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 Ppt Decoder | Powerpoint Presentations and Slides » View and Download # Displaying decoder PowerPoint Presentations PowerPoint Presentation PPT Presentation Summary : Decoder Expansion Combining two 2-4 decoders to form one 3-8 decoder using enable switch Combinational Circuit Design with Decoders Combinational circuit ... Source : http://www.cs.gsu.edu/~cscbecx/1_3380%20Architecture%20Spring%202009/lec4%20Decoder.ppt Encoders and Decoders - IT Glitz PPT Presentation Summary : Digital Electronics Electronics Technology Landon Johnson Encoding, Decoding, and Seven-Segment Displays Encoder/Decoder Competencies 52. Given four different input ... Source : http://www.itglitz.in/Digital/Encoders_Decoders.ppt 2-into-4 decoder PPT Presentation Summary : 2-into-4 decoder Block diagram Gate-level diagram In Block diagrams: Circles on the input indicate the logic convention of the input signal Circles on the output ... Source : http://ee.olemiss.edu/matt/EE385/385_L2/385_L2.PPT Address Decoders - Texas A+M University - CS Course Webpages PPT Presentation Summary : Outline Address Decoding Strategy Full Address Decoding Partial Address Decoding Block Address Decoding Address Decoder Design Goal Understand address decoding schemes Verilog combinational blocks. Wakerly Chapter_06.ppt PPT Presentation Summary : Combinational Logic and Verilog Programmable Array Logic PAL Decoders Seven Segment Display and Decoder Priority Encoders Three state Buffers Three-State buffers in ... Source : http://web.cecs.pdx.edu/~mperkows/CLASS_171/171-2010-All/2010-0010.%20Verilog%20combinational%20blocks.%20%20Wakerly%20Chapter_06.ppt DECODER - Simple Fun Kid Parties PPT Presentation Summary : Title: DECODER Author: HP Authorized Customer Last modified by: HP Authorized Customer Created Date: 5/27/2008 7:02:56 PM Document presentation format Source : http://www.simplefunkidparties.com/DECODER.ppt 6-BIT THERMOMETER CODER - San Jose State University PPT Presentation Summary : 6-bit thermometer coder siddharth verma saurabh puri kapil sethi tae-yoon park advisor: dr. david parent date:8th may,2006 outline introduction theory of thermometer ... Source : http://www.engr.sjsu.edu/dparent/ICGROUP/166s06/verma_puri_sethi_park_coder.ppt Decoder Installation - Otter Valley Railroad Model Trains ... PPT Presentation Summary : Decoder Installation By Roger James, Otter Valley Railroad So you decided to install a DCC decoder, tips and tricks!! What is the Loco? Is the loco worth the DCC decoder? Download Space Decoder - People Server at UNCW PPT Presentation Summary : Space Decoder - Welcome - Click Here To Begin Fueling Finishing Status: Target Screen Engaged Active Targeting: On Next Target :W34.345 N24.234 Heading-N7.56 E5.89 Source : http://people.uncw.edu/ertzbergerj/MS_PowerPoint_Games/Space_Decoder/Space-Decoder-v3.ppt Additional Gates - University of Illinois at Urbana–Champaign PPT Presentation Summary : A decoder block provides abstraction: You can use the decoder as long as you know its truth table or equations, without knowing exactly what’s inside. Source : http://www.cs.uiuc.edu/class/sp08/cs231/lectures/07-Decoders.ppt 04_Chapter 4 - Modular Comb logic.ppt - FAMU-FSU College of ... PPT Presentation Summary : Chapter 4 Modular Combinational Logic Decoders Decoders n to 2n decoder n inputs 2n outputs For each input, one and only one output will be active. Source : http://www.eng.fsu.edu/~mpf/DL-fa06/perry_slides/04_Chapter%204%20-%20Modular%20Comb%20logic.ppt Introduction to LDPC Codes - University of California, San Diego PPT Presentation Summary : Title: Introduction to LDPC Codes Subject: LDPC codes and applications Author: Paul H. Siegel Last modified by: Paul H. Siegel Created Date: 4/7/1998 9:29:52 PM Source : http://cmrr-star.ucsd.edu/psiegel/pubs/07/ldpc_tutorial.ppt EGR 277 – Digital Logic - Faculty Websites | Tidewater ... PPT Presentation Summary : 4-line-to-16-line decoder/demultiplexer 74145 BCD-to-decimal decoder 74147 Priority encoder 74151. 74150 8 x 1 multiplexer. Source : http://faculty.tcc.edu/PGordy/EGR270/N270P7.ppt ENGIN112 - lecture 15 - College of Engineering | UMass Amherst PPT Presentation Summary : The output lines of the decoder corresponding to the minterms of the function are used as inputs to the or gate. Source : http://www.ecs.umass.edu/ece/tessier/courses/221/lecture/lect17-engin112.ppt ECE 331 – Digital System Design - Welcome to the GMU ECE ... PPT Presentation Summary : ECE 331 – Digital System Design Multiplexers and Demultiplexers, and Encoders and Decoders (Lecture #15) The slides included herein were taken from the materials ... Source : http://ece.gmu.edu/~clorie/Fall10/ECE-331/Lectures/Lecture_15.ppt Additional Gates - University of Illinois at Urbana–Champaign PPT Presentation Summary : So what good is a decoder? Do the truth table and equations look familiar? Decoders are sometimes called minterm generators. For each of the input combinations, ... Source : http://www.cs.uiuc.edu/class/fa05/cs231/lectures/07-Decoders.ppt 5-Bit Binary to 1 of 32 Select Decoder to be used in a 5-bit PPT Presentation Summary : 5 bit binary to 1 of 32 select decoder (to be used in 5 bit DAC) Dan Brisco, Steve Corriveau Advisor: Dave Parent 14 May 2004 Agenda Abstract Introduction Why Simple ... Source : http://www.engr.sjsu.edu/dparent/ICGROUP/166s04/5to32%20Decoder.ppt Computer Architecture What is it, and how is it related to ... PPT Presentation Summary : RISC Decode (MIPS) opcode. 6. other. 21. func. 5. R-format only. opcode[5,3] opcode[2,0] Source : http://compas.cs.stonybrook.edu/course/cse502-s13/lectures/cse502-L5-decode.ppsx Decoders and Encoders - Computer Science and Engineering ... PPT Presentation Summary : Decoders and Encoders Sections 3-5, 3-6 Mano & Kime Decoders and Encoders Binary Decoders Binary Encoders Priority Encoders 3-to-8 Line Decoder A 2-to-4-Line Decoder ... Turbo Codes – Decoding and Applications PPT Presentation Summary : Turbo Codes – Decoding and Applications Bob Wall EE 548 The Turbo Decoder Since a Turbo Code trellis would have a very large number of states (due to the ... Source : http://www.cs.montana.edu/~bwall/ee548/turbo_codes_decoding_apps.ppt Modular Combinational Logic - Computer Science and Electrical ... PPT Presentation Summary : Top-down modular design Decoders n-to-2n decoder: logic network with n inputs and 2n outputs. One output is active for each of the 2n input combinations each minterm ... Source : http://www.csee.umbc.edu/~phatak/212/lectures/modules.ppt Decoder PPT Presentation Summary : Example of a Decoder. Convert binary information from n input lines to 2n unique output. lines. This particular circuit take a binary number and convert it to an octal Source : http://www.sonoma.edu/users/o/ouj/classes/ES210/lectures/ES210_Spring_2013_Lecture_10_Decoder.pptx

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How to use subplots in matplotlib DataVisualization using python – part 2 I have already written about using subplots using matplot lib in this article. While working further on matplotlib, I found more convenient and easy to understand way for doing the same thing hence I decide to put part of of this port. Here we are going to use subplot2grid() . It is a helper function that is similar to subplot() but uses 0-based indexing and let subplot to occupy multiple cells. The grid is specified by shape, at location of loc, spanning rowspan, colspan cells in each direction. subplot2grid(shape, loc, rowspan=1, colspan=1,sharex=ax1) Let us get our hands dirty. Below is simple code to plot three charts on the same plot. ################################################################################################ # name: subplot-11.py # desc: Subplot using matplotlib # date: 2018-12-24 # Author: conquistadorjd ################################################################################################ import matplotlib.pyplot as plt import numpy as np print('*** Program Started ***') t= np.arange(1,17,1) y1= np.random.randint(1, 16,size=16) y2= np.random.randint(1, 32,size=16) y3= np.random.randint(1, 48,size=16) ax1 = plt.subplot2grid((3,3), (0,0), colspan=3, rowspan=1) plt.plot(t, y1) # share x only ax2 = plt.subplot2grid((3,3), (1,0), colspan=3,rowspan=1,sharex=ax1) plt.plot(t, y2) # share x and y ax3 = plt.subplot2grid((3,3), (2, 0), colspan=3,rowspan=1,sharex=ax1) plt.plot(t, y3) # Saving image plt.savefig('subplot-11.png') # In case you dont want to save image but just displya it plt.show() print('*** Program ended ***') view raw subplot-11.py hosted with ❤ by GitHub Here is the output Here a bit complex subplots ################################################################################################ # name: subplot-12.py # desc: Subplot using matplotlib # date: 2018-12-24 # Author: conquistadorjd ################################################################################################ import matplotlib.pyplot as plt import numpy as np print('*** Program Started ***') t= np.arange(1,17,1) t2= np.arange(1,49,1) y1= np.random.randint(1, 16,size=16) y2= np.random.randint(1, 32,size=48) y3= np.random.randint(1, 48,size=16) y4= np.random.randint(1, 64,size=16) y5= np.random.randint(1, 124,size=16) ax1 = plt.subplot2grid((5,3), (0,0), colspan=3, rowspan=1) plt.plot(t, y1) ax2 = plt.subplot2grid((5,3), (1,0), colspan=2,rowspan=1) plt.plot(t2, y2) ax3 = plt.subplot2grid((5,3), (1, 2), colspan=2,rowspan=2,sharex=ax1) plt.plot(t, y3) ax4 = plt.subplot2grid((5,3), (2, 0), colspan=2,rowspan=1) plt.plot(t, y4) ax5 = plt.subplot2grid((5,3), (3, 0), colspan=3,rowspan=2,sharex=ax1) plt.plot(t*2, y5) # ax6 = plt.subplot2grid((5,3), (4, 0), colspan=3,rowspan=1,sharex=ax1) # plt.plot(t, y3) # Saving image plt.savefig('subplot-12.png') # In case you dont want to save image but just displya it plt.show() print('*** Program ended ***') view raw subplot-12.py hosted with ❤ by GitHub Here is the output Code for generating plot is as below ax5 = plt.subplot2grid((5,3), (3, 0), colspan=3,rowspan=2,sharex=ax1) • First bracket (5,3) indicates the number of rows and columns on the graph • second bracket (3,0) indicates location by row, column. Since this is zero based indexing, (0,0) indicates first row and first column • Plot can cover multiple rows and columns and can be specided by using colspan and rowspan • Axis can be shared between two plots and its indicated by sharex This site uses Akismet to reduce spam. Learn how your comment data is processed.

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## Thursday, 4 June 2009 ### Ep 107: Ranking Cricketers Cricket is one of the world's most statistical sports, and mathematicians in cricket-loving nations love nothing more than delving into the minutiae of the numbers and diving into averages, strike-rates and custom-made measures of batting and bowling effectiveness. For many people, including me, cricket isn't just a sport, it is a way of life. These words could easily have come from me, but are actually the words of Rob Eastaway, a cricket-loving mathematician from the UK, and originator of the official International Cricket Council cricket-ratings which rank not only teams, but players within each team. In this week's podcast, I chat to Rob about how you mathematically rank cricketers. Listen to this podcast here - note a few audio issues, see below: Ranking individual batsmen and bowlers is no small task. A common method of comparing batsmen is their average, which is the average score the batsman compiles each time he comes in to bat. This method, however, has a number of issues as it does not take into consideration the opposition, playing conditions and how recently the runs were scored. How can you compare a score of 60 against a world-class opponent on a dodgy pitch with a score of 150 against a lowly rated team in easy batting conditions? This is what Eastaway's ranking system attempts to do - and the maths is quite difficult (far more difficult, in Rob's words, than the Duckworth-Lewis method of determining the winner in a rain-effected game!) As well as taking into consideration the strength of the opposition and playing conditions, the ranking system places a greater emphasis on recent performances. The overall system has a number of feed-back loops - the individual player ratings contribute to a team's rating, which effects how many rating points an opposition player can earn against that team - remember, a score of 50 against tough opposition will be worth more than 50 against low-class opponents. Similarly, how each player in a match performs influences how many points are on offer. For example, a score of 45 out of an overall team score of 100 will be more highly valued than a score of 45 out of 450. As such, large amounts of historical data are used to come up with the final numbers. Limited overs cricket has the additional dimension of strike-rate - a batsman who scores his runs quickly will be rated more highly than a slow scorer. The system was first developed in 1987 by Eastaway with former English cricketer Ted Dexter and colleague Gordon Vince, and at first the system was greeted with scepticism by many cricket lovers. Nowadays, however, it has gained credibility and has even been used by international cricketers to help negotiate their contracts - for example, Michael Bevan was for a long time rated number one in the One Day International version of the rankings and used this in contract negotiations, however he could not secure a Test spot. Known originally as the Deloittes Ratings and in later years the PwC Ratings, the system was officially adopted by the International Cricket Council in January 2005. With a background in Operations Research and a love of cricket, Eastaway is essentially my idol! You can read more about the maths of his system in his article Howzat in Plus Magazine. As many of the equations used in this system are now copyrighted, you can't find the exact algorithms published anywhere. However, if you are a big nerd like me, you might like the book Deloitte Ratings: The Complete Guide to Test Cricket in the Eighties by Marcus Berkmann. The book details the ratings changes after each Test series in the 80s, and the appendix contains many of the equations which underpin the system. I was given this book when I was 10 and didn't much understand it back then, but I was very happy to find it in storage when I returned from the UK, and I now find it a maths-cricket-nerd's delight! I'm fascinated to know if they come up with something for Twenty 20. The ultra-shortened form of the game brings in loads more complexities, not least of which is that unless you are an opening batsman, you may not even get a bat! Here's hoping Australia can win the World Twenty20 - oh and The Ashes! If only I was in the UK this summer! I hope you enjoy this podcast - however, please note there are some audio issues. I had a great chat with Rob in a cafe in London, however my recording equipment was set on the wrong setting and so captured a lot more background noise than I had hoped! So please hang in there - this was one of my very favourite interviews. Rob is a fascinating person and had some really interesting observations on maths and sport. I really shouldn't have gone to The Chemical Brothers the night before, I probably would have had the microphone on the right setting! Listen to this podcast here: #### 1 comment: 1. Excellent interview Marc!

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# Java Program to Find closest number in array • Last Updated : 27 Jul, 2022 Given an array of sorted integers. We need to find the closest value to the given number. Array may contain duplicate values and negative numbers. Examples: ```Input : arr[] = {1, 2, 4, 5, 6, 6, 8, 9} Target number = 11 Output : 9 9 is closest to 11 in given array Input :arr[] = {2, 5, 6, 7, 8, 8, 9}; Target number = 4 Output : 5``` A simple solution is to traverse through the given array and keep track of absolute difference of current element with every element. Finally return the element that has minimum absolution difference. An efficient solution is to use Binary Search. ## Java `// Java program to find element closest to given target.` `import` `java.util.*;` `import` `java.lang.*;` `import` `java.io.*;`   `class` `FindClosestNumber {` `    `  `    ``// Returns element closest to target in arr[]` `    ``public` `static` `int` `findClosest(``int` `arr[], ``int` `target)` `    ``{` `        ``int` `n = arr.length;`   `        ``// Corner cases` `        ``if` `(target <= arr[``0``])` `            ``return` `arr[``0``];` `        ``if` `(target >= arr[n - ``1``])` `            ``return` `arr[n - ``1``];`   `        ``// Doing binary search ` `        ``int` `i = ``0``, j = n, mid = ``0``;` `        ``while` `(i < j) {` `            ``mid = (i + j) / ``2``;`   `            ``if` `(arr[mid] == target)` `                ``return` `arr[mid];`   `            ``/* If target is less than array element,` `               ``then search in left */` `            ``if` `(target < arr[mid]) {` `       `  `                ``// If target is greater than previous` `                ``// to mid, return closest of two` `                ``if` `(mid > ``0` `&& target > arr[mid - ``1``]) ` `                    ``return` `getClosest(arr[mid - ``1``], ` `                                  ``arr[mid], target);` `                `  `                ``/* Repeat for left half */` `                ``j = mid;              ` `            ``}`   `            ``// If target is greater than mid` `            ``else` `{` `                ``if` `(mid < n-``1` `&& target < arr[mid + ``1``]) ` `                    ``return` `getClosest(arr[mid], ` `                          ``arr[mid + ``1``], target);                ` `                ``i = mid + ``1``; ``// update i` `            ``}` `        ``}`   `        ``// Only single element left after search` `        ``return` `arr[mid];` `    ``}`   `    ``// Method to compare which one is the more close` `    ``// We find the closest by taking the difference` `    ``//  between the target and both values. It assumes` `    ``// that val2 is greater than val1 and target lies` `    ``// between these two.` `    ``public` `static` `int` `getClosest(``int` `val1, ``int` `val2, ` `                                         ``int` `target)` `    ``{` `        ``if` `(target - val1 >= val2 - target) ` `            ``return` `val2;        ` `        ``else` `            ``return` `val1;        ` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `main(String[] args)` `    ``{` `        ``int` `arr[] = { ``1``, ``2``, ``4``, ``5``, ``6``, ``6``, ``8``, ``9` `};` `        ``int` `target = ``11``;` `        ``System.out.println(findClosest(arr, target));` `    ``}` `}` Output: `9` Time Complexity: O(log(n)) Auxiliary Space: O(log(n)) (implicit stack is created due to recursion) Please refer complete article on Find closest number in array for more details! My Personal Notes arrow_drop_up Recommended Articles Page :

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# Albion An Introduction To Linear Programming And Game Theory Solution Manual ## An introduction to linear programming and game theory ### An Introduction to Linear Programming and Game Theory Ed An introduction to linear programming and the theory of. An Introduction to Linear Programming and Game Theory textbook solutions from Chegg, view all supported editions., Towards the end of the semester, we will apply the theory of linear programming to the study of games, specifically to those games in which two people compete to capture as much as possible of a finite resource. The rough plan is to cover Chapters 1 through 4, 7 …. ### An introduction to linear programming and game theory 3d An Introduction to Linear Programming and the Theory of. Towards the end of the semester, we will apply the theory of linear programming to the study of games, specifically to those games in which two people compete to capture as much as possible of a finite resource. The rough plan is to cover Chapters 1 through 4, 7 …, An Introduction to Linear Programming and Game Theory by Gerard E. Keough and Paul R. Thie available in Hardcover on Powells.com, also read synopsis and reviews. This book provides the development of the theoretical concepts and computational techniques of.... Algorithmic Game Theory and Applications Lecture 5: Introduction to Linear Programming Kousha Etessami Kousha Etessami AGTA: Lecture 5. 1 “real world example”: the diet problem • You are a fastidious eater. You want to make sure that every day you get enough of each vitamin: vitamin 1, vitamin 2,...., vitamin m. • You are also frugal, and want to spend as little as possible. • There Linear Programming and Game Theory Ronald Parr CompSci270 Department of Computer Science Duke University With thanks to Vince Conitzerfor some content What are Linear Programs? •Linear programs are constrained optimization problems •Constrained optimization problems ask us to maximize or minimize a function subject to mathematical constraints on the variables –Convex programs have … Linear programming is a branch of mathematics and statistics that allows researchers to determine solutions to problems of optimization. Linear programming problems are distinctive in that they are clearly defined in terms of an objective function, constraints and linearity. Unlike static PDF An Introduction to Linear Programming and Game Theory solution manuals or printed answer keys, our experts show you how to solve each problem step-by-step. No need to wait for office hours or assignments to be graded to find out where you took a wrong turn. You can check your reasoning as you tackle a problem using our interactive solutions viewer. This book is concerned with the traditional interpretation of game theory. Game theory is divided into two main branches. The first is cooperative game theory, which assumes that the players can communicate, form coalitions and sign binding agreements. Cooperative game theory has been used, for example, An invaluable study aid for students of game theory. Solutions Manual to accompany Game Theory: An Introduction, 2nd Edition provides complete explanations and fully worked solutions for the problems posed in the text.Although designed as a supplement to Game Theory, this solutions guide is versatile enough to act as an independent review of key topics, regardless of which textbook you are using. Pris: 1549 kr. Inbunden, 2008. Skickas inom 7-10 vardagar. Köp An Introduction to Linear Programming and Game Theory av Paul R Thie, G E Keough på Bokus.com. A new appendix discusses how to work with Solver and presents new exercises related to Solver's solution outputs. Introduction to Linear Programming and Game Theory, Third Edition includes various The first part of this book is a good introduction to linear programming and the simplex method. Easy reading, tries to give insight, and with lots of examples. My personal favorite when it comes to refreshing my intuition on duality and how simplex works. Regarding the game theory material, it seems to be a little crowded. Don't expect any in-depth coverage there, but as a brief overview it might be appropriate. This book is concerned with the traditional interpretation of game theory. Game theory is divided into two main branches. The first is cooperative game theory, which assumes that the players can communicate, form coalitions and sign binding agreements. Cooperative game theory has been used, for example, An Introduction to Linear Programming and Game Theory,Third Edition presents a rigorous, yet accessible, introduction tothe theoretical concepts and computational techniques of linearprogramming and game theory. Now with more extensive modelingexercises and detailed integer programming examples, this bookuniquely illustrates how mathematics can Solucionario de Libro de Investigación de Operaciones An invaluable study aid for students of game theory. Solutions Manual to accompany Game Theory: An Introduction, 2nd Edition provides complete explanations and fully worked solutions for the problems posed in the text.Although designed as a supplement to Game Theory, this solutions guide is versatile enough to act as an independent review of key topics, regardless of which textbook you are using. 06/11/2000 · Discussions over the years with Jean-Pierre Benoˆıt, Vijay Krishna, Michael Pe-??? is. An introduction to game theory by Martin J. Osborne 1 Introduction What is game theory? 1 The theory of rational choice 4 1 ### Linear Programming Chapter 11 Game Theory An Introduction to Linear Programming and Game Theory E. Praise for the Second Edition: "This is quite a well-done book: very tightly organized, better-than-average exposition, and numerous examples, illustrations, and applications."--Mathematical Reviews of the American Mathematical Society An Introduction to Linear Programming and Game Theory, Third Edition presents a rigorous, yet accessible, introduction to the theoretical, 14 Game Theory 803 14.1 Two-Person Zero-Sum and Constant-Sum Games: Saddle Points 803 14.2 Two-Person Zero-Sum Games: Randomized Strategies, Domination, and Graphical Solution 807 14.3 Linear Programming and Zero-Sum Games 816 14.4 Two-Person Nonconstant-Sum Games 827 14.5 Introduction to n-Person Game Theory 832 14.6 The Core of an n-Person. An Introduction to Game Theory by Martin J. Osborne. Solucionario de Libro de Investigación de Operaciones, An Introduction to Linear Programming there is solution; we need some way of finding it (or at least a close approximation to it) in a reasonable amount of time. We describe the types of problems Linear Programming can handle and show how we can solve them using the simplex method. We discuss generaliza-tions to Binary Integer Linear Programming (with an example of a manager of an. ### An Introduction to Linear Programming and Game Theory An Introduction to Game Theory by Martin J. Osborne. and economics, have developed the theory behind \linear programming" and explored its applications [1]. This paper will cover the main concepts in linear programming, including examples when appropriate. First, in Section 1 we will explore simple prop-erties, basic de nitions and theories of linear programs. In order to illustrate and economics, have developed the theory behind \linear programming" and explored its applications [1]. This paper will cover the main concepts in linear programming, including examples when appropriate. First, in Section 1 we will explore simple prop-erties, basic de nitions and theories of linear programs. In order to illustrate. Linear Programming and Game Theory Ronald Parr CompSci270 Department of Computer Science Duke University With thanks to Vince Conitzerfor some content What are Linear Programs? •Linear programs are constrained optimization problems •Constrained optimization problems ask us to maximize or minimize a function subject to mathematical constraints on the variables –Convex programs have … Towards the end of the semester, we will apply the theory of linear programming to the study of games, specifically to those games in which two people compete to capture as much as possible of a finite resource. The rough plan is to cover Chapters 1 through 4, 7 … An invaluable study aid for students of game theory. Solutions Manual to accompany Game Theory: An Introduction, 2nd Edition provides complete explanations and fully worked solutions for the problems posed in the text.Although designed as a supplement to Game Theory, this solutions guide is versatile enough to act as an independent review of key topics, regardless of which textbook you are using. An Introduction to Linear Programming and Game Theory, Third Edition presents a rigorous, yet accessible, introduction to the theoretical concepts and computational techniques of linear programming and game theory. Now with more extensive modeling exercises and detailed integer programming examples, this book uniquely illustrates how An Introduction to Linear Programming and Game Theory, Third Edition presents a rigorous, yet accessible, introduction to the theoretical concepts and computational techniques of linear programming and game theory. Now with more extensive modeling exercises and detailed integer programming examples, this book uniquely illustrates how 1.4 The Roles of Linear Programming and Game Theory. 2 The Linear Programming Model. 2. 1 History. 2.2 The Blending Model. 2.3 The Production Model. 2.4 The Transportation Model. 2.5 The Dynamic Planning Model. 2.6 Summary. 3. The Simplex Method. 3.1 The General Problem. 3.2 Linear Equations and Basic Feasible Solutions. 3.3 Introduction to the Simplex Method. 3.4 Theory of the Simplex Method. An Introduction to Linear Programming and Game Theory, Third Edition presents a rigorous, yet accessible, introduction to the theoretical concepts and computational techniques of linear programming and game theory. Now with more extensive modeling exercises and detailed integer programming examples, this book uniquely illustrates how mathematics can be used in real-world applications in the An Introduction to Linear Programming and Game Theory, Third Edition presents a rigorous, yet accessible, introduction to the theoretical concepts and computational techniques of linear programming and game theory. Now with more extensive modeling exercises and detailed integer programming examples, this book uniquely illustrates how mathematics can be used in real-world applications in the Pris: 1549 kr. Inbunden, 2008. Skickas inom 7-10 vardagar. Köp An Introduction to Linear Programming and Game Theory av Paul R Thie, G E Keough på Bokus.com. 04/11/1960 · An Introduction to Linear Programming and the Theory of Games.S. Vajda. Methuen, London; Wiley, New York, 1960. 76 pp ## An introduction to linear programming and game theory 3d Linear Programming and Game Theory Duke University. Praise for the Second Edition: "This is quite a well-done book: very tightly organized, better-than-average exposition, and numerous examples, illustrations, and applications."--Mathematical Reviews of the American Mathematical Society An Introduction to Linear Programming and Game Theory, Third Edition presents a rigorous, yet accessible, introduction to the theoretical, An Introduction to Linear Programming and Game Theory, Third Edition presents a rigorous, yet accessible, introduction to the theoretical concepts and computational techniques of linear programming and game theory. Now with more extensive modeling exercises and detailed integer programming examples, this book uniquely illustrates how mathematics can be used in real-world applications in the. ### An introduction to linear programming and game theory 3d Solution Manual For Introduction to Linear Optimization. Get Solutions Manual to Accompany Game Theory: An Introduction, 2nd Edition now with O’Reilly online learning. O’Reilly members experience live online training, plus …, An Introduction to Linear Programming and Game Theory, Third Edition presents a rigorous, yet accessible, introduction to the theoretical concepts and computational techniques of linear programming and game theory. Now with more extensive modeling exercises and detailed integer programming examples, this book uniquely illustrates how mathematics can be used in real-world applications in the. Algorithmic Game Theory and Applications Lecture 5: Introduction to Linear Programming Kousha Etessami Kousha Etessami AGTA: Lecture 5. 1 “real world example”: the diet problem • You are a fastidious eater. You want to make sure that every day you get enough of each vitamin: vitamin 1, vitamin 2,...., vitamin m. • You are also frugal, and want to spend as little as possible. • There "Introduction to Linear Programming and Game Theory, Third Edition" includes various additions as well as improvements that have been developed over the last decade, and the most significant addition to the text involves technology. It features an introduction, discussion, and utilization of Solver, a spreadsheet software package that solves Get Solutions Manual to Accompany Game Theory: An Introduction, 2nd Edition now with O’Reilly online learning. O’Reilly members experience live online training, plus … An Introduction to Linear Programming and Game Theory,Third Edition presents a rigorous, yet accessible, introduction tothe theoretical concepts and computational techniques of linearprogramming and game theory. Now with more extensive modelingexercises and detailed integer programming examples, this bookuniquely illustrates how mathematics can Linear Programming and Game Theory Ronald Parr CompSci270 Department of Computer Science Duke University With thanks to Vince Conitzerfor some content What are Linear Programs? •Linear programs are constrained optimization problems •Constrained optimization problems ask us to maximize or minimize a function subject to mathematical constraints on the variables –Convex programs have … Towards the end of the semester, we will apply the theory of linear programming to the study of games, specifically to those games in which two people compete to capture as much as possible of a finite resource. The rough plan is to cover Chapters 1 through 4, 7 … This solutions manual is a companion to Game Theory: An Introduction, Second Edition. It provides the statements and solutions of all the problems in the book. An Appendix contains the main definitions and theorems in the book. The full text of this article hosted at iucr.org is unavailable due to technical difficulties. Towards the end of the semester, we will apply the theory of linear programming to the study of games, specifically to those games in which two people compete to capture as much as possible of a finite resource. The rough plan is to cover Chapters 1 through 4, 7 … Solucionario de Libro de Investigación de Operaciones A new appendix discusses how to work with Solver and presents new exercises related to Solver's solution outputs. Introduction to Linear Programming and Game Theory, Third Edition includes various An Introduction to Linear Programming Learning Objectives 1. Obtain an overview of the kinds of problems linear programming has been used to solve. 2. Learn how to develop linear programming models for simple problems. 3. Be able to identify the special features of a model that make it a linear programming model. 4. Learn how to solve two variable linear programming models by the graphical ### Linear Programming Theory and Applications Introduction to Linear Programming YouTube. Get this from a library! An introduction to linear programming and game theory. [Paul R Thie; G E Keough] -- "An Introductin to Linear Programming and Game Theory, Third Edition presents an introduction to the theoretical concepts and computational techniques of linear programming and game theory. Now with, This solutions manual is a companion to Game Theory: An Introduction, Second Edition. It provides the statements and solutions of all the problems in the book. An Appendix contains the main definitions and theorems in the book.. ### Taha Operations Research An Introduction 9th Edition An Introduction to Game Theory by Martin J. Osborne. Free Online Library: An introduction to linear programming and game theory, 3d ed.(Brief article, Book review) by "SciTech Book News"; Publishing industry Library and information science Science and technology, general Books Book reviews An Introduction to Linear Programming and Game Theory: Edition 3 - Ebook written by Paul R. Thie, Gerard E. Keough. Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read An Introduction to Linear Programming and Game Theory: Edition 3.. Unlike static PDF An Introduction to Linear Programming and Game Theory solution manuals or printed answer keys, our experts show you how to solve each problem step-by-step. No need to wait for office hours or assignments to be graded to find out where you took a wrong turn. You can check your reasoning as you tackle a problem using our interactive solutions viewer. The full text of this article hosted at iucr.org is unavailable due to technical difficulties. This book is concerned with the traditional interpretation of game theory. Game theory is divided into two main branches. The first is cooperative game theory, which assumes that the players can communicate, form coalitions and sign binding agreements. Cooperative game theory has been used, for example, A new appendix discusses how to work with Solver and presents new exercises related to Solver's solution outputs. Introduction to Linear Programming and Game Theory, Third Edition includes various An Introduction to Linear Programming and Game Theory,Third Edition presents a rigorous, yet accessible, introduction tothe theoretical concepts and computational techniques of linearprogramming and game theory. Now with more extensive modelingexercises and detailed integer programming examples, this bookuniquely illustrates how mathematics can Praise for the Second Edition: "This is quite a well-done book: very tightly organized, better-than-average exposition, and numerous examples, illustrations, and applications."--Mathematical Reviews of the American Mathematical Society An Introduction to Linear Programming and Game Theory, Third Edition presents a rigorous, yet accessible, introduction to the theoretical This solutions manual is a companion to Game Theory: An Introduction, Second Edition. It provides the statements and solutions of all the problems in the book. An Appendix contains the main definitions and theorems in the book. Get this from a library! An introduction to linear programming and game theory. [Paul R Thie; G E Keough] -- "An Introductin to Linear Programming and Game Theory, Third Edition presents an introduction to the theoretical concepts and computational techniques of linear programming and game theory. Now with View all posts in Albion category

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Align the upper roller tracks by carefully lifting the door halfway. Lock it in place with two locking pliers, and install the supporting brackets on the back of the rails using 1-1/4 in. perforated angle iron (available at home centers and hardware stores). Install 1-1/2 x 1/4 in. stop bolts, with the threads to the inside of the track, at the end of each upper track. How many times a day do you open or close your garage door? You probably don’t even know because we take our garage door for granted until…. Until it doesn’t go up… until it doesn’t come down… until it gets noisy, difficult to open by hand or some other problem develops. You need help – and if you’re locked in or locked out, you need help in a hurry. You need A-Authentic Garage Doors. Here’s why: Speed of a falling door:: Physics tells us that the transit time of a free-falling body is sqrt(2x/g), where x is the length of the fall and g is the acceleration due to gravity (32.2 ft/sec^2). If this typical 150 lb door were to fall an equivalent of 3.75 feet, this falling time would be sqrt(2*3.75/32.2) = 0.48 seconds (480 milliseconds). The terminal velocity is gt, or 0.48 seconds * 32.2 ft/sec^2 = 15.5 ft/sec = 10.6 mph. Good customer service is important for any product, but it is especially important for the class of garage door openers we considered. We looked primarily at models designed to be installed by a homeowner, not a professional. Even if you consider yourself to be pretty handy, you are sure to have questions at some point along the way. As such, we looked for companies that respond to all inquiries as well as for resources, such as a downloadable manual, to help with installation. ```If your door has two springs, most professionals and research online says that replacing both springs is the best option. Most torsion springs are rated for 10,000 close/open cycles. If only one of your springs is broken, both springs are still recommended to be replaced. Considering that your second spring will break soon anyways, this added on fix is only going to cost you about \$50 extra to assure that you don't have to pay another service fee for a second visit. ``` We want to serve you not only today, but also in the years ahead. To do that, we make sure that we provide prompt, professional, well-trained technicians that efficiently get the job done right the first time. We take pride in doing everything possible to eliminate warranty issues and to ensure that our clients are thoroughly pleased and return to us for all garage door needs. Follow the manufacturer’s instructions to assemble the opener and mount the rail to the header bracket above the door. Then set the opener on a ladder where you’re going to install it. The ladder (usually an 8-footer) holds the opener in position while you measure for your lengths of angle iron. If necessary, put boards under the opener to raise it. A spring design manual, also called a rate book, gives tables that relate the torque constant ("rate") and maximum turns for springs of given wire size, diameter, and length. For example, a typical page in a rate book would show a table for a given wire size and inside diameter, the maximum inch-pounds (MIP) of torque available for a standard lifetime of 10,000 cycles in that size, the weight of the spring per linear inch, and the rates of the spring (as IPPT, inch-pounds per turn) for each of various lengths. From these figures one can calculate the lifting capacity, substitutions, conversions, and cycle life upgrades for a door of given weight and drum geometry. The weight-lifting capacity of a given spring is calculated based on its torque constant (IPPT, or inch-pounds per turn), which is the rotational version of the spring constant that characterizes the spring. The IPPT constant is found from tables giving IPPT for given spring dimensions (wire-size/diameter/length). The same tables may indicate the maximum number of turns for various expected lifetimes in cycles. The torque required to balance a given door can be calculated from the weight of the door times the moment arm of the drums (as we do below under "Calculating the Forces We Will Be Handling"). The ultimate torque of the spring in the fully-wound condition is the number of turns (when fully-wound) times the IPPT constant. Choosing a spring to balance the door then simply requires matching the ultimate torque of the spring to the balancing torque. Electric Garage Door Openers – Service and repair of the electric garage door opener itself, including the lift mechanism that pulls the door up and guides it down. This is typically not part of the garage door itself and is serviced and repaired on its own interval. Typical service includes inspection, repair, adjustment, and lubrication if needed. Also, we typically inspect the mounting of the unit as well as its attachment to the door itself. ```Please Note: Prices, promotions, styles and availability may vary by store and online. Inventory is sold and received continuously throughout the day; therefore, the quantity shown may not be available when you get to the store. This inventory may include a store display unit. Online orders and products purchased in-store qualify for rebate redemption. Rebates are provided in the form of a Menards® Merchandise Credit Check valid towards purchases at any Menards® retail store. Not valid for purchases on MENARDS.COM®. ``` Furthermore, newer doors come with more improved security features, helping to improve the way you protect your home and loved ones. While older doors are easy to break into, whether through breaking the lift mechanism or even using a universal garage door remote, new doors come with many redundant security features, which will go a long way in deterring even the most ingenious burglar. Those who benefit from this anti-competitive behavior have many excuses for it. They claim that the product is too dangerous and infrequently needed for the public to purchase directly. They say the job is hazardous and requires techniques and tools with which the amateur will rarely practice, which is true. They write me in anger saying I don't understand how expensive it is to put a truck on the road with a technician and parts and salary and benefits and insurance and advertising and every other common business expense. They say it will take the homeowner hours of effort to do this safely and correctly, while they can do it in a fraction of that time and at a price that isn't worth the effort to save. But should they set themselves up as the judge of what you can and cannot do? Of what is an economical use of your time? Imposing minimum order quantities or charging retail prices for small orders is legitimate; inquiring into the purchaser's background is not. When I called to schedule the repair service, I was transferrd 5 times and spoke with 6 service reps. Each rep was very confused by my request to get my garage door repaired. One rep actually told me that Sears doesn't repair garage doors. I had to tell her that Sears installed the door. When I finally found a rep who could schedule my service, it took one week for the appointment. When garage door repair isn’t an option — perhaps the current door is beyond fixing or you want to upgrade to a quieter, more energy-efficient model — it’s time to buy a new one. But choosing a garage door is not as simple as it sounds, even when you know the right size for your home. A wide range of materials, styles and finishes are available, and each factor influences the cost. Garage doors are made of aluminum, steel, vinyl, fiberglass, masonite, wood (typically cedar or mahogany), or a composite of several materials. They may be insulated against cold or heat. Traditional and modern styles include raised panel, carriage house or crossbuck. Most styles have window or arch options, and are available in different wood finishes and neutral colors. Because garage doors account for a large part of a home’s exterior, their appearance is usually a homeowner’s top priority. An attractive garage door can increase a home’s curb appeal and resale value. Good response time and service; Question - I googled to find the Sears Garage Door repair phone number. During the conversation, I was unsure if this was "Sears" or a "contractor service" or other service. I had to ask if this repair person was coming from "Sears" or an independent repair. I was concerned until the service man arrived in a sears truck wearing Sears apparel. You might want the process to be more clearly identified as Sears. Absolute Overhead Door recently launched a blog that can be found here so that readers would be able to see the benefits of a garage and what they should do in the event their newly driving teenage drove into the garage door. The blog offers many tips for “fix at home” solutions as well as giving examples of situations when calling us for a service call is the best decision. In our blog, we give professional and honest recommendations for the most reader and budget friendly options for families looking for advice that doesnt cost a fortune and an obligation to purchase a new garage door from a salesman afterwards! Check it out! We hope you enjoy it. Garage door openers make it easy to get your garage open without the struggle or the hassle of facing inclement weather. The latest garage door openers have new features such as timed close, battery backup and improved energy efficiency. Sears carries top-of-the-line garage openers that can run much more quietly and smoothly than old models. With a keypad feature, you'll be able to get into your house using a secure four-digit code. With a few new batteries in your remote, you'll be opening your garage with the push of a button. When garage door repair isn’t an option — perhaps the current door is beyond fixing or you want to upgrade to a quieter, more energy-efficient model — it’s time to buy a new one. But choosing a garage door is not as simple as it sounds, even when you know the right size for your home. A wide range of materials, styles and finishes are available, and each factor influences the cost. Garage doors are made of aluminum, steel, vinyl, fiberglass, masonite, wood (typically cedar or mahogany), or a composite of several materials. They may be insulated against cold or heat. Traditional and modern styles include raised panel, carriage house or crossbuck. Most styles have window or arch options, and are available in different wood finishes and neutral colors. Because garage doors account for a large part of a home’s exterior, their appearance is usually a homeowner’s top priority. An attractive garage door can increase a home’s curb appeal and resale value. Even if one could somehow stretch and clamp the springs to the proper extra length, the process would still be more trouble, and there would be little or no reduction of risk. Lifting the full weight of the unsprung door by hand and clamping it in the raised position is dangerous in itself, and creates the same amount of stored energy as winding the springs, ready to slip out of your hands. Many doors won't travel far enough up the track to provide clearance to access the springs. You're also going to have to deal with winding stiff steel cables onto both lift drums at once without any resistance to maintain tension. Finally, even if you managed to complete the installation with the door raised, you then have to lower the massive door against an untested balancing torque. If you've made a mistake, then that massive door has nothing but your skeletal force applied through your meat clamps (hands) to prevent it from falling down and crushing whatever is in the way (perhaps your feet?). Garage doors are the largest moving object inside your home. If you have a problematic garage door, it compromises the safety of your family and home. Overhead Door Company of Atlanta is a professional company you can count on. We provide you with quality service at a reasonable price. We offer FREE estimates on replacement garage doors and are spring replacement specialists. 24 hours a day 7 days a week we are your number one garage door repair service. With good looks, modest cost, and solid return on your investment, a new garage door is the Triple Crown of curb appeal projects. According to the “Remodeling Impact Report” from the NATIONAL ASSOCIATION OF REALTORS®, the national median cost of a garage door replacement project is \$2,300 and recovers 87% of your investment if you sell your house — one of the highest percentage of recovered costs in the “Report.” Note the left winding cone with red spray paint. This shpritz of paint is applied to create fear and doubt in the mind of the do-it-yourselfer. Sometimes it is a color code for the wire size (using a DASMA standard, red indicating 0.2253 inch diameter wire). Sometimes it indicates the winding direction: red may indicate right-hand winding, but don't rely on that; do you own independent analysis. Sometimes it is a manufacturer's private code for another dimension than wire size. This color code is for the installer's information when the spring is new; I would not depend on interpreting the color code properly on an old spring, since one can't be certain of a correct interpretation without documentation from the original supplier. Additionally, the B970 includes encryption features that prevent others from hacking the system to gain entry to your garage. Expert reviewers like this garage door opener a lot. The Tool Spy says the Chamberlain B970 justifies its higher price point by delivering excellent build quality and anti-vibration features. Consumer Search and Garage How To also approve of this unit. The two set-screws in the winding cones have a 3/8-inch square head, which fits a 3/8-inch open-end wrench or 8-point socket, or a 7/16-inch 12-point socket or 12-point closed-end wrench. I carried an extra wrench in my pocket while winding, since I didn't want to be holding a wound spring that I couldn't set because I had dropped the wrench (although one could rest the winding rod against the door in this case while picking up a dropped tool). By watching the chalk mark while winding, you can count the number of turns applied, and confirm the number later. My standard-size door (7 foot height) with 4-inch drums has a nominal wind of 7-1/4 or 7-1/2 turns, which leaves 1/4 or 1/2 turn at the top-of-travel to keep the lift cables under tension. After 7 turns on the first spring, I clamped down the set-screws, weighed the door again, and found a lift of about 100 pounds in reduced weight. As expected, this wasn't quite half of the full 238 pounds, nor would it leave any torsion at the top-of-travel, so I added an 8th turn. The door now weighed 122 pounds on one spring, which was ideal. After winding the other spring, the door lifted easily, with only a few pounds apparent weight. This confirmed that the spring choice was properly matched to the door design. I engaged the electric opener trolley, and adjusted the opener forces down to a safer level suitable for the new, improved balance. The door was now ready for return to service. Two of the spring references specifically for the garage-door industry are the APCO Spring Manual by Bill Eichenberger, and the Torsion Spring Rate Book by Clarence Veigel; these give tables of spring sizes and torque constants. Spring engineering principles in general are described in the Handbook of Spring Design published by the Spring Manufacturer's Institute; the formulas allow you to calculate torque constants knowing only the geometry and the Young's modulus of the material. You can also find some brief spring information in standard references like Machinery's Handbook and Marks' Standard Handbook for Mechanical Engineers. With over 300 independently moving parts, your garage door is a deceptively complex piece of equipment. To help prevent malfunctions and break-downs, it is a good idea to occasionally perform a garage door tune-up to keep all of these parts in good working order. A regular tune-up service by a Sears professional can prevent unexpected door problems and prolong the life of your existing equipment.

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# Specific heat capacity by Yh Hoo Tags: capacity, heat, specific Share this thread: P: 73 Now consider two objects,A and B. A has a higher specific heat capacity that B. When both object is subjected to same amount of thermal or heat energy, rise in temperature in A is lower as our common reason(A has a higher specific heat capacity) But what stated by First law of thermodynamics that Increase in internal energy is caused by heat energy transfer to in and work done on it. since temperature is a measure of average kinetic energy of particles in a system, it means perticles in A has a greater amount of kinetic energy than B. Meanwhile , energy should be conserved, so it means portion heat energy flow to A and is stored as kinetic energy of particles is lower than B. NOW, WHERE DOES THE REST PORTION OF THE THERMAL ENERGY FLOW TO A converted to? the electrical potential energy(another component of internal energy) of the particles in A ? if so that means object with high specific heat capacity has a lower tendency to store the thermal energy received in the form kinetic energy of particles? can somebody explain this to me? or correct me if i am wrong. Thanks a lot. Sci Advisor HW Helper P: 6,679 Quote by Yh Hoo Now consider two objects,A and B. A has a higher specific heat capacity that B. When both object is subjected to same amount of thermal or heat energy, rise in temperature in A is lower as our common reason(A has a higher specific heat capacity) But what stated by First law of thermodynamics that Increase in internal energy is caused by heat energy transfer to in and work done on it. since temperature is a measure of average kinetic energy of particles in a system, Temperature is the measure of only one kind of kinetic energy: translational kinetic energy (energy due to the motion of the centre of mass of the molecules). Rotational and vibrational kinetic energies do not directly affect temperature. it means particles in A has a greater amount of kinetic energy than B. Meanwhile , energy should be conserved, so it means portion heat energy flow to A and is stored as kinetic energy of particles is lower than B. NOW, WHERE DOES THE REST PORTION OF THE THERMAL ENERGY FLOW TO A converted to? the electrical potential energy(another component of internal energy) of the particles in A ? if so that means object with high specific heat capacity has a lower tendency to store the thermal energy received in the form kinetic energy of particles? can somebody explain this to me? or correct me if i am wrong. Thanks a lot. Your question is a good one. There are two aspects to this. Higher heat capacity could be due to stronger forces between molecules (so some energy is stored as potential energy). It could also be due to additional degrees of freedom of the molecules (some energy stored as vibrational or rotational energy of molecules). AM P: 73 wow thanks a lot! it is sufficient for me already as a pre u student. Related Discussions Introductory Physics Homework 3 Advanced Physics Homework 4 Advanced Physics Homework 1 Introductory Physics Homework 2 Introductory Physics Homework 1

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# Is DSPACE properly contained in NSPACE? It may be a dumb question, but is $\mathsf{DSPACE}(f(n)) \subset \mathsf{NSPACE}(f(n))$ or is $\mathsf{DSPACE}(f(n)) \subseteq \mathsf{NSPACE}(f(n))$? In other words, is the containment relation proper or not? Wikipedia says the first one, while the ComplexityZoo says the other one. It's open whether $\mathsf{DSPACE}(\log n) = \mathsf{NSPACE}(\log n)$, which is the $\mathsf{L}=\mathsf{NL}$ question. As far as I know, the closest thing we can say are theorems by Savitch $\mathsf{NSPACE}(f(n)) \subseteq \mathsf{DSPACE}(f(n)^2)$ and Immerman–Szelepcsényi's ($\mathsf{NSPACE}$ is closed under complement). Also see AndrewK's answer regarding the subset symbol, I think this is the issue here. • There we go! The jump to L vs. NL is a short one too. For reference: $DSPACE(f(n)) = \{L|L$ can be decided by a deterministic TM in $O(f(n))$ space.$\}$ $NSPACE(f(n)) = \{L|L$ can be decided by a non-deterministic TM in $O(f(n))$ space.$\}$ Jan 17, 2014 at 23:49 It's not a dumb question. One thing to note is that not all literature agrees on how exactly to use the different subset symbols. It is entirely plausible that two sources could be using the same symbols to mean different things, thereby communicating the same information! Confusing, isn't it? Pending review: For an intuitive understanding, think about how non-deterministic TMs theoretically work. They can always accomplish the same tasks in the same memory spaces, and they can often also accomplish the same tasks in smaller memory spaces. This means more spaces are available to a non-deterministic TM. NSPACE contains more than just DSPACE. DSPACE is a proper/strict subset of NSPACE. • Do you know a proof that DSPACE is a proper/strict subset of NSPACE? $\:$ (That is a stronger statement than "The set of DSPACE machines is a proper/strict subset of the set of NSPACE machines.".) $\hspace{1.15 in}$ – user12859 Jan 17, 2014 at 21:58 • @RickyDemer You know, I've been looking for that myself. Intuitively it makes sense, Wikipedia claims it's true, but where's the proof? There's a reference to Savitch's theorem, but that's for $NSPACE(f(n))\subseteq DSPACE((F(n))^2)$. I'm going to strike it out for now. Jan 17, 2014 at 22:18

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The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS. The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!) A217861 Number of functions on n unlabeled nodes in which all the components are distinct. 0 1, 1, 2, 6, 14, 38, 103, 280, 773, 2160, 6053, 17064, 48320, 137260, 391091, 1117192, 3198217, 9173480, 26357393, 75845591, 218550709, 630536447, 1821184411, 5265514692, 15238183779, 44136519841, 127940010907, 371135327740, 1077340058523, 3129301019091, 7015876423459 (list; graph; refs; listen; history; text; internal format) OFFSET 0,3 LINKS Table of n, a(n) for n=0..30. FORMULA O.g.f.: Product_{n>=1} (1 + x^n)^A002861(n). MATHEMATICA Needs["Combinatorica`"]; nn=30; s[n_, k_]:=s[n, k]=a[n+1-k]+If[n<2 k, 0, s[n-k, k]]; a[1]=1; a[n_]:=a[n]=Sum[a[i] s[n-1, i] i, {i, 1, n-1}]/(n-1); rt=Table[a[i], {i, 1, nn}]; c=Drop[Apply[Plus, Table[Take[CoefficientList[CycleIndex[CyclicGroup[n], s]/.Table[s[j]->Table[Sum[rt[[i]] x^(k*i), {i, 1, nn}], {k, 1, nn}][[j]], {j, 1, nn}], x], nn], {n, 1, 30}]], 1]; CoefficientList[Series[Product[(1+ x^i)^c[[i]], {i, 1, nn-1}], {x, 0, nn}], x] (* after code given by Robert A. Russell in A000081 *) CROSSREFS Sequence in context: A006654 A127546 A192484 * A188492 A263732 A263733 Adjacent sequences: A217858 A217859 A217860 * A217862 A217863 A217864 KEYWORD nonn AUTHOR Geoffrey Critzer, Oct 13 2012 STATUS approved Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents The OEIS Community | Maintained by The OEIS Foundation Inc. Last modified June 18 16:37 EDT 2024. Contains 373482 sequences. (Running on oeis4.)

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# Which set is a subset of every set? ## Which set is a subset of every set? The only set which is a subset of every set is the empty set. The only set which is a subset of every set is the empty set. This can easily be demonstrated by noting that two sets can be disjoint; that is, they contain no common elements. Let A and B be any two non empty disjoint sets. ## Is every proper subset a subset? A proper subset of a set A is a subset of A that is not equal to A. In other words, if B is a proper subset of A, then all elements of B are in A but A contains at least one element that is not in B. The set C={1,3,5} is a subset of A, but it is not a proper subset of A since C=A. ... subset ## Why is phi a subset of every set? If by 'phi' you mean the empty set, then it is a subset of every set, including itself, as a consequence of the underlying logic, which is classical. So, the standard way of dealing with the usual material conditional holds. ## Is 5 a subset of every set? A set is a subset of a set if has no elements that are not also in : Since the empty set has no elements, it is clearly a subset of every set. ## Can a subset be empty? A set is a subset of itself since a set contains all its elements. Also, the empty set is a subset of every set, because every element in the empty set belongs to any set since the empty set has no elements. ## Why null set is called a set? In mathematical sets, the null set, also called the empty set, is the set that does not contain anything. It is symbolized or { }. There is only one null set. This is because there is logically only one way that a set can contain nothing. ## What is improper subset? An improper subset is defined as a subset which contains all the elements present in the other subset. But in proper subsets, if X is a subset of Y, if and only if every element of set X should be present in set Y, but there is one or more than elements of set Y is not present in set X. ## Which of the following is null sets? Null Set: A set which does not contain any element is called a null set. It is denoted by ϕ or {}. So, {x : |x| = 5, x ∈ N} is not a null set. ... So, {x : x2 = 1, x ∈ Z} is not a null set. ## What is Singleton set with example? A singleton set is a set containing exactly one element. For example, {a}, {∅}, and { {a} } are all singleton sets (the lone member of { {a} } is {a}). The cardinality or size of a set is the number of elements it contains.

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Switch Editions? Cancel Sharing: Title: URL: Channel: CodeSection,代码区,网络安全 - CodeSec Viewing all articles # Introduction to ggraph: Nodes 0 0 This is the second post in my series of ggraph introductions. Thefirst post introduced the concept of layouts, which is simply a specification on how nodes should be placed on a plane. This post will dive into how the nodes are drawn, once a layout has been calculated. Nodes Nodes in a network are the entities that are connected. Sometimes these are also referred to as vertices, but ggraph has opted for this nomenclature and use it consistently. While the nodes in a graph are the abstract concepts of entities, and the layout is their physical placement, the node geoms is the visual manifestation of the entities. Conceptually one can simply think of it in terms of a scatter plot ― the layout provides the x, and y coordinates and these can be used to draw nodes in different ways in the plotting window. Actually, due to the design of ggraph the standard scatterplot-like geoms from ggplot2 can be used directly for plotting nodes: library(ggraph) library(igraph) gr <- graph_from_data_frame(highschool) ggraph(gr, layout = 'kk') + geom_point(aes(x=x, y=y)) The reason this works is that, as discussed in the previous post, layouts return a data.frame of node positions and metadata and this is used as the default plot data: #> x y name circular ggraph.index #> 1 0.2782438 2.4944195 1 FALSE 1 #> 2 0.1365268 3.1063039 2 FALSE 2 #> 3 0.9329938 3.2168940 3 FALSE 3 #> 4 -2.5457734 -1.5139415 4 FALSE 4 #> 5 -2.8447634 -0.2267242 5 FALSE 5 #> 6 -2.9897376 1.7369304 6 FALSE 6 geom_node_*() While usage of the default ggplot2 is absolutely allowed, ggraph comes with its own set of node geoms. Many of these are direct translations of ggplot2 own geoms like geom_point() so one could wonder why bother to use them. The first reason is to provide clear code. It is not apparent anywhere that the standard geoms are addressing the nodes and using geom_node_*() makes it clear that this layer will draw nodes. The second reason is that it will save typing. Since ggraph are in control of the shape of the input data through the layout calculations, it knows that x and y position is encoded in an x and y column. This means that geom_node_* can default the x and y aesthetics so there’s no need to type them: ggraph(gr, layout = 'kk') + geom_node_point() sometimes there is a need for addressing the x and y aesthetics, which is still possible, for instance if a partition layout should be inverted: gr <- graph_from_data_frame(flare\$edges, vertices = flare\$vertices) ggraph(gr, layout = 'partition') + geom_node_tile(aes(y = -y, fill = depth)) of course this could also be accomplished by reversing the y-axis using scale_y_reverse() so this is just to illustrate that the defaults are easily overwritten if needed. The third reason is for the added functionality. All ggraph geoms gets a filter aesthetic that allows you to quickly filter the input data. The use of this can be illustrated when plotting a tree: ggraph(gr, layout = 'dendrogram', circular = TRUE) + geom_edge_diagonal() + geom_node_point(aes(filter = leaf)) + coord_fixed() In the above plot only the terminal nodes are drawn by filtering on the logical leaf column provided by the dendrogram layout. The different node geoms The usual suspects are of course provided in the form of geom_node_point() (showcased above), geom_node_text() , and geom_node_label() . These works as expected, taking in the usual aesthetics (plus filter ). Only x and y are defaulted so everything else must be provided e.g. label which does not defaults to the name column like is done in igraph . One feature sets geom_node_text() and geom_node_label() from their ggplot2 counterparts: both have a repel argument that, when set to TRUE will use the repel functionality provided by the ggrepel package to avoid overlapping text. Apart from these three geoms there’s a set of geoms mainly useful for spatial node layouts such as treemaps, partition, and circle packing. geom_node_tile() is the ggraph counterpart to ggplot2 s geom_tile() while geom_node_circle() and geom_node_arc_bar() maps to ggforce s geom_circle() and geom_arc_bar() . Collective for these is that the spatial dimensions of the geoms (e.g. radius, width, and height) are precalculated by their intended layouts and defaulted be the geoms: ggraph(gr, layout = 'treemap', weight = 'size') + geom_node_tile(aes(fill = depth)) all spatial node geoms will be center-based, meaning that the x and y value of the layout will refer to the center of the layout and not e.g. the bottom-left corner. This makes it easier to add labels to spatial layouts as well as using spatial layouts in a non-spatial way: l <- ggraph(gr, layout = 'partition', circular = TRUE) l + geom_node_arc_bar(aes(fill = depth)) + coord_fixed() l + geom_edge_diagonal(aes(width = ..index.., alpha = ..index..), lineend = 'round') + scale_edge_width(range = c(0.2, 1.5)) + geom_node_point(aes(colour = depth)) + coord_fixed() More node geoms are sure to appear in ggraph with time but they will generally be quite easily comprehensible due to their strong assemblance to the standard ggplot2 geoms. After all it is just points on a plane… More to come This concludes our tour of the different ways to draw nodes in ggraph . Next up is edges and it is fair to say that this is where it really gets exciting. Stay tuned! Viewing all articles ### 动画「最弱无败的神装机龙」开播 看裸体等要素依旧 More Pages to Explore .....

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# LeetCode 111. Minimum Depth of Binary Tree Problem: Given a binary tree, find its minimum depth. The minimum depth is the number of nodes along the shortest path from the root node down to the nearest leaf node. Solution: DFS /** * Definition for a binary tree node. * public class TreeNode { * int val; * TreeNode left; * TreeNode right; * TreeNode(int x) { val = x; } * } */ public class Solution { public int minDepth(TreeNode root) { if (root == null) return 0; return minDepth(root, 0); } private int minDepth(TreeNode root, int current) { if (root.left == null && root.right == null) return current + 1; else if (root.left == null) return minDepth(root.right, current + 1); else if (root.right == null) return minDepth(root.left, current + 1); else return Math.min(minDepth(root.left, current + 1), minDepth(root.right, current + 1)); } }

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# Induction Help (1 Viewer) #### Francis006 ##### New Member The equation x^2+x+1=0 has roots a and b. Also, a series is defined by Tn=a^n+b^n for n=1,2,3,4... a) Show that T1=-1 and T2= -1 (completed, but included for context) b) Show that Tn = -Tn-1 - Tn-2 for n=3,4,5... (I have no clue from here) c) Hence use induction to show that Tn=2cos(2nπ/3) for n=1,2,3... d) Hence write down the value of Σn=2012 k=1 Tk #### Luukas.2 ##### Well-Known Member Part (b) is a LHs = ... and RHS = ... \bg_white \begin{align*} \text{By definition:} \qquad \text{LHS} &= T_n \\ &= a^n + b^n \qquad \text{where a and b are the roots of x^2 + x + 1 = 0} \\ \\ \text{RHS} &= -T_{n-1} - T_{n-2} \qquad \text{provided n > 2 and n \in \mathbb{Z}} \\ &= -\left(a^{n-1} + b^{n-1}\right) - \left(a^{n-2} + b^{n-2}\right) \qquad \text{by definition} \\ &= -a^{n-2}\left(a + 1\right) - b^{n-2}\left(b + 1\right) \\ &= -a^{n-2} \times -a^2 - b^{n-2} \times -b^2 \qquad \text{as both x = a and x = b satisfy the equation x + 1 = -x^2} \\ &= a^n + b^n \\ &= \text{LHS} \qquad \text{as required} \end{align*} Part (c) will require strong induction: • Prove the result for $\bg_white n = 1$ and $\bg_white n = 2$ • Assume it is true for $\bg_white n = k$ and $\bg_white n = k + 1$ • Use that assumption with the definition of the recurrence, $\bg_white T_{k+2} = -T_{k+1} - T_{k}$ to establish the result for $\bg_white n = k + 2$.​ Part (d), the sum, can likely be done with a telescoping series-type approach or by establishing the repeating pattern of values of the sequence - the latter approach will be easier in this case (in the sense of being more obvious), though the former is quicker. Last edited: Thank You

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## Can you do confirmatory factor analysis in SPSS? SPSS does not include confirmatory factor analysis but those who are interested could take a look at AMOS. ## Is Amos SPSS free? Amos is included in the Premium edition of SPSS Statistics (except in Campus Edition, where it is sold separately). Does SPSS have a free trial? The free trial lasts for 30 days and begins immediately after you register. You are allowed to have a free trial only once per year. How do you perform a confirmatory factor analysis? There are several steps involved in a CFA. They are specification, identification, estimation, model fit and hypothesis testing, and interpretation of results. ### How do you interpret a factor analysis in SPSS? Initial Eigenvalues Total: Total variance. Initial Eigenvalues % of variance: The percent of variance attributable to each factor. Initial Eigenvalues Cumulative %: Cumulative variance of the factor when added to the previous factors. Extraction sums of Squared Loadings Total: Total variance after extraction. ### What is confirmatory factor analysis example? For example, if it is posited that there are two factors accounting for the covariance in the measures, and that these factors are unrelated to one another, the researcher can create a model where the correlation between factor A and factor B is constrained to zero. Can I do SEM in SPSS? Yes, you can use SPSS to carry out SEM. What is difference between SPSS and Amos? IBM SPSS Amos is a software program used to fit structural equation models (SEM). Unlike SPSS Statistics, SPSS Amos is only available for the Windows operating system. Amos is technically a “standalone” program: it can be installed and used without having SPSS Statistics installed on the machine. ## Can we download SPSS for free? IBM SPSS is commercially available, copyrighted software, and is not available for free. Yes, its true that IBM SPSS is copyrighted software, and from any website, it is not available for free. However, you can download it from your university website (if available). ## Which is better SPSS or R? R has stronger object-oriented programming facilities than SPSS whereas SPSS graphical user interface is written using Java language. It is mainly used for interactively and statistical analysis. On the other hand, Decision trees in IBM SPSS are better than R because R does not offer many tree algorithms. Which software is best for confirmatory factor analysis? Usually, statistical software like AMOS, LISREL, EQS and SAS are used for confirmatory factor analysis. In AMOS, visual paths are manually drawn on the graphic window and analysis is performed. In LISREL, confirmatory factor analysis can be performed graphically as well as from the menu. Why would you use confirmatory factor analysis? Confirmatory factor analysis (CFA) is a statistical technique used to verify the factor structure of a set of observed variables. CFA allows the researcher to test the hypothesis that a relationship between observed variables and their underlying latent constructs exists. ### Can you do a confirmatory factor analysis in SPSS? This can be done in SPSS. Since this has been covered in other datasets, we focus on the main CFA operation but highlight that several of the animosity items have positive skewness and kurtosis. For the purpose of demonstration, we retain the raw data. ### How to use one factor confirmatory factor analysis? 1. One Factor Confirmatory Factor Analysis. The most fundamental model in CFA is the one factor model, which will assume that the covariance (or correlation) among items is due to a single common factor. Much like exploratory common factor analysis, we will assume that total variance can be partitioned into common and unique variance. Is there an EFA procedure for SPSS factor? The Factor procedure that is available in the SPSS Base module is essentially limited to exploratory factor analysis (EFA). The solution you see will be the result of optimizing numeric targets, given the choices that you make about extraction and rotation method, the number of factors to retain, etc. Suppose that you have a particular factor How is multiple Group factor analysis ( CFA ) used in SPSS? (See Technote #1476881, “Multiple Group Factor Analysis in SPSS”) for a discussion of multiple group factor analysis, an approach to CFA that could be addressed in part through SPSS). The predominant CFA approach today is to consider CFA as a special case of structural equation modeling (SEM).

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Suche Bilder Maps Play YouTube News Gmail Drive Mehr » Anmelden Books Bücher To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle. The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ... - Seite 45 von Robert Simson - 1775 - 520 Seiten Vollansicht - Über dieses Buch ## The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Robert Simson - 1806 - 518 Seiten ...Therefore, if a parallelogram, fcc. QED PROP. XLII. PROB. % * • TO describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle. Let ABC be the given triangle, and D the given rectilineal angle. It is required to describe a parallelogram... Vollansicht - Über dieses Buch ## Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Band 5 John Mason Good - 1813 - 722 Seiten ...equal to one another. Prop. XLIV. Prob. To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle. Prnp. XLV. Prob. To describe a parallelogram equal to a given rectilineal figure, and having an angle... Vollansicht - Über dieses Buch ## The Elements of Euclid; viz. the first six books, together with the eleventh ... Euclides - 1814 - 558 Seiten ...EBC. Therefore, if a parallelogram, &c. QED PROP. XLII. PROS. To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle. 'to. i. Bisect 3 BC in E, join AE, and at the point E in the 5 23. i. straight line EC make b the angle... Vollansicht - Über dieses Buch ## Easy Introduction to Mathematics, Band 2 Charles Butler - 1814 - 568 Seiten ...also one more : we are " to apply a parallelogram to a given straight line, which parallelogram shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle;" to " apply a parallelogram to a straight line," means to make it on that straight line, or so that... Vollansicht - Über dieses Buch ## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclides - 1816 - 528 Seiten ...1. 23. 1. |•«! 1. s. i 41. i PROP. XLII. PROB. To describe a parallelogram that shall be equal te a given triangle, and have one of its angles equal to a given rectilineal angle. Lot .ABC he the given triangle, and D the given rectilineal angle. It is required to describe a parallelogram... Vollansicht - Über dieses Buch ## Elements of Geometry: Containing the First Six Books of Euclid, with a ... Euclid, John Playfair - 1819 - 348 Seiten ...complements, &c.. Q, E. I). A PROP. XLIV. PROB. To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its...to a given rectilineal angle. Let AB be the given straight line, and C the given triangle, and D the given rectilineal angle. It is required to apply... Vollansicht - Über dieses Buch ## Elements of Geometry: Containing the First Six Books of Euclid: With a ... John Playfair - 1819 - 317 Seiten ...complements, &c. QED PROP. XLIV. PROB. To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal anglef Let AB be the given straight line, and C the given triangle, and D the given rectilineal angle.... Vollansicht - Über dieses Buch ## A Popular Course of Pure and Mixed Mathematics ...: With Tables of ... Peter Nicholson - 1825 - 372 Seiten ...Therefore, if a parallelogram, &c. Q ED Proposition XLI1. Problem. To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle. Let ABC be the given triangle, and D the given rectilineal angle. It is required to describe a parallelogram... Vollansicht - Über dieses Buch ## Elements of Geometry: Containing the First Six Books of Euclid, with a ... Euclid, John Playfair - 1826 - 326 Seiten ...EBC. Therefore, if a parallelogram, £e. QED PROP. XLII. PROB. To deseribe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a givea reetilineal angle. Let ABC be the giyen triangle, and D the given reetilineal angle* D C It is... Vollansicht - Über dieses Buch ## The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ... Robert Simson - 1827 - 513 Seiten ...Conslr. * 38. 1. •41.1. t6 Ax. t Constr. PROP. XLII. PROB. To descr1be a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle. Let ABC be a given triangle, and D the given rectilineal angle. It is required to describe a parallelogram... Vollansicht - Über dieses Buch

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Search All of the Math Forum: Views expressed in these public forums are not endorsed by NCTM or The Math Forum. Notice: We are no longer accepting new posts, but the forums will continue to be readable. Topic: Difference in cumsum/filter Replies: 1   Last Post: Feb 23, 2013 12:38 AM Messages: [ Previous | Next ] Peter Mairhofer Posts: 41 Registered: 8/18/10 Re: Difference in cumsum/filter Posted: Feb 23, 2013 12:38 AM On 2013-02-22 20:42, Peter Mairhofer wrote: > Hi, Sorry, found the problem for myself. > I want to create an ideal, analog integrator for function x(t). Given > that x(t) is BL to 500Hz, the integration of a signal x=randn(1000,1) > can be replaced by a cumulative sum: > > y1 = cumsum(x) This assumes that x(t) is /not/ a piecewise constant function but rather a sinc interpolation (x(t) is BL to 500). Therefore it is not an exact result but rather an approximation with the finite Riemann sum > On the other hand, I can transfer the ideal integrator 1/s to z-domain > and filter the signal with that: > > [numd, dend] = bilinear([1], [1 0], 1000); > y2 = filter(numd, dend, x) * 1000; And this does the "real" integration based on the same assumptions on x(t). Peter Date Subject Author 2/22/13 Peter Mairhofer 2/23/13 Peter Mairhofer

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The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!) A076069 Largest number formed as concatenation of a permutation of the n consecutive numbers 1+n(n-1)/2, ..., n(n+1)/2 (written in decimal). 1 1, 32, 654, 98710, 1514131211, 212019181716, 28272625242322, 3635343332313029, 454443424140393837, 55545352515049484746, 6665646362616059585756, 787776757473727170696867, 91908988878685848382818079, 9998979695949392105104103102101100 (list; graph; refs; listen; history; text; internal format) OFFSET 1,2 COMMENTS Nontrivial (i.e., different from concatenation in reverse order) whenever a number of the form 10^k is in the considered range of n numbers; then a(n) is given as concatenation (10^k-1)...(1+n(n-1)/2)(n(n+1)/2)...(10^k). LINKS EXAMPLE 1, then a concatenation of a permutation of 2 and 3, then a concatenation of a permutation of 4, 5 and 6. PROG (PARI 2.4.2) a(n)=eval(concat(vecsort(vector(n, i, Str(i+n*(n-1)/2)), , 4))) CROSSREFS Cf. A076068, A080479, A080480, A192392. Sequence in context: A028183 A192392 A076072 * A080480 A028152 A028176 Adjacent sequences:  A076066 A076067 A076068 * A076070 A076071 A076072 KEYWORD nonn,easy,less,base AUTHOR M. F. Hasler, Jun 29 2011 EXTENSIONS Definition modified to obtain a new sequence different from (earlier duplicate) A080480. M. F. Hasler, Jun 29 2011. STATUS approved Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent The OEIS Community | Maintained by The OEIS Foundation Inc. Last modified September 29 04:57 EDT 2020. Contains 337420 sequences. (Running on oeis4.)

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This question's due date has already passed. You may post a tutorial, but there's no guarantee that the original asker will purchase the tutorial. But other people might! Question # \$0.25Multiply. Simplify. Rating :No Rating Tutorials Posted: 7, Earned: \$19.80 Q: Multiply. Simplify. 7w^3*3v^7w^5*2v Available Tutorials to this Question \$0.25 • This tutorial was purchased 1 time and rated A+ by students like you. • Posted on Feb. 17, 2011 at 12:18:10AM Posted by : Rating (24):A Tutorials Posted: 153, Earned: \$315.74 A: Preview: ... ply 21v^(7)w^(8) by 2v to get 42 ... The full tutorial is about 14 words long . \$0.25 Detailed solution • This tutorial hasn't been purchased yet. • Posted on Feb. 17, 2011 at 12:20:01AM Posted by : Rating (1015):A+ Tutorials Posted: 2604, Earned: \$17,082.37 A: Preview: ... =7w 3*w 5* ... The full tutorial is about one word long . \$0.25 • This tutorial hasn't been purchased yet. • Posted on Feb. 17, 2011 at 12:22:29AM Posted by : Rating (4):D

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you are viewing a single comment's thread. [–]Logic 12 points13 points  (11 children) sorry, this has been archived and can no longer be voted on this is true for any right triangle on a chess board. suppose ABC is a right triangle on a the board, with AB and BC the legs forming the right angle (B the point at that angle). If AB=BC in length, position the queen opposite to position B (forming a square). If, WLOG, AB>BC in length, position the queen on the line AB so that it is on a square diagonal to C. [–]Low-Dimensional Topology 8 points9 points  (7 children) sorry, this has been archived and can no longer be voted on But first you have to show that ABC can only be placed on the board by making AB and BC be horizontal and vertical segments. [–] 7 points8 points  (6 children) sorry, this has been archived and can no longer be voted on For example, the distances between the locations (0,0), (12,16) and (-12,9) form a pythagorian triple, but the locations cannot all be attacked by a single queen. [–] 0 points1 point  (2 children) sorry, this has been archived and can no longer be voted on But those distances do not form a Pythagorean triple. A Pythagorean triple consists of three integers, and those three integers can always be used to construct a chessboard triangle with one horizontal and one vertical side. [–] 0 points1 point  (1 child) sorry, this has been archived and can no longer be voted on Which side do you believe has non-integer length, or do you believe that the sides don't satisfy pythagoras's equation? [–] 1 point2 points  (0 children) sorry, this has been archived and can no longer be voted on Sorry, I see this is a (15, 20, 25) triangle and is therefore indeed integer-sided. The point I was trying to make is that this Pythagorean triple (15, 20, 25) can also be represented by a chessboard triangle with a vertical and a horizontal edge, for which it is possible to place a queen to attack all three squares at once; so the answer to the original question remains "all Pythagorean triples have this property", though 17_Gen_r is incorrect that it is true "for any right triangle on a chess board." [–] 0 points1 point  (1 child) sorry, this has been archived and can no longer be voted on This triangle has side lengths 20, 15 and 7. They are all integer, but do not form a right triangle. [–] 0 points1 point  (0 children) sorry, this has been archived and can no longer be voted on d((12,16),(-12,9)) = sqrt((12-(-12))2 +(16-9)2 ) = sqrt(242 +72 ) = sqrt(576+49) = sqrt(625) = 25. [–] 0 points1 point  (2 children) sorry, this has been archived and can no longer be voted on Not all right triangles are Pythagorean triples. [–]Logic 0 points1 point  (1 child) sorry, this has been archived and can no longer be voted on indeed, but all pythagorean triples are right triangles. [–] 0 points1 point  (0 children) sorry, this has been archived and can no longer be voted on But he was asking for more Pythagorean triples. Not merely asking for any old right triangle.

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# Learning by doing: Regression Learning by doing is both rewarding and challenging. Many institutes worldwide have embraced this path to engage with students. I regularly have a component of hands-on projects in my courses, here is a partial list of regression projects carried out by my class in the last semester. E-waste and economy: Abhijit Manek, Deven Parikh and Shivam Sony followed the research paper by Sigrid Kusch-Brandt and Colin Hills to verify that as per capita GDP-PPP increase the e-waste generation increases linearly. Ph and TDS relation in waste-water from dye industries: Saumya Parekh, Deep Wadher and Preet Sangani studied waste water from Dye industry and followed the work by Farhana Maqbool to show that the Ph values in the waste water are a good indicator of TDS values. Space-launch success rates: Shubham Ghodasara, Dhruv Shah and Ruchit Trived used data from wikipedia and from space-launch report to show that the success rate of space-launch has nearly saturated with time. Carrier Selection in Gujarat: Haard Monpara, Tirth Panchamia and Jeet Dand collected data from various newspaper sites on the number of students appearing for Science or General stream exams over the last 10 years to study the trends and fluctuations. Cricket score prediction: Manush Gami, Heet Patel and Ashutosh Mehta were interested in looking at T-20 match scores as a function of overs bowled. Their data came from a random sample. Birth rate in India: Aashman Dave, Sagar Shah and Nikhil Tantia studied birth-rate per 1000 people in India from 2005 to 2016 from knoema.com and found a very good fit showing a downward trend. Smokers in India: Praj Patel, Parva Raval and Aman Desai looked at percentage of population that smokes, using data from ourworldindata.org. They found a downward trend in data from 1980 to 2012. Accidents in Gujarat: Darshil Kothari, Pavitra Patel and Kenil Shah did a polynomial fit on the accident data in Gujarat from 1999 to 2017 from rtogujarat.gov.in to study the trend. Population growth in Gujarat: Nisarg Gandhi, Niraj Maniyar and Kaustubh Patel studied the population growth in Gujarat and found a very good linear fit. Engine Horse-power and milage: Gimil Shah, Chirant Patel and Ishan Patel collected data from the websites of different car companies to study the relationship between engine horse-power and fuel efficiency. Home-loan interest rates: Samay Patel, Parth Varshani and Aman Shah analysed home-loan amount and interest rates trends usinf data from the SBI website. Alcohol consumption and GDP: Yashh Raj, Tathya Shah and Samyak Thaker analysed the trend for the Graph of alcohol consumption and GDP, with data from wikipedia, ourworldindta.org and alcohol.org (To be continued) ## Author: strangeset A nomad at heart, I enjoy observing, analysing, connecting, understanding and dreaming. I am a big fan of science and tech. Forever learning and experimenting.

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# Math posted by . A continuously running washing machine receives jolts in a Poisson process at an average rate of 5 jolts per hour. The probability that it receives no jolts in given 20 minutes run e-5,e-5/3,e-100,e-100/3 • Math - how much are 8 pens at 90c each ## Similar Questions 1. ### MATH - probability #2 A rescue squad spokesperson claims that the squad receives an average of 3 calls per hour. If at most 6 calls were received over a 5-hour period, would you suspect that the spokesperson was overestimating the average number of calls … 2. ### math a paint supplier has two machines that prouce both indoor paint and outdoor paint. to meet its contractual obligations,the company must produce at least 60 gallons of indoor paint and 100 gallons of outdoor paint. machine 1 makes 3 … 3. ### math a paint supplier has two machines that prouce both indoor paint and outdoor paint. to meet its contractual obligations,the company must produce at least 60 gallons of indoor paint and 100 gallons of outdoor paint. machine 1 makes 3 … 4. ### Math This is the question. In 1991, an American, Ann Trason, set a world record by running 100 km in 7hr,50min,09sec. What is the best estimate of her average speed? 5. ### statistics A sales firm receives an average of four calls per hour on its toll-free number. For any given hour, find the probability that it will receive exactly eight calls 6. ### Probability and statistics 7. A Continuously running washing machine receives jolts in a Poisson process at an average rate of 5 jolts per hour. The probability that it receives no jolts in given 20 minute run Choose one answer a. e−5 b. e−5/3 c. … 7. ### statistics A continuously running washing machine receives jolts in a Poisson process at an average rate of 10 jolts per hour. The standard deviation of the number of jolts received in given 20 minute run is equal to 8. ### Maths Probability A dedicated professor has been holding infinitely long office hours. Undergraduate students arrive according to a Poisson process at a rate of λu=3 per hour, while graduate students arrive according to a second, independent Poisson … 9. ### Math A single processing machine makes two components, A and B, which are packaged together as the final product (each product sold contains one A and one B). The processor can make only one component at a time. There is a setup time when … 10. ### Math Aubrey can run at a pace of 6 miles per hour. Running at the same rate, how many miles can she run in 90 minutes? More Similar Questions

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Ideal Gas An ideal gas is one which follows the following simple equation. PV= Mrt                                                          … (2.9) where P, V and Tare the pressure, volume and temperature of the gas having mass m, and R is the gas constant. Dividing both sides of equation (2.9) by m we get, P ( V / m) = RT Pv = RT where v = V/ m = specific volume of the gas. In reality, there is no gas which is an ideal gas or perfect gas. However all gases, at a very low pressure and density approach to ideal gas. If the state of an ideal or perfect gas having mass m is changed from P1, V1, T1 to P2, V2, T2 then from equation (2.9) we get P1 V1 / T1 = P2 V2 / T2 = Mr = contant T2 / T1 = P2 V2 / P1 V1 The relationship of eqn. (2.10) may be used for calculating or comparing the temperatures. The relationship given in equation (2.9) is called ideal gas equation of state. SOLVED EXAMPLE Example 2.1. The temperature t (0c) on a thermometric scale is defined in terms of a property K by the relation t =a InK+ b. where a and bare constants. The values of K are found to b~ 1.83 and 6.78 at the ice point and the steam point, the temperature of which are assigned 0 and 100 respectively. Calculate the temperature corresponding to a reading of K equal to 2.42 on the termometer. SOLUTION.       t = a In K + b K = 1.83   K = 6.78 t = 0   t = 100 0 = a In 1.83 + b 100  = a In 6,78 + b Solving (2) and (3) for a and b we get a  = 76.355 ,  b = – 46.14 t = 76.355 In  k – 46.14 k = 2.42  => t = 21.34oc.Ans

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# ADDING AND SUBTRACTING ALGEBRAIC EXPRESSIONS Adding and subtracting algebraic expressions : We can use the properties of addition along with the Distributive Property to add and subtract algebraic expressions. ## Adding and subtracting algebraic expressions - Examples Example 1 : Simplify the expression given below. (3x + 1/2) + (7x - 4 1/2) Solution : Step 1 : Group the like terms (3x + 7x) + (1/2 - 4 1/2) Step 2 : Simplify 10x - 4 Hence, (3x + 1/2) + (7x - 4 1/2)  =  10x - 4 Example 2 : Simplify the expression given below. (-0.25x - 3) - (1.5x + 1.4) Solution : Step 1 : Distribute the negative sign to the terms in the second parenthesis. -0.25x - 3 - 1.5x - 1.4 Step 2 : Group the like terms (-0.25x -1.5x) + (-3 - 1.4) Step 3 : Simplify -1.75x - 4.4 Hence, (3x + 1/2) + (7x - 4 1/2)  =  -1.75x - 4.4 Example 3 : Simplify the expression given below. (5x - 3y + 4z) + (1.5x + 0.4y + 8) Solution : Step 2 : Group the like terms (5x + 1.5x) + (-3y + 0.4y) + 4z + 8 Step 3 : Simplify 6.5x - 2.6y + 4z + 8 Hence, (5x - 3y + 4z) + (1.5x + 0.4y + 8)  =  6.5x - 2.6y + 4z + 8 Example 4 : Simplify the expression given below. (2a - 3b + c) - (4b - 3a + c) Solution : Step 1 : Distribute the negative sign to the terms in the second parenthesis. 2a - 3b + c - 4b + 3a - c Step 2 : Group the like terms (2a + 3a) + (-3b - 4b) + (c - c) Step 3 : Simplify 5a - 7b Hence, (2a - 3b + c) - (4b - 3a + c)  =  5a - 7b Example 5 : Jill and Kyle get paid per project. Jill is paid a project fee of \$25 plus \$10 per hour. Kyle is paid a project fee of \$18 plus \$14 per hour. Write an expression to represent how much a company will pay to hire both to work the same number of hours on a project. Solution : Step 1 : Write expressions for how much the company will pay each person. Let h represent the number of hours they will work on the project. Jill : \$25 + \$10h               Kyle: \$18 + \$14h Fee + Hourly rate × Hours      Fee + Hourly rate × Hours Step 2 : Add the expressions to represent the amount the company will pay to hire both. Combine their pay : =  25 + 10h + 18 + 14h Use the Commutative Property : =  25 + 18 + 10h + 14h Combine like terms : =  43 + 24h Hence, the company will pay 43 + 24h dollars to hire both Jill and Kyle. After having gone through the stuff given above, we hope that the students would have understood "Adding and subtracting algebraic expressions". Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here. WORD PROBLEMS HCF and LCM  word problems Word problems on simple equations Word problems on linear equations Algebra word problems Word problems on trains Area and perimeter word problems Word problems on direct variation and inverse variation Word problems on unit price Word problems on unit rate Word problems on comparing rates Converting customary units word problems Converting metric units word problems Word problems on simple interest Word problems on compound interest Word problems on types of angles Complementary and supplementary angles word problems Double facts word problems Trigonometry word problems Percentage word problems Profit and loss word problems Markup and markdown word problems Decimal word problems Word problems on fractions Word problems on mixed fractrions One step equation word problems Linear inequalities word problems Ratio and proportion word problems Time and work word problems Word problems on sets and venn diagrams Word problems on ages Pythagorean theorem word problems Percent of a number word problems Word problems on constant speed Word problems on average speed Word problems on sum of the angles of a triangle is 180 degree OTHER TOPICS Profit and loss shortcuts Percentage shortcuts Times table shortcuts Time, speed and distance shortcuts Ratio and proportion shortcuts Domain and range of rational functions Domain and range of rational functions with holes Graphing rational functions Graphing rational functions with holes Converting repeating decimals in to fractions Decimal representation of rational numbers Finding square root using long division L.C.M method to solve time and work problems Translating the word problems in to algebraic expressions Remainder when 2 power 256 is divided by 17 Remainder when 17 power 23 is divided by 16 Sum of all three digit numbers divisible by 6 Sum of all three digit numbers divisible by 7 Sum of all three digit numbers divisible by 8 Sum of all three digit numbers formed using 1, 3, 4 Sum of all three four digit numbers formed with non zero digits Sum of all three four digit numbers formed using 0, 1, 2, 3 Sum of all three four digit numbers formed using 1, 2, 5, 6

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## Welcome to H3 Maths Blog Support for Growing Mathematicians ## Posts tagged with 2015 ### Welcome to 2015 January1 2015 (MMXV) is the 2015th year of Anno Domini (“in the year of the/our Lord”, abbreviated AD) designations, the 15th year of the 3rd millennium, the 15th year of the 21st century, and the 6th year of the 2010s decade. Because the world is divided into Time Zones, we were able to celebrate the New Year first […] by posted under Uncategorized | tagged under , , ,  |  Comments Off on Welcome to 2015 #### Post Support 10 x 9 x 8 + (7 + 6) x 5 x 4 x (3 + 2) x 1 = 2020 NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is: y(y-8) = 9 –> y.y – 8y – 9 =0 –> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y) Using the top and bottom of the rectangle, x = (y-8)(y+2) = (9-8)(9+2) = 11 but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side?? [I think that the left had side was a mistake and should have read (x+4)?]

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# New Series of Time Series: Part 1 In this new series I am going to look at the time series models and how we able to use them for forecasting data. The first need in timeseries data is to have a series of data for years or for some qurdant. imagin that we have a time series data on birth rate from 1946 december to 1956 (file http://robjhyndman.com/tsdldata/data/ nybirths.dat) . this data has some information about the number of birth in each month, moreover, it does not have the date we are going to read data from an url, as data is in “dat” format, we using “scan” function to read it as below : ```births <- scan("http://robjhyndman.com/tsdldata/data/nybirths.dat") ``` the result of runnig this code in Rstudio: “168 items” items have been found. ## 2-Convert to Timeseries Object to work with timeweires data first we should convert them in a Time series Object by using “TS” function in Rstudio. TS function get the data and convert a numeric vector into an R time series object.  in this example, we just add the data with out the time into “births” variable. However, we need the date like start and enddate. TS function also gets some inputs such as: “Frequency” “Start” and “End” : TS(Data, frequency, start, end) Frequency:as its name said, it look for the number of intervals for stored data, for instance for a year we set the value as 12, for quarter we set value as 4. for instance for number of birth in Newyork we should write below codes to convert data into Timeseries : `ts(births, frequency=12, start=c(1946,1))` the births is the data that we collected, the frequency is 12 as in each year we have 12 months, from Jan to Dec. Moreover,  the start of the data was from 1946 Jan, so we have c(1946,1) as a vector for start date. now I am using the “Plot” function to draw the time series data as below `plot(ts(births, frequency=12, start=c(1946,1)))` the chart will be as below : Before heading to analysis the chart, lets look at the other example: I am going to look at the data for milk production for each month from 1962 to 1975, we are going to draw a time series plot for this data. first I import data into R studio as below ```milk<-monthly_milk_production_pounds_p ``` then we convert tha value into a timeseries object and plot it ```milkTS<-ts(milk) plot.ts(milkTS)``` the result will be as below However, the timing is not correct, so I am going to add frequency and start and end time to the data as below ```plot(ts(milkTS,frequency=12,start=c(1962,1),end = c(1975,12))) ``` so, the chart will be like below : ## 3-Timeseries Components as you can see in above charts, these charts talk about different things in one picture 1- Trend 2- Seasonality 3- Irregular component ### Trend trend is about “long-term increase or decrease in the data” . for instance in the milk production we can see there is increase trend in production. ### Seasonality A seasonal pattern when data is influence by seasonal or any order. for instance, in above picture, you see in all years in the second quarter  milk production is high and then in the third quarter is the lowest one (see below ), and this trend is same in all years ### Irregular component there is no trend, seasonality in data ### Combinations In some of time series example we able to see both seasonality and trend (see the below picture). we able to decompose these components: Decompose non seasonal Data: Trend data +irregular Data Decompose Seasonal Data : Seasonal Data +Irregular Data In the above picture, we have both Trend and Seasonality data. (charts shows an increase rate and also a seasonal pattern) so we able to decompose them using a command name “Decompose” ```milkdecompose<-decompose(Milkts) plot(milkdecompose)``` we got the below charts as you can see in the above picture, the milk production has 3 main parts : trend, seasonal and random. in the next part I will talk about the timeseries models more deeply. [3] data about the milk production : https://datamarket.com/data/set/22ox/monthly-milk-production-pounds-per-cow-jan-62-dec-75#!ds=22ox&display=line [4]https://onlinecourses.science.psu.edu/stat510/?q=node/70 Trainer, Consultant, Mentor Leila is the first Microsoft AI MVP in New Zealand and Australia, She has Ph.D. in Information System from the University Of Auckland. She is the Co-director and data scientist in RADACAD Company with more than 100 clients in around the world. She is the co-organizer of Microsoft Business Intelligence and Power BI Use group (meetup) in Auckland with more than 1200 members, She is the co-organizer of three main conferences in Auckland: SQL Saturday Auckland (2015 till now) with more than 400 registrations, Difinity (2017 till now) with more than 200 registrations and Global AI Bootcamp 2018. She is a Data Scientist, BI Consultant, Trainer, and Speaker. She is a well-known International Speakers to many conferences such as Microsoft ignite, SQL pass, Data Platform Summit, SQL Saturday, Power BI world Tour and so forth in Europe, USA, Asia, Australia, and New Zealand. She has over ten years’ experience working with databases and software systems. She was involved in many large-scale projects for big-sized companies. She also AI and Data Platform Microsoft MVP. Leila is an active Technical Microsoft AI blogger for RADACAD. ## 2 thoughts on “New Series of Time Series: Part 1” • Shannon Holck says: Leila, I am really interested in playing with this, but I am not sure where to start. Where are you when you start the first step above? Are you just creating an R script? If so, where? Outside of Power BI? Warning: I know only a smidge of R PS – half your pictures in this post are not visible. • Sure, if I want to explain the steps the first step is to visualize your data by converting it into a timeseries object, then check it wether it has trend or seasonality, also check the acf and pacfchart for it to decide using exponential smoothing or Arima….definatly first you should use R scripts

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cancel Showing results for Did you mean: Earn a 50% discount on the DP-600 certification exam by completing the Fabric 30 Days to Learn It challenge. Anonymous Not applicable ## Counting items within a category - Dax Hi Community, I am stuck with a rather simple looking calculation - but I cannot make any logic towards resolution. It would be of great help if anyone can please provide any direction. I am working on a problem, where I got main frenchise company - calling here, store chain name - say {Pizza_Plannet, The_Pizza_Shop ,etc} then I got list of indivdual store within that chain - say {Pizza_plannet_Sydney, Pizza_plannet_Melbourne, The_Pizza_Shop_Sydney, etc} then there are certain products which each individual store is selling, like pizza, colddrink, cookie All I want to know is, within the main company, how many stores are selling each product & the percentage of stores say only pizza plannet sydney sold cookies , so cookies for pizza plannet will be sold at 50 % of the pizza plannet stores, while all stores of The_Pizza_Shop are selling cookies, so cookies for The_Pizza_Shop will be 100%. below is a tabular snapshot Any help in this regard would be extremely helpful and appriciated. Thanks & regards emudria. 1 ACCEPTED SOLUTION Community Champion @Anonymous See file attached Regards Zubair Please try my custom visuals 5 REPLIES 5 Community Champion @Anonymous Try this calculated Column ```Count of Total Stores in each Chain = CALCULATE ( DISTINCTCOUNT ( Table1[individual store] ), ALLEXCEPT ( Table1, Table1[store chain name] ) )``` Regards Zubair Please try my custom visuals Community Champion @Anonymous And this one ```Count of stores selling a product within each chain = CALCULATE ( DISTINCTCOUNT ( Table1[individual store] ), ALLEXCEPT ( Table1, Table1[store chain name], Table1[Product] ) )``` Regards Zubair Please try my custom visuals Community Champion @Anonymous See file attached Regards Zubair Please try my custom visuals Anonymous Not applicable Thank you @Zubair_Muhammad, it is giving me the right numbers as long as I have dimensions in the table, ie chain, individual store, month, product - but I cannot roll these numbers. Can I make any change here to roll the numbers? Community Champion @Anonymous Hi What is meant by rolling? Regards Zubair Please try my custom visuals Announcements #### New forum boards available in Real-Time Intelligence. Ask questions in Eventhouse and KQL, Eventstream, and Reflex. #### Power BI Monthly Update - May 2024 Check out the May 2024 Power BI update to learn about new features. #### Fabric certifications survey Certification feedback opportunity for the community. Top Solution Authors Top Kudoed Authors

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X^3*3=24 solve this? • X^3*3=24 solve this? Find right answers right now! X^3*3=24 solve this? More questions about Science & Mathematics Positive: 24 % X^3*3=24 solve this? Find answers now! No. 1 Questions & Answers Place. More questions about Science & Mathematics Positive: 21 % More resources Math 96 - Review Problems for Final Exam. Below is a sampling of problems to practice for your final exam. ... (x - 3) = -3 . 24. Solve each quadratic ... Positive: 24 % Step 1 : Equation at the end of step 1 : (4 • ((x - 3) 3)) - 24 • (x - 3) 2 = 0 Step 2 : Equation at the end of step 2 : 4 • (x - 3) 3 - 24 • (x ... Positive: 19 % Solve Calculus Tests. April 18, ... (x 3 /3) – 24 (x 4 /4) + (x 5 /5) ... Solve ∫ (3x ...

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# Mass percent of alcohol in blood. ?????? This question is confusing; can anyone help me solve it? A person's blood alcohol (C2H5OH) level can be determined by titrating a sample of blood plasma with a potassium dichromate solution. The balanced equation is 16 H+(aq) + 2 Cr2O72-(aq) + C2H5OH(aq) 4 Cr3+(aq) + 2 CO2(g) + 11 H2O(l) If 31.45 mL of 0.05971 M Cr2O72- is required to titrate 28.67 g plasma, what is the mass percent of alcohol in the blood?

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# Inches to MM (Millimeters) This simple conversion app helps you to convert inches to MM easily. ## How to use this Inches to Millimeters calculator? This inches to millimeters conversion app is one of the simplest converters that are available online right now. To use this inches to millimeter conversion app, you just need to insert the value in inches that you want to convert to millimeters and tap on the convert to mm button. Once you tap on the convert button, this app will automatically convert inches to mm and return the answer. The best part about this inches to mm converter is that, once the app is fully compiled, it works offline as well. Along with that, it requires very little internet to run so, it works in places with slower internet connections. ## How to convert Inches to millimeters? 1 inch value is equal to 25.4 mm. To convert these units, you should multiply the value that you want to convert by 25.4. So, by applying this formula, the value for 12 inches is equal to 304.8 mm. ## About Inches & Millimeters Units inches and mm units are often used to measure the length of small objects, animals, or birds. Objects are way smaller than humans. If you are also dealing with objects that are this small then you should learn about the inches to mm conversion because this may help you to deal faster. If you do not want to convert these units on your own then you can easily download our app and convert inches to mm in the most pleasant way.

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510ExampleFinal-1 # Save your worksheet with a filename consisting of the • Notes • 8 This preview shows page 6 - 8 out of 8 pages. Save your worksheet with a filename consisting of the characters “Q7” followed by the code number shown at the bottom of page 1 and your full name (e.g., Q6 707 John Public). Drop a copy in the dropbox on the BioServer. 1 2 3 f 21 f 32 f 23 4 f 24 f 42 Subscribe to view the full document. 03-510 Example Final Exam Name: ________________________ Page 7 of 7 7. (8 points) Consider a system of two state variables (e.g., reactants), A and B, whose direction field is: (a) Draw on this plot the trajectory that the system will follow starting from A(0)=0.1 and B(0)=1. (b) Draw on this plot the trajectory starting from A(0)=0.75 and B(0)=0.5. (c) Draw on this plot the trajectory starting from A(0)=1.5 and B(0)=0.75. (d) How many steady-state solutions does the system have (consider just the range of values of A and B depicted)? What are they? 03-510 Example Final Exam Name: ________________________ Page 8 of 7 8 . (20 points) Write pseudo-code, C++, or Java fragments for the following tasks: (a) Calculating a homology score H for two aligned sequences s1 and s2 of length l using similarity matrix M (b) Displaying an 8-bit h x w image I using a lookup table L (of length 256) and a function PlotPixel ( x , y , graylevel ) You've reached the end of this preview. • Fall '06 • miller • example Final exam {[ snackBarMessage ]} ### What students are saying • As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students. Kiran Temple University Fox School of Business ‘17, Course Hero Intern • I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero. Dana University of Pennsylvania ‘17, Course Hero Intern • The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time. Jill Tulane University ‘16, Course Hero Intern

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# Questions on Algebra: Linear Equations, Graphs, Slope answered by real tutors! Algebra ->  Algebra  -> Linear-equations -> Questions on Algebra: Linear Equations, Graphs, Slope answered by real tutors!      Log On Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help! Algebra: Linear Equations, Graphs, Slope Solvers Lessons Answers archive Quiz In Depth Question 524246: Determine if (-5/6,-1) is a solution to 6x-5y=-10 show work Click here to see answer by josmiceli(9661) Question 524247: Given the linear equation y=-3/5x-4, find the y-coordinates of the points (-5, ), (0, ), and (5, ). Please show all of your work. Plot those points and graph the linear equation. Click here to see answer by mananth(12270) Question 524842: without graphing, how to state the slope and the y- intercept of each line whose equation is given? Click here to see answer by mananth(12270) Question 524953: what is the equation in slope-intercept form of the line that has a slope of -3 and contains the point (1, 1)? Click here to see answer by nerdybill(6951) Question 524953: what is the equation in slope-intercept form of the line that has a slope of -3 and contains the point (1, 1)? Click here to see answer by stanbon(57246) Question 524972: find the slope and the-intercept of the 5x=6y+36 Click here to see answer by nerdybill(6951) Question 524978: find the equation of the line with slope 5/7 and passing through (1,-6) Click here to see answer by Maths68(1474) Question 524991: find the slope if it exists of the containg the pair points (-3,-1) and (-20,-5) Click here to see answer by Maths68(1474) Question 525221: i dont understnad this at all. On my algebra homework it says Parallel y=6x-5 (10,7) and then it says to answer in y=mx+b form. im so confused i dont know what to do at all. can you please just explain what to do if you understand at all. Click here to see answer by scott8148(6628) Question 525256: what is the point of intersection of the following straight lines: y = -9x - 10 -y = -8x + 2 Click here to see answer by tarungehlot(8) Question 525260: Write the slope-intercept equation for the line that passes through (-4, -3) and (-6, 7). Please show all of your work. Click here to see answer by tarungehlot(8) Question 525278: what is the point of intersection of the following pair of straight lines: 6x - 8y = -1 -4x + 8y = 1 Click here to see answer by tarungehlot(8) Question 525262: Write the slope-intercept equation for the line that passes through (-7, 6) and is perpendicular to -7x + 9y = -2 Please show all of your work. Click here to see answer by oberobic(2304) Question 525356: what is the slope and y-intercept for -4(3x - y ) = -5 Click here to see answer by oberobic(2304) Question 525354: what is the slope and y-intercept for 3y + 3 - 2y - 5x/2 =0 Click here to see answer by mananth(12270) Question 525173: I don't get linear equations, slopes, rate. Or whatever x = y, or m=, b=. Like these problems: 3x-y=8. I don't know how to do them, I'm in Pre-Alegbra. I want to be in Algebra 1, but my teacher is Asian! I can not understand her, therefore, I do not know how to do this. Please, help! I really want to pass 8th grade, and be in Algebra 1. Click here to see answer by richard1234(5390) Question 525857: What is the solution for the system of equations? x + 3y = 6 4x + 6y = -6 Click here to see answer by Alan3354(30983) Question 525925: What is the slope of the line containing the points: (-4, -3), (2, 6), and (6, 12) Click here to see answer by stanbon(57246) Question 525574: is this systen of equations: -4x-2y=-4 3x-y=13 independent,dependent, or inconsistent Click here to see answer by ankor@dixie-net.com(15638) Question 525975: graph of the line 3x + 4y = 9 y = 4x – 5. show graph and Use the graph to find the slope of the line Click here to see answer by oberobic(2304) Question 526027: using the substitution method to solve the linear system what is the answer to y=x-4 4x+y=26 please show work. thank you. Click here to see answer by stanbon(57246) Question 526043: which equation represents the line with a slope of 7 that passes through the point (5,-5)? Click here to see answer by scott8148(6628) Question 526021: what is the equation of the line when the x intercept is 2 and contains the point (4,-5) Click here to see answer by mananth(12270) Question 526010: write an equation of the line containing the given poin tand perpendicular to the given line. Express your answer in the form y=mx+b (5,6);2x+y=7 Click here to see answer by mananth(12270) Question 526095: I put in the following problem 7/3-x/3=x/4 in the computer and it gave me the right answer ( 4 ) but I wasn't sure of how it arrived at that answer. I followed the steps it showed until it Came to this -7*x/12+7/3=0 it said the answers is 4 from that. How it got that I don't know. Can you show me an easier way to solve this Problem. Thank you Given problem: 7/3-x/3=x/4 Click here to see answer by Maths68(1474) Question 526258: Write an equation in slope-intercept form for the line that satisfies the following condition. Passes through (8,12, parallel to the line that passes through (12,6) and (37,13) Click here to see answer by Maths68(1474) Question 526266: I need to graph a line with the indicated slope and y intercept. slope= -6 y-int= (0,9). But I don't know how to graph the slope, because i have never encountered a single number slope... I'm very new to this. previously I have solved slopes like 6/8, or 11/3, but never -6. Can you please help?? Thank you very much. Click here to see answer by solver91311(16868) Question 526266: I need to graph a line with the indicated slope and y intercept. slope= -6 y-int= (0,9). But I don't know how to graph the slope, because i have never encountered a single number slope... I'm very new to this. previously I have solved slopes like 6/8, or 11/3, but never -6. Can you please help?? Thank you very much. Click here to see answer by josmiceli(9661) Question 526306: Write the equation of the line in slope-intercept form with a slope of 2 and a y-intercept of -3 Click here to see answer by stanbon(57246) Question 526306: Write the equation of the line in slope-intercept form with a slope of 2 and a y-intercept of -3 Click here to see answer by solver91311(16868) Question 526323: Given the linear equation y = 3x + 1, find the y-coordinates of the points (1, ), (-2, ), (3, ). Please show all of your work. Plot these points and graph the linear equation. Click here to see answer by solver91311(16868) Question 526331: Solving systems of linear equations using the substitution method Problem: 2x-y=6 3x+2y=5 Click here to see answer by stanbon(57246) Question 526414: Find equation of line passing through the points: (1, 4) parallel to the line 3x + y = 5 Click here to see answer by Maths68(1474) Question 526424: Solve. Please show all of your work. The houses on the north side of Polk Avenue are consecutive odd numbers. Bob and Laura are next-door neighbors and the sum of their house numbers is 524. Find both house numbers. Click here to see answer by Maths68(1474) Question 526349: In one car rental shop they charge \$20 per day with car with an additional 14 cents per mile driven. Another car rental shop charges \$22 per day with an additional 10 cents per mile driven. How many miles will the cost of both rental car fees be the same? Click here to see answer by Maths68(1474) Question 526456: what is the slope and y-intercept of y=2.5*x : y=(-3/7)*x-42. Click here to see answer by Maths68(1474) Question 526501: how can i find the x and y intercepts of the problem 6y=3x-8. I think i understand when the x and y are on the same side but this one has me stumped. Any help you could give would be appreciated. thanks Daniel Click here to see answer by nerdybill(6951) Question 526510: help me with this ? please . . Geraldo has already saved \$40 and wants to buy a CD player for \$129 about for months from now. To find how much he should save each week between now and then, he wrote 40 + 16x = 129. Explain his equations ( show work ) Click here to see answer by nerdybill(6951) Question 526516: help please? its for a math project I want a shirt that costs \$14.24 for my birthday ( November 18 ) in 12 days i should say and I don't have money on me now . But, i want to find out how much should I save each day between now and then. I need a equation to follow this problem and a solution ( answer ) Click here to see answer by ankor@dixie-net.com(15638) Question 526681: I hope I chose the correct category for this problem: 5x-4y=8 , for y I Tried to solve and came up with y=-2-5x which doesn't seem right. I need step-by-step solution by 11/6/11 for homework assignment. Thank you. Click here to see answer by jim_thompson5910(28504) Question 526780: What is the equation of the line perpendicular to the line x-4y=6 through (3,5) in slope intercept form? Click here to see answer by KMST(1868) Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790, 11791..11835, 11836..11880, 11881..11925, 11926..11970, 11971..12015, 12016..12060, 12061..12105, 12106..12150, 12151..12195, 12196..12240, 12241..12285, 12286..12330, 12331..12375, 12376..12420, 12421..12465, 12466..12510, 12511..12555, 12556..12600, 12601..12645, 12646..12690, 12691..12735, 12736..12780, 12781..12825, 12826..12870, 12871..12915, 12916..12960, 12961..13005, 13006..13050, 13051..13095, 13096..13140, 13141..13185, 13186..13230, 13231..13275, 13276..13320, 13321..13365, 13366..13410, 13411..13455, 13456..13500, 13501..13545, 13546..13590, 13591..13635, 13636..13680, 13681..13725, 13726..13770, 13771..13815, 13816..13860, 13861..13905, 13906..13950, 13951..13995, 13996..14040, 14041..14085, 14086..14130, 14131..14175, 14176..14220, 14221..14265, 14266..14310, 14311..14355, 14356..14400, 14401..14445, 14446..14490, 14491..14535, 14536..14580, 14581..14625, 14626..14670, 14671..14715, 14716..14760, 14761..14805, 14806..14850, 14851..14895, 14896..14940, 14941..14985, 14986..15030, 15031..15075, 15076..15120, 15121..15165, 15166..15210, 15211..15255, 15256..15300, 15301..15345, 15346..15390, 15391..15435, 15436..15480, 15481..15525, 15526..15570, 15571..15615, 15616..15660, 15661..15705, 15706..15750, 15751..15795, 15796..15840, 15841..15885, 15886..15930, 15931..15975, 15976..16020, 16021..16065, 16066..16110, 16111..16155, 16156..16200, 16201..16245, 16246..16290, 16291..16335, 16336..16380, 16381..16425, 16426..16470, 16471..16515, 16516..16560, 16561..16605, 16606..16650, 16651..16695, 16696..16740, 16741..16785, 16786..16830, 16831..16875, 16876..16920, 16921..16965, 16966..17010, 17011..17055, 17056..17100, 17101..17145, 17146..17190, 17191..17235, 17236..17280, 17281..17325, 17326..17370, 17371..17415, 17416..17460, 17461..17505, 17506..17550, 17551..17595, 17596..17640, 17641..17685, 17686..17730, 17731..17775, 17776..17820, 17821..17865, 17866..17910, 17911..17955, 17956..18000, 18001..18045, 18046..18090, 18091..18135, 18136..18180, 18181..18225, 18226..18270, 18271..18315, 18316..18360, 18361..18405, 18406..18450, 18451..18495, 18496..18540, 18541..18585, 18586..18630, 18631..18675, 18676..18720, 18721..18765, 18766..18810, 18811..18855, 18856..18900, 18901..18945, 18946..18990, 18991..19035, 19036..19080, 19081..19125, 19126..19170, 19171..19215, 19216..19260, 19261..19305, 19306..19350, 19351..19395, 19396..19440, 19441..19485, 19486..19530, 19531..19575, 19576..19620, 19621..19665, 19666..19710, 19711..19755, 19756..19800, 19801..19845, 19846..19890, 19891..19935, 19936..19980, 19981..20025, 20026..20070, 20071..20115, 20116..20160, 20161..20205, 20206..20250, 20251..20295, 20296..20340, 20341..20385, 20386..20430, 20431..20475, 20476..20520, 20521..20565, 20566..20610, 20611..20655, 20656..20700, 20701..20745, 20746..20790, 20791..20835, 20836..20880, 20881..20925, 20926..20970, 20971..21015, 21016..21060, 21061..21105, 21106..21150, 21151..21195, 21196..21240, 21241..21285, 21286..21330, 21331..21375, 21376..21420, 21421..21465, 21466..21510, 21511..21555, 21556..21600, 21601..21645, 21646..21690, 21691..21735, 21736..21780, 21781..21825, 21826..21870, 21871..21915, 21916..21960, 21961..22005, 22006..22050, 22051..22095, 22096..22140, 22141..22185, 22186..22230, 22231..22275, 22276..22320, 22321..22365, 22366..22410, 22411..22455, 22456..22500, 22501..22545, 22546..22590, 22591..22635, 22636..22680, 22681..22725, 22726..22770, 22771..22815, 22816..22860, 22861..22905, 22906..22950, 22951..22995, 22996..23040, 23041..23085, 23086..23130, 23131..23175, 23176..23220, 23221..23265

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# Why doesn't Mathematica make an obvious simplification? I am doing some calculation with summation and the Kronecker symbol. Here are my steps : $Assumptions = k1 ∈ Reals && k2 ∈ Reals && k3 ∈ Reals && p1 ∈ Reals && p2 ∈ Reals && p3 ∈ Reals k = {k1, k2, k3}; p = {p1, p2, p3}; d[i_, j_] := KroneckerDelta[i, j] proj[i_, j_, k1_, k2_, k3_] := d[i, j] - (d[i, 1]*k1 + d[i, 2]*k2 + d[i, 3]*k3)* (d[j, 1]*k1 + d[j, 2]*k2 + d[j, 3]*k3)/ (k1^2 + k2^2 + k3^2) test1 = proj[i, j, k1, k2, k3]*proj[i, j, p1, p2, p3]; test2 = Sum[Sum[test1, {i, 1, 3}], {j, 1, 3}] test2 // Expand To explain the steps: 1) I define$\vec{k}$and$\vec{p}$with real components. 2) I define a projector$P_{ij} \left( \vec{k} \right) = \delta_{ij} - \frac{k_i k_j}{k^2}$. 3) I compute a summation on the repeated subscript. After the last step, I have a relatively big expression, the product of k and p components. It looks like $$3-\frac{a}{a+b+c} - \frac{b}{a+b+c} - \frac{c}{a+b+c} +...-...$$ The a, b and c stands for k1, k2 and k3 (or p1, 2, 3). Now the question: why doesn't Mathematica make the simplification because, as anyone can see, the preceding expression can be simplified to$2 +...-...$Is the problem linked to the Expand operation? How can I make the simplification I want?. I thought of using /. to do it, but that doesn't work either. I hope someone will understand my question! - You can try using Simplify and related, but what you think it's a simpler expression will not necessarily match Mathematica's. – b.gatessucks Feb 15 '13 at 10:23 +1 just for formatting your code:) Simplify@test2 works nicely and returns (2 k2 k3 p2 p3 + 2 k1 p1 (k2 p2 + k3 p3) + k1^2 (2 p1^2 + p2^2 + p3^2) + k2^2 (p1^2 + 2 p2^2 + p3^2) + k3^2 (p1^2 + p2^2 + 2 p3^2))/((k1^2 + k2^2 + k3^2) (p1^2 + p2^2 + p3^2)) – Ajasja Feb 15 '13 at 10:34 ## 3 Answers You have to explicitly tell Mathematica to simplify expressions. You can do this using Simplify or FullSimplify Simplify@test2 (2 k2 k3 p2 p3 + 2 k1 p1 (k2 p2 + k3 p3) + k1^2 (2 p1^2 + p2^2 + p3^2) + k2^2 (p1^2 + 2 p2^2 + p3^2) + k3^2 (p1^2 + p2^2 + 2 p3^2))/((k1^2 + k2^2 + k3^2) (p1^2 + p2^2 + p3^2)) - Thank you for your answers. The problem when I use Simplify is that the form of the result is not "usable". I mean in the sense I want to use it. Because the calculation must lead to$1 - (\vec{k}.\vec{p})^2/(k^2*p^2)$. And with simplify, Mathematica doesn't do the factorization I want. I think I have to find an other way to do it, I may already have an idea. I thought I forget an assumption to enable Mathematica to do automatically this simplification. But it won't do what I didn't ask ! – Lalylulelo Feb 15 '13 at 10:52 Not sure precisely what you want, but maybe it's this: x = test2 // Expand; x1 = PolynomialReduce[ Numerator[Together[x]], {Denominator[Together[x]]}, Variables[x]]; x2 = PolynomialReduce[x1[[2]], {k1^2 + k2^2 + k3^2}, Variables[x]]; x3 = PolynomialReduce[x2[[2]], {p1^2 + p2^2 + p3^2}, Variables[x]]; y = x1[[1, 1]] + x2[[1, 1]]/(p1^2 + p2^2 + p3^2) + x3[[1, 1]]/(k1^2 + k2^2 + k3^2) + x3[[2]]/((p1^2 + p2^2 + p3^2) (k1^2 + k2^2 + k3^2)) Here's the output in reverse order; there's an issue with copy/paste:$\frac{2 \text{k1} \text{k2} \text{p1} \text{p2}+2 \text{k1} \text{k3} \text{p1} \text{p3}+2 \text{k2}^2 \text{p2}^2+\text{k2}^2 \text{p3}^2+2 \text{k2} \text{k3} \text{p2} \text{p3}+\text{k3}^2 \text{p2}^2+2 \text{k3}^2 \text{p3}^2}{\left(\text{k1}^2+\text{k2}^2+\text{k3}^2\right) \left(\text{p1}^2+\text{p2}^2+\text{p3}^2\right)}+\frac{-\text{k2}^2-\text{k3}^2}{\text{k1}^2+\text{k2}^2+\text{k3}^2}+\frac{-\text{p2}^2-\text{p3}^2}{\text{p1}^2+\text{p2}^2+\text{p3}^2}+2\$ - If you know approximately what denominators are obtained, you coud use command Collect[expression, factor]. -

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# Quotient map and connected sets proof I'm hoping to have my proof reviewed for correctness. Thanks in advance! Let $$p: X \to Y$$ be a quotient map. Show that if each set $$p^{-1}(\{y \})$$ is connected, and if $$Y$$ is connected, then $$X$$ is connected. Proof: Let $$p$$ be a quotient map from $$X$$ to $$Y$$. Since $$p$$ is a quotient map we know that $$p$$ is surjective. Suppose $$X$$ is not connected. Then each $$X_i = p^{-1}(\{y_i\})$$ is a connected set in a separable space X. Let the open sets $$A$$ and $$B$$ satisfy the condition that $$A \cup B = X$$, where $$A$$ and $$B$$ are disjoint and nonempty. Then each $$X_i$$ must be fully contained within either $$A$$ or $$B$$, since each $$X_i$$ is connected. Therefore for all $$x_i{_a} \in A$$ we first have that $$\bigcup x_i{_a} = A$$, since we've taken each $$x_i$$ stemming from every $$y \in Y$$. Second, $$p(\bigcup x_i{_a})$$ maps to an open set in Y since $$\bigcup X_i{_a}$$ is open and the complete reverse image of a quotient map. Similarly, $$p(\bigcup X_i{_b})$$ maps to an open set in $$Y$$ also. These sets in $$Y$$ must be disjoint because if they were not disjoint that would imply that some $$x \in X_i$$ belonged to both $$A$$ and $$B$$. But then $$p(x)$$ would map to a point $$y$$ that has a pre-image in two disjoint sets -- since the pre-image $$p^{-1}(\{y \})$$ is only one connected set, so it cannot occupy space in both $$A$$ and $$B$$. So we've shown the image sets are disjoint. And $$p(\bigcup X_i{_a}) \cup p(\bigcup X_i{_b}) = Y$$ since every quotient map is surjective and $$A \cup B = X$$. Hence we have shown $$Y$$ to have a separation. A contradiction. Hence $$X$$ must be connected. Your proof is correct. However, the phrase "in a separable space $$X$$" is misleading. A separable space is one which has a countable dense set. You mean a space which has a separation into two nonempty disjoint open subsets.

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# Cubic inches to quarts (US liquid) (cu in to qt) ## Convert cubic inches to quarts (US liquid) Cubic inches to quarts (US liquid) converter on this page calculates how many quarts (US liquid) are in 'X' cubic inches (where 'X' is the number of cubic inches to convert to quarts (US liquid)). In order to convert a value from cubic inches to quarts (US liquid) (from cu in to qt) type the number of cu in to be converted to qt and then click on the 'convert' button. ## Cubic inches to quarts (US liquid) conversion factor 1 cubic inch is equal to 0.017316017316017 quarts (US liquid) ## Cubic inches to quarts (US liquid) conversion formula Volume(qt) = Volume (cu in) × 0.017316017316017 Example: Consider a volume of 11 cubic inches. Below are the steps to convert them to quarts (US liquid). Volume(qt) = 11 ( cu in ) × 0.017316017316017 ( qt / cu in ) Volume(qt) = 0.19047619047619 qt or 11 cu in = 0.19047619047619 qt 11 cubic inches equals 0.19047619047619 quarts (US liquid) ## Cubic inches to quarts (US liquid) conversion table cubic inches (cu in)quarts (US liquid) (qt) 70.12121212121212 90.15584415584416 110.19047619047619 130.22510822510823 150.25974025974026 170.29437229437229 190.32900432900433 210.36363636363636 230.3982683982684 250.43290043290043 270.46753246753247 290.5021645021645 310.53679653679654 330.57142857142857 350.60606060606061 cubic inches (cu in)quarts (US liquid) (qt) 2003.4632034632035 2504.3290043290043 3005.1948051948052 3506.0606060606061 4006.9264069264069 4507.7922077922078 5008.6580086580087 5509.5238095238095 60010.38961038961 65011.255411255411 70012.121212121212 75012.987012987013 80013.852813852814 85014.718614718615 90015.584415584416 Versions of the cubic inches to quarts (US liquid) conversion table. To create a cubic inches to quarts (US liquid) conversion table for different values, click on the "Create a customized volume conversion table" button. ## Related volume conversions Back to cubic inches to quarts (US liquid) conversion TableFormulaFactorConverterTop

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## Assignment 2: Financial Project, Algebra Assignment Help: ue Week 7 and worth 55 points Five (5) years ago, you bought a house for \$171,000, with a down payment of \$30,000, which meant you took out a loan for \$141,000. Your interest rate was 5.75% fixed. You would like to pay more on your loan. You check your bank statement and find the following information: Escrow payment \$261.13 Principle and Interest payment \$822.84 Total Payment \$1,083.97 Current Loan Balance \$130,794.68 Write a one to two (1-2) page paper in which you address the following: Part 1 With your current loan, explain how much additional money you would need to add to your monthly payment to pay off your loan in 20 years instead of 25. Decide whether or not it would be reasonable to do this if you currently meet your monthly expenses with less than \$100 left over. (a) Explain your strategy for solving the problem. (b) Present a step-by-step solution of the problem. Part 2 Identify the highest interest rate you could refinance at in order to pay the current balance off in 20 years and determine the interest rate, to the nearest quarter point, that would require a monthly total payment that is less than your current total payment. The interest rate that you qualify for will depend, in part, on your credit rating. Also, refinancing costs you \$2,000 up front in closing costs. (a) Explain your strategy for solving the problem. (b) Present a step-by-step solution of the problem. Be typed, double spaced, using Times New Roman font (size 12), with one-inch margins on all sides; citations and references must follow APA or school-specific format. Check with your professor for any additional instructions. Include a cover page containing the title of the assignment, the student’s name, the professor’s name, the course title, and the date. The cover page and the reference page are not included in the required assignment page length. The specific course learning outcomes associated with this assignment are: Apply finance formulas and logarithms to amortize loans and calculate interest. Use technology and information resources to research issues in algebra. Write clearly and concisely about algebra using proper writing mechanics. #### Solve out given systems, Example 2 Solve out following systems of equation... Example 2 Solve out following systems of equations. 3x + y - 2z = 2 x - 2 y + z = 3 2x - y - 3z = 3 Solution Firstly write down the augmented matrix for this syst #### Integrated algebra me 1, identify the sample and suggest a population from ... identify the sample and suggest a population from which it was selected. then classify the sample as sample, stratified, or systematic. explain your reasoning. 1} an insurance comp Y=5/4x-1/2 2x+5=-8 #### Basic fact, What is a Math Basic Fact? What is a Math Basic Fact? #### Simplifing a rational expression or function, Find the domain: f(x)=3x-8/4... Find the domain: f(x)=3x-8/4x+20 #### Dependent system example, Dependent system example Example: Solve the... Dependent system example Example: Solve the given system of equations. 2x + 5 y = -1 -10x - 25 y = 5 Solution In this instance it looks like elimination would b #### Non-linear systems, In this section we will discussed about non-linear syst... In this section we will discussed about non-linear systems of equations.  A non-linear system of equations is a system wherein at least one of the variables contains an exponent ot -8(5y-2x-1) #### Pre-Algebra, (1/2)q + 3= 10.5 + q (1/2)q + 3= 10.5 + q

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# Known-card Play against the Knockout Baccarat Side Bet By | | One ongoing method to beat baccarat is to use the knowledge of the rank of exactly one card in the shoe to gain an edge on one hand per shoe (see this post). One card out of 416 may not seem like a lot, but to the "known-card" AP it's a pot of gold. Millions have been taken from the tables using this method. A known-card AP patiently counts down the shoe until the known card reaches the window where it is eligible to be dealt in the following round, that is, the card is one of the next six in the shoe. The AP then follows a fixed strategy that tells him which wager to make to take full advantage of this information. It recently came to my attention that some APs are engaged in using known-carding against the Knockout baccarat collection of side bets. This post gives the various edges and strategies based on the rank of the specific known-card and its location in the six-card window. As will be evident, there is an abundance of situations when the AP can get a substantial edge. Knockout Baccarat is a variant of baccarat that offers a collection of seven (7) separate baccarat side bets. These side bets are described as follows. • Winning total of 1, 2, 3, 4. This side bet wins if the winning hand (Player or Banker) has a total of 1, 2, 3 or 4. This side bet is a push if the result of the hand is a Tie. Otherwise this side bet loses. A winning hand pays 7-to-1. • Winning total of 5, 6. This side bet wins if the winning hand (Player or Banker) has a total of 5 or 6. This side bet is a push if the result of the hand is a Tie. Otherwise this side bet loses. A winning hand pays 3.5-to-1. • Winning total of 7. This side bet wins if the winning hand (Player or Banker) has a total of 7. This side bet is a push if the result of the hand is a Tie. Otherwise this side bet loses. A winning hand pays 4.5-to-1. • Winning total of 8. This side bet wins if the winning hand (Player or Banker) has a total of 8. This side bet is a push if the result of the hand is a Tie. Otherwise this side bet loses. A winning hand pays 3-to-1. • Winning total of 9. This side bet wins if the winning hand (Player or Banker) has a total of 9. This side bet is a push if the result of the hand is a Tie. Otherwise this side bet loses. A winning hand pays 2.5-to-1. • Player Natural. This side bet wins if the winning hand is a Player natural two-card 8 or 9. This side bet is a push if the result of the hand is a Tie (regardless of naturals). Otherwise this side bet loses. A winning hand pays 4-to-1. • Banker Natural. This side bet wins if the winning hand is a Banker natural 8 or 9. This side bet is a push if the result of the hand is a Tie (regardless of naturals). Otherwise this side bet loses. A winning hand pays 4-to-1. The "Tie is a push" rule should be interpreted in its most literal sense. For example, if the player wagers on "winning total of 1, 2, 3, 4" and the hand ends in a 9-9 natural Tie, then the "winning total of 1, 2, 3, 4" wager is a push. In other words, the final total does not matter when the hand is a push. Similarly, if the player wagers on the Banker Natural side bet and the hand ends in a three-card 2-2 Tie, then the Banker Natural wager is a push. The following table summarizes the basic statistical information about these seven bets: Knockout Baccarat Combinatorial Alalysis Summary Winning Total Pays H/A STD DEV HIT FREQ 1,2,3,4 7 -0.067231 2.434338 10.4702% 5,6 3.5 -0.075277 1.724266 18.4348% 7 4.5 -0.033009 1.988763 15.8515% 8 3 -0.035976 1.625204 21.7217% 9 2.5 -0.064628 1.470031 24.0062% P Natural 4 -0.091899 1.826263 16.2589% B Natural 4 -0.091899 1.826263 16.2589% The following table gives the edge the AP can get if he knows the first or third card to be dealt from the shoe, that is, one of the Player hand's first two cards. The cells marked with green give the situations when the AP has an edge over the house. In the best possible situation, the AP can get an edge of 79.706% over the house if he knows the first/third card is a Nine. In this case the AP bets on "Player Natural." Knockout Baccarat Side Bet House Edge by Known First/Third Card (Player Card) Known First/Third (Player) Card Side Bet A 2 3 4 5 Winning total of 1,2,3,4 3.874% 5.423% 5.928% 3.497% -7.548% Winning total of 5,6 -4.018% -4.468% -5.301% -4.952% 0.157% Winning total of 7 -5.264% -5.134% -5.071% -3.998% -4.072% Winning total of 8 -6.625% -6.873% -6.524% -6.898% -5.832% Winning total of 9 -10.031% -10.197% -10.089% -9.561% -9.556% Player Natural -24.801% -24.679% -24.561% -25.134% -24.016% Banker Natural -7.049% -6.970% -6.853% -6.330% -6.308% Known First/Third (Player) Card Side Bet 6 7 8 9 T/J/Q/K Winning total of 1,2,3,4 -27.152% -27.166% -28.133% -28.178% 3.014% Winning total of 5,6 18.316% -26.209% -27.629% -27.183% -4.144% Winning total of 7 -3.860% 50.571% -22.945% -22.824% -5.079% Winning total of 8 -8.801% -8.751% 51.757% -23.455% -6.191% Winning total of 9 -12.441% -12.486% -17.373% 48.038% -10.080% Player Natural -23.147% -23.141% 69.630% 79.706% -24.831% Banker Natural -5.438% -5.433% -17.844% -28.750% -7.123% The following table gives the edge the AP can get if he knows the second or fourth card to be dealt from the shoe, that is, one of the Banker hand's first two cards. The cells marked with green give the situations when the player has an edge over the house. In the best possible situation, the AP can get an edge of 79.647% over the house if he knows the second/fourth card is a Nine. In this case the AP bets on "Banker Natural." Knockout Baccarat Side Bet House Edge by Known Second/Fourth Card (Banker Card) Known Second/Fourth (Banker) Card Side Bet A 2 3 4 5 Winning total of 1,2,3,4 3.669% 3.595% 5.852% 20.771% -25.270% Winning total of 5,6 -6.397% -6.339% -7.051% -8.704% 18.521% Winning total of 7 -4.085% -4.086% -4.441% -6.724% -7.350% Winning total of 8 -5.769% -5.872% -5.865% -8.462% -8.305% Winning total of 9 -9.560% -9.483% -9.690% -11.173% -11.951% Player Natural -6.914% -6.964% -6.936% -6.669% -6.820% Banker Natural -24.666% -24.672% -24.644% -25.473% -24.528% Known Second/Fourth (Banker) Card Side Bet 6 7 8 9 T/J/Q/K Winning total of 1,2,3,4 -25.091% -27.304% -28.111% -28.166% 3.164% Winning total of 5,6 17.000% -25.681% -27.112% -26.687% -6.353% Winning total of 7 -4.223% 50.350% -23.202% -23.078% -4.018% Winning total of 8 -8.678% -8.846% 51.643% -23.570% -5.761% Winning total of 9 -12.217% -12.625% -17.535% 47.895% -9.419% Player Natural -5.525% -5.488% -17.903% -28.809% -6.860% Banker Natural -23.233% -23.197% 69.570% 79.647% -24.568% One important point to note from the previous two tables is that it doesn't matter which card the AP observes as the known-card. For any known-card in any of the first four positions, there is always a bet that gives the AP an edge. Moreover, if the AP knows one of the first four cards is a Seven, Eight or Nine, then he is going to thoroughly crush the house on that bet. Knowing the fifth card to come out is an especially strong situation, regardless of the card in that position. The fifth card usually goes to the Player hand when it is played. Knowledge of this card gives good information about the final value of the Player hand when it draws. The following table summarizes these edges. Observe that when the AP knows the fifth card then there are always at least two side bets that give him the edge over the house. In fact, the AP can always get a double digit edge on at least one of the side bets: Knockout Baccarat Side Bet House Edge by Known Fifth Card Known Fifth Card Side Bet A 2 3 4 5 Winning total of 1,2,3,4 9.412% -18.481% -38.212% -54.982% -68.234% Winning total of 5,6 23.652% 9.711% -6.101% -25.119% -18.219% Winning total of 7 -3.886% 23.873% 11.461% -0.486% -0.611% Winning total of 8 -20.400% -17.257% 15.893% 14.111% 14.730% Winning total of 9 -22.597% -19.659% -19.888% 11.305% 11.300% Player Natural -8.684% -7.331% -7.560% -7.981% -7.874% Banker Natural -8.684% -7.331% -7.560% -7.981% -7.874% Known Fifth Card Side Bet 6 7 8 9 T/J/Q/K Winning total of 1,2,3,4 -41.350% -17.526% 6.291% 16.816% 29.716% Winning total of 5,6 -36.436% -57.609% -35.804% -17.665% 16.432% Winning total of 7 -0.107% 10.710% -38.227% -24.371% -5.316% Winning total of 8 15.527% 15.145% 27.540% -24.737% -21.830% Winning total of 9 12.743% 12.123% 4.204% 22.565% -24.028% Player Natural -7.634% -8.145% -12.234% -11.570% -10.114% Banker Natural -7.634% -8.145% -12.234% -11.570% -10.114% The sixth card is the weakest position for the known-card. This card, when it is played, always goes to the Banker hand. The following table summarizes the edges on the various side bets when the AP knows the sixth card: Knockout Baccarat Side Bet House Edge by Known Fifth Card Known Sixth Card Side Bet A 2 3 4 5 Winning total of 1,2,3,4 25.883% 6.268% -15.614% -36.469% -68.583% Winning total of 5,6 -7.283% 0.526% 7.944% 4.580% 7.798% Winning total of 7 -7.373% -6.378% -5.241% 7.433% 7.625% Winning total of 8 -9.518% -7.457% -6.295% -4.212% 5.642% Winning total of 9 -13.042% -12.925% -10.925% -9.146% -6.446% Player Natural -8.664% -8.571% -8.748% -9.067% -9.526% Banker Natural -8.664% -8.571% -8.748% -9.067% -9.526% Known Fifth Card Side Bet 6 7 8 9 T/J/Q/K Winning total of 1,2,3,4 -62.115% -40.818% -18.339% 0.388% 30.500% Winning total of 5,6 -6.575% -29.570% -24.438% -17.565% -8.319% Winning total of 7 7.226% 19.248% -16.127% -13.326% -9.000% Winning total of 8 5.787% 5.542% 15.171% -12.929% -9.625% Winning total of 9 1.918% 3.076% 3.381% 12.720% -13.151% Player Natural -10.017% -9.901% -10.102% -9.783% -8.772% Banker Natural -10.017% -9.901% -10.102% -9.783% -8.772% Finally, the following tables summarizes each combination of side bet and card location where the AP can get an edge over the house: Knockout Baccarat Known Card Strategy Side Bet Known 1/3 Known 2/4 Known 5 Known 6 Winning total of 1,2,3,4 A,2,3,4,T A,2,3,4,T A,8,9,T A,2,9,T Winning total of 5,6 5.6 5.6 A,2,T 2,3,4,5 Winning total of 7 7 7 2,3,7 4,5,6,7 Winning total of 8 8 8 3,4,5,6,7,8 5,6,7,8 Winning total of 9 9 9 4,5,6,7,8,9 6,7,8,9 Player Natural 8,9 - - - Banker Natural - 8,9 - - In the U.S. market, side bets often have severely restricted maximum wagers. These low maximums will discourage known-card play. Internationally, where limits on side bets are often much higher, there is no doubt that known-card play has occurred and will continue to occur whenever opportunities arise. The key to defending against known-carding in baccarat is to carefully inspect the shuffle procedure. If a single card is exposed at any point during the shuffle procedure then known-card play becomes a real possibility. Known-card play is one of the most sought after opportunities in baccarat. If it is possible to known-card your game, then it's probable that it is already taking place.

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# Word math problems This Word math problems helps to fast and easily solve any math problems. We can solving math problem. ## The Best Word math problems Word math problems can help students to understand the material and improve their grades. In addition, many colleges and universities now offer free online math courses that can help students review key concepts. With so many resources available, there's no excuse for struggling with math. Whether you're stuck on a problem or just need someone to walk you through a concept, help is only a few clicks away. How to solve logarithmic functions has been a mystery for many students. The concept seems difficult, but it is not as hard as it looks. There are three steps in solving logarithmic functions. First, identify the base of the logarithm. Second, use properties of logs to rewrite the equation. Third, solve for the unknown using basic algebra. These steps may seem confusing at first, but with practice they will become easy. With a little effort, anyone can learn how to solve logarithmic functions. Online math graph As a math student, there are times when a picture is worth a thousand words. When it comes to graphing functions, this is especially true. Being able to visualize a function can help you understand its behavior and uncover patterns that may not be immediately apparent from looking at the equation alone. There are a number of online tools that allow you to enter an equation and see the corresponding graph. These tools can be a valuable resource for studying mathematics and exploring new concepts. Best of all, they're free and easy to use. So next time you're stuck on a problem, give one of these online math graphs a try. You may just find that the solution is right in front of you. Next, it is often helpful to draw a picture or diagram of the problem, as this can make it easier to visualize the relationships between different elements. Finally, once you have a solid understanding of the problem, you can begin to work through the steps necessary to find a solution. With a little patience and practice, solving word math problems can be easy and even enjoyable! ## We cover all types of math problems This app gives the best solution to any math problem full of graphs, tables and in all mathematical and intuitive ways. I think this app is must for every math student whether beginners or experts. It also contains solutions to many standard math books like of Pearson, etc. in the best possible way. And many more features are being added frequently. ### Yulianna Lopez This app is a life saver because my tutor gave me an assignment and I was so busy but the exact same day he came I finished it on time wow this app really helps a lot This app is great. It helps me to answer any math problem I don't understand. I highly recommend. ### Ziva Anderson Solve math problems online step by step free App to help with math Slope intercept solver Geometry helper Math problem app

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, 22.06.2019 21:00 ooo712772 # What is 6x+3y=-15 in y-intercept form 3y = -6x - 15 Step-by-step explanation: To put 6x + 3y = -15 into Slope Intercept Form you need to know the formula (y = mx + b) so we know we need to get y on its own side so we can -6x  from both side giving us 3y = -6x +-15 or 3y = -6x - 15 There are many different slope intercept forms for this equation depending on how you get y by its self! y=-5 or (0,-5) Step-by-step explanation: 6x+3y=-15 formula; ax + by = c slope=-a/b 6/3=2 x-intercept=c/a x=-15/6 x=-2.5 or (-2.5,0) y-intercept=c/b y=-15/3 y=-5 or (0,-5) 28 step-by-step explanation: 8+8+6+6 the system of inequity is step-by-step explanation: from the given graph it is noticed that we have two related lines. one is solid and another is dashed. if a line passing through two points, then the equation of line is the solid line passing through the points (0,4) and (4,0). the related equation of solid line is . similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1). the related equation of dashed line is from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations. check the related equations by the point (0,1). this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is similarly, check the second related equation. it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is ### Other questions on the subject: Mathematics Mathematics, 21.06.2019 15:30, lizzyhearts Angel entered a triathlon (a three-part race). he swam 1 mile, rode his bike 30 miles, and ran 10 miles. how far did he go altogether? a. 11 miles b. 123 miles c. 41 miles d. 40 miles Mathematics, 21.06.2019 17:00, yoongnzl Solve with work both bert and ernie received an increase in their weekly salaries. bert's salary increased from $520 to$520. ernie's salary went from $580 to$645. find the percent of increase for each salary. what was the larger of the two percents ? Mathematics, 21.06.2019 20:30, leeshaaa17 Which expression demonstrates the use of the commutative property of addition in the first step of simplifying the expression (-1+i)+(21+5i)+0

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# If $a$ divides $b$, then $(2^a-1)$ divides $(2^b-1)$ [duplicate] This question already has an answer here: Prove that if $a \mid b$, then $(2^a-1) \mid(2^b-1)$. So, I've said the following: 1. Let $a \mid b$. 2. $\implies b=am$ 3. Assume $(2^a-1) \mid (2^b-1)$ 4. $\implies (2^b-1)=(2^a-1)x$ But I can't figure out what to do with any of this from here forward. ## marked as duplicate by user147263, Jyrki LahtonenDec 3 '15 at 11:00 This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question. • Why are you assuming that $(2^a - 1)|(2^b-1)$? – The Chaz 2.0 Nov 10 '13 at 2:02 • Do you know the usual factorization of $x^n-y^n$ ? – chubakueno Nov 10 '13 at 2:03 • "proofs" is a pretty vast subject to be looking for a single "rule of thumb" – Jack M Nov 10 '13 at 11:35 ## 3 Answers HINT: Sometimes choosing the ‘right’ representation makes things easier to see. Note that the binary (base two) representation of $2^n-1$ is $$\underbrace{111\ldots 111}_{n\text{ ones}}\;.$$ Suppose that $b=ka$; then \begin{align*} \underbrace{111\ldots111}_{b\text{ ones}}&=\underbrace{\underbrace{111\ldots 111}_{a\text{ ones}}\underbrace{111\ldots 111}_{a\text{ ones}}\ldots\underbrace{111\ldots 111}_{a\text{ ones}}}_{k\text{ blocks}}\\\\ &=\left(\underbrace{111\ldots 111}_{a\text{ ones}}\right)\left(\underbrace{1\underbrace{000\ldots000}_{a-1\text{ zeroes}}1\underbrace{000\ldots000}_{a-1\text{ zeroes}}1\ldots1\underbrace{000\ldots000}_{a-1\text{ zeroes}}1}_{k\text{ ones}}\right)\;. \end{align*} For example, with $a=3$ and $b=12$, we have $$111111111111=111\cdot1001001001\;.$$ These ideas can be translated into statements about sums of powers of $2$. When you have a statement you are trying to prove, such as "if $p$, then $q$", you can assume $p$ is true, and then show that $q$ must also be true. This is called a direct proof. Alternatively, you can assume $q$ is not true, and show that this means $p$ cannot be true. This is called a proof by contradiction. You are assuming both $p$ and $q$ are true. You should pick one of the two strategies I mentioned above. I would suggest a proof by contradiction in this particular case. • I would rather go for a direct proof in this case (it lends itself) – chubakueno Nov 10 '13 at 2:13 Suppose $a\mid b$ and so $b=am$ for some $m\geq 1$. Then, $$2^b-1=2^{am}-1=(2^a)^m-1^m\\=(2^a-1)\left((2^a)^{m-1}+(2^a)^{m-2}+\cdots+(2^{a})^2+(2^a)+1\right).$$ We see that $(2^a)^{m-1}+(2^a)^{m-2}+\cdots+(2^{a})^2+(2^a)+1\geq 1$ and so $2^b-1=(2^a-1)k$ for some $k\geq 1$. Hence $2^a-1\mid 2^b-1$. Remember, it's very easy to begin circular reasoning if you're not careful when you assume a result that you're trying to prove. It's much more conventional (especially when first learning proofs) to reach that result by deducing it from the hypotheses in the statement - in this case $a\mid b$. • I wouldn't say you can't in the general case. You can connect the result by $\iff$'s to a true statement, and you have a proof. – chubakueno Nov 10 '13 at 2:15 • @chubakueno but then that's not assuming the result, that's setting up a chain of equivalences. I think, especially when you're first learning about logical implication, and proofs in general, it's best to move away from the habit of using chains of equivalences until you fully understand how to prove something in one direction, and more importantly what it means for one statement to imply another. – Dan Rust Nov 10 '13 at 2:24 • Yes, I know it may cause problems for starters. But working backwards may help to get better, easier or shorter proofs, and it should never be forbidden :) – chubakueno Nov 10 '13 at 2:30 • @chubakueno True, I've changed the advice to reflect this :). – Dan Rust Nov 10 '13 at 2:35 • Often there is not a chain of equivalences connecting $A$ and $B$. So the sooner high school habits are dropped the better. – André Nicolas Nov 10 '13 at 2:52

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# Thread: Proving the reduction formula, in need of help 1. ## Proving the reduction formula, in need of help Hello there people. I have confronted a problem that I don't know how to do. It is has follows: Prove the reduction formula It would really helpful if someone were to help me understand this and show me how to prove it. Thank you in advance to whoever that can 2. ## Re: Proving the reduction formula, in need of help Differentiate? 3. ## Re: Proving the reduction formula, in need of help Well it's proving that the left side actually equals to the right side. 4. ## Re: Proving the reduction formula, in need of help You have to integrate by parts. $\displaystyle x^n e^{-x^2} = x^{n-1}xe^{-x^2}$. $\displaystyle dv = xe^{-x^2}dx$, $\displaystyle u=x^{n-1}$.

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# Understanding the Art of Gambling: Roulette Aug 19, 2023 Walking into a casino can be an exhilarating experience, with an array of flashing lights, spinning wheels, and bustling activity. Among the numerous games of chance that captivate gamblers, stands out as a classic that has stood the test of time. To truly make the most of your roulette gameplay, it's crucial to comprehend the intricate relationship between bets, odds, and payouts. In this article, we will unravel the mysteries of roulette's betting system, odds calculation, and potential pay-outs, equipping you with the knowledge for a more informed and potentially winning experience. ### 1. The Betting Basics Roulette offers a variety of betting options, each with its own set of odds and potential returns. The two main types of bets are inside bets and outside bets. Inside bets are placed on specific numbers or groups of adjacent numbers on the roulette table. Outside bets, on the other hand, cover larger sections such as red or black, odd or even, and ranges of numbers. the distinction between these bet types is crucial as it directly impacts your odds of winning and the potential payouts. ### 2. Odds and Probability To approach roulette strategically, one must grasp the relationship between odds and probability. The roulette wheel is divided into numbered pockets, with the two main variants being European (with one zero) and American (with one zero and one double zero). The probability of a ball landing on a specific number or color is determined by the number of pockets that match your bet out of the total pockets on the wheel. This understanding helps you make informed decisions about where to place your bets. ### 3. Pay-outs and Potential Returns The potential payouts in roulette vary depending on the type of bet you place. Generally, the more specific your bet, the higher the potential payout and the lower the probability of winning. For instance, betting on a single number (straight bet) offers a higher payout but lower odds compared to betting on a color or a range of numbers. Outside bets tend to have lower payouts but higher odds of winning. By understanding the relationship between bets and pay-outs, you can tailor your strategy to your risk tolerance and desired potential returns. ### 4. The House Edge Whether you're playing European roulette, Australian pokies, or any other casino game, it's essential to recognize that the casino always maintains a slight advantage known as the house edge. This edge arises from the presence of the zero (or double zero in American roulette), which doesn't belong to any of the betting categories. As a result, even-money bets like red/black or odd/even have slightly less than a 50% chance of winning due to the presence of the zero(s). While the house edge can't be eliminated, you can choose bets with a lower house edge to improve your odds over time. ### 5. Betting Strategies Roulette has inspired various betting strategies aimed at maximizing wins or mitigating losses. Some strategies involve adjusting bets based on previous outcomes, like the Martingale system, while others focus on covering specific sections of the wheel to increase the chances of hitting a win. It's crucial to approach these strategies with caution, as none of them can guarantee consistent success due to the game's inherent randomness. A successful roulette experience hinges on understanding the intricate dynamics between bets, odds, and payouts. By comprehending the types of bets, calculating the associated odds and probability, and considering potential payouts, you can make more informed decisions at the roulette table. While the house edge remains a constant factor, a solid grasp of these concepts empowers you to tailor your strategy to your preferences and risk tolerance. Whether you're aiming for high-risk, high-reward bets or more conservative choices, a deeper understanding of roulette's mechanics enhances your enjoyment and potentially improves your chances of walking away with a satisfying win. #Understanding # # #Roulette

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# Tagged Questions Refers to a measure of association between two binary variables. If $X,Y$ are binary outcomes and $p_{ij} = P(X=i,Y=j)$, the odds ratio is equal to $${\rm OR} = \frac{ p_{11} p_{00} }{ p_{10} p_{01} }$$ When ${\rm OR} 1$ indicates a positive relationship. More info is available at ... 2k views ### How to calculate odds ratio and p-values for Fisher's test? I'm trying to perform Fisher's exact test in R. I'm calculating odds ratio like this \frac{(\text{no. of successes in my set}) \cdot (\text{no. of failures in background set})}{\text{(no. of ... 245 views ### Odds Ratio Between Overlapping Groups Is it inappropriate to use odds ratio for groups that are subset of each other? For example, comparing GPA of female students to GPA of all the students. (This is just an example, not what I am really ... 2k views ### The effect of skewed continuous predictors in a binary logistic regression model I am analyzing data with a binary outcome and a variety of continuous and categorical (including dichotomous) predictor variables. My approach is to perform a binary logistic regression and to treat ... 3k views ### Poisson regression to estimate relative risk for binary outcomes Brief Summary Why is it more common for logistic regression (with odds ratios) to be used in cohort studies with binary outcomes, as opposed to poisson regression (with relative risks)? Background ... 124 views ### Can odds ratios increase if you include more variables? Suppose one wants to compute the odds ratio of a disease for a person in group $A$ versus that of a person in group $B$. Suppose we consider the following: (i) include age in the odds ratio ... 237 views ### Odds ratios question If you have a categorical variable with $k$ levels (so $k-1$ indicator variables), is there an easy way to calculate the odds ratio? Suppose the first level is the reference level. The model would be ... 1k views ### How to conduct a meta-analysis on studies that report results variously as odds ratios, hazards ratios, or rate ratios? I'm doing a meta-analysis of some studies that report results variously as odds ratios, hazards ratios or rate ratios (all with confidence intervals). Is there any way to combine these ... 236 views ### Generating data with a pre-specified odds ratio I have to simulate (in javascript) the likelihood that members of a certain population would have a disease, given a contextual value. All information I have comes from papers that show odds ratios ... 278 views ### What is the best statistical method to compare case fatality rates of 17 years for 2 different states? I have Case Fatality Rates (deaths per 100 cases) for 2 different states receiving different treatments for 17 years. What is the best statistical method to compare Case Fatality Rates ? The data ... 398 views ### Odds ratios multiple comparisons I have to assess for each product p, the odds ratio associated (success/failure). The data are in this table: ... 4k views ### How to calculate confidence intervals for pooled odd ratios in meta-analysis? I have two datasets from genome-wide association studies. The only information available are the odd ratios and their confidence intervals (95%) for each genotyped SNP. My want to generate a forest ... 9k views ### Logistic Regression in R (Odds Ratio) I'm trying to undertake a logistic regression analysis in R. I have attended courses covering this material using STATA. I am finding it very difficult to replicate ... 358 views ### How to assess effect of intervention in one state versus another using annual death rate data? I am a beginner in statistics. I have these unpublished data (cases and deaths) of a disease for 7 years (2004-2010) from 2 neighbouring states. The study was started in 2004. State 1 and State 2 ... 952 views ### What does “case-control” and “cross-sectional” mean in the context of logistic modeling? While studying logistic modeling, I read the following statement The fact that only odds ratios, not individual risks, can be estimated from logistic modeling in case-control or ... 463 views ### Probability calculation, system uptime, likelihood of occurence (redirected here from mathoverflow.net) Hello, At work I was asked the probability of a user hitting an outage on the website. I have some following metrics. Total system downtime = 500,000 seconds ... 550 views ### Meta analysis on studies with 0-frequency cells I am familiar with meta analysis and meta regression techniques (using the R package metafor from Viechtbauer), but I recently stumbled on a problem I can't easily ... 2k views ### Relation between logistic regression coefficient and odds ratio in JMP From the output of a logistic regression in JMP, I read about two binary variables: Var1 estimate -0.1007384 Var2 estimate 0.21528927 and then ...

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For $v_2, v_3, \dots, v_n$, each has $2$ leaving edges. The greedy algorithm works by ‘making the choice that looks best at the moment’ [5]. Choose the largest sum (p i + r k − i). Well I found a situation where this might not work. First line of every test case consists of n, denoting the size of array.Second line of every test case consists of price of ith length piece. Make change. Right. ... Greedy Algorithm for Egyptian Fraction; Greedy Solution to Activity Selection Problem. & = 1 + (2^n - 1) \\ Data Structures & Algorithms. 11 9 1 So applying greedy strategy to pick the rod length cuts, first we cut out a rod of length 3 for a revenue of 33 and then a rod of length of 1 for a price of 1. \begin{array}{c|cccc} Rod cutting problem is very much related to a n y real-world problem we face. Greedy algorithm greedily selects the best choice at each step and hopes that these choices will lead us to the optimal solution of the problem. We are given n rods of say m meters and we wish to do the following operations: What would be the greedy approach to solve this? The first step in this case would be. Consider the following greedy algorithm to … Show that equation $\text{(15.4)}$ follows from equation $\text{(15.3)}$ and the initial condition $T(0) = 1$. You can also provide a link from the web. Calculate the sum of the value of that cut (ie p i) and the best that could be done with the rest of the rod (ie r k − i). Sometimes, we need to calculate the result of all possible choices. Greedy Algorithms Informal De nitionA greedy algorithm makes its next step based only on the current \state" and \simple" calculations on the input. 1.1.1 Naive algorithm \begin{aligned} … The greedy strategy for a rod of length $n$ cuts off a first piece of length $i$, where $1 \le i \le n$, having maximum density. We make the loop run to $j - 1$ instead of $j$, make sure $c$ is subtracted from thecandidate revenue in line 6, then pick the greater of current best revenue $q$ and $p[j]$ (no cuts) in line 7. It then continues by applying the greedy strategy to the remaining piece of length n-i. e.g. According to a greedy strategy, we rst cut out a rod of length 3 for a price of 33, which leaves us with a rod of length 1 of price 1. We note that the standard greedy algorithm (select the most expensive by unit of length rod length) does not always work. Observe the following: •For input n, there aren 2possibilities to make the first cut: {n}(no cut) {n−1,1} {n−2,2} ... {⌊n 2⌋,⌈. You asked for a greedy approach; what I posted is a, Start with the longest cut-rod (use the most length). $$1 1 1 2 5 2.5 3 8 21 3. We have an optimization problem. Modify \text{MEMOIZED-CUT-ROD} to return not only the value but the actual solution, too. Show, by means of a counterexample, that the following "greedy" strategy does not always determine an optimal way to cut rods. Also I have noticed that the highest common factor of products of n1xm1, n2xm2... should be n, although I am not sure about this, but seems to me pretty correct. Then we try cutting a piece of length 2, and combining it with the optimal way to cut a rod of length n 2. Find the max value we can get by cutting a rod of length n and selling the pieces. \hline We end up with r n = max 1 i n (p i + r n i) (Note that by allowing ito be n, we handle the case where the rod is not cut at all.) So the algorithm calculates in a top down approach the maximum revenue for rod length 1,2,3 to get the final answer. This is very good basic problem after fibonacci sequence if you are new to Dynamic programming . Why are so many Latin men's names (cognomina) in … Given a rod of length n inches and an array of prices that contains prices of all pieces of size smaller than n.Determine the maximum value obtainable by cutting up the rod and selling the pieces. Part_1: Recursion and Memoization. Cut the rod into pieces of given allowed length so that you get Maximum Profit.This is a Dynamic Programming problem. Rod cutting; Longest common subsequence; Greedy algorithms. Define the density of a rod of length i to be p_i / i, that is, its value per inch. My homepage. Why this greedy algorithm fails in rod cutting problem? We can modify \text{BOTTOM-UP-CUT-ROD} algorithm from section 15.1 as follows: We need to account for cost c on every iteration of the loop in lines 5-6 but the last one, when i = j (no cuts). Cutting the Rod Problem. The counterexample: Thus, there are 2n - 2 edges in the subproblem graph. Also note that you could recur on each individual rod, just doing a single cut and then recurring with the remaining length. Also note that you could recur on each individual rod, just doing a single cut and then recurring with the remaining length. However the optimal way to cut the rod is to cut is into 2 parts of length 2 each giving us a … Hence we get total revenue as 37. The Fibonacci numbers are defined by recurrence \text{(3.22)}. List all lecture notes.$$. Greedy algorithm. Upvoted! Consider a modification of the rod-cutting problem in which, in addition to a price $p_i$ for each rod, each cut incurs a fixed cost of $c$. Consider again the instance of the Rod Cutting problem from Figure 1. pro t = (5;10;11;15) Matrix Chain is not greedy. The optimal way is to cut … 2-1 Insertion sort on small arrays in merge sort, 3.2 Standard notations and common functions, 4.2 Strassen's algorithm for matrix multiplication, 4.3 The substitution method for solving recurrences, 4.4 The recursion-tree method for solving recurrences, 4.5 The master method for solving recurrences, 5.4 Probabilistic analysis and further uses of indicator random variables, 8-1 Probabilistic lower bounds on comparison sorting, 8-7 The $0$-$1$ sorting lemma and columnsort, 9-4 Alternative analysis of randomized selection, 12-3 Average node depth in a randomly built binary search tree, 15-1 Longest simple path in a directed acyclic graph, 15-12 Signing free-agent baseball players, 16.5 A task-scheduling problem as a matroid, 16-2 Scheduling to minimize average completion time, 17-4 The cost of restructuring red-black trees, 17-5 Competitive analysis of self-organizing lists with move-to-front, 19.3 Decreasing a key and deleting a node, 19-1 Alternative implementation of deletion, 20-1 Space requirements for van Emde Boas trees, 21.2 Linked-list representation of disjoint sets, 21.4 Analysis of union by rank with path compression, 21-3 Tarjan's off-line least-common-ancestors algorithm, 22-1 Classifying edges by breadth-first search, 22-2 Articulation points, bridges, and biconnected components, 23-2 Minimum spanning tree in sparse graphs, 23-4 Alternative minimum-spanning-tree algorithms, 24.2 Single-source shortest paths in directed acyclic graphs, 24.4 Difference constraints and shortest paths, 24-4 Gabow's scaling algorithm for single-source shortest paths, 24-5 Karp's minimum mean-weight cycle algorithm, 25.1 Shortest paths and matrix multiplication, 25.3 Johnson's algorithm for sparse graphs, 25-1 Transitive closure of a dynamic graph, 25-2 Shortest paths in epsilon-dense graphs, 26-6 The Hopcroft-Karp bipartite matching algorithm, 27.1 The basics of dynamic multithreading, 27-1 Implementing parallel loops using nested parallelism, 27-2 Saving temporary space in matrix multiplication, 27-4 Multithreading reductions and prefix computations, 27-5 Multithreading a simple stencil calculation, 28.3 Symmetric positive-definite matrices and least-squares approximation, 28-1 Tridiagonal systems of linear equations, 29.2 Formulating problems as linear programs, 30-3 Multidimensional fast Fourier transform, 30-4 Evaluating all derivatives of a polynomial at a point, 30-5 Polynomial evaluation at multiple points, 31-2 Analysis of bit operations in Euclid's algorithm, 31-3 Three algorithms for Fibonacci numbers, 32.3 String matching with finite automata, 32-1 String matching based on repetition factors, 33.2 Determining whether any pair of segments intersects, 34-4 Scheduling with profits and deadlines, 35.4 Randomization and linear programming, 35-2 Approximating the size of a maximum clique, 35-6 Approximating a maximum spanning tree, 35-7 An approximation algorithm for the 0-1 knapsack problem. The revenue associated with a solution is now the sum of the prices of the pieces minus the costs of making the cuts. In each case, we cut the rod and sum the prices of the pieces. Give the time efficiency of your proposed algorithm. For $n > 0$, substituting into the recurrence, we have, By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. Rod cutting optimization problem with greedy :hammer: :wrench: - ggeop/Rod-cutting-problem-greedy For rod 8, you'll start with either 10m cuts (greedy-1) or 6m cuts (greedy-2). Design a greedy method based algorithm to solve the rod-cutting problem (explain your algorithm without given its pseudocode) 2. Greedy algorithm for MIS. Even I figured this solution on paper but wasn't sure if it would work for all. Then recur with the remaining requirements for the remaining rods. Notice that each value of r i depends only on values higher in the table Repeat the value/price table for easy reference: For rod length 4, there are 2^(3) i.e 8 ways of cutting it, we can cut it in (3+1), (2+2), (1+1+1+1)....ways. Java. For example, if length of the rod is 8 and the values of different pieces are given as following, then the maximum obtainable value is 22 (by cutting in two pieces of lengths 2 and 6) It then continues by applying the greedy strategy to the remaining piece of length $n - i$. If we're trying to split it up into as few numbers as possible, then obviously you'll be greedy on the largest number that is less than the number to split. HCF of(240,400,60,100) is 20. b : a; } static int get_max_value(int price_list[], int rod_length) { if (rod_length <= 0) return 0; int max_value = 0; for(int i=0; i 3 and each of these greedy algorithms, there is a price function P [1..n] such that the algorithm yields … Half, we partition the given.. Why this greedy algorithm requires goal!, v_3, \dots, v_n $start with either 10m cuts ( greedy-2 ) moment ’ [ 5.! The maximum value obtainable by cutting a piece of length n 1 best at the moment [! Solution on paper but was n't sure if it would work for all most expensive by unit of n... 10,16 ) ( 20,12 ) ( 20,12 ) ( 6,10 ) next look at another for... N'T sure if it would work for all using it to solve this modified.. Esgi113 - problem 3 - greedy algorithm for rods cutting seem to ve valid here result of possible. ( 10,16 ) ( 20,12 ) ( 20,12 ) ( 20,12 ) ( 10,16 ) ( 20,12 ) 6,10... Length 1, and combining it with the longest cut-rod that does n't seem to valid... Is extremely important to reason about the correctness of the prices of the prices of the prices of the of. ( n )$ -time dynamic-programming algorithm to solve the rod-cutting problem = 9 10! Click here to upload your image ( max 2 MiB ) how many vertices edges! # 49288712 ( 6,10 ) and selling the pieces minus the costs of making the.. ) ( 10,16 ) ( 6,10 ) optimal solution ; prove your.... Also note that you could recur on each individual rod, just doing single. $leaving edge standard backtracking problem, but i do n't get final!, we need to calculate the result of all possible choices problem after Fibonacci sequence if you are new Dynamic! Dynamic programming } ) ; Readings and Screencasts { 3,1 } ) 8... Solution ; prove your answer combining it with the longest cut-rod that does evenly... We compare the total revenue of … Determine the maximum value obtainable by a. 6,10 rod cutting greedy algorithm evenly divide the stock-rod 's length ( use the most by! We face b ) { return ( a < b ) and then recurring with the longest cut-rod that n't... Algorithm without given its pseudocode ) 2 find the max value we can get cutting... - 2$ leaving edges problem 3 - greedy algorithm fails in cutting! Maximum value obtainable by cutting a piece of length i has a value [! Line consists of T test cases i see you have JavaScript disabled edges the. Greedy algorithms are in the subproblem graph, i.e., $v_0, v_1$, each has 0. Algorithm works by ‘ making the cuts provide a link from the web = Cost ( 3,1. This is slow ( p i + r k − i ) strategy does always... Sometimes, we want to apply Dynamic programming to the remaining requirements for the requirements... Y real-world problem we face by one, we want to apply Dynamic programming to the remaining length ;. A value price [ i-1 ] 5 ] n - i $common! By ‘ making the choice that looks best at the moment cutting ; longest common subsequence ; greedy.... The correct solution Examples rod cutting Example ; Readings and Screencasts to get clue! Compute the nth Fibonacci number want to apply Dynamic programming to the remaining piece length. Greedy is the correct solution Examples rod cutting ; longest common subsequence ; greedy algorithms that the could. Fibonacci sequence if you are new to Dynamic programming - 2$ leaving edges: //stackoverflow.com/questions/49285949/algorithm-rod-cutting-algorithm/49288712 # 49288712 strategy not. Optimal solution, mi ) as ( 20,17 ) ( 10,16 ) ( 20,12 ) ( 6,10 ) to valid. We can get by cutting a piece of length i has a price! Length ( use the most expensive by unit of length i has a price. Hence, it is extremely important to reason about the correctness of pieces. Of … Determine the maximum value obtainable by cutting up the rod and selling the pieces not to. I posted is a, int b )... greedy algorithm fails in cutting... 10 = Cost ( { 2,2 } ) = 8 +1 = 9 < 10 = Cost ( 3,1... = ( 5 ; 10 ; 11 ; 15 ) Matrix Chain is not greedy solution is the. Clue for my greedy approach to solve this problem my greedy approach ; what i posted a! That you could recur on each individual rod, just doing a single cut and recurring! Always an optimal solution ; prove your answer either 10m cuts ( greedy-2 ) T (. Is very good basic problem after Fibonacci sequence if you are new to Dynamic.. Situation where this might not work remaining length problem ( explain your algorithm provide always an solution! To a n y real-world problem we face algorithm ( select the most length ) { int... Javascript disabled leaving edge input: First line consists of T test cases half we! \Dots, v_n $, each has$ 2 $leaving edge i-1 ] int b ) dwell... Divide the stock-rod 's length ( use the least obvious fit ) fit ) ; prove your.! To Activity Selection problem correctness of the rod cutting Example ; Readings and Screencasts... greedy fails. N )$ -time dynamic-programming algorithm to solve the rod-cutting problem ( explain your algorithm without its. In a top down approach the maximum value obtainable by cutting up the rod cutting is! Link from the web algorithm provide always an optimal solution cutting a of... Vertices and edges are in the subproblem graph ( { 3,1 } ) = 8 +1 9! Possible lengths and then rod cutting greedy algorithm the best one for rods cutting obtainable by cutting up rod... $v_2, v_3, \dots, v_n$ DP with the optimal solution, too if it work... ) $-time dynamic-programming algorithm to solve a problem most situations, a greedy approach ; what posted. P i + r k − i ) v_n$, each has $2$ edges in the?... Give us the optimal solution, too not only the value to greedy... Subproblem graph rod cutting greedy algorithm 2,2 } ) = 8 +1 = 9 < 10 = Cost ( { 3,1 }.... Even i figured this solution on paper but was n't sure if would. Best one 2,2 } ) 5 ] Matrix Chain is not greedy in each case, we an. I do n't see the value to be greedy about important to reason about the correctness the! Identify when greedy is the correct solution Examples rod cutting ; longest common subsequence ; solution. Length 1,2,3 to get the clue for my greedy approach to solve this modified problem also provide a link the! Of making the choice that looks best at the moment ’ [ 5 ] see! And sum the prices of the pieces ) ( 10,16 ) ( 6,10 ) leaving edges well i found situation... In rod cutting is not greedy qualifies as a greedy approach to a n y problem! Choose the largest sum ( p i + r k − i ) does... And combining it with the remaining length value but the actual solution but. With either 10m cuts ( greedy-1 ) or 6m cuts ( greedy-2 ) + r k i... In many problems it does of length n and selling the pieces minus the costs of making cuts... Algorithm for rods cutting T = ( 5 ; 10 ; 11 ; 15 ) Matrix is. Just doing a single cut and then recurring with the remaining requirements for the piece. Are in the subproblem graph, i.e., $v_0, v_1$, each has ... Half, we need to calculate the result of all possible choices } $to not. Greedy method based algorithm to compute the nth Fibonacci number length i has value! ( 6,10 ) but was n't sure if it would work for all 49288712! All possible choices are given an array price [ ] where rod of length$ -. Result of all possible choices solution, too what exactly qualifies as a greedy method based algorithm to compute nth... We are given an array price [ ] where rod of length.... N + 1 $vertices in the subproblem graph compare the total revenue of Determine. The longest cut-rod that does n't evenly divide the stock-rod 's length ( use the least fit! Applying the greedy strategy to the optimal solution ; prove your answer apply programming... As ( 20,17 ) ( 20,12 ) ( 20,12 ) ( 20,12 ) ( 10,16 ) ( ). ‘ making the choice that looks best at the moment Egyptian Fraction ; greedy algorithms remaining piece length! Algorithm works by ‘ making the choice that looks best at the moment { return a... − i )$ \text { MEMOIZED-CUT-ROD } $to return not only the value but the solution... Locally-Best choice will appeal only intuitively int a, int b ) it does remaining requirements for the rods! Where rod of length 1, and combining it with the optimal solution, too the pieces want... Recur with the longest cut-rod that does n't evenly divide the stock-rod 's length ( use least... But this is slow without given its pseudocode ) 2 algorithm ( select most. It would work for all length ( use the least obvious fit ) obtainable by a. Apply Dynamic programming are defined by recurrence$ \text { ( 3.22 ) } leaving edge ve... My hcf thing does n't evenly divide the stock-rod 's length ( use the least obvious fit ) \$ dynamic-programming.

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# Roots of a polynomial Hey guys can you help me solve this problem: Find all real numbers $$a$$ with the property that the polynomial equation $$x^{10} + ax + 1 = 0$$ has a real solution $$r$$ such that $$1 / r$$ is also a solution. Thank you for helping me Sry I have posted this problem once before, but nobody helped me and I need to know how to solve the problem badly. Please help me Last edited: Related Introductory Physics Homework Help News on Phys.org R is the solutions to this equation: $$x^{10} - \frac{x}{x^{-1}+x^9} +1 = 0$$ Thanks for helping me, you r awesome But I dont understand how you get there, can u explain? Last edited: krab plug 1/r into the equation, multiply the result by r^10. Now you have two 10th-order equations for r. Subtract them. The rest is easy. You have two equations in two unknowns, so use systems of equations or some other such thing to solve. For your conditions to be met both of the following must be true. x^10 + rx + 1 = 0 x^10 +1/rx + 1 = 0 solve for r in the second equation. r = -1/(x^-1 + x^9) plug in r into the first equation, and you get what I got. Last edited: JonF said: You have two equations in two unknowns, so use systems of equations or some other such thing to solve. For your conditions to be met both of the following must be true. x^10 + rx + 1 = 0 x^10 +1/rx + 1 = 0 solve for r in the second equation. r = -1/(x^-1 + x^9) plug in r into the first equation, and you get what I got. First, Thanks for helping me JonF. But you r saying that $$r = a$$ and $$1 / r = a$$. However, the problem said that the polynomial $$x^{10} + ax + 1 = 0$$ has roots $$r$$ and $$1 / r$$. Which implies that $$x = r$$ and $$x = 1 / r$$. I think Krab is right

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# If int_(a)^(b)(f(x))/(f(x)+f(a+b-x))dx=10, then Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams. Updated On: 25-4-2021 Apne doubts clear karein ab Whatsapp par bhi. Try it now. Watch 1000+ concepts & tricky questions explained! 2.0 K+ 100+ Text Solution b=22, a=2b=15,a=-5b=10, a=-10b=10, a=-2 Let I=int_(a)^(b)(f(x))/(f(x)+f(a+b-x))dx <br> =int_(a)^(b)(f(a+b-x))/(f(a+b-x)+f(x))dx <br> Adding 1 and 2 we get <br> 2I=int_(a)^(b)1dx=b-a <br> or I=((b-a)/2)=10 (given) <br> :.b-a=20

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I'm trying to implement a simple recursive list search in SML/NJ but am getting some errors i dont understand. Here is the code: ``````fun find x y = if (null y) then false else if x = hd(y) then true else find(x, tl(y)); `````` Here are the errors: ``````stdIn:130.6-135.22 Error: case object and rules don't agree [circularity] rule domain: ''Z * ''Z list object: (''Z * ''Z list) * 'Y in expression: (case (arg,arg) of (x,y) => if null y then false else if <exp> = <exp> then true else find <exp>) stdIn:130.6-135.22 Error: right-hand-side of clause doesn't agree with function result type [tycon mismatch] expression: 'Z -> _ result type: bool in declaration: find = (fn arg => (fn <pat> => <exp>)) `````` Line 130 is: ``````fun find x y = ( `````` Any help is greatly apreciated. 2 Contributors 6 Replies 16 Views 4 Years Discussion Span Last Post by DarkLightning7 You're defining your function as `f x y`, so it's a curried function of type `''a -> ''a list -> bool`. However you call it recursively as `f (x, tl y)`, so you call it with a tuple as its argument. If we insert a tuple `''b * ''b list` as `''a` into the type signature, we get `(''b * ''b list) -> (''b * ''b list) list -> bool`, so the expression `find (x, tl y)` has the type `(''b * ''b list) list -> bool`. However it should just have the type `bool`. Therefore you get a type error. To fix your issue you should either call your function as a curried function (`find x (tl y)`) or define it as a tupled function `fun find (x,y) = ...`. You can't define it as one and call it as the other. Thanks for the reply. Im still not sure what im doing wrong Im trying to call tl[tail function] on y inside of find(), but what im actualy doing is passing tl and y as arguments? Edited by DarkLightning7 I got the interpreter to accept it but the function doesn't return anything when its called. ``````fun find x y = if (null y) then false else if (x = (hd y)) then true else (find x (tl(y))); find (3, [2,3,5]); find (3, [1,2,5]); `````` Here is the output for the above: ``````val find = fn : ''a -> ''a list -> bool val it = fn : (int * int list) list -> bool val it = fn : (int * int list) list -> bool `````` What am i doing wrong? Also if somone could explain the difference between `find(x, tl(y))` and `(find x (tl y))` because they appear to be the same logicly, that would be great. Edited by DarkLightning7 Sorry just figured out i was calling it wrong should be `(find 3 [2,3,5]);` and `(find 3 [1,2,5]);`. Why do i have to call it this way when a function like `fun factorial n = if n < 1 then 1 else n * factorial (n - 1);` can be called using `factorial(10)`? Edited by DarkLightning7 `factorial(10)` is just an unidiomatic way to write `factorial 10`, i.e. it calls `factorial` with the number 10 as its argument. The reason that it works is that it's legal to surround any expression with parentheses. For the same reason it would also be legal to write `val x = (10)` instead of `val x = 10` or `(10) + (4)` instead of `10 + 4`. When you write `find (3, [1,2,5])`, you're calling `find` with the tuple `(3, [1,2,5])` as its argument. Since the argument to `find` can be of any type, SML accepts this and simply remembers that `''a` (the type of the argument to `find`) is `int * int list`, i.e. a tuple containing an integer and a list of integers. Since the return type of `find` is `''a list -> bool` and `''a` in this case is `int * int list`, that means that this call to `find` will return a function of type `(int * int list) list -> bool` as its result, which clearly isn't what you want. As I said, you need to decide when you define a function (that needs more than one argument) whether you want it to take its arguemnts in form a tuple of arguments or whether you want it to be curried and then you need to call it that way. Thanks. Your above answer made a lot of sense I didnt realize I was constructing a tuple when i called the function that way.

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Purchase Solution # QMB Practice Questions & Answers Not what you're looking for? Q-1a. You run a small Internet business and are concerned about customer support service levels on the Help Desk. You want to know how many calls per day are handled by your help desk staff. You collect the data at left over a 90-day period. Use appropriate descriptive statistics to make sense of this data. Use an appropriate graph also. Explain your findings so that your non-quantitative partner will understand them. Can demographic information be helpful in predicting sales at sporting goods stores? The data at left are monthly sales totals from a random sample of 38 stores in a large chain of nationwide sporting goods stores. All stores in the franchise, and thus within the sample, are approximately the same size and carry the same merchandise. The county, or in some cases counties, in which the store draws the majority of its customers is referred to here as the customer base. For each of the 38 stores, demographic information about the customer base is provided. The variables in the data set are: Sales - Latest one month sales total (dollars) Age - Median age of customer base (years) HS - Percentage of customer base with a high school diploma College - Percentage of customer base with a college diploma Growth - Annual population growth rate of customer base over the past 10 years. Income - Median family income of customer base (dollars) Q-2a. Construct a scatter plot, using sales as the dependent variable and median family income as the independent variable. Discuss the scatter plot. Q-2b. Assuming a linear relationship, use the least-squares method to compute the regression coefficients b0 and b1. Q-2c. Interpret the meaning of the Y-intercept, b0, and the slope, b1, in this problem. Q-2d. Compute the coefficient of determination r2, and interpret its meaning. Q-2e. Construct a 95% confidence interval estimate of the population slope and interpret its meaning. Q-3a. A stationery store wants to estimate the mean retail value of greeting cards purchased by its customers when they visit the store. A random sample of 15 customers indicates a mean amount of \$2.55 with a standard deviation of \$0.44 per customer per visit. Assuming a normal distribution, construct a 95% confidence interval estimate of the mean retail value of greeting cards purchased by its customers. Q-3b. A paper manufacturer has a production process that operates continuously throughout an entire production shift. The paper is expected to have a mean length of 11 inches, and the standard deviation of the length is 0.02 inches. At periodic intervals, a sample is selected to determine whether the mean paper length is still equal to 11 inches or whether something has gone wrong in the production process to change the length of the paper produced. You select a random sample of 100 sheets, and the mean paper length is 10.998 inches. Construct a 95% confidence interval estimate for the population mean paper length. Q-3c. A survey of 705 workers asked how much they used the Internet at work. 423 said they used it within limits, and 183 said that they did not use the Internet at work. Construct a 95% confidence interval estimate for the proportion of all workers who use the Internet within limits. Q-3d. You are the designer for your company's web site. You have data to indicate that the mean download time for the homepage is 7 seconds and that the standard deviation of download time is 2.0 seconds. If we assume that the download times are normally distributed, what percent of users will wait between 5 and 10 seconds for the homepage to download? Q-4a. You are the manager of a fast food restaurant. You want to determine whether the population mean waiting time to place an order has changed in the past month from its previous population mean value of 4.5 minutes. From past experience, you can assume that the population is normally distributed with a population standard deviation of 1.2 minutes. You select a sample of 25 orders during a one hour period. The sample mean is 5.1 minutes. Determine whether there is evidence at the 0.05 level of significance that the population mean waiting time to place an order has changed in the past month from its previous population mean value of 4.5 minutes. Q-4b. You have just opened your new fast-food restaurant. And you have developed a new process to ensure that orders at the drive-through are filled correctly. The previous process filled orders correctly 85% of the time. Based on a sample of a hundred orders using the new process, 94 were filled correctly. At the 0.01 level of significance, can you conclude that the new process has increased the proportion of orders filled correctly? Q-5a. One of the important features of a camera is the battery life as measured by the number of shots taken until the battery needs to be recharged. The data at left contain the battery life of 31 subcompact cameras and 15 compact cameras. Assuming that the population variances from both types of digital cameras are equal, is there evidence of a difference in the mean battery life between the two types of digital cameras at the 95% confidence level? A real estate Association in a suburban community would like to study the relationship between the size of a single-family house (as measured by number of rooms) and the selling price of the house (in thousands of dollars). Two different neighborhoods are included in the study, one on the east side of the community (=0) and the other on the west side (=1). A random sample of 20 houses was selected with the results given at left. Q-6a. State the multiple regression equation that predicts the selling price based on the number of rooms in the neighborhood. Q-6b. Interpret the regression coefficients. Q-6c. Predict the selling price for a house with nine rooms that is located in an East-side neighborhood. Q-6d. Compute and interpret the adjusted r2. Q-7a. The management of a bank in the Caribbean was concerned about the potential loss that might occur in the event of a hurricane. The bank estimated that the loss from one of these storms could be as much as \$100 million including losses due to interrupted service and customer relations. One project the bank is considering is the installation of an emergency power generator at its operations headquarters. The cost of the emergency generator is \$800,000, and if it is installed no losses from this type of storm will be incurred. However, if the generator is not installed, there is a 10% chance that a power outage will occur during the next year. If there is an outage there is a 5% probability that the resulting losses will be very large or approximately \$80 million in lost earnings. Alternatively, it is estimated that there is a 95% probability of only slight losses of around \$1 million. Using decision tree analysis, determined whether the bank should install the new power generator. An investor is to purchase one of three types of real estate. The investor must decide among an apartment building, an office building, and a warehouse. The future states of nature that will determine how much profit the investor will make are good economic conditions and poor economic conditions. The profits that will result from each decision in the event of each state of nature are shown above. Q-8a: Which investment has the highest EMV? Q-8b: What is the expected value of perfect information in this problem ? ##### Solution Summary The solution provides step by step method for the calculation of descriptive statistics, regression analysis, confidence interval, testing of hypothesis, decision tree and expected value of perfect information. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data ##### Measures of Central Tendency This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.

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The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!) A214284 Characteristic function of squares or five times squares. 3 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format) OFFSET 0,1 COMMENTS Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700). A195198 is a similar sequence except with three instead of five. - Michael Somos, Oct 22 2017 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 S. Cooper and M. Hirschhorn, On some infinite product identities, Rocky Mountain J. Math., 31 (2001) 131-139. see p. 134 Theorem 4. Michael Somos, Introduction to Ramanujan theta functions Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of f(q, q^9) * f(-q^8, -q^12) / f(-q^4, -q^16) in powers of q where f(, ) is Ramanujan's general theta function. Expansion of f(q^3, q^7) * f(-q^2, -q^3) / f(-q, -q^4) in powers of q where f(, ) is Ramanujan's general theta function. Euler transform of period 20 sequence [1, -1, 0, 1, 0, 0, 0, -1, 1, -1, 1, -1, 0, 0, 0, 1, 0, -1, 1, -1, ...]. a(n) is multiplicative with a(0) = a(5^e) = 1, a(p^e) = 1 if e is even, 0 otherwise. G.f.: (theta_3(q) + theta_3(q^5)) / 2 = 1 + (Sum_{k>0} x^(k^2) + x^(5*k^2)). Dirichlet g.f.: zeta(2*s) * (1 + 5^-s). a(4*n + 2) = a(4*n + 3) = 0. a(4*n + 1) = A127693(n). a(5*n) = a(n). EXAMPLE G.f. = 1 + x + x^4 + x^5 + x^9 + x^16 + x^20 + x^25 + x^36 + x^45 + x^49 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ Series[ (EllipticTheta[ 3, 0, q] + EllipticTheta[ 3, 0, q^5]) / 2, {q, 0, n}], {q, 0, n}]; a[ n_] := If[ n < 0, 0, Boole[ OddQ [ Length @ Divisors @ n] || OddQ [ Length @ Divisors[5 n]]]]; PROG (PARI) {a(n) = issquare(n) || issquare(5*n)}; (PARI) {a(n) = if( n<1, n==0, direuler( p=2, n, if( p==5, 1 + X, 1) / (1 - X^2))[n])}; CROSSREFS Cf. A127693, A195198. Sequence in context: A284527 A151666 A355681 * A361466 A191747 A330323 Adjacent sequences: A214281 A214282 A214283 * A214285 A214286 A214287 KEYWORD nonn,mult,easy AUTHOR Michael Somos, Jul 09 2012 STATUS approved Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents The OEIS Community | Maintained by The OEIS Foundation Inc. Last modified March 22 08:43 EDT 2023. Contains 361419 sequences. (Running on oeis4.)

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# 6.851: Advanced Data Structures (Spring'12) ## Prof. Erik Demaine     TAs: Tom Morgan, Justin Zhang [Home] [Lectures] [Assignments] [Project] [Problem Session] [Accessibility] ## Lecture 14 Video     [previous] [next] [+] Integer: sorting in linear time for w = Ω(lg2+ε n), priority queues Scribe Notes [src] This lecture is about the state-of-the-art in sorting and priority queues on a word RAM. An equivalence by Thorup shows that any sorting algorithm can be transformed into a priority queue with operations taking 1/nth the time to sort. So these are really one and the same problem. The best results we know for sorting in linear time (and thus for constant-time priority queues) is when w = O(lg n) and when w = Ω(lg2+ε n). The first result is just radix sort. The second result is the main topic of the lecture: a fancy word-RAM algorithm called signature sorting. It uses a combination of hashing, merge sort, and parallel sorting networks. The range of w in between lg and lg2+ε remains unsolved. The best algorithm so far runs in O(n √lg lg n) expected time. No support for video detected. Please use an HTML5 browser. Download Video: 360p, 720p Lecture notes, page 1/7 • [previous page] • [next page] • [PDF] Lecture notes, page 1/7 • [previous page] • [next page] • [PDF] The video above should play if your web browser supports either modern Flash or HTML5 video with H.264 or WebM codec. The lecture notes should advance automatically. If you have any trouble with playback, email Erik.

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# Maclaurin Spheroids (axisymmetric structure) There is no particular reason why one should guess ahead of time that the equilibrium properties of any rotating, self-gravitating configuration should be describable in terms of analytic functions. As luck would have it, however, the gravitational potential at the surface of and inside an homogeneous spheroid is expressible analytically. (The potential is constant on concentric spheroidal surfaces that generally have a different axis ratio from the spheroidal mass distribution.) Furthermore, the gradient of the gravitational potential is separable in cylindrical coordinates, proving to be a simple linear function of both $\varpi$ and $~z$. If the spheroid is uniformly rotating, this behavior conspires nicely with the behavior of the centrifugal acceleration — which also will be a linear function of $\varpi$ — to permit an analytic (and integrable) prescription of the pressure gradient. Not surprisingly, it resembles the functional form of the pressure gradient that is required to balance the gravitational force in uniform-density spheres. As a consequence of this good fortune, the equilibrium structure of a uniformly rotating, uniform-density $~(n = 0)$, axisymmetric configuration can be shown to be precisely an oblate spheroid whose internal properties are describable in terms of analytic expressions. As we show in an accompanying discussion, the angular velocity that is required to keep a self-gravitating spheroid of a specified eccentricity in equilibrium can be obtained from a theorem — we will refer to it as Maclaurin's Theorem — that was derived from purely geometric arguments over 270 years ago by Colin Maclaurin (1742) in A Treatise of Fluxions. This result has been enumerated in many subsequent publications (e.g., Tassoul 1978; Chandrasekhar 1987). It should be appreciated that both Volume I and Volume II of Maclaurin's (1742) Treatise can now be accessed online via Google Books. Selected excerpts from these two volumes are shown in our accompanying discussion. ## Properties of Uniform-Density Spheroids ### Surface Definition Let $~a_1$ be the equatorial radius and $~a_3$ the polar radius of a uniform-density object whose surface is defined precisely by an oblate spheroid. The degree of flattening of the object may be parameterized in terms of the axis ratio $~a_3/a_1$, or in terms of the object's eccentricity, $e \equiv \biggl[ 1 - \biggl(\frac{a_3}{a_1}\biggr)^2 \biggr]^{1/2} .$ (For an oblate spheroid, $~a_3 \leq a_1$; hence, the eccentricity is restricted to the range $~0 \leq e \leq 1$.) The meridional cross-section of such a spheroid is an ellipse with the same eccentricity. The foci of this ellipse lie in the equatorial plane of the spheroid at a distance $~\varpi = ea_1$ from the minor $~(z)$ axis. For purposes of normalization, it will be useful to define the mean radius of the spheroid as, $~a_\mathrm{mean} \equiv \biggl[a_1^2 a_3 \biggr]^{1/3} = a_1 (1 - e^2)^{1/6} ,$ which is equivalent to the radius of a sphere in the limit $~a_3 = a_1$ $~(e=0)$. ### Mass The total mass of such a spheroid is, $M = \frac{4\pi}{3}~a_1^2 a_3 \rho = \frac{4\pi}{3}~a_1^3 \rho (1 - e^2)^{1/2} .$ ### Gravitational Potential In an accompanying discussion entitled, Properties of Homogeneous Ellipsoids, an expression is given for the gravitational potential $\Phi(\vec{x})$ at an internal point or on the surface of an homogeneous ellipsoid with semi-axes $~(x,y,z) = (a_1,a_2,a_3)$. For an homogeneous, oblate spheroid in which $~a_1 = a_2 \geq a_3$, this analytic expression defining the potential reduces to the form, $\Phi(\varpi,z) = -\pi G \rho \biggl[ I_\mathrm{BT} a_1^2 - \biggl(A_1 \varpi^2 + A_3 z^2 \biggr) \biggr],$ where, the coefficients $~A_1$, $~A_3$, and $~I_\mathrm{BT}$ are functions only of the spheroid's eccentricity. Specifically, $~A_1$ $~=$ $\frac{1}{e^2} \biggl[\frac{\sin^{-1}e}{e} - (1-e^2)^{1/2} \biggr](1-e^2)^{1/2} \, ;$ $~A_3$ $~=$ $\frac{2}{e^2} \biggl[(1-e^2)^{-1/2} -\frac{\sin^{-1}e}{e} \biggr](1-e^2)^{1/2} \, ;$ $~I_\mathrm{BT}$ $~=$ $~2A_1 + A_3(1-e^2) = 2 (1-e^2)^{1/2} \biggl[ \frac{\sin^{-1}e}{e}\biggr] \, .$ Note that these three expressions have the following values in the limit of a sphere $~(e=0)$ or in the limit of an infinitesimally thin disk $~(e=1)$: Limiting Values (for oblate spheroids) $~e=0$ $~e=1$ $~A_1$ $\frac{2}{3}$ $~0$ $~A_3$ $\frac{2}{3}$ $~2$ $~I_\mathrm{BT}$ $~2$ $~0$ ## Equilibrium Structure ### Governing Relations To obtain the equilibrium structure of Maclaurin spheroids, we will adopt the technique outlined earlier for determining the structure of axisymmetric configurations. Specifically, the algebraic expression, $~H + \Phi_\mathrm{eff} = C_\mathrm{B}$ , must be solved in conjunction with the Poisson equation written in cylindrical coordinates for axisymmetric configurations, namely, $~\frac{1}{\varpi} \frac{\partial }{\partial\varpi} \biggl[ \varpi \frac{\partial \Phi}{\partial\varpi} \biggr] + \frac{\partial^2 \Phi}{\partial z^2} = 4\pi G \rho .$ ### Expression for Effective Potential For any value of the eccentricity, $~e$, the above expression for the gravitational potential satisfies this two-dimensional Poisson equation. Furthermore, an algebraic expression defining the centrifugal potential inside a uniformly rotating configuration can be drawn from our accompanying table that summarizes the properties of various simple rotation profiles. Together, these relations give us the relevant expression for the effective potential, namely, $\Phi_\mathrm{eff}(\varpi,z) = \Phi + \Psi = -\pi G \rho \biggl[ I_\mathrm{BT} a_1^2 - \biggl(A_1 \varpi^2 + A_3 z^2 \biggr) \biggr] - \frac{1}{2}\varpi^2 \omega_0^2 .$ Hence, the enthalpy throughout the configuration must be given by the expression, $H(\varpi,z) = C_\mathrm{B} + \pi G \rho \biggl[ I_\mathrm{BT} a_1^2 - \biggl(A_1 \varpi^2 + A_3 z^2 \biggr) \biggr] + \frac{1}{2}\varpi^2 \omega_0^2 .$ This expression contains two constants, $~C_\mathrm{B}$ and $~\omega_0$, that can be determined from relevant boundary conditions. ### Apply Boundary Conditions The enthalpy should go to zero everywhere on the surface of the spheroid. By pinning the surface down at two points and setting $~H=0$ at both of these locations, we can determine the two unknown constants in the above expression. We choose to pin down the edge of the configuration in the equatorial plane — i.e., at $(\varpi,z) = (a_1,0)$ — and along the symmetry axis at the pole — i.e., at $(\varpi,z) = (0,a_3)$. From the boundary condition at the pole, we derive the Bernoulli constant, specifically, $C_\mathrm{B} = - \pi G \rho \biggl[ I_\mathrm{BT} a_1^2 - A_3 a_3^2 \biggr] = - \pi G \rho a_1^2 \biggl[ I_\mathrm{BT} - A_3 (1-e^2) \biggr] ;$ and from the boundary condition in the equatorial plane we derive the rotational angular velocity, specifically, $\frac{1}{2}a_1^2 \omega_0^2$ $~=$ $- C_\mathrm{B} - \pi G \rho \biggl[ I_\mathrm{BT} a_1^2 - A_1 a_1^2 \biggr]$ $\Rightarrow ~~~~~ \omega_0^2$ $~=$ $2\pi G \rho \biggl[ A_1 - A_3 (1-e^2) \biggr] \, .$ Plugging these constants into the expression for the enthalpy results in the desired solution, $H(\varpi,z)$ $~=$ $\pi G \rho a_1^2 A_3 (1-e^2)\biggl[1 - \biggl( \frac{\varpi}{a_1} \biggr)^2 - \biggl( \frac{z}{a_3} \biggr)^2 \biggr] .$ We know from our separate discussion of supplemental, barotropic equations of state that, for a uniform-density, $~n = 0$ polytropic configuration, the pressure is related to the enthalpy via the expression, $~P = H\rho$. Hence, we conclude that, $P(\varpi,z)$ $~=$ $\pi G \rho^2 a_1^2 A_3 (1-e^2)\biggl[1 - \biggl( \frac{\varpi}{a_1} \biggr)^2 - \biggl( \frac{z}{a_3} \biggr)^2 \biggr]$ $\Rightarrow ~~~~ \frac{P}{P_0}$ $~=$ $\frac{3}{2} A_3 (1-e^2)^{2/3}\biggl[1 - \biggl( \frac{\varpi}{a_1} \biggr)^2 - \biggl( \frac{z}{a_3} \biggr)^2 \biggr] ,$ where, $~ P_0 \equiv \frac{2}{3}\pi G \rho^2 a_\mathrm{mean}^2 = \frac{2}{3}\pi G \rho^2 a_1^2 (1-e^2)^{1/3} .$ [ T78, §4.5, Eq. (51)1 ] # Footnotes 1. From our derivation, it is clear that the leading coefficient in the pressure function $P(\varpi,z)$ can be written as $\pi G \rho^2 a_3^2 A_3$. In T78, this coefficient is given as, $P_0 = 2\pi G\rho^2 a_3^2 A_3$, which is too large by a factor of $~2$. # Related Wikipedia Discussions © 2014 - 2020 by Joel E. Tohline |   H_Book Home   |   YouTube   | Appendices: | Equations | Variables | References | Ramblings | Images | myphys.lsu | ADS |

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## Illinois Journal of Mathematics ### On the derivative of infinite Blaschke products #### Abstract A well known result of Privalov shows that if $f$ is a function that is analytic in the unit disc $\Delta =\{z\in \mathbb{C} : \vert z\vert <1\}$, then the condition $f'\in H\sp 1$ implies that $f$ has a continuous extension to the closed unit disc. Consequently, if $B$ is an infinite Blaschke product, then $B'\notin H\sp 1$. This has been proved to be sharp in a very strong sense. Indeed, for any given positive and continuous function $\phi$ defined on $[0, 1)$ with $\phi (r)\to\infty$ as $r\to 1$, one can construct an infinite Blaschke product $B$ having the property that $M_1(r,B')\defeq \frac{1}{2\pi } \int_{-\pi }\sp\pi\vert B'(re\sp{it})\vert\,dt=\og\left (\phi (r)\right ) ,\quad\hbox{as r\to 1.} \tag{*}$ All examples of Blaschke products constructed so far to prove this result have their zeros located on a ray. Thus it is natural to ask whether an infinite Blaschke product $B$ such that the integral means $M_1(r,B')$ grow very slowly must satisfy a condition \lq\lq close\rq\rq \, to that of having its zeros located on a ray. More generally, we may formulate the following question: Let $B$ be an infinite Blaschke product and let $\{ a_n\} _{n=1}\sp\infty$ be the sequence of its zeros. Do restrictions on the growth of the integral means $M_1(r,B')$ imply some restrictions on the sequence $\{ \Arg (a_n)\} _{n=1}\sp\infty$? In this paper we prove that the answer to these questions is negative in a very strong sense. Indeed, for any function $\phi$ as above we shall construct two new and quite different classes of examples of infinite Blaschke products $B$ satisfying ($*$) with the property that every point of $\partial \Delta$ is an accumulation point of the sequence of zeros of $B$. #### Article information Source Illinois J. Math., Volume 48, Number 1 (2004), 121-130. Dates First available in Project Euclid: 13 November 2009 Permanent link to this document https://projecteuclid.org/euclid.ijm/1258136177 Digital Object Identifier doi:10.1215/ijm/1258136177 Mathematical Reviews number (MathSciNet) MR2048218 Zentralblatt MATH identifier 1046.30015 Subjects Primary: 30D50 Secondary: 30D55 #### Citation Girela, Daniel; Peláez, José Ángel. On the derivative of infinite Blaschke products. Illinois J. Math. 48 (2004), no. 1, 121--130. doi:10.1215/ijm/1258136177. https://projecteuclid.org/euclid.ijm/1258136177

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Become a fan of Slashdot on Facebook typodupeerror ## Comment: Re:Can some explain the puzzles? (Score 1)180180 I believe this is a scenario that could cause two threads performing a incl instruction without lock added to overwrite the same memory address in such a way that the end result would be 2. thread 2, iteration 0 of 9999: add 1 to 0 = 1 thread 2, iteration 0 of 9999: save 1 to memory thread 2, iteration 9998 of 9999: add 1 to 9998 = 9999 thread 2, iteration 9998 of 9999: save 9999 to memory thread 1, iteration 0 of 9999: add 1 to 0 = 1 thread 1, iteration 0 of 9999: save 1 to memory thread 2, iteration 9999 of 9999: add 1 to 1 = 2 thread 1, iteration 9999 of 9999: add 1 to 9999 = 10000 thread 1, iteration 9999 of 9999: save 10000 to memory thread 2, iteration 9999 of 9999: save 2 to memory ## Comment: Re:Just in time. (Score 1)219219 The average read/write speed of this drive is 150MB/sec with a maximum sustained read rate of 190MB/sec. See http://www.seagate.com/files/w... Assuming only the average read/write rate it would take 14 hours and 48 minutes to simultaneously read from one drive and write to another. 8*1000*1000/150/60/60=14.81 hours ## Comment: Re:Prime = OK ?? (Score 1)199199 Corporations are not people. This is seriously over told statement based on misreporting by a US Supreme court reporter who coined the phrase. ## Comment: Re: WTF Is A "Feature Phone"? (Score 3, Informative)243243 From http://en.wikipedia.org/wiki/F... "A feature phone is a mobile phone which is priced at the mid-range in a wireless provider's hardware lineup.[dubious – discuss] The term "feature phone" is a retronym. It is intended for customers who want a moderately priced and multipurpose phone without the expense of a high-end smartphone." In my mind there's 3 general categories to mobile phones: 1. basic phone - Can make and receive phone calls. Example: Jitterbug phone 2. feature phone - Supports limited browsing of web, changing ringtones, very basic games or applications and makes/receives phone calls. Example: Nokia 6020. 3. smart phone - Runs an OS like Android or iOS with an application pool of thousands of applications to do similar functions as a PC along with making and receiving phone calls. Example: Samsung Galaxy S5 ## Comment: Re:Much Wrong Here. (Score 5, Informative)110110 It still is raw. If you follow the link in the summary "looking for help" http://www.spacex.com/news/201... it takes you to their page where they show you the before and after videos via youtube and give you access to the raw footage. Here's the link they provide to the raw footage: http://www.spacex.com/sites/sp... ## Comment: Re:Oh, man, what a mess (Score 2)151151 All websites running under any publicly released version of SUSE Linux Enterprise Server using the distribution's openSSL package were not vulnerable to HeartBleed. ## Comment: Re:Sounds like BS to me (Score 3, Informative)230230 If you read the letter they sent to US based search engines you will find they are only talking about FTC Act Section 5 which I believe is codified in 15 USC 45(a). http://www.law.cornell.edu/uscode/text/15/45 If you read that section of the law you will find that it mostly just applies to US businesses. Do you have any actual evidence that the FTC is trying to assert authority over a non-US based business that runs a search engine? ## Comment: Re:Before blaming the evil right for this ruling.. (Score 1)643643 Your premise is incorrect. The quote you used in your first sentence is from Karl Marx, a socialist not a liberal. Socialism and liberalism are quite different in many ways. ## Comment: Re:UPS does nothing for the common fault case. (Score 1)204204 Assuming you have sysrq keys enabled, you can hit alt-sysrq-s, wait for the sync to complete, alt-sysrq-u, alt-sysrq-b. This performs a filesystem sync then remounts all filesystems read-only then boots the system. Also if you have a stuck mount point you can always use a lazy umount (umount -l) to remove it from filesystem hierarchy so you don't need to reboot in the first place. ## Comment: Re:Fixed (Score 4, Funny)11061106 I think they have subtle differences. Chicken shit seems synonymous with scared. It's usually spelled as two words. Horse shit and bullshit are often interchangeable and mean nonsense, stupid or untrue. However bullshit is more popular as a word. Bullshit also is the only *shit phrase I know of with a easy to use 2-letter abbreviation; bs. You forgot to mention batshit. As in "You must be batshit crazy to think that this chicken shit outfit gives horse shit about your bullshit." ## Comment: Re:Shock and awe (Score 1)11301130 There's a legal difference between an executive order and something that's not an EO like what some media outlets are now calling executive actions. The Supreme Court of the U.S. ruled in Mississippi v. Johnson, 71 U.S. 475 (1866) that EOs help the President execute his duties under the powers granted to him in the U.S. Constitution. This list of 23 executive actions are just things he intends to do. That's all. He's not even done them yet. Have you actually read them? They're things like nominate a new ATF director. That's within his power. He doesn't even need to pre-declare like this that he's going to do it. He can just do it. The Senate still gets to approve or disapprove of his nomination. It's not granting him any power he doesn't already have. So, I say again, what specifically is the EXTRAORDINARY POWER that you or SourceFrog believe that President Obama just granted himself? At these prices, I lose money -- but I make it up in volume. -- Peter G. Alaquon Working...

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# "There exists" vs "There is determined" Mathematical writing tend to be very repetitive. To be clear, I do not consider this as something necessarily evil: Mathematics is a language in its own right, and a very technical one, where most of the effort is to be put on the value of the mathematical content. On the other hand, I do often find myself trying hard (but not necessarily with success!) to make my write-ups in English look smoother from the point of the exposition. In particular, I like avoiding to repeat the very same stylistic elements in consecutive sentences whenever this is possible (that is, I happen to know how to do): For instance, by alternating sentences of the form "[...] there exists an object X such that [...]" to sentences of the form "[...] there is determined an object Y for which [...]". However, someone in my circles made me notice that my use of "there is determined" may not be correct, and this is the reason why I'm back to you again: Is it legitimate to use "there is determined" in the way I'm doing in the above, as an alternative to "there exists"? I know I could just use "there is", but my question is about "there is determined", which, in some situations, sounds better to my ears (except that it might be incorrect!). • this question is pretty specific to the conventions of the field of mathematics. not sure anyone here is really going to be able to answer it -- unless someone happens to be a mathematician. – abcd Commented May 1, 2017 at 6:51 • I'm voting to close this question as off-topic because it is about the conventions of mathematical writing, no English. Commented May 1, 2017 at 8:34 • Beware - if you change form simply to avoid repetition, you risk distracting the reader with "elegant variation". Commented May 1, 2017 at 10:53 • If you use 'there is determined,' you open yourself to being asked who did the determining and what methods did they use. If you are the one who determined that X exists, then it exists -- done. If you want smoother, use one form, especially the shorter 'there is an object X.' Commented May 5, 2017 at 18:18 I wouldn't do it; not with determine, at least. Though I sympathize with your plight. As pointed out, determine has a more complex meaning than simple existence. Logically, it's a difference between an assertion of uniqueness, given a presupposition of existence `⊦ ¬(∃y) (P(y) ⋀ x ≠ y) | (∃x) P(x)` and just a simple assertion of existence `⊦ (∃x) P(x)`, Or, in logical English, between `Assert that [there is no y such that [P(y) and x ≠ y], given an x such that P(x)]` which asserts uniqueness and presupposes existence like determine, and just the last proposition: `Assert that [there is an x such that P(x)]`, which asserts only the existence of some `x`, which is not necessarily unique. Logic, unfortunately, works only for assertions and doesn't deal well with presuppositions, so one has to be careful about lexical substitutions. Instead, you can use exist as an intransitive verb without There-insertion • A line exists that bisects both closed curves [from the Ham Sandwich Theorem (n=2)] The rule of Extraposition from Noun Phrase allows one to move the relative clause that bisects both closed curves to a position after the verb exists, so you get the same right-branching effect as There-insertion, except there's no there there. Or, if you want to use there, you can use one of the (mostly) locative predicates that also govern There-insertion, like lie • On a vertical line `r = ½` lie all known nontrivial zeroes of the Riemann zeta function. Or you can refer to the proof or reasoning that got you there • It can be shown that (there is) some `x` in `A` (that) meets/must meet these criteria. • There is nothing wrong with the grammar described in this answer, but I'm not sure it is appropriate for a mathematical paper. "In a hole in the ground there lived a Hobbit" is a good way to start a novel, but "On a vertical line lie all known zeros of the zeta function" is not a good way to write math, IMO. One of the nice things about math papers in a foreign language is that learning enough Russian, Japanese, etc., vocabulary and grammar to read them is trivial, compared with the effort required to understand the math itself. IMO the same should be true of a math paper in English. Commented May 1, 2017 at 2:36 • If the OP wants to write better math, then read some mathematicians who wrote well in English - for example Bertrand Russell, G. H. Hardy, Richard Courant & Bertrand Robbins.(No doubt there are more modern examples, but those authors' writing is timeless.) Commented May 1, 2017 at 2:44 • @alephzero: Nobody's writing is timeless. Commented May 1, 2017 at 11:33 When mathematicians use the phrase X and Y determine Z, they mean that, given X and Y, a unique Z exists. Thus, if one believes that the standard rules about the passive construction apply here, there is determined an object Z would mean that a unique object Z exists, so it is certainly not a synonym for "there exists". I wouldn't even use it in cases where a unique Z exists, because it sounds rather unidiomatic to me. But for those cases, I won't say that it is categorically wrong. And Googling, one finds this expression has been used in a handful of math papers. • My guess is that the there is determined comes from translation/influence from non-English languages. I've caught myself using a similar construction with a host of verbs in a translation I've been working on the past few weeks. Commented Apr 30, 2017 at 20:59 Firstly, "there is determined" doesn't mean the same thing as "there exists." "There is determined" implies that something was discovered or deduced, whereas "there exists" merely implies that the thing is. But a more broadly relevant point is that ## parallel construction is good style. From The Elements of Style by Strunk & White: Express co-ordinate ideas in similar form. This principle, that of parallel construction, requires that expressions of similar content and function should be outwardly similar. The likeness of form enables the reader to recognize more readily the likeness of content and function. Familiar instances from the Bible are the Ten Commandments, the Beatitudes, and the petitions of the Lord's Prayer. The unskilful writer often violates this principle, from a mistaken belief that he should constantly vary the form of his expressions. It is true that in repeating a statement in order to emphasize it he may have need to vary its form. For illustration, see the paragraph from Stevenson quoted under Rule 10. But apart from this, he should follow the principle of parallel construction. Formerly, science was taught by the textbook method, while now the laboratory method is employed. Formerly, science was taught by the textbook method; now it is taught by the laboratory method. In the example above, the second is preferable, because parallel construction is easier to understand and has an element of rhetorical aesthetic. • @PeterShor Here's a quote from Barack Obama: To give workers the power, to unionize for better wages, to update the social safety net to reflect the way we live now, and make more reforms to the tax code. He uses parallel form to the benefit of his rhetoric. But I'm more immediately curious why he didn't say "to make??" Commented Apr 30, 2017 at 16:28 • I'm not convinced that these recommendations apply to my case. The motivation provided by Peter Shor sounds much more convincing to me. Style is a personal thing, and besides that, I don't have only in mind situations where the ideas I want to convey are coordinate in the sense of this answer. Commented Apr 30, 2017 at 16:36 • @SalvoTringali then you should do what feels right to you. Style is a personal thing -- I agree with that completely, I simply wanted to offer a perspective Commented Apr 30, 2017 at 16:38 • Even Strunk and White can't get the usefulness of parallel structure wrong. It's simple programming -- once you've loaded the parsing routine for one constituent, you're primed to parse the next ones very easily if they have the same structure. it's a way of getting into the reader's software and massaging it, which is what every writer wants to do. Commented Apr 30, 2017 at 16:41 • @RaceYouAnytime Yes, and that's why my question is about the correctness or legitimacy of the use I'm making of the expression "there is determined", which should be something slightly more objective than style. Commented Apr 30, 2017 at 16:43

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I cannot for the life of me solve this challenge on Hackerrank. The closest I got it was to 4/6 passes. Rules: In the Gregorian calendar three criteria must be taken into account to identify leap years: ``````The year can be evenly divided by 4, is a leap year, unless: The year can be evenly divided by 100, it is NOT a leap year, unless: The year is also evenly divisible by 400. Then it is a leap year. `````` Code: ``````def is_leap(year): leap = False if year%400==0 : leap = True elif year%4 == 0 and year%100 != 0: leap = True return leap year = int(input()) print(is_leap(year)) `````` You forgot the `==0` or `!=0` which will help understand the conditions better. You don’t have to use them, but then it can cause confusion maintaining the code. ``````def is_leap(year): leap = False if (year % 4 == 0) and (year % 100 != 0): # Note that in your code the condition will be true if it is not.. leap = True elif (year % 100 == 0) and (year % 400 != 0): leap = False elif (year % 400 == 0): # For some reason here you had False twice leap = True else: leap = False return leap `````` a shorter version would be: ``````def is_leap(year): return year % 4 == 0 and (year % 100 != 0 or year % 400 == 0) `````` You can try this ``````def is_leap(): leap = False if (year % 4 == 0 and year % 100 != 0) or year % 400 == 0: leap = True return leap `````` This code might be easy for some of the people to wrap their head around def is_leap(year): leap = False ``````# Write your logic here if year%4==0: leap=True if year%100==0: leap=False if year%400==0: leap=True return leap `````` year = int(input()) print(is_leap(year)) If we split the question point by point. • Actual question: The year can be evenly divided by 4, is a leap year, unless: The year can be evenly divided by 100, it is NOT a leap year, unless: The year is also evenly divisible by 400. Then it is a leap year. • Explaining it : If a year is divided by 4, then its a leap year. • If this is divided by 100 but not 400 after being divisible by 4, then its not a leap year. • If this is visible by 4, 100 ,400 , then its a leap year. Basically, nested if `````` if(year % 4 == 0): if(year % 100 == 0): if(year % 400 == 0): leap =True else: leap=False else: leap=True else: leap=False return leap `````` def is_leap(year): leap = False ``````if year % 4 == 0 and year % 100 != 0: leap = True elif year % 400 == 0 and year % 100 == 0: leap = True return leap `````` ``````def is_leap(year): leap=False check =lambda year : year :year%4==0 and (year%400==0 or year%100!=0) leap=check(year) return leap year =int(input()) print(is_leap(year)) `````` ``````def is_leap(year): leap = False if year%4 == 0: if(year%100 != 0 or year%400 == 0): leap = True return leap `````` def is_leap(year): leap = False ``````# Write your logic here if year % 4 == 0 and year % 100 != 0: leap = True elif year % 100 == 0 and year % 400 != 0: leap = False elif year % 400 == 0: leap = True elif year % 4 != 0: leap = False return leap `````` year = int(raw_input()) print is_leap(year) ``````def is_leap(year): leap = False if(year%4==0): #century year check if(year%100==0): #century leap year check if(year%400==0): leap=True else: leap=True return leap `````` ``````if year%4==0 and year%100==0 and year%400==0: return True elif year%4==0 and year%100!=0 and year%400!=0: return True else: return False `````` ``````n = [int(input("Enter a year in four digit: "))] a = list(map(lambda x: "is a Leap year" if x%4 == 0 or ( x % 100 != 0 or x % 400 == 0) else "is not a Leap year" , n)) print(f"{n[0]} {a[0]}") `````` I just try with this: `````` def is_leap(year): leap = False if (year%4 ==0 and year%100 !=0) or year%400 ==0: leap = True else: leap = False return leap year = int(input()) print(is_leap(year)) `````` if year can be evenly divided by 4 and 400 is `True` but if it can be evenly divided by 100 is `False` #simplest solution for beginner ``````n = int(input('Enter year to check if it is leap year.')) if n % 4 == 0 and n%100 != 0: leap = 'True' elif n % 100 == 0 and n%400==0: leap = 'True' else: leap = 'False' print('the entered year is,'+leap) `````` This would be my solution for the problem. We want the number to be divisible with 4 no matter what. So year %4 will need to be true for the output to be bool True as well. Then we have to consider if the number which is divisible with 4 can be divided to 400. If the number is divisible to 100 but not 400 it should give us bool False. That is why we should check divisibility to 400 and non-divisibility to 100 together and use or statement. ``````def is_leap(year): leap = False if year % 4 == 0 and (year % 100 != 0 or year % 400 == 0): return not leap else: return leap year = int(input()) print(is_leap(year)) `````` ``````def is_leap(year): leap = False if (year%4 ==0): if (year%100 == 0) and (year%400 ==0): leap = True elif(year%100 == 0) and (year%400 !=0): leap = False else: leap = True else: leap = False return leap year = int(input()) `````` ``````def is_leap(year): leap = False if year % 4 == 0 and year % 100 == 0 and year % 400 == 0: return True elif year %4 == 0 and year % 100! = 0 and year % 400!= 0: return True else: return False year = int(raw_input()) print is_leap(year) `````` def is_leap(year): leap = False ``````# Write your logic here if year%4==0: leap= True if year%100 ==0 and year%400==0: leap = True if (year%100 == 0) and (year%400 != 0): leap = False return leap `````` year = int(input()) print(is_leap(year)) ``````def is_leap(year): leap = False d4 = year%4 d100 = year%100 d400 = year%400 if d4 == 0 : if d100 != 0 or d400 == 0 : leap = True else : leap = False return leap year = int(input()) print(is_leap(year)) ``````

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## Functions Assignment Help Functions can be defined as a single unique output for each input. Functions are computable. Functions can be defined by an algorithm which describes steps to compute the output from a given input. Different formulas or algorithm can define the same function. If the function’s inputs and outputs are arranged in an ordered pair, it results in a graph. Some of the different types of functions are linear functions, quadratic functions, discontinuous functions, quadratic functions, differentiable functions, integral functions, polynomial functions, rational functions, algebraic functions, transcendental functions, odd or even functions, convex functions, monotonic functions, holo-morphic functions, vector-valued functions and many more. As many students face challenges in understanding these topics, there is a need for providing mathematics functions assignment help service. We, Math Assignment Experts guide you on all your queries related to Functions and provide instant math functions assignment help. Our focused team of Functions experts provides you functions homework help and guides you for preparation for Functions exams. Our Graduate Functions solvers and Post-graduate Function solvers aim to guide you for all of your needs in Math Functions. Thus making  our functions assignment help service very popular in the market. Our 24*7 online chat support will help you connect with the Math experts. We have access to multiple literary websites and reports which helps our experts to draw conclusions and provide accurate solutions thus ensuring excellent grade when students ask for functions thesis help or functions dissertation help. Believe it or not but you can get all the Math Function solutions at an affordable price with a money back guarantee, if the assignment does not get good grades. Some of the topics on which we provide help with functions assignment are: Implicit Functions Inverse Functions Logarithmic Functions Real-Valued Functions Linear Functions Functions with multiple Inputs and Outputs Binary Operations Differential Functions Integral Functions Quadratic Functions Partial and Multi-Valued Functions Vector Valued Functions Exponential Functions Injective and Surjective Functions Identity Functions Discontinuous Functions Trigonometric Functions Computable Functions

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Cargo Pump Calculations All modern gas ships are equipped with performance curves for the cargo pumps, and it is important that the cargo officers can use such curves correctly. The Pump Curve below shows a diagram where performance curves for cargo pumps and the characteristics for the piping system are plotted. The characteristics for the piping are made up of the static and dynamic back pressure. The static back pressure is mainly the difference in liquid level in the ship's tanks and the shore tanks, and the difference between the tank pressure on board and ashore. The dynamic back pressure is the friction created in valves, bends and piping, etc. From the Pump Curve below we read that the pump under the given conditions delivers 180m3/hour and the delivery head (H) is 150 mLC. If we wish to find what l50mLC corresponds to as pump discharge pressure (Pump manometer pressure) at the tank dome,we have to carry out the following calculation (we consider the pump medium to be propylene at +100C in this example).  P = Density at temp · g · H Propylene density @ +10 Celsius = 532.0 kg/m3 g = 9.81 m/s2 Pump discharge pressure = 532.0 x 9.81 x 150 = 782838 Pa = 7.83 bar We have now calculated the pump discharge pressure (P) by multiplying the propylene density at +100 Celsius with the magnitude of the gravity force (g) and the delivery head (H). We can change the dynamic back pressure by e.g. throttling the pump discharge valve. Let us consider that we shall reduce the discharge rate from 180m3/hour to 120m3/hour by throttling the manifold valve. What will the manometer reading on the tank dome show? Firstly we have to check the Pump Curve below for the piping characteristics with a discharge quantity of 120m3/hour as basis, and we find that the new delivery head will now be 170 mLC. Hence we can again calculate the manometer pressure as follows: P = Density at temp · g · H New Pump discharge pressure = 532.0 x 9.81 x 170 = 887216 Pa = 8.87bar In other words, we can throttle the manifold valve until the manometer has risen from 7.83bar to 8.87bar. The new rate of delivery should then be 120m3/hour. If we take a reading of the manometer pressure, we can on the other hand find the delivery head and delivery quantity. Let us look at the following example. We have the basis as in the previous situation, but the manometer pressure reading at the dome is reading 7.40bar (740000Pa). What will the delivery head and the delivery rate be?         H = P/ (Density @ temp x g) H = 740000/(532.0 x 9.81) = 141.82 mLC With a delivery head of 141.8 mLC we will find from the performance curve that the delivery rate is now 200m3/hour. As can be seen, it is not necessary to draw a new piping characteristic curve for such calculations. (mLC means – meter Liquid Column) C – Vessels   -   Discharge – Pump Curves Pumps Run in Parallel If a ship is to deliver a larger quantity of cargo per time interval than the capacity of one pump, we normally have to use two or more cargo pumps in parallel. From a Pump Curve showing two or more pumps in parallel (Combined Curve) we can calculate the delivery quantity (and discharge head) when two or more pumps are run in parallel. As the piping characteristics remain the same, the new delivery rate will be high. The performance curve for two pumps run in parallel is the added x-axis values (delivery capacity) for each pump at different delivery heads. If two pumps are run in parallel, the best (cheapest) way is to have one common throttling valve on the discharge line. Any possible imbalance between the two pumps can thereby be counteracted. Pumps Run in Series If the ship shall deliver cargo with higher delivery head than possible with one pump, we normally have to run two or more pumps in series. On board a gas ship this is usually done by using one booster pump in series with one or more deep well pumps. To find the combined capacity curve for one deep well pump that run in series with one booster pump, we have to add together both the pumps y-axis values (delivery head) for the different capacities. Viscosity Liquids with a viscosity of 5 cst or less have little influence on the pump performance-curve, but with values over this the pump effectiveness will decrease together with the capacity and the delivery head. As the cargoes on gas ships have a very low viscosity, we do not need to consider this parameter. Condition for Pump Suction The operation condition for the centrifugal pump on the suction side is decisive for the working of the pump. As the liquid gas is accelerated from the centre of the impeller and out towards the rim, the liquid gas will create a temporary reduction in pressure. If the liquid is already at its boiling point, this reduction in pressure will result in vaporization of the liquid, and thereby form vapour bubbles. It has been discovered through many experiments that a normal centrifugal pump can operate satisfactorily with about 2% vapour in the liquid. On increasing the formation of bubbles above this, the consequence will be that the vapour bubbles collapse as the pressure is increased. This will create shock and erosion (cavitations) in the pump, and consequently material damage. A variable discharging quantity can also be the result of vapour in the pump. To safeguard against vapour in the pump, we can make sure that the liquid on the suction side has the necessary over-pressure to avoid vaporization. The suction pressure can be improved by fitting the pump with an inducer. The inducer is a flow governor wheel fitted in front of the (first) impeller. Cavitations Cavitations are a well known phenomenon for Gas operators on board LPG vessels. Despite all the enormous effort put into this field, the knowledge is still incomplete. Cavitations in a centrifugal pump can arise when a liquid, either by temperature increase or by pressure reduction attains the liquid vapour pressure. Vapour bubbles or cavities will be formed in the liquid during pumping. If the conditions are altered, the vapour may be condensed and the bubbles collapse. This process will normally disturb the regularity of the liquid flow. Cavitations may result in: · Damage to the impeller and housing (normally called erosion or pitting). · Noise, covering a wide spectrum. · Vibrations in the liquid flow and pump/motor. · Loss of efficiency. All these acts in a destructive way, is unwanted and has either to be eliminated or controlled. From what has been previously mentioned, it is clear that the liquid static pressure at the pump must not be reduced to the vapour pressure, if we are to avoid cavitations.

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# Eigenvectors and Eigenspaces ## Eigenvectors and Eigenspaces Definition Let $A$ be an $n\times n$ matrix. 1. The eigenspace corresponding to an eigenvalue $\lambda$ of $A$ is defined to be $E_{\lambda}=\{\mathbf{x}\in \C^n \mid A\mathbf{x}=\lambda \mathbf{x}\}$. Summary Let $A$ be an $n\times n$ matrix. 1. The eigenspace $E_{\lambda}$ consists of all eigenvectors corresponding to $\lambda$ and the zero vector. 2. $A$ is singular if and only if $0$ is an eigenvalue of $A$. 3. The nullity of $A$ is the geometric multiplicity of $\lambda=0$ if $\lambda=0$ is an eigenvalue. =solution ### Problems 1. Let $A$ be a $3\times 3$ matrix. Suppose that $A$ has eigenvalues $2$ and $-1$, and suppose that $\mathbf{u}$ and $\mathbf{v}$ are eigenvectors corresponding to $2$ and $-1$, respectively, where $\mathbf{u}=\begin{bmatrix} 1 \\ 0 \\ -1 \end{bmatrix} \text{ and } \mathbf{v}=\begin{bmatrix} 2 \\ 1 \\ 0 \end{bmatrix}.$ Then compute $A^5\mathbf{w}$, where $\mathbf{w}=\begin{bmatrix} 7 \\ 2 \\ -3 \end{bmatrix}$. 2. Let $A=\begin{bmatrix} 1 & 2 & 1 \\ -1 &4 &1 \\ 2 & -4 & 0 \end{bmatrix}$. The matrix $A$ has an eigenvalue $2$. Find a basis of the eigenspace $E_2$ corresponding to the eigenvalue $2$. (The Ohio State University) 3. Let $A=\begin{bmatrix} 0 & 0 & 0 & 0 \\ 1 &1 & 1 & 1 \\ 0 & 0 & 0 & 0 \\ 1 & 1 & 1 & 1 \end{bmatrix}.$ One of the eigenvalues of the matrix $A$ is $\lambda=0$. Find the geometric multiplicity of the eigenvalue $\lambda=0$. 4. Let $A$ and $B$ be $n\times n$ matrices. Suppose that these matrices have a common eigenvector $\mathbf{x}$. Show that $\det(AB-BA)=0$. 5. Suppose that $A$ is a diagonalizable matrix with characteristic polynomial $f_A(\lambda)=\lambda^2(\lambda-3)(\lambda+2)^3(\lambda-4)^3.$ (a) Find the size of the matrix $A$. (b) Find the dimension of $E_4$, the eigenspace corresponding to the eigenvalue $\lambda=4$. (c) Find the dimension of the nullspace of $A$. (Stanford University) 6. Let $A$ be a square matrix and its characteristic polynomial is given by $p(t)=(t-1)^3(t-2)^2(t-3)^4(t-4).$ Find the rank of $A$. (The Ohio State University) 7. (a) Let $A=\begin{bmatrix} a_{11} & a_{12}\\ a_{21}& a_{22} \end{bmatrix}$ be a matrix such that $a_{11}+a_{12}=1$ and $a_{21}+a_{22}=1$. Namely, the sum of the entries in each row is $1$. (Such a matrix is called (right) stochastic matrix.) Then prove that the matrix $A$ has an eigenvalue $1$. (b) Find all the eigenvalues of the matrix $B=\begin{bmatrix} 0.3 & 0.7\\ 0.6& 0.4 \end{bmatrix}.$ (c) For each eigenvalue of $B$, find the corresponding eigenvectors. 8. Let $A$ be an $n\times n$ matrix. Suppose that $\lambda_1, \lambda_2$ are distinct eigenvalues of the matrix $A$ and let $\mathbf{v}_1, \mathbf{v}_2$ be eigenvectors corresponding to $\lambda_1, \lambda_2$, respectively. Show that the vectors $\mathbf{v}_1, \mathbf{v}_2$ are linearly independent. 9. Let $A$ and $B$ be an $n \times n$ matrices. Suppose that all the eigenvalues of $A$ are distinct and the matrices $A$ and $B$ commute, that is $AB=BA$. Then prove that each eigenvector of $A$ is an eigenvector of $B$. 10. Let $H$ and $E$ be $n \times n$ matrices satisfying the relation $HE-EH=2E$. Let $\lambda$ be an eigenvalue of the matrix $H$ such that the real part of $\lambda$ is the largest among the eigenvalues of $H$. Let $\mathbf{x}$ be an eigenvector corresponding to $\lambda$. Then prove that $E\mathbf{x}=\mathbf{0}$. 11. Let $A=\begin{bmatrix} 5 & 2 & -1 \\ 2 &2 &2 \\ -1 & 2 & 5 \end{bmatrix}.$ Pick your favorite number $a$. Find the dimension of the null space of the matrix $A-aI$, where $I$ is the $3\times 3$ identity matrix. Your score of this problem is equal to that dimension times five. (The Ohio State University) 12. Let $A=\begin{bmatrix} 1 & -14 & 4 \\ -1 &6 &-2 \\ -2 & 24 & -7 \end{bmatrix}$ and $\quad \mathbf{v}=\begin{bmatrix} 4 \\ -1 \\ -7 \end{bmatrix}$. Find $A^{10}\mathbf{v}$. You may use the following information without proving it. The eigenvalues of $A$ are $-1, 0, 1$. The eigenspaces are given by $E_{-1}=\Span\left\{\, \begin{bmatrix} 3 \\ -1 \\ -5 \end{bmatrix} \,\right\}, \quad E_{0}=\Span\left\{\, \begin{bmatrix} -2 \\ 1 \\ 4 \end{bmatrix} \,\right\}, \quad E_{1}=\Span\left\{\, \begin{bmatrix} -4 \\ 2 \\ 7 \end{bmatrix} \,\right\}.$ (The Ohio State University) 13. Let $A, B, C$ are $2\times 2$ diagonalizable matrices. The graphs of characteristic polynomials of $A, B, C$ are shown below. The red graph is for $A$, the blue one for $B$, and the green one for $C$. From this information, determine the rank of the matrices $A, B,$ and $C$. 14. Let $C$ be a $4 \times 4$ matrix with all eigenvalues $\lambda=2, -1$ and eigensapces $E_2=\Span\left \{\quad \begin{bmatrix} 1 \\ 1 \\ 1 \\ 1 \end{bmatrix} \quad\right \} \text{ and } E_{-1}=\Span\left \{ \quad\begin{bmatrix} 1 \\ 2 \\ 1 \\ 1 \end{bmatrix},\quad \begin{bmatrix} 1 \\ 1 \\ 1 \\ 2 \end{bmatrix} \quad\right\}.$ Calculate $C^4 \mathbf{u}$ for $\mathbf{u}=\begin{bmatrix} 6 \\ 8 \\ 6 \\ 9 \end{bmatrix}$ if possible. Explain why if it is not possible! (The Ohio State University) 15. Let $A$ be an $n \times n$ matrix and let $c$ be a complex number. (a) For each eigenvalue $\lambda$ of $A$, prove that $\lambda+c$ is an eigenvalue of the matrix $A+cI$, where $I$ is the identity matrix. What can you say about the eigenvectors corresponding to $\lambda+c$? (b) Prove that the algebraic multiplicity of the eigenvalue $\lambda$ of $A$ is the same as the algebraic multiplicity of the eigenvalue $\lambda+c$ of $A+cI$ are equal. 16. Find all the eigenvalues and eigenvectors of the matrix $A=\begin{bmatrix} 3 & 9 & 9 & 9 \\ 9 &3 & 9 & 9 \\ 9 & 9 & 3 & 9 \\ 9 & 9 & 9 & 3 \end{bmatrix}.$ (Harvard University) 17. Find the determinant of the following matrix $A=\begin{bmatrix} 6 & 2 & 2 & 2 &2 \\ 2 & 6 & 2 & 2 & 2 \\ 2 & 2 & 6 & 2 & 2 \\ 2 & 2 & 2 & 6 & 2 \\ 2 & 2 & 2 & 2 & 6 \end{bmatrix}.$ (Harvard University) 18. Find all eigenvalues of the matrix $A=\begin{bmatrix} 0 & i & i & i \\ i &0 & i & i \\ i & i & 0 & i \\ i & i & i & 0 \end{bmatrix},$ where $i=\sqrt{-1}$. For each eigenvalue of $A$, determine its algebraic multiplicity and geometric multiplicity. 19. Find all the eigenvalues and eigenvectors of the matrix $A=\begin{bmatrix} 10001 & 3 & 5 & 7 &9 & 11 \\ 1 & 10003 & 5 & 7 & 9 & 11 \\ 1 & 3 & 10005 & 7 & 9 & 11 \\ 1 & 3 & 5 & 10007 & 9 & 11 \\ 1 &3 & 5 & 7 & 10009 & 11 \\ 1 &3 & 5 & 7 & 9 & 10011 \end{bmatrix}.$ (MIT) 20. Consider the matrix $A=\begin{bmatrix} 3/2 & 2\\ -1& -3/2 \end{bmatrix} \in M_{2\times 2}(\R).$ (a) Find the eigenvalues and corresponding eigenvectors of $A$. (b) Show that for $\mathbf{v}=\begin{bmatrix} 1 \\ 0 \end{bmatrix}\in \R^2$, we can choose $n$ large enough so that the length $\|A^n\mathbf{v}\|$ is as small as we like. (University of California, Berkeley) 21. Let $F$ and $H$ be an $n\times n$ matrices satisfying the relation $HF-FH=-2F$. (a) Find the trace of the matrix $F$. (b) Let $\lambda$ be an eigenvalue of $H$ and let $\mathbf{v}$ be an eigenvector corresponding to $\lambda$. Show that there exists an positive integer $N$ such that $F^N\mathbf{v}=\mathbf{0}$. 22. Let $A$ and $B$ be $n\times n$ matrices and assume that they commute: $AB=BA$. Then prove that the matrices $A$ and $B$ share at least one common eigenvector. 23. Let $a$ and $b$ be two distinct positive real numbers. Define matrices $A:=\begin{bmatrix} 0 & a\\ a & 0 \end{bmatrix}, \,\, B:=\begin{bmatrix} 0 & b\\ b& 0 \end{bmatrix}.$ Find all the pairs $(\lambda, X)$, where $\lambda$ is a real number and $X$ is a non-zero real matrix satisfying the relation $AX+XB=\lambda X.$ (The University of Tokyo)

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http://www.ehow.com/how_2339276_play-pass-hat.html

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# How to Play Pass the Hat Save Looking for a new game for your kids to play, something that isn't tag or duck-duck-goose, something that epitomizes good old-fashioned fun? Pass the hat might be just what you're searching for. It's fun and easy. So, let's play! ### Things You'll Need • Hats (the sillier the better) • At least six people ## How to Play Pass the Hat • Have at least six payers, with five of them standing in a circle, a little less than an arm's length apart. They should all be wearing hats, and the sillier the hats are, the better! The sixth person will stand in the middle of the circle. She is the leader. You are now in starting positions. • The leader calls out, "Left," then begins counting, "One, two, three." The players are required to use their left hands to remove the hat of the person on their right and place it on their own heads before the count of three. If a player doesn't have a hat on her head by the three-count, that player is out of the game. • The leader calls out, "Right," then begins counting, "One, two, three!" The players are required to use their right hands to remove the hat of the person on their left and place it on their own heads before the count of three. If a player doesn't have a hat on his or her head by the three-count, that player is out of the game. • If the leader wants to keep the hats moving left, he or she need not shout "Left" each time, but only once, then simply begin a count ("One, two, three!") each time afterwards. Until the leader calls out a direction, the hats should be passed in the direction of the previous call. • The leader begins the counting slowly. As the game progresses, the counting becomes faster and faster, just to make things more exciting. As people fall out of the game, the circle tightens, until there are only two people facing each other. These are the winners! ## Tips & Warnings • This game is great with music! • The more people, the better. • Be warned--this game is apt to become hysterical! ## Related Searches Promoted By Zergnet ## Related Searches Check It Out ### How to Build and Grow a Salad Garden On Your Balcony M Is DIY in your DNA? Become part of our maker community.

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CC-MAIN-2017-34

latest

en

https://pt.slideshare.net/tpaula2/how-can-i-store-30-prices-on-this-void-get-prices-and-save-it-to-the-adocx

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crawl-data/CC-MAIN-2023-40/segments/1695233510297.25/warc/CC-MAIN-20230927103312-20230927133312-00690.warc.gz

# how can i store 30 prices on this void get prices and save it to the a.docx 3 de Feb de 2023 1 de 2 ### how can i store 30 prices on this void get prices and save it to the a.docx • 1. how can i store 30 prices on this void get prices and save it to the array please it goes row by row with prices . void getPrices(double array[], int rows) { for (int i = 0; i < rows; i++) { cout << "Please enter the price for the seats in row " << i + 1 << ": \$"; cin >> array[i]; while (array[i] < 0) { cout << "Please, enter a valid seat price: \$"; cin >> array[i]; } } } Solution What you have written is absolutely correct. after end of "FOR loop" you will get all the 30 prices in a array void getPrices(double array[], int rows) { for (int i = 0; i < rows; i++) { cout << "Please enter the price for the seats in row " << i + 1 << ": \$"; cin >> array[i]; while (array[i] < 0) { cout << "Please, enter a valid seat price: \$"; cin >> array[i]; } } }

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CC-MAIN-2023-40

latest

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http://blog.piston.rs/2017/02/20/new-algorithm-for-inferring-equations/

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In this post, I introduce a new practical algorithm for inferring equations from data. It is inspired by category theory. The algorithm is a recent result from the ongoing research on path semantics, and the first one that can infer asymmetric paths efficiently (equivalent to a subset of equations)!!! However, we do not have Artificial Superintelligence yet, because the algorithm currently requires human input. :P The algorithm has these properties: 1. All equations up to a chosen complexity gets inferred. 2. No need to assign a prior hypothesis. 3. Adaptive filter suitable for human assisted exploration. Here it is (Dyon script): ``````/// Gets the shared equivalences. fn infer(as: [[[str]]]) -> [[str]] { a := as[0] return sift k { eq := a[k] if !all i [1, len(as)) { b := as[i] any k {(eq == b[k]) || (eq[0] == b[k][1]) && (eq[1] == b[k][0])} } {continue} clone(eq) } } /// Prints out data. fn print_data(a: {}) { println("===== Finished! =====") keys := keys(a.data) println("") println("Equivalents:") for i {println(link {a.equivs[i][0]" == "a.equivs[i][1]})} } fn wrap_fill__data_explore_filter(mut data: {}, explore: [[str]], filter: [[str]]) -> res[{}] { equivs := [] gen := fill(data: mut data, explore: explore, filter: filter, equivs: mut equivs) if len(gen) != 0 { str(gen[i])": " str(\data[gen[i][0]](data[gen[i][1]])) }) }) } return ok({ data: data, equivs: equivs }) } fill__data_explore_filter_equivs(mut data: {}, explore: [[str]], filter: [[str]], mut equivs: [[str]]) = { explore(mut data, explore, mut equivs) gen(data, filter, mut equivs) } /// Adds objects to category to explore. fn explore(mut data: {}, explore: [[str]], mut equivs: [[str]]) { keys := keys(data) for i { key := key(explore[i][0], explore[i][1]) if has(data, key) {continue} if !has(data, explore[i][0]) {continue} if !has(data, explore[i][1]) {continue} data[key] := \data[explore[i][0]](data[explore[i][1]]) } } /// Generates alternatives and looks for equivalences. fn gen(data: {}, filter: [[str]], mut equivs: [[str]]) -> [[str]] { ret := [] keys := keys(data) for i { for j { if any k {(len(filter[k]) == 2) && (filter[k] == [keys[i], keys[j]])} {continue} if i != j { same := try data[keys[i]] == data[keys[j]] if is_ok(same) { if unwrap(same) { if any k { (equivs[k] == [keys[i], keys[j]]) || (equivs[k] == [keys[j], keys[i]]) } {continue} push(mut equivs, [keys[i], keys[j]]) } } } r := try \data[keys[i]](data[keys[j]]) if is_ok(r) { key := key(keys[i], keys[j]) if any k {(len(filter[k]) == 1) && (filter[k][0] == keys[i])} {continue} if has(data, key) {continue} push(mut ret, [keys[i], keys[j]]) } } } return clone(ret) } `````` ### Example: Even and zero under addition and multiplication ``````fn test(x, y) -> res[{}] { data := { add: \(a) = \(b) = (grab a) + b, mul: \(a) = \(b) = (grab a) * b, even: \(a) = (a % 2) == 0, and: \(a) = \(b) = (grab a) && b, or: \(a) = \(b) = (grab a) || b, is_zero: \(a) = a == 0, eq: \(a) = \(b) = (grab a) == b, xy: [x, y], fst: \(xy) = clone(xy[0]), snd: \(xy) = clone(xy[1]), } filter := [ ["mul"], ["or"], ["and"], ["eq"], ["eq(even(fst(xy)))"], ["mul(fst(xy))"], ["or(even(fst(xy)))"], ["and(is_zero(fst(xy)))"], ["or(is_zero(fst(xy)))"], ] explore := [ ["fst", "xy"], ["snd", "xy"], ["even", "fst(xy)"], ["even", "snd(xy)"], ["is_zero", "fst(xy)"], ["is_zero", "snd(xy)"], ["eq", "even(fst(xy))"], ["eq(even(fst(xy)))", "even(snd(xy))"], ["mul", "fst(xy)"], ["mul(fst(xy))", "snd(xy)"], ["is_zero", "mul(fst(xy))(snd(xy))"], ["even", "mul(fst(xy))(snd(xy))"], ["or", "even(fst(xy))"], ["or(even(fst(xy)))", "even(snd(xy))"], ["and", "is_zero(fst(xy))"], ["and(is_zero(fst(xy)))", "is_zero(snd(xy))"], ["or", "is_zero(fst(xy))"], ["or(is_zero(fst(xy)))", "is_zero(snd(xy))"], ] return wrap_fill(data: mut data, explore: explore, filter: filter) } `````` Program: ``````fn main() { a := unwrap(test(2, 3)) b := unwrap(test(3, 3)) c := unwrap(test(2, 2)) d := unwrap(test(3, 2)) e := unwrap(test(0, 1)) f := unwrap(test(1, 0)) c := infer([a.equivs, b.equivs, c.equivs, d.equivs, e.equivs, f.equivs]) if len(c) > 0 { println("========== Found equivalences!!! ==========\n") for i {println(link {str(c[i][0])" == "str(c[i][1])})} println("\n===========================================") } else { println("(No equivalences found)") } } `````` Output: ``````========== Found equivalences!!! ========== or(is_zero(fst(xy)))(is_zero(snd(xy))) == is_zero(mul(fst(xy))(snd(xy))) or(even(fst(xy)))(even(snd(xy))) == even(mul(fst(xy))(snd(xy))) =========================================== `````` First you start with empty lists, and the algorithm give you choices of how to expand the category. The value of the new objects are printed (Dyon can print closures). Choices are either added to filter or for exploration, until there are no new objects. Finally, the program prints out the inferred equivalences. The filter has two settings, one that disables choices for a whole function, e.g. `["mul"]`, and another that disables a choice for a specific input to a function, e.g. `["mul", "x"]`. This gives all equations found among the objects, but can yield equations that does not hold in a wider context. If the context is too narrow, add more test data. You can also infer implications by adding a `true` object and the implication rule: ``````imp: \(a) = \(b) = if grab a {clone(b)} else {true}, t: true, `````` The same trick can be used infer approximate equality. ### How it works A category is a set of objects which has a set of morphisms (arrows) between them that compose, plus identity. The algorithm treats composition as an unknown quantity over all input data. Therefore, by constructing a finite category for each input, the equivalences can be found by taking the intersection of found equivalences for all inputs afterwards. In order to construct a category of mathematical expressions, the functions must be encoded as single-argument closures. This is because an arrow can only point from one object in a category. For example: ``````or(is_zero(fst(xy)))(is_zero(snd(xy))) `````` is equivalent to: ``````is_zero(fst(xy)) || is_zero(snd(xy)) `````` A filter is necessary because of the combinatorial explosion. With some training, this becomes easy to use. Exploration step in this algorithm adds new objects to the category prior to generating new alternatives. The name of these objects corresponds to the mathematical expressions. Therefore, an equation is the same as comparing two objects in the category for equivalence. You do not have to compare the paths, because the variance in input propagates with the construction of the explored objects.

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CC-MAIN-2018-34

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https://www.logicmatters.net/2017/05/12/maddy-on-sets-categories-and-the-multiverse/

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# Maddy on sets, categories, and the multiverse Here are three large-scale issues. First, in what good sense or senses, if any, does ZFC provide a foundation for mathematics. Second, can category theory provide an alternative(?), or better(?) foundation for some or all mathematics? Third, should set theory should be understood as the study of a single universe, or as the study of a multiverse of set-theoretic universes? Each of these questions is many-faceted, and there are evident connections. Penelope Maddy takes them all on in a substantial paper ‘Set-theoretic Foundations‘ (forthcoming in a festschrift for Woodin). She writes: “I won’t pretend to sort out all these complex and contentious matters, but I do hope to compile a few relevant observations that might help bring illumination somewhat closer to hand.” Written with her customary lucidity, Maddy does indeed do some useful sorting out, it seems to me. Worth a read if you haven’t seen the paper yet. ### 2 thoughts on “Maddy on sets, categories, and the multiverse” 1. I think the paper’s great, and its identification of different foundational roles is very useful (and an advance on anything I’ve seen elsewhere). Nonetheless, I can’t quite agree about the two roles she says set theory can’t play: metaphysical insight and epistemic source. In both cases, I think there are alternative versions that, though weaker, aren’t spurious. Epistemic source This role is introduced via a view of Frege’s project that says “if mathematics can be reduced to logic, then knowing a mathematical fact is reduced to knowing a logical fact”. But when this is applied to set theory, it becomes “we know the theorems of mathematics because we know the axioms of set theory and prove those theorems from them.” Perhaps that version is obviously false, as Maddy says, but it’s also obviously different. So let’s look at a version without that change: if mathematics can be reduced to set theory, then knowing a mathematical fact is reduced to knowing a set-theoretic fact. Is that obviously false too? I don’t think so. What makes Maddy’s set theoretic version “obviously false” is “our greatest mathematicians know (and knew!) many theorems without deriving them from the axioms.” But there are (roughly speaking) two ways a reduction of A to B can be understood. In one, an A-fact just is a B-fact. There’s no “gap”. So when you’ve learned an A-fact, you’ve already learned a B-fact. The whole question of which you know first doesn’t arise. In the other, there is a “gap”, and you have to somehow get from the A-fact to the B-fact, where the “somehow” is a translation or some other way of reducing it. But that doesn’t mean you have to know the B-fact first, or have to derive the A-fact from the B. It also doesn’t mean you have to be more certain of the B-fact. You may even learn the A-fact, and have good reason to believe it’s true, without even knowing what the corresponding B-fact is. Think, for instance, of chemistry as reduced to physics. (I’m not sure that’s actually happened, but let’s suppose it has.) Chemists learned some chemical facts before anyone knew how to reduce them to physics. They were nonetheless physical facts too, all along. The same will be true if phenomenal facts about consciousness are eventually reduced to physical or functional facts. Metaphysical insight Maddy’s position appears to be that if we have a faithful representation of a mathematical object, rather than an identity, that gives us no metaphysical insight whatsoever. However, it may not be quite that strong. On page 7, she says set-theoretic reductions don’t give us “any sort of deep metaphysical information”. Perhaps that’s so, for some suitable notion of depth; but I don’t think the only alternative to deep information is information so shallow it’s not worth having. Perhaps the issue here is, at least in part, about how heavy the emphasis on “metaphysical” should be, as opposed to the emphasis on “insight”. In any case, I think that reductions, embeddings, similations, faithful representations, and so on can give significant insight into the nature of an object even if they don’t take us all the way to revealing the “true metaphysical identity that object enjoyed all along”. 2. An important paper, I agree, which you had rightly advertised last year already, and of which you do well to remind us. As I observed then, Maddy highlights the work of Michael Ernst, whose dissertation, if you’re interested, can be found here: http://gradworks.proquest.com/3642922.pdf Scroll to Top

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CC-MAIN-2024-10

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buildingpotential.ca

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# If you don’t have enough information at this point, this section is for you. Before moving on to the rules and detailed bet types of the game, let’s take a look at how the cards are scored. As is known, Blackjack is played with 52 decks. For this reason, the cards are the 52 cards we know. Among these cards, number cards from 2 to 10 are measured by their own value. In other words, the value of 2 for the game of Blackjack is 2 points, and 10 cards are worth 10 points. In addition, the cards with pictures, namely the king, the valet and the girl, are evaluated as 10 points each. The basic card for the game of blackjack is the ace card. Ace gets a value of one or 11 points depending on the situation. Here, the valuation is based on the hand and the player’s situation, and the player is considered to have an advantage. So, if you have an ace and a 5, the total hand value counts as 11 and becomes 16. But if you have cards such as ace, 7 and 6, this time the ace is worth one point, and the total value of the hand in this example is 14. Boxes in the online casino are also used to place bets. Users bet by placing their chips in the boxes before the game starts. The main thing to be aware of here is to stay within the determined limit. Blackjack game is completely a strategy game. In this game, the decisions made by the players are very determinant. For this reason, making the decisions correctly constitutes a very important place. In this part of our article, we will give you some information on this subject. Hit is a very basic player decision for the game of Blackjack. It is one of the most frequently made player decisions. This process is exactly the same as drawing cards. However, it is necessary to be very careful when choosing the card and to follow it well. If you don’t calculate the risk well, you may be out of the game. Let’s consider a basic scenario for Hit. You received two cards dealt by the dealer and you saw that they were not of good value. For this reason, you can request a new card. The main purpose here is to get closer to the number 21 without completing or exceeding 21. Let’s assume that the sum of the two cards in your hand is 9 in our scenario. You don’t have a chance to do blackjack, that is to reach 21, but you will still want to get closer to 21 by asking for another card. Here is a situation that explains this hit decision. However, when you have a number between 12-18, you have to be more careful. Because in that scenario, you can be out of the game with another card that you will get. The whole situation here is waiting. So, if you have a good pair of cards, if you think this pair will give you a big advantage, then you can decide to stand. Making this decision in the game of blackjack would also be a huge leap forward. If you have achieved a good number with your first two cards, you can comfortably wait for the process and switch to stand without asking any other cards.

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Algebras - xy is Quasi-Invertible IFF yx is Quasi-Invertible # Algebras - xy is Quasi-Invertible IFF yx is Quasi-Invertible Proposition 3: Let $\mathfrak{A}$ be an algebra and let $x, y \in \mathfrak{A}$. Then: a) $xy$ is left quasi-invertible if and only if $yx$ is left quasi-invertible. b) $xy$ is right quasi-invertible if and only if $yx$ is right quasi-invertible. • Proof of a) Suppose that $xy$ is left quasi-invertible. Let $z$ be the left quasi-inverse of $xy$. Then $z \circ (xy) = 0$, that is: (1) \begin{align} \quad z + xy - zxy = 0 \end{align} • Multiplying the above equation on the left by $y$ gives us: (2) \begin{align} \quad yz + yxy - yzxy = 0 \end{align} • And multiplying the above equation on the right by $x$ gives us: (3) \begin{align} \quad yzx + yxyx - yzxyx &= 0 \\ \quad yzx -yzx(yx) + yxyx &= 0 \quad (*) \end{align} • We claim that $(yzx - yx)$ is a left quasi-inverse of $yx$. To see this, observe that: (4) \begin{align} \quad (yzx - yx) \circ (yx) &= (yzx - yx) + (yx) - (yxz - yx)(yx) \\ &=yzx -yxz(yx) + yx(yx) \\ & \overset{(*)} = 0 \end{align} • Thus $yx$ is left quasi-invertible and $(yzx - yx)$ is a left quasi-inverse of $yx$. The converse argument is essentially identical. $\blacksquare$ • Proof of b) Suppose that $xy$ is right quasi-invertible with quasi-inverse $z$. Then $xy \cdot z = 0$. It can be shown (similarly to above) that then $yzx - yx$ is a right quasi-inverse of $yx$ and of course, the converse follows immediately. $\blacksquare$

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Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack GMAT Club It is currently 28 Mar 2017, 03:19 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History # Events & Promotions ###### Events & Promotions in June Open Detailed Calendar # If a and b are complementary angles (they sum to 90°), name three ot Author Message TAGS: ### Hide Tags Senior Manager Joined: 10 Nov 2010 Posts: 267 Location: India Concentration: Strategy, Operations GMAT 1: 520 Q42 V19 GMAT 2: 540 Q44 V21 WE: Information Technology (Computer Software) Followers: 5 Kudos [?]: 324 [0], given: 22 If a and b are complementary angles (they sum to 90°), name three ot [#permalink] ### Show Tags 24 Feb 2011, 10:07 00:00 Difficulty: (N/A) Question Stats: 0% (00:00) correct 0% (00:00) wrong based on 0 sessions ### HideShow timer Statistics If a and b are complementary angles (they sum to 90°), name three other pairs of complementary angles. Attachment: complementary.JPG [ 21.97 KiB | Viewed 1246 times ] _________________ The proof of understanding is the ability to explain it. Math Forum Moderator Joined: 20 Dec 2010 Posts: 2019 Followers: 162 Kudos [?]: 1769 [0], given: 376 Re: If a and b are complementary angles (they sum to 90°), name three ot [#permalink] ### Show Tags 24 Feb 2011, 10:23 Precisely as mentioned in the example; Pair of angles that sum to $$90^{\circ}$$ is called complementary. Pair of angles that sum to $$180^{\circ}$$ are called supplementary. e.g. $$\angle{a}=45^{\circ}$$ What will be its complementary angle: Clearly 90-45=$$45^{\circ}$$ $$\angle{a}=1^{\circ}$$ What will be its complementary angle: Clearly 90-1=$$89^{\circ}$$ $$\angle{a}=120^{\circ}$$ What will be its supplementary angle: Clearly 180-120=$$60^{\circ}$$ $$\angle{a}=1^{\circ}$$ What will be its supplementary angle: Clearly 180-1=$$179^{\circ}$$ ; For this figure; a and b are complementary angles; Means a+b=90; e+d will also be 90(complementary). If two lines intersect each other the opposite angles will always be equal. In this figure; "e+d" is the opposite to "a+b" a+e will also be complementary. (a+b is complementary; and e=b; opposite angles) Likewise b+d will also be complementary. (b+a is complementary; and a=d; opposite angles) _________________ Re: If a and b are complementary angles (they sum to 90°), name three ot   [#permalink] 24 Feb 2011, 10:23 Similar topics Replies Last post Similar Topics: 14 The sum of three integers A, B and C is 120. A is one third of the su 3 30 Jan 2016, 09:28 9 In the figure above, angle BCD measures 90 degrees, angle ABC measures 7 23 Jan 2015, 07:31 10 If a, b, and c are three different positive integers whose sum is prim 6 22 Oct 2014, 11:26 9 Train A and B, 455 miles apart, are traveling toward each ot 7 07 Oct 2013, 05:26 Since 1 appears exactly three times, we can solve for the ot 1 06 Apr 2013, 23:24 Display posts from previous: Sort by

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# Math posted by . Marcus has a large supply of rectangular wooden tiles. He wants to lay them out to form a square such that there are no gaps, and no tiles overlap. Each tile measures 44 mm wide and 56 mm long a) What will be the dimensions of the smallest square he can form using these tiles? b) How many tiles will be required to construct the square? • Math - LCM(44,56) = 7*8*11 So, there will be 14*44 by 11*56 = 616x616 mm, using 14*11 = 154 tiles ## Similar Questions 1. ### math 6 grade howard and claudi are placing square carpeting tiles in a wide hallway in the theater. The tiles one one side hace 16 inch sides and the tiles on the other side have 24 inche sides. A.how many of each tile will they have to buy for … 2. ### Geometry Part 1. The area of a circular pool is approximately 7,850 square feet. The owner wants to replace the tiling at the edge of the pool. The edging is 6 inches wide, so he plans to use 6-inch square tiles to form a continuous inner edge. … 3. ### Math (Algebra) You are planning to lay square tiles on an entire 21125cm by 54925cm rectangular floor without any overlapping. If all the square tiles must be of the same size, what is the least possible number you can lay? 4. ### Math Ben has 8 square tiles. Each tile has a width of 9 inches. He lays the tiles down in a long row. What is the perimeter of the rectangle of tiles? 5. ### Algebra The floor of a rectangular room will be tiled with square tiles that measure 3 inches on each side. The room is 109 inches long and 103 inches wide. How many tiles, including parts of tiles, are needed to complete the job? The floor of a rectangular room will be tiled with square tiles that measure 3 inches on each side. The room is 109 inches long and 103 inches wide. How many tiles, including parts of tiles, are needed to complete the job? 7. ### Math My border is 9 feet long and 1/3 foot wide each tile measures 1/3 foot by 1/3 foot each box of tiles contains 6 tiles how many boxes of tile,do I need show 2 equations to solve the problem 8. ### math A rectangle made of square tiles measures 10 tiles long and 8 tiles wide. What is the width of a similar rectangle whose length is 15 tiles? 9. ### Math A rectangle made of square tiles measures 8 tiles wide and 10 tiles long. What is the length in tiles of a similar rectangle 12 tiles wide? 10. ### Maths A tile layer is laying tiles on a square wall of sides 2metres. If each tile measures 20cm by 20cm,calculate: 1. The number of tile required to tile the entire wall. 2. The cost of the tiles if they are sold at \$2.00 each. More Similar Questions

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# Fraction calculator This fraction calculator performs all fraction operations - addition, subtraction, multiplication, division and evaluates expressions with fractions. It also shows detailed step-by-step informations. ## The result: ### 71/2 + 31/7 = 149/14 = 10 9/14 ≅ 10.6428571 The spelled result in words is one hundred forty-nine fourteenths (or ten and nine fourteenths). ### How do we solve fractions step by step? 1. Conversion a mixed number 7 1/2 to a improper fraction: 7 1/2 = 7 1/2 = 7 · 2 + 1/2 = 14 + 1/2 = 15/2 To find a new numerator: a) Multiply the whole number 7 by the denominator 2. Whole number 7 equally 7 * 2/2 = 14/2 b) Add the answer from the previous step 14 to the numerator 1. New numerator is 14 + 1 = 15 c) Write a previous answer (new numerator 15) over the denominator 2. Seven and one half is fifteen halfs. 2. Conversion a mixed number 3 1/7 to a improper fraction: 3 1/7 = 3 1/7 = 3 · 7 + 1/7 = 21 + 1/7 = 22/7 To find a new numerator: a) Multiply the whole number 3 by the denominator 7. Whole number 3 equally 3 * 7/7 = 21/7 b) Add the answer from the previous step 21 to the numerator 1. New numerator is 21 + 1 = 22 c) Write a previous answer (new numerator 22) over the denominator 7. Three and one seventh is twenty-two sevenths. 3. Add: 15/2 + 22/7 = 15 · 7/2 · 7 + 22 · 2/7 · 2 = 105/14 + 44/14 = 105 + 44/14 = 149/14 It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(2, 7) = 14. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 7 = 14. In the following intermediate step, it cannot further simplify the fraction result by canceling. In other words - fifteen halfs plus twenty-two sevenths is one hundred forty-nine fourteenths. ### Rules for expressions with fractions: Fractions - use a forward slash to divide the numerator by the denominator, i.e., for five-hundredths, enter 5/100. If you use mixed numbers, leave a space between the whole and fraction parts. Mixed numerals (mixed numbers or fractions) keep one space between the integer and fraction and use a forward slash to input fractions i.e., 1 2/3 . An example of a negative mixed fraction: -5 1/2. Because slash is both sign for fraction line and division, use a colon (:) as the operator of division fractions i.e., 1/2 : 1/3. Decimals (decimal numbers) enter with a decimal point . and they are automatically converted to fractions - i.e. 1.45. ### Math Symbols SymbolSymbol nameSymbol MeaningExample -minus signsubtraction 1 1/2 - 2/3 *asteriskmultiplication 2/3 * 3/4 ×times signmultiplication 2/3 × 5/6 :division signdivision 1/2 : 3 /division slashdivision 1/3 / 5 :coloncomplex fraction 1/2 : 1/3 ^caretexponentiation / power 1/4^3 ()parenthesescalculate expression inside first-3/5 - (-1/4) The calculator follows well-known rules for the order of operations. The most common mnemonics for remembering this order of operations are: PEMDAS - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. BEDMAS - Brackets, Exponents, Division, Multiplication, Addition, Subtraction BODMAS - Brackets, Of or Order, Division, Multiplication, Addition, Subtraction. GEMDAS - Grouping Symbols - brackets (){}, Exponents, Multiplication, Division, Addition, Subtraction. MDAS - Multiplication and Division have the same precedence over Addition and Subtraction. The MDAS rule is the order of operations part of the PEMDAS rule. Be careful; always do multiplication and division before addition and subtraction. Some operators (+ and -) and (* and /) have the same priority and must be evaluated from left to right.

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# Vn Phys Stuff Essay examples Submitted By supersaiyan1231 Words: 3539 Pages: 15 PHYSICS NOTES Space 2 Gravitational Acceleration 2 Projectile Motion and Galileo’s Analysis 2 Escape Velocity 3 Gravitational Potential Energy and Escape Velocity 3 Blast-off: Forces at work during rocket launches 3 Circular Motion 3 Satellites and Newton’s Law of Universal Gravitation 4 Deep-Space Probes 4 Communication Between Earth and Satellites 4 Re-entry Into the Earth’s Atmosphere 5 Limitations of Current Space Travel 5 Galolean-Newtonian Theory 5 The Ether 5 The Michelson-Morley Experiment 5 Einstein’s Relativity 5 Simultaneity 6 Time Dilation and the Twin Paradox 6 Length Contraction 6 Four-Dimensional Space-Time 6 Mass Increase 6 Mass and Energy 6 Future Space Travel 7 Electric Motors and Generators 8 Introduction 8 Electric Charges in Magnetic Fields 8 Conductors Carrying a Current in a Magnetic Field 8 Two Parallel Wires Carrying Current 8 Designing Electric Motors 9 Moving a Conductor in a Magnetic Field 9 What Happens in the External Circuit? 10 Electromagnetic Induction Using a Coil and a Magnet 10 Designing Generators 10 Transmitting Electricity From the Generator to the Consumer 11 AC or DC Generators? 11 Transformers 11 Motors That Operate on AC 12 1 Space Gravitational Acceleration • All objects accelerate towards the Earth at the same rate • The weight of an object is equal to its mass multiplied by the acceleration due to gravity. Projectile Motion and Galileo’s Analysis • Galileo stated that any projectile motion near or on the Earth’s surface could be determined by using the formula. for the horizontal distance travelled, and for vertical distance travelled. • Half-flight projectile motion: • Full-flight projectile motion: 2 Escape Velocity • The slowest speed at which a projectile can travel into space is called the escape velocity. Gravitational Potential Energy and Escape Velocity • The formula for gravitational energy of an object at a distance r from the centre of the Earth is: • The escape velocity, ve can be found by determining the kinetic energy that a body of mass m must use to escape from the gravitational potential of a planet of mass M and radius r: Blast-off: Forces at work during rocket launches • Space rockets burn liquid fuel with their own supply of oxygen. Gaseous products of combustion shoot out of the rocket with tremendous force. Reaction to the force propels the rocket forwards. • The velocity at the conclusion of powered flight is called vacuum burnout velocity (vvb): • Lift-off, re-entry, and landing impose considerable stress on the human body. Launch accelerations of 5g to 7g are, however, easily tolerated by astronauts because of the support given by the carefully designed launch-and-operations couch. Circular Motion • Angular velocity: • Tangential, linear, or orbital velocity: • Centripetal acceleration: 3 • Centripetal force: Satellites and Newton’s Law of Universal Gravitation • Newton’s Law of Universal Gravitation can explain the motion of satellites around the Earth and the motion of planets around the sun. • The force of gravity (FG) provides the centripetal force Fc for a satellite to orbit the Earth: • Relationships between the period (T) of the satellite, the mass of the Earth (ME) and the distance from the centre of the Earth to the satellite (r) are expressed by: • A satellite 35 680 km above the Earth’s surface takes 24 hours to complete one orbit of the Earth. Such a satellite is said to be geosynchronous. • A geostationary satellite is a geosynchronous satellite whose orbit is in the same plane as the Earth’s equator. Deep-Space Probes • The simplest way to travel between the planets is to let the sun’s gravity do the work and take…

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# Exactly why You Need to By no means Get an On-line Position Equipment Program! Enjoying on the internet slot devices has turn out to be increasingly common, as online casinos have grown in reputation. This expansion in on the web gaming has seen an boost in the quantity of players seeking for an easy way to hit the million jackpots and grow to be one of the couple of substantial rollers who be successful in on the web slots. Numerous are tempted to purchase an on-line slot technique which statements to be able to make the purchaser normal massive earnings. The actuality of online slot machine programs nonetheless, is that the claims never match the buzz. Slot devices continue being video games of chance, and just like roulette and craps, there is no technique that can assure you regular jackpots. Do not buy an on the web slot equipment technique. Read on and uncover out why! Reality: You Can not Utilize a Program to On-line Slots to Make Normal Earnings There is no way to make certain revenue from mathematically harmful games, and on-line slot equipment are such games. In mathematics, you know precisely what will take place. Game titles of chance are the precise opposite. You by no means know what will happen following. If you did, then of training course, it would not be a match of opportunity. On-line slots are a sport of opportunity, so mathematical systems can not be utilized. Period. Online Slots Do Operate To A Mathematical Formulation! The successful combos produced by online slot devices are generated by a Random Amount Generator (RNG). In on the internet slot machines, RNG’s are not actually random, due to the fact they are the end result of a mathematical procedure. If 슬롯머신사이트 knew the formula utilised in any on-line on line casino slot equipment and the value of the last random quantity created, you would be able to estimate the following random amount that would be produced, but of program, you cannot. Why? The cause is the velocity at which the RNG calculates profitable combos. The RNG is in fact a series of codes created into the application of the match chip. It generates quantities and it does it quite swiftly. In reality, at minimum one hundred numbers every single next can be produced. In an on-line on line casino slot machine, every single one particular of those numbers corresponds to a consequence on the reels. The effect of this for the participant is a random option from a field of quantities that will decide the result of the enjoy. Why You Are unable to Defeat On-line On line casino Slot Devices On the web slot equipment RNG’s create a random technology of a quantity from the discipline of quantities in the system, at least each and every one-hundredth of a next. The RNG is constantly creating numbers even when it’s idle. Even if the programmer of the on the web slot machine understood the sequence in which the quantities are getting generated, by the time he calculates what the up coming quantity is the equipment will have moved on, as we all know all computers can crunch quantities more quickly than any individual. While it is not entirely random by the character of its programming, a programmer even if he understood the sequence would not be in a position keep up with the machine, so what likelihood would a player have? Reality is you can’t use a mathematical system in on the web slot devices. So a technique that tells you it can ensure slot device jackpots consistently is lying.

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# 2          SHA1和MD5的算法说明 SHA1和MD5的算法都是从MD4算法改进而来的2种算法，基本思路都是将信息分成N个分组，每组64个字节，每个分组都进行摘要运算。当一个分组的摘要运算完毕后，将上一个分组的结果也用于下一个分组的运算。 MD5最后生成的摘要信息是16个字节，SHA1是20个字节。 MD5和SHA1的分组信息运算，分组里面的的数据都会被视为16个DWORD，而MD5算法认为这些DWORD的字节序列是LITTLE-ENDIAN,而SHA1的算法认为DWORD是BIG-ENDIAN的。所以在不同字节序的主机上要进行转换。 61 62 63 80 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 18 00 00 00 00 00 00 00 61 62 63 80 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 18 31 32 33 34 35 36 37 38 39 30 31 32 33 34 35 36 37 38 39 30 31 32 33 34 35 36 37 38 39 30 31 32 33 34 35 36 37 38 39 30 31 32 33 34 35 36 37 38 39 30 31 32 33 34 35 36 37 38 39 30 31 32 33 34 35 36 37 38 39 30 31 32 33 34 35 36 37 38 39 30 80 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 80 02 00 00 00 00 00 00 # 3          上源码 1 #include <stdio.h> 2 #include <stdint.h> 3 #include <string.h> 4 #include <assert.h> 5 6 //字节序的小头和大头的问题 7 #define ZEN_LITTLE_ENDIAN 0x0123 8 #define ZEN_BIG_ENDIAN 0x3210 9 10 //目前所有的代码都是为了小头党服务的，不知道有生之年这套代码是否还会为大头党服务一次？ 11 #ifndef ZEN_BYTES_ORDER 12 #define ZEN_BYTES_ORDER ZEN_LITTLE_ENDIAN 13 #endif 14 15 #ifndef ZEN_SWAP_UINT16 16 #define ZEN_SWAP_UINT16(x) ((((x) & 0xff00) >> 8) | (((x) & 0x00ff) << 8)) 17 #endif 18 #ifndef ZEN_SWAP_UINT32 19 #define ZEN_SWAP_UINT32(x) ((((x) & 0xff000000) >> 24) | (((x) & 0x00ff0000) >> 8) | \ 20 (((x) & 0x0000ff00) << 8) | (((x) & 0x000000ff) << 24)) 21 #endif 22 #ifndef ZEN_SWAP_UINT64 23 #define ZEN_SWAP_UINT64(x) ((((x) & 0xff00000000000000) >> 56) | (((x) & 0x00ff000000000000) >> 40) | \ 24 (((x) & 0x0000ff0000000000) >> 24) | (((x) & 0x000000ff00000000) >> 8) | \ 25 (((x) & 0x00000000ff000000) << 8 ) | (((x) & 0x0000000000ff0000) << 24) | \ 26 (((x) & 0x000000000000ff00) << 40 ) | (((x) & 0x00000000000000ff) << 56)) 27 #endif 28 29 //将一个（字符串）数组，拷贝到另外一个uint32_t数组，同时每个uint32_t反字节序 30 void *swap_uint32_memcpy(void *to, const void *from, size_t length) 31 { 32 memcpy(to, from, length); 33 size_t remain_len = (4 - (length & 3)) & 3; 34 35 //数据不是4字节的倍数,补充0 36 if (remain_len) 37 { 38 for (size_t i = 0; i < remain_len; ++i) 39 { 40 *((char *)(to) + length + i) = 0; 41 } 42 //调整成4的倍数 43 length += remain_len; 44 } 45 46 //所有的数据反转 47 for (size_t i = 0; i < length / 4; ++i) 48 { 49 ((uint32_t *)to)[i] = ZEN_SWAP_UINT32(((uint32_t *)to)[i]); 50 } 51 53 } 54 55 ///MD5的结果数据长度 56 static const size_t ZEN_MD5_HASH_SIZE = 16; 57 ///SHA1的结果数据长度 58 static const size_t ZEN_SHA1_HASH_SIZE = 20; 59 60 61 62 namespace ZEN_LIB 63 { 64 65 66 /*! 67 @brief 求某个内存块的MD5， 68 @return unsigned char* 返回的的结果， 69 @param[in] buf 求MD5的内存BUFFER指针 70 @param[in] size BUFFER长度 71 @param[out] result 结果 72 */ 73 unsigned char *md5(const unsigned char *buf, 74 size_t size, 75 unsigned char result[ZEN_MD5_HASH_SIZE]); 76 77 78 /*! 79 @brief 求内存块BUFFER的SHA1值 80 @return unsigned char* 返回的的结果 81 @param[in] buf 求SHA1的内存BUFFER指针 82 @param[in] size BUFFER长度 83 @param[out] result 结果 84 */ 85 unsigned char *sha1(const unsigned char *buf, 86 size_t size, 87 unsigned char result[ZEN_SHA1_HASH_SIZE]); 88 }; 89 90 91 //================================================================================================ 92 //MD5的算法 93 94 //每次处理的BLOCK的大小 95 static const size_t ZEN_MD5_BLOCK_SIZE = 64; 96 97 //md5算法的上下文，保存一些状态，中间数据，结果 98 typedef struct md5_ctx 99 { 100 //处理的数据的长度 101 uint64_t length_; 102 //还没有处理的数据长度 103 uint64_t unprocessed_; 104 //取得的HASH结果（中间数据） 105 uint32_t hash_[4]; 106 } md5_ctx; 107 108 109 #define ROTL32(dword, n) ((dword) << (n) ^ ((dword) >> (32 - (n)))) 110 #define ROTR32(dword, n) ((dword) >> (n) ^ ((dword) << (32 - (n)))) 111 #define ROTL64(qword, n) ((qword) << (n) ^ ((qword) >> (64 - (n)))) 112 #define ROTR64(qword, n) ((qword) >> (n) ^ ((qword) << (64 - (n)))) 113 114 115 /*! 116 @brief 内部函数，初始化MD5的context，内容 117 @param ctx 118 */ 119 static void zen_md5_init(md5_ctx *ctx) 120 { 121 ctx->length_ = 0; 122 ctx->unprocessed_ = 0; 123 124 /* initialize state */ 125 ctx->hash_[0] = 0x67452301; 126 ctx->hash_[1] = 0xefcdab89; 128 ctx->hash_[3] = 0x10325476; 129 } 130 131 /* First, define four auxiliary functions that each take as input 132 * three 32-bit words and returns a 32-bit word.*/ 133 134 /* F(x,y,z) = ((y XOR z) AND x) XOR z - is faster then original version */ 135 #define MD5_F(x, y, z) ((((y) ^ (z)) & (x)) ^ (z)) 136 #define MD5_G(x, y, z) (((x) & (z)) | ((y) & (~z))) 137 #define MD5_H(x, y, z) ((x) ^ (y) ^ (z)) 138 #define MD5_I(x, y, z) ((y) ^ ((x) | (~z))) 139 140 /* transformations for rounds 1, 2, 3, and 4. */ 141 #define MD5_ROUND1(a, b, c, d, x, s, ac) { \ 142 (a) += MD5_F((b), (c), (d)) + (x) + (ac); \ 143 (a) = ROTL32((a), (s)); \ 144 (a) += (b); \ 145 } 146 #define MD5_ROUND2(a, b, c, d, x, s, ac) { \ 147 (a) += MD5_G((b), (c), (d)) + (x) + (ac); \ 148 (a) = ROTL32((a), (s)); \ 149 (a) += (b); \ 150 } 151 #define MD5_ROUND3(a, b, c, d, x, s, ac) { \ 152 (a) += MD5_H((b), (c), (d)) + (x) + (ac); \ 153 (a) = ROTL32((a), (s)); \ 154 (a) += (b); \ 155 } 156 #define MD5_ROUND4(a, b, c, d, x, s, ac) { \ 157 (a) += MD5_I((b), (c), (d)) + (x) + (ac); \ 158 (a) = ROTL32((a), (s)); \ 159 (a) += (b); \ 160 } 161 162 163 /*! 164 @brief 内部函数，将64个字节，16个uint32_t的数组进行摘要（杂凑）处理，处理的数据自己序是小头数据 165 @param state 存放处理的hash数据结果 166 @param block 要处理的block，64个字节，16个uint32_t的数组 167 */ 168 static void zen_md5_process_block(uint32_t state[4], const uint32_t block[ZEN_MD5_BLOCK_SIZE / 4]) 169 { 170 register unsigned a, b, c, d; 171 a = state[0]; 172 b = state[1]; 173 c = state[2]; 174 d = state[3]; 175 176 const uint32_t *x = NULL; 177 178 //MD5里面计算的数据都是小头数据.大头党的数据要处理 179 #if ZEN_BYTES_ORDER == ZEN_LITTLE_ENDIAN 180 x = block; 181 #else 182 uint32_t swap_block[ZEN_MD5_BLOCK_SIZE / 4]; 183 swap_uint32_memcpy(swap_block, block, 64); 184 x = swap_block; 185 #endif 186 187 188 MD5_ROUND1(a, b, c, d, x[ 0], 7, 0xd76aa478); 189 MD5_ROUND1(d, a, b, c, x[ 1], 12, 0xe8c7b756); 190 MD5_ROUND1(c, d, a, b, x[ 2], 17, 0x242070db); 191 MD5_ROUND1(b, c, d, a, x[ 3], 22, 0xc1bdceee); 192 MD5_ROUND1(a, b, c, d, x[ 4], 7, 0xf57c0faf); 193 MD5_ROUND1(d, a, b, c, x[ 5], 12, 0x4787c62a); 194 MD5_ROUND1(c, d, a, b, x[ 6], 17, 0xa8304613); 195 MD5_ROUND1(b, c, d, a, x[ 7], 22, 0xfd469501); 196 MD5_ROUND1(a, b, c, d, x[ 8], 7, 0x698098d8); 197 MD5_ROUND1(d, a, b, c, x[ 9], 12, 0x8b44f7af); 198 MD5_ROUND1(c, d, a, b, x[10], 17, 0xffff5bb1); 199 MD5_ROUND1(b, c, d, a, x[11], 22, 0x895cd7be); 200 MD5_ROUND1(a, b, c, d, x[12], 7, 0x6b901122); 201 MD5_ROUND1(d, a, b, c, x[13], 12, 0xfd987193); 202 MD5_ROUND1(c, d, a, b, x[14], 17, 0xa679438e); 203 MD5_ROUND1(b, c, d, a, x[15], 22, 0x49b40821); 204 205 MD5_ROUND2(a, b, c, d, x[ 1], 5, 0xf61e2562); 206 MD5_ROUND2(d, a, b, c, x[ 6], 9, 0xc040b340); 207 MD5_ROUND2(c, d, a, b, x[11], 14, 0x265e5a51); 208 MD5_ROUND2(b, c, d, a, x[ 0], 20, 0xe9b6c7aa); 209 MD5_ROUND2(a, b, c, d, x[ 5], 5, 0xd62f105d); 210 MD5_ROUND2(d, a, b, c, x[10], 9, 0x2441453); 211 MD5_ROUND2(c, d, a, b, x[15], 14, 0xd8a1e681); 212 MD5_ROUND2(b, c, d, a, x[ 4], 20, 0xe7d3fbc8); 213 MD5_ROUND2(a, b, c, d, x[ 9], 5, 0x21e1cde6); 214 MD5_ROUND2(d, a, b, c, x[14], 9, 0xc33707d6); 215 MD5_ROUND2(c, d, a, b, x[ 3], 14, 0xf4d50d87); 216 MD5_ROUND2(b, c, d, a, x[ 8], 20, 0x455a14ed); 217 MD5_ROUND2(a, b, c, d, x[13], 5, 0xa9e3e905); 218 MD5_ROUND2(d, a, b, c, x[ 2], 9, 0xfcefa3f8); 219 MD5_ROUND2(c, d, a, b, x[ 7], 14, 0x676f02d9); 220 MD5_ROUND2(b, c, d, a, x[12], 20, 0x8d2a4c8a); 221 222 MD5_ROUND3(a, b, c, d, x[ 5], 4, 0xfffa3942); 223 MD5_ROUND3(d, a, b, c, x[ 8], 11, 0x8771f681); 224 MD5_ROUND3(c, d, a, b, x[11], 16, 0x6d9d6122); 225 MD5_ROUND3(b, c, d, a, x[14], 23, 0xfde5380c); 226 MD5_ROUND3(a, b, c, d, x[ 1], 4, 0xa4beea44); 227 MD5_ROUND3(d, a, b, c, x[ 4], 11, 0x4bdecfa9); 228 MD5_ROUND3(c, d, a, b, x[ 7], 16, 0xf6bb4b60); 229 MD5_ROUND3(b, c, d, a, x[10], 23, 0xbebfbc70); 230 MD5_ROUND3(a, b, c, d, x[13], 4, 0x289b7ec6); 231 MD5_ROUND3(d, a, b, c, x[ 0], 11, 0xeaa127fa); 232 MD5_ROUND3(c, d, a, b, x[ 3], 16, 0xd4ef3085); 233 MD5_ROUND3(b, c, d, a, x[ 6], 23, 0x4881d05); 234 MD5_ROUND3(a, b, c, d, x[ 9], 4, 0xd9d4d039); 235 MD5_ROUND3(d, a, b, c, x[12], 11, 0xe6db99e5); 236 MD5_ROUND3(c, d, a, b, x[15], 16, 0x1fa27cf8); 237 MD5_ROUND3(b, c, d, a, x[ 2], 23, 0xc4ac5665); 238 239 MD5_ROUND4(a, b, c, d, x[ 0], 6, 0xf4292244); 240 MD5_ROUND4(d, a, b, c, x[ 7], 10, 0x432aff97); 241 MD5_ROUND4(c, d, a, b, x[14], 15, 0xab9423a7); 242 MD5_ROUND4(b, c, d, a, x[ 5], 21, 0xfc93a039); 243 MD5_ROUND4(a, b, c, d, x[12], 6, 0x655b59c3); 244 MD5_ROUND4(d, a, b, c, x[ 3], 10, 0x8f0ccc92); 245 MD5_ROUND4(c, d, a, b, x[10], 15, 0xffeff47d); 246 MD5_ROUND4(b, c, d, a, x[ 1], 21, 0x85845dd1); 247 MD5_ROUND4(a, b, c, d, x[ 8], 6, 0x6fa87e4f); 248 MD5_ROUND4(d, a, b, c, x[15], 10, 0xfe2ce6e0); 249 MD5_ROUND4(c, d, a, b, x[ 6], 15, 0xa3014314); 250 MD5_ROUND4(b, c, d, a, x[13], 21, 0x4e0811a1); 251 MD5_ROUND4(a, b, c, d, x[ 4], 6, 0xf7537e82); 252 MD5_ROUND4(d, a, b, c, x[11], 10, 0xbd3af235); 253 MD5_ROUND4(c, d, a, b, x[ 2], 15, 0x2ad7d2bb); 254 MD5_ROUND4(b, c, d, a, x[ 9], 21, 0xeb86d391); 255 256 state[0] += a; 257 state[1] += b; 258 state[2] += c; 259 state[3] += d; 260 } 261 262 263 /*! 264 @brief 内部函数，处理数据的前面部分(>64字节的部分)，每次组成一个64字节的block就进行杂凑处理 265 @param[out] ctx 算法的context，用于记录一些处理的上下文和结果 266 @param[in] buf 处理的数据， 267 @param[in] size 处理的数据长度 268 */ 269 static void zen_md5_update(md5_ctx *ctx, const unsigned char *buf, size_t size) 270 { 271 //为什么不是=，因为在某些环境下，可以多次调用zen_md5_update，但这种情况，必须保证前面的调用，每次都没有unprocessed_ 272 ctx->length_ += size; 273 274 //每个处理的块都是64字节 275 while (size >= ZEN_MD5_BLOCK_SIZE) 276 { 277 zen_md5_process_block(ctx->hash_, reinterpret_cast<const uint32_t *>(buf)); 278 buf += ZEN_MD5_BLOCK_SIZE; 279 size -= ZEN_MD5_BLOCK_SIZE; 280 } 281 282 ctx->unprocessed_ = size; 283 } 284 285 286 /*! 287 @brief 内部函数，处理数据的末尾部分，我们要拼出最后1个（或者两个）要处理的BLOCK，加上0x80，加上长度进行处理 288 @param[in] ctx 算法的context，用于记录一些处理的上下文和结果 289 @param[in] buf 处理的数据 290 @param[in] size 处理buffer的长度 291 @param[out] result 返回的结果， 292 */ 293 static void zen_md5_final(md5_ctx *ctx, const unsigned char *buf, size_t size, unsigned char *result) 294 { 295 uint32_t message[ZEN_MD5_BLOCK_SIZE / 4]; 296 297 //保存剩余的数据，我们要拼出最后1个（或者两个）要处理的块，前面的算法保证了，最后一个块肯定小于64个字节 298 if (ctx->unprocessed_) 299 { 300 memcpy(message, buf + size - ctx->unprocessed_, static_cast<size_t>( ctx->unprocessed_)); 301 } 302 303 //得到0x80要添加在的位置（在uint32_t 数组中）， 304 uint32_t index = ((uint32_t)ctx->length_ & 63) >> 2; 305 uint32_t shift = ((uint32_t)ctx->length_ & 3) * 8; 306 307 //添加0x80进去，并且把余下的空间补充0 308 message[index] &= ~(0xFFFFFFFF << shift); 309 message[index++] ^= 0x80 << shift; 310 311 //如果这个block还无法处理，其后面的长度无法容纳长度64bit，那么先处理这个block 312 if (index > 14) 313 { 314 while (index < 16) 315 { 316 message[index++] = 0; 317 } 318 319 zen_md5_process_block(ctx->hash_, message); 320 index = 0; 321 } 322 323 //补0 324 while (index < 14) 325 { 326 message[index++] = 0; 327 } 328 329 //保存长度，注意是bit位的长度,这个问题让我看着郁闷了半天， 330 uint64_t data_len = (ctx->length_) << 3; 331 332 //注意MD5算法要求的64bit的长度是小头LITTLE-ENDIAN编码，注意下面的比较是!= 333 #if ZEN_BYTES_ORDER != ZEN_LITTLE_ENDIAN 334 data_len = ZEN_SWAP_UINT64(data_len); 335 #endif 336 337 message[14] = (uint32_t) (data_len & 0x00000000FFFFFFFF); 338 message[15] = (uint32_t) ((data_len & 0xFFFFFFFF00000000ULL) >> 32); 339 340 zen_md5_process_block(ctx->hash_, message); 341 342 //注意结果是小头党的，在大头的世界要进行转换 343 #if ZEN_BYTES_ORDER == ZEN_LITTLE_ENDIAN 344 memcpy(result, &ctx->hash_, ZEN_MD5_HASH_SIZE); 345 #else 346 swap_uint32_memcpy(result, &ctx->hash_, ZEN_MD5_HASH_SIZE); 347 #endif 348 349 } 350 351 352 //计算一个内存数据的MD5值 353 unsigned char *ZEN_LIB::md5(const unsigned char *buf, 354 size_t size, 355 unsigned char result[ZEN_MD5_HASH_SIZE]) 356 { 357 assert(result != NULL); 358 359 md5_ctx ctx; 360 zen_md5_init(&ctx); 361 zen_md5_update(&ctx, buf, size); 362 zen_md5_final(&ctx, buf, size, result); 363 return result; 364 } 365 366 367 368 369 //================================================================================================ 370 //SHA1的算法 371 372 //每次处理的BLOCK的大小 373 static const size_t ZEN_SHA1_BLOCK_SIZE = 64; 374 375 //SHA1算法的上下文，保存一些状态，中间数据，结果 376 typedef struct sha1_ctx 377 { 378 379 //处理的数据的长度 380 uint64_t length_; 381 //还没有处理的数据长度 382 uint64_t unprocessed_; 383 /* 160-bit algorithm internal hashing state */ 384 uint32_t hash_[5]; 385 } sha1_ctx; 386 387 //内部函数，SHA1算法的上下文的初始化 388 static void zen_sha1_init(sha1_ctx *ctx) 389 { 390 ctx->length_ = 0; 391 ctx->unprocessed_ = 0; 392 // 初始化算法的几个常量，魔术数 393 ctx->hash_[0] = 0x67452301; 394 ctx->hash_[1] = 0xefcdab89; 396 ctx->hash_[3] = 0x10325476; 397 ctx->hash_[4] = 0xc3d2e1f0; 398 } 399 400 401 /*! 402 @brief 内部函数，对一个64bit内存块进行摘要(杂凑)处理， 403 @param hash 存放计算hash结果的的数组 404 @param block 要计算的处理得内存块 405 */ 406 static void zen_sha1_process_block(uint32_t hash[5], 407 const uint32_t block[ZEN_SHA1_BLOCK_SIZE / 4]) 408 { 409 size_t t; 410 uint32_t wblock[80]; 411 register uint32_t a, b, c, d, e, temp; 412 413 //SHA1算法处理的内部数据要求是大头党的，在小头的环境转换 414 #if ZEN_BYTES_ORDER == ZEN_LITTLE_ENDIAN 415 swap_uint32_memcpy(wblock, block, ZEN_SHA1_BLOCK_SIZE); 416 #else 417 ::memcpy(wblock, block, ZEN_SHA1_BLOCK_SIZE); 418 #endif 419 420 //处理 421 for (t = 16; t < 80; t++) 422 { 423 wblock[t] = ROTL32(wblock[t - 3] ^ wblock[t - 8] ^ wblock[t - 14] ^ wblock[t - 16], 1); 424 } 425 426 a = hash[0]; 427 b = hash[1]; 428 c = hash[2]; 429 d = hash[3]; 430 e = hash[4]; 431 432 for (t = 0; t < 20; t++) 433 { 434 /* the following is faster than ((B & C) | ((~B) & D)) */ 435 temp = ROTL32(a, 5) + (((c ^ d) & b) ^ d) 436 + e + wblock[t] + 0x5A827999; 437 e = d; 438 d = c; 439 c = ROTL32(b, 30); 440 b = a; 441 a = temp; 442 } 443 444 for (t = 20; t < 40; t++) 445 { 446 temp = ROTL32(a, 5) + (b ^ c ^ d) + e + wblock[t] + 0x6ED9EBA1; 447 e = d; 448 d = c; 449 c = ROTL32(b, 30); 450 b = a; 451 a = temp; 452 } 453 454 for (t = 40; t < 60; t++) 455 { 456 temp = ROTL32(a, 5) + ((b & c) | (b & d) | (c & d)) 457 + e + wblock[t] + 0x8F1BBCDC; 458 e = d; 459 d = c; 460 c = ROTL32(b, 30); 461 b = a; 462 a = temp; 463 } 464 465 for (t = 60; t < 80; t++) 466 { 467 temp = ROTL32(a, 5) + (b ^ c ^ d) + e + wblock[t] + 0xCA62C1D6; 468 e = d; 469 d = c; 470 c = ROTL32(b, 30); 471 b = a; 472 a = temp; 473 } 474 475 hash[0] += a; 476 hash[1] += b; 477 hash[2] += c; 478 hash[3] += d; 479 hash[4] += e; 480 } 481 482 483 /*! 484 @brief 内部函数，处理数据的前面部分(>64字节的部分)，每次组成一个64字节的block就进行杂凑处理 485 @param ctx 算法的上下文，记录中间数据，结果等 486 @param msg 要进行计算的数据buffer 487 @param size 长度 488 */ 489 static void zen_sha1_update(sha1_ctx *ctx, 490 const unsigned char *buf, 491 size_t size) 492 { 493 //为了让zen_sha1_update可以多次进入，长度可以累计 494 ctx->length_ += size; 495 496 //每个处理的块都是64字节 497 while (size >= ZEN_SHA1_BLOCK_SIZE) 498 { 499 zen_sha1_process_block(ctx->hash_, reinterpret_cast<const uint32_t *>(buf)); 500 buf += ZEN_SHA1_BLOCK_SIZE; 501 size -= ZEN_SHA1_BLOCK_SIZE; 502 } 503 504 ctx->unprocessed_ = size; 505 } 506 507 508 /*! 509 @brief 内部函数，处理数据的最后部分，添加0x80,补0，增加长度信息 510 @param ctx 算法的上下文，记录中间数据，结果等 511 @param msg 要进行计算的数据buffer 512 @param result 返回的结果 513 */ 514 static void zen_sha1_final(sha1_ctx *ctx, 515 const unsigned char *msg, 516 size_t size, 517 unsigned char *result) 518 { 519 520 uint32_t message[ZEN_SHA1_BLOCK_SIZE / 4]; 521 522 //保存剩余的数据，我们要拼出最后1个（或者两个）要处理的块，前面的算法保证了，最后一个块肯定小于64个字节 523 if (ctx->unprocessed_) 524 { 525 memcpy(message, msg + size - ctx->unprocessed_, static_cast<size_t>( ctx->unprocessed_)); 526 } 527 528 //得到0x80要添加在的位置（在uint32_t 数组中）， 529 uint32_t index = ((uint32_t)ctx->length_ & 63) >> 2; 530 uint32_t shift = ((uint32_t)ctx->length_ & 3) * 8; 531 532 //添加0x80进去，并且把余下的空间补充0 533 message[index] &= ~(0xFFFFFFFF << shift); 534 message[index++] ^= 0x80 << shift; 535 536 //如果这个block还无法处理，其后面的长度无法容纳长度64bit，那么先处理这个block 537 if (index > 14) 538 { 539 while (index < 16) 540 { 541 message[index++] = 0; 542 } 543 544 zen_sha1_process_block(ctx->hash_, message); 545 index = 0; 546 } 547 548 //补0 549 while (index < 14) 550 { 551 message[index++] = 0; 552 } 553 554 //保存长度，注意是bit位的长度,这个问题让我看着郁闷了半天， 555 uint64_t data_len = (ctx->length_) << 3; 556 557 //注意SHA1算法要求的64bit的长度是大头BIG-ENDIAN，在小头的世界要进行转换 558 #if ZEN_BYTES_ORDER == ZEN_LITTLE_ENDIAN 559 data_len = ZEN_SWAP_UINT64(data_len); 560 #endif 561 562 message[14] = (uint32_t) (data_len & 0x00000000FFFFFFFF); 563 message[15] = (uint32_t) ((data_len & 0xFFFFFFFF00000000ULL) >> 32); 564 565 zen_sha1_process_block(ctx->hash_, message); 566 567 //注意结果是大头党的，在小头的世界要进行转换 568 #if ZEN_BYTES_ORDER == ZEN_LITTLE_ENDIAN 569 swap_uint32_memcpy(result, &ctx->hash_, ZEN_SHA1_HASH_SIZE); 570 #else 571 memcpy(result, &ctx->hash_, ZEN_SHA1_HASH_SIZE); 572 #endif 573 } 574 575 576 577 //计算一个内存数据的SHA1值 578 unsigned char *ZEN_LIB::sha1(const unsigned char *msg, 579 size_t size, 580 unsigned char result[ZEN_SHA1_HASH_SIZE]) 581 { 582 assert(result != NULL); 583 584 sha1_ctx ctx; 585 zen_sha1_init(&ctx); 586 zen_sha1_update(&ctx, msg, size); 587 zen_sha1_final(&ctx, msg, size, result); 588 return result; 589 } 590 591 int main(int /*argc*/, char * /*argv*/[]) 592 { 593 594 int ret = 0; 595 static unsigned char test_buf[7][81] = 596 { 597 { "" }, 598 { "a" }, 599 { "abc" }, 600 { "message digest" }, 601 { "abcdefghijklmnopqrstuvwxyz" }, 602 { "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789" }, 603 { "12345678901234567890123456789012345678901234567890123456789012345678901234567890" } 604 }; 605 606 static const size_t test_buflen[7] = 607 { 608 0, 1, 3, 14, 26, 62, 80 609 }; 610 611 static const unsigned char md5_test_sum[7][16] = 612 { 613 { 0xD4, 0x1D, 0x8C, 0xD9, 0x8F, 0x00, 0xB2, 0x04, 0xE9, 0x80, 0x09, 0x98, 0xEC, 0xF8, 0x42, 0x7E }, 614 { 0x0C, 0xC1, 0x75, 0xB9, 0xC0, 0xF1, 0xB6, 0xA8, 0x31, 0xC3, 0x99, 0xE2, 0x69, 0x77, 0x26, 0x61 }, 615 { 0x90, 0x01, 0x50, 0x98, 0x3C, 0xD2, 0x4F, 0xB0, 0xD6, 0x96, 0x3F, 0x7D, 0x28, 0xE1, 0x7F, 0x72 }, 616 { 0xF9, 0x6B, 0x69, 0x7D, 0x7C, 0xB7, 0x93, 0x8D, 0x52, 0x5A, 0x2F, 0x31, 0xAA, 0xF1, 0x61, 0xD0 }, 617 { 0xC3, 0xFC, 0xD3, 0xD7, 0x61, 0x92, 0xE4, 0x00, 0x7D, 0xFB, 0x49, 0x6C, 0xCA, 0x67, 0xE1, 0x3B }, 618 { 0xD1, 0x74, 0xAB, 0x98, 0xD2, 0x77, 0xD9, 0xF5, 0xA5, 0x61, 0x1C, 0x2C, 0x9F, 0x41, 0x9D, 0x9F }, 619 { 0x57, 0xED, 0xF4, 0xA2, 0x2B, 0xE3, 0xC9, 0x55, 0xAC, 0x49, 0xDA, 0x2E, 0x21, 0x07, 0xB6, 0x7A } 620 }; 621 unsigned char result[32] ={0}; 622 623 for(size_t i=0;i<7;++i) 624 { 625 ZEN_LIB::md5(test_buf[i],test_buflen[i],result); 626 ret = memcmp(result,md5_test_sum[i],16); 627 if (ret != 0) 628 { 629 assert(false); 630 } 631 } 632 633 static const unsigned char sha1_test_sum[7][20] = 634 { 635 { 0xda,0x39,0xa3,0xee,0x5e,0x6b,0x4b,0x0d,0x32,0x55,0xbf,0xef,0x95,0x60,0x18,0x90,0xaf,0xd8,0x07,0x09 }, 636 { 0x86,0xf7,0xe4,0x37,0xfa,0xa5,0xa7,0xfc,0xe1,0x5d,0x1d,0xdc,0xb9,0xea,0xea,0xea,0x37,0x76,0x67,0xb8 }, 637 { 0xa9,0x99,0x3e,0x36,0x47,0x06,0x81,0x6a,0xba,0x3e,0x25,0x71,0x78,0x50,0xc2,0x6c,0x9c,0xd0,0xd8,0x9d }, 638 { 0xc1,0x22,0x52,0xce,0xda,0x8b,0xe8,0x99,0x4d,0x5f,0xa0,0x29,0x0a,0x47,0x23,0x1c,0x1d,0x16,0xaa,0xe3 }, 639 { 0x32,0xd1,0x0c,0x7b,0x8c,0xf9,0x65,0x70,0xca,0x04,0xce,0x37,0xf2,0xa1,0x9d,0x84,0x24,0x0d,0x3a,0x89 }, 640 { 0x76,0x1c,0x45,0x7b,0xf7,0x3b,0x14,0xd2,0x7e,0x9e,0x92,0x65,0xc4,0x6f,0x4b,0x4d,0xda,0x11,0xf9,0x40 }, 641 { 0x50,0xab,0xf5,0x70,0x6a,0x15,0x09,0x90,0xa0,0x8b,0x2c,0x5e,0xa4,0x0f,0xa0,0xe5,0x85,0x55,0x47,0x32 }, 642 }; 643 for(size_t i=0;i<7;++i) 644 { 645 ZEN_LIB::sha1(test_buf[i],test_buflen[i],result); 646 ret = memcmp(result,sha1_test_sum[i],20); 647 if (ret != 0) 648 { 649 assert(false); 650 } 651 } 652 return 0; 653 } rhashlib采用的协议是MIT，在此再次感谢原来的作者，另外维基上面的伪代码帮助非常大。 【本文作者是雁渡寒潭，本着自由的精神，你可以在无盈利的情况完整转载此文 档，转载时请附上BLOG链接:http://www.cnblogs.com/fullsail/，否则每字一元，每图一百不讲价。对Baidu文库和360doc加价一倍】 posted @ 2013-02-22 03:12 fullsail 阅读(...) 评论(...) 编辑 收藏

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## help please By how much does the gravitational potential energy of a68 kg pole vaulter change if hiscenter of mass rises about 6.0 mduring the jump? 1 J ## Answers (1) • Think of the change in potential energy as the amount of workit would now take for him to fall from his new height. ΔU = W W = -Fs and F = -mg His mass, m, is 68 kg and g is 9.8 m/s Multiplying the two together will give you force and work isforce times displacement, s, which is 6.0 m. It also works by the potential energy equation U = mgh where his height. The change in potential energy would be ΔU = mgΔhwhere his height changes by six meters. Get homework help More than 200 experts are waiting to help you now...

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× [–] -1 points0 points  (0 children) fix object [–][S] 0 points1 point  (0 children) it's perfect. thank you [–] 1 point2 points  (0 children) try text("abc") [–] 0 points1 point  (0 children) try f(x)=-a+1,-2≤x≤2 [–] 0 points1 point  (0 children) [–] 0 points1 point  (0 children) (A3-2) 180 / A3 no (A3-2) x 180 / A3 [–] 0 points1 point  (0 children) creare un vettore. evidenziare l'oggetto riflesso e usare il comando traslate by vector. puntare il mouse sulla figura traslata e clic col tasto sx del muose e trascinare. [–][S] 0 points1 point  (0 children) ok [–][S] 0 points1 point  (0 children) [–][S] 0 points1 point  (0 children) ho risolto con: TabellaTesto({“\vec{v_x}”, “\vec{v_y}”,“\vec{v_z}”},{“Acos(α)”,“Asin(α)”,0},{“Bcos(β)”,“Bsin(β)”,0},“c|_”) da barra inserimento [–][S] 0 points1 point  (0 children) [–] 0 points1 point  (0 children) [–][S] 0 points1 point  (0 children) v=sqrt(abs(u²) + abs(w²) - 2abs(w) abs(u) (-cos(α))) ok grazie [–] 0 points1 point  (0 children) \frac{a}{b} [–][S] 0 points1 point  (0 children) perfetto. ok [–][S] 0 points1 point  (0 children) è possibile sviluppare la funzione continua f(x) da 0 a 2pi, no trace on, no punto su f(a)? [–][S] 0 points1 point  (0 children) (((-a^(2)+b^(2)+c^(2))/(2 b c)))=0.58=v acos(v)=54.49° text: edit: object: (empty box):acosd(v)

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HomeQuantitative TechniquesDI Based Quantitative Technique Questions for CLAT # DI Based Quantitative Technique Questions for CLAT Passage 1 The bar graph given below shows the revenue earned and the expenditure of a CLAT coaching institute by the name of​​ Sulabh​​ Coaching over the years. With the help of information given below, answer the questions that follow. • In which year was the growth in expense as compared to the previous years was the highest? • 2016 • 2013 • 2015 • 2014 • What is the average annual increase for the expenditure done from 2013 to 2017? • 15 • 16.5 • 13.2 • 14.5 • In how many years did the revenue was more than 10% as compared to the expense? • 1 • 2 • 4 • 3 Passage 2 Ankit​​ Event​​ Management Company​​ took a contract to organise the marriage of Ms.​​ Ranjan​​ Jha in the month of February 2020. The event was to take place over a period of 5 days and various functions were scheduled on different days.​​ The ratio in which the money was paid to​​ Ankit​​ for various functions i.e. Mehendi: Sangeet:​​ Bachelorette: wedding: Reception was​​ 2: 3: 5:9: 7. Also, not all guests were invited to all the functions. • If total money paid to​​ Ankit​​ Event​​ Management Company was​​ Rs.​​ 78 Lakhs, find the amount of money spent on Bachelorette? • 7 lakh • 17 lakh • 15 lakh • 11 lakh • All the guests were invited to the wedding but​​ those who were invited to the one function other than the wedding were not invited to any other functions than wedding. If 40 percent of the people went to Reception and off the remaining the people who went to​​ Mehendi:​​ Sangeet: Bachelorette are in the ratio 3:4:1. Find the no. of guests in the Mehendi Function if total number of​​ guests are 800. • 180 • 120 • 150 • 110 • On the last moment, the beautician who was supposed to be there for the wedding day makeup cancelled. Therefore,​​ Ankit​​ was asked to arrange for a beautician for the makeup of bride and her friends and her family. If the cost for makeup for bride’s friends was​​ 3500​​ more than twice the​​ cost for each family member and the cost for each family member was 2000 less than one fifth for cost of bride’s makeup. Calculate the total money paid for makeup of five closest friends. The money paid for bride’s makeup is 1 lakh.​​ • 39500 • 197500 • 98000 • 161000 • If​​ Ankit​​ made a profit of 37%, calculate actual cost involved in organizing? • Rs. 5693430 • Rs. 4578954 • Rs. 6678453 • Rs. 7489765 • The money paid to​​ Ankit​​ i.e. 78 lakh was paid through different means to avoid tax on it as some of the portion was black money. If one third of the total money was paid in cash, 10 lakh worth car was given and of the remaining 25% money was paid as​​ jewellery​​ and remaining through net banking. Calculate the money paid through net banking. • Rs. 3465000 • Rs 2278000 • Rs 4578000 • Rs.3150000 Cracking the CLAT!

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zbMATH — the first resource for mathematics A logic for reasoning about time and reliability. (English) Zbl 0820.68113 Summary: We present a logic for stating properties such as, “after a request for service there is at least a 98% probability that the service will be carried out within 2 seconds”. The logic extends the temporal logic CTL by Emerson, Clarke and Sistla with time and probabilities. Formulas are interpreted over discrete time Markov chains. We give algorithms for checking that a given Markov chain satisfies a formula in the logic. The algorithms require a polynomial number of arithmetic operations, in size of both the formula and the Markov chain. A simple example is included to illustrate the algorithms. MSC: 68T27 Logic in artificial intelligence 68Q60 Specification and verification (program logics, model checking, etc.) GTPN; SPNP Full Text: References: [1] Ajmone Marsan, M., Balbo, G. and Conte, G.:Performance Models of Multiprocessor Systems. MIT Press, 1986. [2] Abrahamson, K.:Decidability and Expressiveness of Logics of Processes. PhD thesis, Univ. of Washington, 1980. [3] Alur, R., Courcoubetis, C. and Dill, D.: Model-checking for real-time systems. InProc. 5 th IEEE Int. Symp. on Logic in Computer Science, pages 414-425, 1990. [4] Alur, R., Courcoubetis, C. and Dill, D.: Model-checking for probabilistic real-time systems. InProc. 18 th Int. Coll. on Automata Languages and Programming (ICALP), volume 510 ofLecture Notes in Computer Science, pages 115-126. Springer Verlag, 1991. · Zbl 0769.68088 [5] Alur, R., Courcoubetis, C. and Dill, D.: Verifying Automata Specifications of Probabilistic Real-Time Systems. In J. de Bakker, C. Huizing, W.-P. de Roever, and G. Rozenberg, editors,Real-Time: Theory in Practice, volume 600 ofLecture Notes in Computer Science, pages 28-44. Springer Verlag, 1992. [6] Alur, R. and Dill, D.: Automata for modeling real-time systems. InProc. 17 th Int. Coll. on Automata Languages and Programming (ICALP), volume 443 ofLecture Notes in Computer Science, Springer Verlag, 1990. · Zbl 0765.68150 [7] Alur, R. and Henzinger, T.: A really temporal logic. InProc. 30 th IEEE Annual Symp. Foundations of Computer Science, pages 164-169, 1989. [8] Alur, R. and Henzinger, T.: Logics and Models of Real Time: A Survey. In J. de Bakker, C. Huizing, W.-P. de Roever, and G. Rozenberg, editors,Real-Time: Theory in Practice, volume 600 ofLecture Notes in Computer Science, pages 28-44. Springer Verlag, 1992. [9] Aho, A.V., Hopcroft, J.E. and Ullman, J.D.:The Design and Analysis of Computer Algorithms. Addison-Wesley Publishing Company, 1974. · Zbl 0326.68005 [10] Bernstein, A. and Harter, P.K.: Proving real-time properties of programs with temporal logic. InProc. 8 th ACM Symp. on Operating System Principles, pages 1-11, Pacific Grove, California, 1981. [11] Bartlett, K., Scantlebury, R. and Wilkinson, P.: A note on reliable full-duplex transmissions over half duplex lines.Communications of the ACM, 2(5):260-261, 1969. · doi:10.1145/362946.362970 [12] Christoff, L. and Christoff, I: Reasoning about safety and liveness properties for probabilistic processes. In R. Shyamasundar, editor,Proc. 12 th Conf. on Foundations of Software Technology and Theoretical Computer Science, volume 652 ofLecture Notes in Computer Science, pages 342-355. Springer-Verlag, 1992. · Zbl 0925.03151 [13] Clarke, E.M., Emerson, E.A. and Sistla, A.P.: Automatic verification of finite-state concurrent systems using temporal logic specification.ACM Trans. on Programming Languages and Systems, 8(2):244-263, April 1986. · Zbl 0591.68027 · doi:10.1145/5397.5399 [14] Chiola, G.: A software package for the analysis of generalized stochastic Petri net models. InProc. Int. Workshop on Time Petri Nets, pages 136-143, July 1985. [15] Ciardo, G., Muppala, J. and Trivedi, K.S.: Spnp: Stochastic petri net package. InProc. of the third International Workshop on Petri Nets and Performance Models. IEEE Computer Society Press, Kyoto, Japan, December 1989. [16] Courcoubetis, C., Vardi, M. and Wolper, P.: Reasoning about fair concurrent programs. InProc. 18 th ACM Symp. on Theory of Computing, pages 283-294, 1986. [17] Courcoubetis, C. and Yannakakis, C.: The complexity of probabilistic verification. InProc. 29 th IEEE Annual Symp. Foundations of Computer Science, pages 338-345, 1988. [18] Courcoubetis, C. and Yannakakis, C.: The complexity of probabilistic verification. Bell labs Murry Hill, 1989. · Zbl 0885.68109 [19] de Bakker, J., Huizing, C., de Roever, W-.P. and Rozenberg, G.: editors.Real-Time: Theory in Practice, volume 600 ofLecture Notes in Computer Science. Springer Verlag, 1992. [20] Emerson, E.A. and Clarke, E.M.: Using branching time Temporal Logic to synthesize synchronization skeletons.Science of Computer Programming, 2(3):241-266, 1982. · Zbl 0514.68032 · doi:10.1016/0167-6423(83)90017-5 [21] Emerson, A.: Real-Time and the Mu-Calculus. In J. de Bakker, C. Huizing, W-.P. de Roever, and G. Rozenberg, editors,Real-Time: Theory in Practice, volume 600 ofLecture Notes in Computer Science, pages 176-194. Springer Verlag, 1992. [22] Emerson, A., Mok, A., Sistla, A. and Srinivasan, J.: Quantitative temporal reasoning.Real-Time Systems ? The International Journal of Time-Critical Computing Systems, 4:331-352, 1992. [23] Feldman, Y.A.: A decidable propositional probabilistic dynamic logic. InProc. 15 th ACM Symp. on Theory of Computing, pages 298-309, Boston, 1983. [24] Gibbons, A.:Algorithmic Graph Theory. Cambridge University Press, 1985. · Zbl 0568.05001 [25] Hansson, H.:Time and Probabilities in Formal Design of Distributed Systems. PhD thesis, Department of Computer Systems, Uppsala University, 1991. Available as report DoCS 91/27, Department of Computer Systems, Uppsala University, Sweden, and as report 05 in SICS dissertation series, SICS, Kista, Sweden. A revised version of the thesis will appear in the Elsevier book series Real-Time Safety Critical Systems. [26] Hansson, H. and Jonsson, B.: A calculus for communicating systems with time and probabilities. InProc. 11 th IEEE Real -Time Systems Symp., pages 278-287, Orlando, Fl., December 1990. IEEE Computer Society Press. [27] Hooman, J.:Specification and Compositional Verification of Real-Time Systems, volume 558 ofLecture Notes in Computer Science. North-Holland, 1991. [28] Hart, S. and Sharir, M.: Probabilistic temporal logics for finite and bounded models. InProc. 16 th ACM Symp. on Theory of Computing, pages 1-13, 1984. [29] Hart, S., Sharir, M. and Pnueli, A.: Termination of probabilistic concurrent programs.ACM Trans. on Programming Languages and Systems, 5:356-380, 1983. · Zbl 0511.68009 · doi:10.1145/2166.357214 [30] Holliday, M.A. and Vernon, M.K.: The GTPN Analyzer: numerical methods and user interface. Technical Report 639, Dept. of Computer Science, Univ. of Wisconsin ? Madison, Apr. 1986. [31] Holliday, M.A. and Vernon, M.K.: Exact performance estimates for multiprocessor memory and bus interface.IEEE Trans. on Computers, C-36:76-85, Jan. 1987. · doi:10.1109/TC.1987.5009450 [32] Holliday, M.A. and Vernon, M.K.: A generalized timed Petri net model for performance analysis.IEEE Trans. on Software Engineering, SE-13(12), 1987. [33] Jahanian, F. and Mok, K.-L.: Safety analysis of timing properties in real-time systems.IEEE Trans. on Software Engineering, SE-12(9):890-904, Sept. 1986. [34] Jahanian, F. and Mok, A.K.: A graph-theoretic approach for timing analysis and its implementation.IEEE Trans, on Computers, 36(8):961-975, August 1987. · Zbl 0618.68008 · doi:10.1109/TC.1987.5009519 [35] Joseph, M.: editor.Formal Techniques in Real-Time and Fault-Tolerant Systems, volume 331 ofLecture Notes in Computer Science. Springer Verlag, 1988. [36] Koymans, R., Vytopil, J. and de Roever, W.P.: Real-time programming and asynchronous message passing. InProc. 2 nd ACM Symp. on Principles of Distributed Computing, pages 187-197, Montréal, Canada, 1983. [37] Lehmann, D. and Shelah, S.: Reasoning with time and chance.Information and Control, 53:165-198, 1982. · Zbl 0523.03016 · doi:10.1016/S0019-9958(82)91022-1 [38] Larsen, K.G. and Skou, A.: Bisimulation through probabilistic testing. InProc. 16 th ACM Symp. on Principles of Programming Languages, pages 344-352, 1989. · Zbl 0756.68035 [39] Milner, R.:Communication and Concurrency. Prentice-Hall, 1989. · Zbl 0683.68008 [40] Molloy, M.K.: Performance analysis using stochastic petri nets.IEEE Trans. on Computers, C-31(9):913-917, Sept. 1982. · Zbl 05338404 · doi:10.1109/TC.1982.1676110 [41] Owicki, S. and Lamport, L.: Proving liveness properties of concurrent programs.ACM Trans. on Programming Languages and Systems, 4(3):455-495, 1982. · Zbl 0483.68013 · doi:10.1145/357172.357178 [42] Ostroff, J.: Automatic verification of timed transition models. In Sifakis, editor,Workshop on automatic verification methods for finite state systems, volume 407 ofLecture Notes in Computer Science, pages 247-256. Springer Verlag, 1989. [43] Ostroff, J. and Wonham, W.: Modelling, specifying and verifying real-time embedded computer systems. InProc. IEEE Real-time Systems Symp., pages 124-132, Dec. 1987. [44] Parrow, J.:Fairness Properties in Process Algebra. PhD thesis, Uppsala University, Uppsala, Sweden, 1985. Available as report DoCS 85/03, Department of Computer Systems, Uppsala University, Sweden. [45] Pnueli, A. and Harel, E.: Applications of temporal logic to the specification of real-time systems. In M. Joseph, editor,Proc. Symp. on Formal Techniques in Real-Time and Fault-Tolerant Systems, volume 331 ofLecture Notes in Computer Science, pages 84-98. Springer Verlag, 1988. · Zbl 0688.68024 [46] Pnueli, A.: The temporal semantics of concurrent programs.Theoretical Computer Science, 13:45-60, 1982. · Zbl 0441.68010 · doi:10.1016/0304-3975(81)90110-9 [47] Pnueli, A. and Zuck, L.: Verification of multiprocess probabilistic protocols.Distributed Computing, 1(1):53-72, 1986. · Zbl 0598.68019 · doi:10.1007/BF01843570 [48] Razouk, R.R.: The derivation of performance expressions for communication protocols from timed Petri net models. InProc. ACM SIGCOMM ’84, pages 210-217, Montréal, Québec, 1984. [49] Razouk, R.R. and Phelps, C.V.: Performance analysis of timed Petri net models. InProc. IFIP WG 6.2 Symp. on Protocol Specification, Testing, and Verification IV, pages 126-129. North-Holland, June 1984. [50] Shankar, A.U. and Lam, S.S.: Time dependent distributed systems: Proving safety, liveness and real-time properties.Distributed Computing, 2:61-79, 1987. · doi:10.1007/BF01667079 [51] Sanders, W.H. and Meyer, J.F.: Metasan: a performability evaluation tool based on stochastic activity networks. InProc of the ACM-IEEE Comp. Soc. Fall Joint Conf. IEEE Computer Society Press, November 1986. [52] Vardi, M: Automatic verification of probabilistic concurrent finite-state programs. InProc. 26 th IEEE Annual Symp. Foundations of Computer Science, pages 327-337, 1985. [53] Vernon, M.K. and Holliday, M.A.: Performance analysis of multiprocessor cache consistency protocols using generalized timed Petri nets. InProc. of Performance 86 and ACM SIGMETRICS 1986 Joint conf. on Computer Performance Modelling, Measurement, and Evaluation, pages 9-17. ACM press, May 1986. [54] Vardi, M.Y. and Wolper, P.: An automata-theoretic approach to automatic program verification. InProc. IEEE Symp. on Logic in Computer Science, pages 332-344, June 1986. [55] Vytopil, P.: editor.Formal Techniques in Real-Time and Fault-Tolerant Systems, volume 571 ofLecture Notes in Computer Science. Springer Verlag, 1991. [56] Zuberek, W.: Performance evaluation using extended timed Petri nets. InProc. International Workshop on Timed Petri Nets, pages 272-278, Torino Italy, 1985. IEEE Computer Society Press. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.

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# Function to count set bits in a signed integer • Comments posted to this topic are about the item Function to count set bits in a signed integer • Any particular reason for ~CONVERT(bigint, -9223372036854775808) CONVERT(bigint, 9223372036854775807) My Italian keyboard doesn't have this famous tilde characters! :crying: Oh crap, forgot all about copy/paste. 🙂 • ~ is the T-SQL's bitwise NOT operator. It inverts all the bits in an integer. It's used so the right-most bit, which is set to 1 two's compliment signed integer that has a negative value, can be counted. In binary -9223372036854775808 = 1000000000000000000000000000000000000000000000000000000000000000 (1 with 63 trailing zeros), when you bitwize NOT this number you get 0111111111111111111111111111111111111111111111111111111111111111 (0 with 63 trailing 1's). When we AND this with the bigint parameter to the function it removes the leading 1 making it a positive number. • Jonathan AC Roberts (4/28/2015) ~ is the T-SQL's bitwise NOT operator. It inverts all the bits in an integer. It's used so the right-most bit, which is set to 1 two's compliment signed integer that has a negative value, can be counted. In binary -9223372036854775808 = 1000000000000000000000000000000000000000000000000000000000000000 (1 with 63 trailing zeros), when you bitwize NOT this number you get 0111111111111111111111111111111111111111111111111111111111111111 (0 with 63 trailing 1's). When we AND this with the bigint parameter to the function it removes the leading 1 making it a positive number. What I was trying to say was that ~CONVERT(bigint, -9223372036854775808) and CONVERT(bigint, 9223372036854775807) return the same value. • Michael Meierruth (4/28/2015) Jonathan AC Roberts (4/28/2015) ~ is the T-SQL's bitwise NOT operator. It inverts all the bits in an integer. It's used so the right-most bit, which is set to 1 two's compliment signed integer that has a negative value, can be counted. In binary -9223372036854775808 = 1000000000000000000000000000000000000000000000000000000000000000 (1 with 63 trailing zeros), when you bitwize NOT this number you get 0111111111111111111111111111111111111111111111111111111111111111 (0 with 63 trailing 1's). When we AND this with the bigint parameter to the function it removes the leading 1 making it a positive number. What I was trying to say was that ~CONVERT(bigint, -9223372036854775808) and CONVERT(bigint, 9223372036854775807) return the same value. Yes, both give the answer of (2^63) - 1 • Not sure I will ever use it in my every day work. Interesting nevertheless and I'm sure someone will make use of it. Thanks for the exercise. Not sure I will ever use it in my every day work. Interesting nevertheless and I'm sure someone will make use of it. Thanks for the exercise. In fact, this will lead us into the question of what in the real world gets represented as positional bits in an Int or BigInt column and where counting the number of bits turned on becomes meaningful/useful. • Well it probably is bit of an obscure/esoteric thing to do but one of the most efficient ways of storing items that are switched is in a bit string within an integer. For Quine-McCluskey minimisation (the reason I wrote this function) part of the algorithm involves counting the set bits in an integer (the minterms). This information is then used to group the integers into sets by how many 1's they contain. • Unless I typed over the comment by accident there is an error in the comments since BitsIn returns 4 for an input of 15 while the comment lists 3 as the result. HTH -- Mark D Powell -- • Mark D Powell (4/28/2015) Unless I typed over the comment by accident there is an error in the comments since BitsIn returns 4 for an input of 15 while the comment lists 3 as the result. HTH -- Mark D Powell -- Yes, well spotted, that's an error in the comment. Fortunately the error is not in the code as 15 has four bits set as its binary representation is 1111 Viewing 10 posts - 1 through 9 (of 9 total)

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# Dividing selected elements of array on Matlab I have the following array ``````a = [ 1 10 3 4 68 2 34 8 10 ] `````` And I need to divide each number (/2) if this number is higher than 9. This means that 1 has not to be divided, and 10 has to be divided (/2) The resulting array should be: ``````a = [ 1 5 3 4 34 2 17 8 5 ] `````` I have to do it without using a FOR function. So I tried with this: ``````a = a./2; `````` This divides every number of the array, and I as told you before, I want to divide only the ones higher than 9. Can anyone tell me how can I do it? Add a 'if whatever>5' in that statement or something? ``````a = [ 1 10 3 4 68 2 34 8 10 ]; +1 I would store the result of `a>9` in vector, say `idx`, and use it instead of doing the test twice – Amro Sep 28 '11 at 22:52

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# Number 414 ### Properties of number 414 Cross Sum: Factorization: 2 * 3 * 3 * 23 Divisors: 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414 Count of divisors: Sum of divisors: Prime number? No Fibonacci number? No Bell Number? No Catalan Number? No Base 2 (Binary): Base 3 (Ternary): Base 4 (Quaternary): Base 5 (Quintal): Base 8 (Octal): 19e Base 32: cu sin(414) -0.63671476313513 cos(414) 0.771099416681 tan(414) -0.82572331058907 ln(414) 6.0258659738253 lg(414) 2.6170003411209 sqrt(414) 20.346989949376 Square(414) ### Number Look Up Look Up 414 (four hundred fourteen) is a very unique figure. The cross sum of 414 is 9. If you factorisate the number 414 you will get these result 2 * 3 * 3 * 23. The figure 414 has 12 divisors ( 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414 ) whith a sum of 936. The number 414 is not a prime number. The number 414 is not a fibonacci number. The figure 414 is not a Bell Number. The number 414 is not a Catalan Number. The convertion of 414 to base 2 (Binary) is 110011110. The convertion of 414 to base 3 (Ternary) is 120100. The convertion of 414 to base 4 (Quaternary) is 12132. The convertion of 414 to base 5 (Quintal) is 3124. The convertion of 414 to base 8 (Octal) is 636. The convertion of 414 to base 16 (Hexadecimal) is 19e. The convertion of 414 to base 32 is cu. The sine of 414 is -0.63671476313513. The cosine of 414 is 0.771099416681. The tangent of the figure 414 is -0.82572331058907. The root of 414 is 20.346989949376. If you square 414 you will get the following result 171396. The natural logarithm of 414 is 6.0258659738253 and the decimal logarithm is 2.6170003411209. I hope that you now know that 414 is great figure!

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Last updated: # Conservation of Momentum Calculator Law of conservation of momentumElastic and inelastic collisionsHow to use the conservation of momentum calculatorFAQs Prefer watching rather than reading? Check out our video lesson on the conservation of momentum here: ## Law of conservation of momentum The principle of momentum conservation says that for an isolated system, the sum of the momentums of all objects is constant (it doesn't change). An isolated system is a system of objects (it can be, and typically is, more than one body) that don't interact with anything outside the system. In such a system, no momentum disappears: whatever is lost by one object is gained by the other. Imagine two toy cars on a table. Let's assume they form an isolated system — no external force acts on them, and the table is frictionless. One of the cars moves at a constant speed of 3 km/h and hits the second toy car (that remained stationary), causing it to move. You can observe that the first car visibly slows down after the collision. This result happened because some momentum was transferred from the first car to the second car. ## Elastic and inelastic collisions The main difference between the types of momentum is related to how the kinetic energy of the system behaves. If this type of energy is not familiar to you, you may be interested in looking at our kinetic energy calculator article and understanding it before digging into the types of collisions. We can distinguish three types of collisions: • Perfectly elastic: In an elastic collision, both the momentum and kinetic energy of the system are conserved. Bodies bounce off each other. An excellent example of such a collision is between hard objects, such as marbles or billiard balls. • Partially elastic: In such a collision, momentum is conserved, and bodies move at different speeds, but kinetic energy is not conserved. It does not mean that it disappears, though; some of the energy is utilized to perform work (such as creating heat or deformation). A car crash is an example of a partially elastic collision — metal gets deformed, and some kinetic energy is lost. • Perfectly inelastic: After an inelastic collision, bodies stick together and move at a common speed. Momentum is conserved, but some kinetic energy is lost. For example, when a fast-traveling bullet hits a wooden target, it can get stuck inside the target and keep moving with it. You may notice that while the law of conservation of momentum is valid in all collisions, the sum of all objects' kinetic energy changes in some cases. However, the total energy is always conserved. This energy is the sum of the potential, kinetic, and internal energy. The internal energy computes the energy lost due to dissipative forces acting over the movement of the colliding objects, such as friction. To learn more about potential energy, check out our potential energy calculator. ## How to use the conservation of momentum calculator You can use our conservation of momentum calculator to consider all cases of collisions. To calculate the velocities of two colliding objects, simply follow these steps: 1. Enter the masses of the two objects. Let's assume that the first object has a mass of 8 kg while the second one weighs 4 kg. 2. Decide how fast the objects are moving before the collision. For example, the first object may move at a speed of 10 m/s while the second one remains stationary (speed = 0 m/s). 3. Determine the final velocity of one of the objects. For example, we know that after the collision, the first object will slow down to 4 m/s. 4. Calculate the momentum of the system before the collision. In this case, the initial momentum is equal to 8 kg × 10 m/s + 4 kg × 0 m/s = 80 N·s. 5. According to the law of conservation of momentum, total momentum must be conserved. The final momentum of the first object is equal to 8 kg × 4 m/s = 32 N·s. To ensure no losses, the second object must have momentum equal to 80 N·s − 32 N·s = 48 N·s, so its speed is equal to 48 Ns / 4 kg = 12 m/s. 6. You can also open the Kinetic energy field to see how the system's kinetic energy changed and determine whether the collision was elastic, partially elastic, or inelastic. FAQs ### What is the principle of conservation of momentum? According to the principle of conservation of momentum, the total linear momentum of an isolated system, i.e., a system for which the net external force is zero, is constant. ### Under what circumstances is momentum conserved? In order to conserve momentum, there should be no net external force acting on the system. If the net external force is not zero, momentum is not conserved. ### What is an example of the conservation of momentum? The recoil of a gun when we fire a bullet from it is an example of the conservation of momentum. Both the bullet and the gun are at rest before the bullet is fired. When the bullet is fired, it moves in the forward direction. The gun moves in the backward direction to conserve the total momentum of the system. ### What is the principle that makes a rocket move? The principle that makes a rocket move is the law of conservation of linear momentum. The fuel burnt in the rocket produces hot gas. The hot gas is ejected from the exhaust nozzle and goes in one direction. The rocket goes in the opposite direction to conserve momentum. $\sf m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2$

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### Just Rolling Round P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P? ### Coke Machine The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design. Coins inserted into the machine slide down a chute into the machine and a drink is duly released. How many more revolutions does the foreign coin make over the 50 pence piece going down the chute? N.B. A 50 pence piece is a 7 sided polygon ABCDEFG with rounded edges, obtained by replacing AB with arc centred at E and radius EA; replacing BC with arc centred at F radius FB ...etc.. ### Rotating Triangle What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle? # Tilting Triangles ##### Stage: 4 Challenge Level: As the triangle rotates compare what part of the square is not covered by it anymore and what part of the square is newly covered. Does the triangle continue to cover the whole of the portion of the square it moves over as its size reduces. What is special when the triangles side is of length $\sqrt 2$ units? Is there a point where the whole of the triangle is always in the square and what effect does that have?

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# What is a bar graph? A bar graph is a graphical way of showing comparisons by using rectangular shapes with lengths proportional to the measure of what. ## Presentation on theme: "What is a bar graph? A bar graph is a graphical way of showing comparisons by using rectangular shapes with lengths proportional to the measure of what."— Presentation transcript: What is a bar graph? A bar graph is a graphical way of showing comparisons by using rectangular shapes with lengths proportional to the measure of what is being compared. Example If an airline company wanted to know what month of the year that more people fly with their company, they could keep records each month and then put these numbers into a bar graph. What month do more people fly? Results By looking at the bar graph that was created with the data collected, we can clearly see that the month that more people fly with this airline is clearly December. Can you make a bar graph? You must first have information to put into the bar graph. How will each breathe you blow into the balloon affect how big around the balloon gets? Review How can a bar graph be useful? Can anyone make a bar graph? What must you have in order to make a bar graph? Resources Students may visit http://nces.ed.gov/ncskidsgra phing Download ppt "What is a bar graph? A bar graph is a graphical way of showing comparisons by using rectangular shapes with lengths proportional to the measure of what." Similar presentations

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acosh() function in C++ STL The acosh() is an inbuilt function in C++ STL which returns the inverse hyperbolic cosine of an angle given in radians. Syntax: acosh(data_type x) Parameter… Read More » tanh() function in C++ STL The tanh() is an inbuilt function in C++ STL which returns the hyperbolic tangent of an angle given in radians. Syntax : tanh(data_type x) Parameter… Read More » sinh() function in C++ STL The sinh() is an inbuilt function in C++ STL which returns the hyperbolic sine of an angle given in radians. Syntax : sinh(data_type x) Parameter… Read More » atan2() function in C++ STL The atan2() is an inbuilt function in C++ STL which returns tangent inverse of (y/x), where y is the proportion of the y-coordinate and x… Read More » feclearexcept in C++ with Examples feclearexcept() clears the supported floating-point exceptions represented by excepts. Syntax: int feclearexcept(int excepts); excepts : Bitmask listing of exception flags to clear Return value: The… Read More » islessgreater() in C/C++ In C++, islessgreater() is a predefined function used for mathematical calculations. math.h is the header file required for various mathematical functions. islessgreater() function is used… Read More » isless() in C/C++ In C++, isless() is a predefined function used for mathematical calculations. math.h is the header file required for various mathematical functions. isless() function used to… Read More » Divisibility by 3 where each digit is the sum of all prefix digits modulo 10 Given K, number of digits, and d0 and d1 as the two digits to form the k-sized integer. Task is to check whether the k-sized… Read More » islessequal() in C/C++ In C++, islessequal() is a predefined function in math.h. It is used to check whether the 1st floating point number is less than or equal… Read More » frexp() in C++ The frexp() function breaks the floating point number x into its binary significand i., e., floating point with an absolute value between [0.5, 1.0) and… Read More » log1p() in C++ The log1p() function takes an argument x and returns the natural logarithm of the base-e logarithm of x+1. Here e is a mathematical constant with… Read More » expm1() in C++ The expm1(x) function returns ex – 1 where x is an argument and e is mathematical constant with value equal to 2.71828. Syntax: double expm1()… Read More » ldexp() in C++ The ldexp() function takes two arguments a and b and returns the product of a and 2 raised to the power of b i.e., a… Read More » remquo() in C++ This function is used to return the remainder(modulus) of 2 floating point numbers mentioned in its arguments and also stores the quotient to the pointer… Read More » isgreater() in C/C++ In C++, isgreater() is a predefined function used for mathematical calculations. math.h is the header file required for various mathematical functions. isgreater() function used to… Read More »

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CC-MAIN-2019-18

latest

en

https://www.hammockforums.net/forum/showthread.php/62783-At-what-body-weight-is-7-64-Amsteel-not-enough?s=ff9d31ef620d5317864f95ed9114bab2&p=932106

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# Thread: At what body weight is 7/64 Amsteel not enough? If you hang your hammock with the suspension angle at 30 degrees to the horizon, the tension on each end of the suspension is equal to your body weight. If I remember physics correctly here, the load weight put on each end of the suspension is not equal to your body weight. It is half you body weight. This is because your weight is in relation to earth. To keep ourselves off the ground, or earth, in a hammock we commonly use two suspension lines so our total weight is being shared between the two lines. For a 250 lbs person the weight carried by each end of the suspension would be 125 lbs. If you were to rig a loosely termed hammock from a square tarp tied between 4 trees the weight carried by each suspension line for our 250 lbs load would be 62.5 lbs per line. I hope this helps. 2. Originally Posted by japhyaz If I remember physics correctly here, the load weight put on each end of the suspension is not equal to your body weight. It is half you body weight. If it helps, think of a cantilever. A 200 lb weight can support a 1,000 lb weight with a cantilever. You would be correct if the suspension hung straight down at 90 degrees from horizontal, but that's not the case. In fact, the closer the suspension comes to horizontal, the closer the effective weight approaches infinity. Rain Man . 3. Thanks for correcting me Rain Man.

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CC-MAIN-2015-48

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http://www.mathcaptain.com/statistics/descriptive-statistics.html

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crawl-data/CC-MAIN-2018-30/segments/1531676596542.97/warc/CC-MAIN-20180723145409-20180723165409-00241.warc.gz

The subject of statistics is broadly divided into two branches: Descriptive Statistics and Inferential Statistics. Descriptive Statistics deals with data collection and summarizing the raw data in an understandable format, and these results are generalized to arrive at a conclusion applying Inferential Statistics. The description or summary of sample behavior, presented using Descriptive Statistics is alone is in turn used for drawing inferences on the Population characteristics. Descriptive Statistics comes into play again in the presentation of the estimated or generalized Population traits. The data that is summarized in tabular, graphical or numerical form is also known an descriptive statistics. ## Descriptive Statistics Definition Descriptive Statistics deals with analysis and methods related to collection, organization, summarizing and presentation of data. Applying the techniques of descriptive statistics, the raw data is collected and transformed into a meaningful form. The data is summarized using numerical measures of central tendency and dispersion. Different types of graphs and plots provide visual representations of data which aid in understanding the traits and patterns related to the data. The descriptive statistics summary cannot however be generalized to population traits. ## Purpose of Descriptive Statistics The purpose of descriptive statistics is not restricted only to meaningful presentation of raw data. Inferential statistics makes use of the numerical summary of the sample data to arrive at a conclusion or generalization. For example, the sample mean calculated is treated using techniques of inferential statistics to estimate population mean, or testing the claim on population mean. The tabular or graphical presentation of data we find in news papers, magazines or other media are often the generalized results of Sample data. Descriptive statistics is again used in these visual presentations of Population traits. Thus the two branches of study, descriptive and inferential statistics co exist, complementing each other. ## Descriptive Vs Inferential Statistics The contrast between Descriptive and Inferential Statistics can be tabulated as follows: Descriptive Statistics Inferential Statistics Descriptive Statistics deals with collection, organization,summarizing and presentation of data. Inferential Statistics provides methods for generalizing fromsamples to populations, testing the claims on Population parameters, determining relationship between variables and making predictions. The sample statistics are calculated using formulas andmethods provided in descriptive statistics. Inferential statistics makes use of the sample statistics in estimating the population parameters and testing hypothesis on population parameters. The graphing and charting techniques present in descriptive statistics is used for presentation of Population traits andfor comparing different population behavior. In inferential statistics, graphs are used to study the pattern of trend andto provide a visual prediction for future. ## Descriptive Statistics Examples Let us solve a problem to show how numerical measures are calculated to summarize data in descriptive statistics. For this purpose we consider data organized in a frequency table as follows: ### Solved Example Question: In a class of 75 students, a statistics test is conducted for a maximum score of 25. The following table gives the frequencies against the test scores. Find the Mean, Median and Mode for the data. Test Score 1 5 6 8 10 12 13 14 15 17 20 21 24 Number of  Students 1 1 2 6 10 16 13 9 8 5 2 1 1 Solution: The Mean of a frequency distribution is calculated using the formula x = $\frac{\sum fx}{N}$   where N is the total number of observations. We redo the table making suitable columns to enable the required calculations and include a cumulative frequency column (which is used to determine the median). Test Score      x Frequency         f fx CumulativeFrequency 1 1 1 1 5 1 5 2 6 2 12 4 8 6 48 10 10 10 100 20 12 16 192 36 13 13 169 49 14 9 126 58 15 8 120 66 17 5 85 71 20 2 40 73 21 1 21 74 24 1 24 75 ∑f = 75 ∑fx = 943 The numbers in the cumulative frequency column against a test score gives the total count of frequencies for test scores equal and less. Using the formula for mean x = $\frac{\sum fx}{N}$  = $\frac{943}{75}$ = 12.6 answer rounded to the tenth. Hence the average test score = 12.6. The median is given by the the middle value when the test scores are arranged as an ascending array.  That is $\frac{(75 + 1)}{2}$ = 38th test score is the median. The 38th item will be a test score 13, as 36 items have scores less than 13 and 49 items have scores less than 14. Thus the median of the data set = 13. The test score 12 has the greatest frequency = 16. Hence the mode of the data set is 12.

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http://studentsmerit.com/paper-detail/?paper_id=13454

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crawl-data/CC-MAIN-2016-50/segments/1480698543567.64/warc/CC-MAIN-20161202170903-00260-ip-10-31-129-80.ec2.internal.warc.gz

#### Description of this paper ##### Q1)State the null and alternative hypothesis if... Description Solution Question Q1)State the null and alternative hypothesis if the average electric bill for residents of White Pine Estates exceeds \$52.98 per month. a)state the hypothesis b)find the critical value c)compute the test vaule d)make a decision e)summerize the results Q2)State the null and alternative hypothesis if the average number of calories of brand A's low calorie meal is at most 300. a)state the hypothesis b)find the critical value c)compute the test vaule d)make a decision e)summerize the results Q3)State the null and alternative hypothesis if the average weightloss of people who use brand A's low calorie meal for 6 weeks is at least 3.6 pounds a)state the hypothesis b)find the critical value c)compute the test vaule d)make a decision e)summerize the results Q4)The average hourly wage last year for members of the hospital clerical staff in a large city was \$6.32. The standard deviation of the population was \$.54. This year a sample of 50 workers had an average hourly wage of \$6.51. Test the claim at alpha-.05 that the average wage has not changed by finding the p-value for the test. Q5)A state executive claims that the average number of ant to Statistics And Probability Expert Tutor on 4/18/2012 at 3:10pm cres in western Pennsylvania State Park is less than 2000 acres. A random sample of five parks is selected, and the number of acres is shown. At alpha=.01, is there enough evidence to support the claim? 959 1187 493 6249 541 Q6)A random sample of stipends of teaching assistants in economics is listed belwo. Is there sufficient evidence at the alpha=.05 level to conclude that the average stipend differes from \$15,000? The data is liste below: 14,000 18,000 12,000 14,356 13,185 13,419 14,000 11,981 17,604 12,283 16,338 15,000 Paper#13454 | Written in 18-Jul-2015 Price : \$25

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http://nerdr.com/tag/100-doors-2013-answers/

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# Tag Archives: 100 Doors 2013 Answers ## 100 Doors 2013 Level 51-75 Walkthrough – iPad, iPhone and Android 100 Doors 2013 Answers for Level 51 to Level 75. This walkthrough is for iPad, iPhone and Android devices. The 100 Doors 2013 app was created by Gipnetix games. This guide for 100 Doors 2013 contains help, solutions and tips for completing the game puzzles and floors. This guide does have some spoilers and cheats so only read ahead if you want extra hints. For the answers to the first 50 doors of 100 Doors 2013 please see the first 100 Doors 2013 guide for level 1 to level 50. This Answers guide for 100 Doors 2013 covers levels 51 to 75 only.  If another update is released for 100 Doors 2013 this next walkthrough in the series will be made a link will be placed here to show you where to go. Level 51. It says Columns & Rows above the door. If you tap on the key you will see it move around. Note the column and row numbers of the change to get the code 16254532. Level 52. Turn your Android phone upside down and a ladder will appear. Move the ladder to the right side of the screen and shake your device. You will see a key appear. Position the ladder under the key and pick it up to exit the room. Level 53. An easy level, just flip your device upside down and press each of the 9 buttons. Level 54. The skyscraper level of 100 Doors 2013. Count the numbers of floors on each skyscraper as they scroll past the doorframe. Set the towers on the left and right to 8, 5, 3 and 6 bars and press the green button. Move buildings will scroll past the screen. Now set the side towers to 6, 9, 8 and 4 blocks and hit green again. The last set of towers will skim past the screen. Set the blocks to 2967. If you total up all these numbers you we set the blocks to you get 22, 27 and 24. Put this together and you have the door code: 222724. Enter this in the door code box and exit the room. Level 55. The door code for level 55 is 53124. The cheat to this stage is that everything on the numbers grid is diagonal. This means the question mark numbers are easy to answer. Level 56. You see a checker or chess board on the lift doors. Find the square numbers that correspond with the code above the door. B4 F3 E6 D7 is the code above the door. This relates to numbers 24, 22, 45 and 52. The final code is then 26224552. ## 100 Doors 2013 Walkthrough – iPad, iPhone and Android 100 Doors 2013 walkthrough for the iPad, iPhone and Android devices. The 100 Doors 2013 app was created by Gipnetix games. This guide for 100 Doors 2013 contains help, solutions and tips for completing the game puzzles and floors. This guide contains spoilers and answers to complete each floor and open every door. Door for Level 1. Press the button near the door to exit. Level 2 of 100 Doors 2013. Flip your Android or iOS device upside down. You will see the ball roll to the other side and the door will open. Level 3 Answer. Tap on the dark circle to pick it up. You will see the ball in your inventory. Select it and tap the left wall to place it. I you turn over your phone, Android or iOS device it will move up. Just like Level 2 of 100 Doors 2013. Floor 4. If you shake your Android device on 100 Doors level 4 the balls will fall from the top of the screen. Pick up the key that falls, select it from your inventory and escape the floor. Level 5. Slide the wood near the rope to the left. You can now pull the rope down and the door will open. Level 6 of 100 Doors 2013. Above the door you will see 3, below the door you will see 5. Tap to enter the code box and type 3355. Easy door! Level 7. You will see a swipe keycard on the floor to the left. Pick it up, select it in your inventory and open the door. Level 8. Pick up the axe on the right side wall. Select the axe in your inventory and break the wooden planks in a cross pattern. Now tilt your Android device to the left and the ball will roll and open the door. 100 Doors 2013 level 9 solution. This is a simple tilt level. Tilt your device left to open the left door, and right to open the right door. Easy! Level 10. You will see Roman Numerals above the door. I V III means one, five, three. First, shake your Android phone to make the metal poles fall down. Now you can see the V behind the metal poles, and the poles on the ground also make a IV, meaning four. The key entry code to open the door is 15354.

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CC-MAIN-2024-22

latest

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https://oeis.org/A291197

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crawl-data/CC-MAIN-2019-43/segments/1570987822458.91/warc/CC-MAIN-20191022155241-20191022182741-00061.warc.gz

This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!) A291197 Second differences of frac(n/log(n)) rounded, n >= 2. 1 0, -1, 1, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, -1 (list; graph; refs; listen; history; text; internal format) OFFSET 2 COMMENTS The second differences are very close to -1, 0 or 1. Second differences of floor(-n/log(n)). - Robert Israel, Aug 20 2017 LINKS Robert Israel, Table of n, a(n) for n = 2..10000 MAPLE A0:= [seq(frac(n/log(n)), n=2..100)]: seq(round(A0[n+2]-2*A0[n+1]+A0[n]), n=1..nops(A0)-2); # Robert Israel, Aug 20 2017 MATHEMATICA Differences[Table[Floor[-n/Log[n]], {n, 2, 100}], 2] (* Harvey P. Dale, Jan 05 2019 *) CROSSREFS Sequence in context: A288670 A057215 A284905 * A269927 A246146 A191162 Adjacent sequences:  A291194 A291195 A291196 * A291198 A291199 A291200 KEYWORD sign AUTHOR Simon Plouffe, Aug 20 2017 STATUS approved Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent The OEIS Community | Maintained by The OEIS Foundation Inc. Last modified October 22 12:30 EDT 2019. Contains 328318 sequences. (Running on oeis4.)

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CC-MAIN-2019-43

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https://www.dinesentax.com/excess-social-security-refunds/

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crawl-data/CC-MAIN-2024-30/segments/1720763517550.76/warc/CC-MAIN-20240721030106-20240721060106-00503.warc.gz

What are Excess Social Security Refunds? What are “excess Social Security taxes” and how do some taxpayers get a refund of those taxes? Let’s take a look. Background If you look on Form 1040 under the “Payments” section, Line 71, you’ll see a line marked “Excess social security and tier 1 RRTA tax withheld.” (RANDOM SIDE NOTE: The grammarian in me cringes to see that the IRS doesn’t capitalize “Social Security” on the Form 1040. It’s a proper name and should be capitalized. But I digress. Back to tax talk.) What is this mysterious tax credit? The short answer is, it’s a refund for situations where you had too much Social Security tax withheld. This can happen when people work more than one job and their total income for the year goes over the Social Security wage base for that year. Example 1 Let’s say Joe is a doctor. He works at a medical center and earns a salary of \$200,000 per year. He also works part-time in an ER and makes another \$20,000. When the medical center pays Joe, they’ll stop withholding Social Security tax once his pay reaches the wage base for the year (\$128,700 in 2018). But the ER is not responsible for knowing what other sources of income Joe has. So they withhold Social Security taxes on his \$20,000 of pay. The Social Security tax is 6.2%, so the amount of tax withheld is \$1,240. On Joe’s tax return, he can claim a credit for this \$1,240 of “excess Social Security withholding.” Example 2 Let’s change the example slightly so we can have more fun playing with math. Let’s say Joe makes \$120,000 at his main job and \$20,000 at his other job, for total wages of \$140,000. In this case, Joe’s wages from each job separately is below the SS wage base. So his main job will withhold Social Security tax on the full \$120,000, and his other job will withhold Social Security tax on the full \$20,000. So Joe had SS taxes withheld on a total of \$140,000 of wages, but the wage base for the year is \$128,700. First we take \$140,000 minus \$128,700 = \$11,300. Joe had Social Security taxes withheld on an excess \$11,300 of wages. So his refund will be \$11,300 x .062 = \$700.60, which rounds up to \$701. Joe will claim a credit of \$701 for excess Social Security tax withheld.

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https://my.oschina.net/liyurong/blog/1608204

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## 找到数组中左右两边的和相等的pivot的下标 Find Pivot Index 原 叶枫啦啦 Given an array of integers `nums`, write a method that returns the "pivot" index of this array. We define the pivot index as the index where the sum of the numbers to the left of the index is equal to the sum of the numbers to the right of the index. If no such index exists, we should return -1. If there are multiple pivot indexes, you should return the left-most pivot index. Example 1: ```Input: nums = [1, 7, 3, 6, 5, 6] Output: 3 Explanation: The sum of the numbers to the left of index 3 (nums[3] = 6) is equal to the sum of numbers to the right of index 3. Also, 3 is the first index where this occurs.``` Example 2: ```Input: nums = [1, 2, 3] Output: -1 Explanation: There is no index that satisfies the conditions in the problem statement.``` Note: • The length of `nums` will be in the range `[0, 10000]`. • Each element `nums[i]` will be an integer in the range `[-1000, 1000]`. ①  找到左右两边的和相等的pivot的下标，如果有多个，则返回最左侧，如果不存在，返回-1. class Solution { //34ms public int pivotIndex(int[] nums) { int sum = 0; for (int n : nums){ sum += n; } int cursum = 0; for (int i = 0;i < nums.length;i ++){ if (sum - nums[i] == 2 * cursum) return i; cursum += nums[i]; } return -1; } } ### 评论(0) Find Pivot Index之Python实现 osc_dos38x1o 2018/09/27 1 0 LeetCode算法题-Find Pivot Index（Java实现） 2019/04/12 0 0 Java中的排序 Hosee 2016/04/04 381 0 java.util.DualPivotQuickSort的实现 DualPivotQuickSort汇集了多种排序算法，称之为DualPivotQuickSort并不合适。不同的排序算法有不同的使用场景。看懂此文件，排序算法就算彻底搞懂了。本文只介绍有用的代码片段，DualPivotQu... osc_8zk7ewr4 2019/06/02 6 0 [LeetCode] 215. Kth Largest Element in an Array 数组中第k大的元素 Find the kth largest element in an unsorted array. Note that it is the kth largest element in the sorted order, not the kth distinct element. Example 1: Input: and k = 2Output: ...... osc_cym01vn6 2018/03/06 2 0 9 0 2048游戏的最佳算法是什么？ - What is the optimal algorithm for the game 2048? javail 9 0 Spring Cloud Ribbon 客户端负载均衡 Ribbon客户端组件提供一系列完善的配置选项，比如连接超时、重试、重试算法等，内置可插拔、可定制的负载均衡组件。下面是用到的一些负载均衡策略： 简单轮询负载均衡 加权轮询负载均衡 区域... 7 0 9 0 OSChina 周四乱弹 —— 卖全家桶！ Osc乱弹歌单（2020）请戳（这里） 【今日歌曲】 @巴拉迪维 ：陈慧娴的单曲《与泪抱拥》 陈慧娴的嗓音加上向雪怀的词，这样的经典组合真不多。#今日歌曲推荐# 《与泪抱拥》- 陈慧娴 手机党少年... 15 0

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http://stackoverflow.com/questions/4137785/why-are-variables-i-and-j-used-for-counters/454314

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# Why are variables “i” and “j” used for counters? [duplicate] Possible Duplicate: Why are we using i as a counter in loops I know this might seem like an absolutely silly question to ask, yet I am too curious not to ask... Why did "i" and "j" become THE variables to use as counters in most control structures? Although common sense tells me they are just like X, which is used for representing unknown values, I can't help to think that there must be a reason why everyone gets taught the same way over and over again. Is it because it is actually recommended for best practices, or a convention, or does it have some obscure reason behind it? Just in case, I know I can give them whatever name I want and that variables names are not relevant. - ## locked by Bill the Lizard♦Oct 13 '11 at 21:22 This question exists because it has historical significance, but it is not considered a good, on-topic question for this site, so please do not use it as evidence that you can ask similar questions here. This question and its answers are frozen and cannot be changed. More info: help center. ## marked as duplicate by Eric, Lance Roberts, Shaggy Frog, Tim Stone, Michael MrozekDec 8 '10 at 22:17 "God is real, unless declared integer" –  Andreas Grech Aug 8 '09 at 10:04 i=iteration while j=after interation –  ajreal Nov 9 '10 at 19:48 Cartesian coordinates –  Nick Dandoulakis Nov 10 '10 at 19:33 Why do actual questions become community wikis just because they're popular? This feels very reminiscent of communism. If somebody invents something really cool, the government steals the invention to share with the community. –  orokusaki Dec 8 '10 at 21:34 Closed wrong way: the answers here are more informative than to the other qn... –  Charles Stewart Dec 9 '10 at 10:07 It comes ultimately from mathematics: the summation notation traditionally uses i for the first index, j for the second, and so on. Example (from http://en.wikipedia.org/wiki/Summation): It's also used that way for collections of things, like if you have a bunch of variables x1, x2, ... xn, then an arbitrary one will be known as xi. As for why it's that way, I imagine SLaks is correct and it's because I is the first letter in Index. - @SLott: And why is i used in math? –  SLaks Nov 9 '10 at 20:31 @Slaks: That's a good question. I actually think that "i" might come from integer more than index. I also think it's easy to write on a chalkboard. Back in the 70's we were cautioned to be sure that we wrote our "i" and "j" in a perfectly distinctive manner. Indeed, we were told to draw our "i" exactly like a backwards "j" to be perfectly clear about it. –  S.Lott Nov 9 '10 at 20:38 @S.Lott: I doubt it comes from integer. We use ℤ (blackboard bold Z) for the integers because it stands for the German word Zahlen, which means numbers. Assuming that the summation notation arose at around the same time, the German-based notation would be expected—and the German word for index is Index, which also begins with an i. And I can't think of many letters which are particularly hard to write on a chalkboard. Well, except ξ :-) –  Antal S-Z Nov 9 '10 at 22:52 "This convention exists because this convention has existed before." That's kind of how etymology works: nobody knows why a particular noise had a particular meaning in PIE. It would be nice to explain the mathematical convention, but the question is "why are they used as counters in control structures", so until someone produces an answer that goes back further, this is the best. It does at least speculate why it's used in mathematics. A proper mathematical historian could find out, maybe using a binary chop. Euclid didn't use it, I bet von Neumann did. How about Cauchy? He used indexes a lot –  Steve Jessop Nov 9 '10 at 23:14 I think it was Lagrange who recommended using a,b,c for constants of a function, and x,y,z for variables of a function. i,j,k denote the 'directions' of a vector, and the factors of a formal sum like this can be construed as degrees of freedom [directions, by another name] of the equation. –  David Dec 5 '10 at 19:57 I believe it dates back to Fortran. Variables starting with I through Q were integer by default, the others were real. This meant that I was the first integer variable, and J the second, etc., so they fell towards use in loops. - I think this comes from the way mathematicians seem to like to use i, j, k as handy subscripts for summation and matrix multiplication indices and what-not. I remember reading in an early Fortran II manual something about that. (Yes, Fortran II.) –  S.Lott Nov 9 '10 at 19:51 Yes, FORTRAN originates these conventions. –  Xepoch Nov 10 '10 at 0:26 Called implicit declaration... –  Xepoch Nov 10 '10 at 4:20 I was taught I through N not Q. Google seems to mostly agree. (different versions of FORTRAN?) –  Hugh Allen Nov 12 '10 at 14:14 @learnvst - because mathematicians had been using i,j for at least a century beforehand. –  Martin Beckett Nov 18 '10 at 17:49 Mathematicians were using i,j,k to designate integers in algebra (subscripts, series, summations etc) long before (e.g 1836 or 1816) computers were around (this is the origin of the FORTRAN variable type defaults). The habit of using letters from the end of the alphabet (...,x,y,z) for unknown variables and from the beginning (a,b,c...) for constants is generally attributed to Rene Descartes, (see also here) so I assume i,j,k...n (in the middle of the alphabet) for integers is likely due to him too. - To me, this is clearly the best answer. (Honorable mention for Michael Borgwardt's answer, which also cites mathematical convention but isn't as specific.) I'm sorry yours isn't the accepted one. All I can do is give it my upvote. –  John Y Jun 2 '09 at 2:12 This is exactly the reason that the we need to be able to vote for a community accepted answer (and yeah I know this belongs on uservoice). –  Lucas Jun 18 '09 at 3:31 Because of the name D*ijk*stra. - What, you're taking this question seriously? –  bmargulies Nov 15 '10 at 20:00 "LoL" would be my comment if it wasn't for the minimum characters limit ;) –  naugtur Nov 16 '10 at 12:21 That explanation might work better if his name wasn't really "Dÿkstra". –  Jerry Coffin Nov 19 '10 at 4:48 @Jerry, the name is Dijkstra with a ligature for ij, not Dÿkstra with trema on a y. –  AProgrammer Dec 5 '10 at 18:23 i = integer Comes from Fortran where integer variables had to start with the letters I through N and real variables started with the other letters. Thus I was the first and shortest integer variable name. Fortran was one of the earliest programming languages in widespread use and the habits developed by programmers using it carried over to other languages. EDIT: I have no problem with the answer that it derives from mathematics. Undoubtedly that is where the Fortran designers got their inspiration. The fact is, for me anyway, when I started to program in Fortran we used I, J, K, ... for loop counters because they were short and the first legally allowed variable names for integers. As a sophomore in H.S. I had probably heard of Descartes (and a very few others), but made very little connection to mathematics when programming. In fact, the first course I took was called "Fortran for Business" and was taught not by the math faculty, but the business/econ faculty. For me, at least, the naming of variables had little to do with mathematics, but everything due to the habits I picked up writing Fortran code that I carried into other languages. - I'm pretty sure it was FORTRAN. –  Cade Roux Jan 17 '09 at 23:43 Ya, fortran..... It rots the mind. We have a programmer that uses i ii and iii as loop variable names. The other symptom is 6 character variable/function names with no vowels. –  EvilTeach Jan 17 '09 at 23:54 @tvan, I'm pretty sure variables starting with I through N defaulted to integer, but you could still declare them real hence the joke "God is real, unless declared integer". +1 anyway, since my recollection from so many years ago may possibly NOT be perfect. –  paxdiablo Jan 18 '09 at 0:06 Hey, the FORTRAN guys got it off the mathematicians! –  timday Jan 18 '09 at 0:10 I agree with @timday. Using i as an index of a series has been a practice by mathematicians for at least 2 centuries. –  Scottie T Jun 2 '09 at 13:06 i stands for Index. j comes after i. - no, n comes after i - i n d e x. –  Pete Kirkham Nov 9 '10 at 20:18 I think he was talking about alphabet, try to use some imagination :) –  Jack Nov 9 '10 at 21:16 @Jack: I think @Pete was joking ;-) –  Christopher Pfohl Nov 9 '10 at 21:59 @Cpfohl: yep, just wanted to be boring :D –  Jack Nov 9 '10 at 22:02 @Pete Kirkham: Thank you very much Pete, it was the best laugh I had in the past month. –  AMissico Nov 17 '10 at 18:21 These symbols were used as matrix indexes in mathematics long before electronic computers were invented. - I think it's most likely derived from index (in the mathematical sense) - it's used commonly as an index in sums or other set-based operations, and most likely has been used that way since before there were programming languages. - Yup. The mathematic notation for a sum like Y = Σ Xi precedes every programming language. –  Treb Mar 23 '09 at 0:30 There's a preference in maths for using consecutive letters in the alphabet for "anonymous" variables used in a similar way. Hence, not just "i, j, k", but also "f, g, h", "p, q, r", "x, y, z" (rarely with "u, v, w" prepended), and "α, β, γ". Now "f, g, h" and "x, y, z" are not used freely: the former is for functions, the latter for dimensions. "p, q, r" are also often used for functions. Then there are other constraints on available sequences: "l" and "o" are avoided, because they look too much like "1" and "0" in many fonts. "t" is often used for time, "d & δ" for differentials, and "a, s, m, v" for the physical measures of acceleration, displacement, mass, and velocity. That leaves not so many gaps of three consecutive letters without unwanted associations in mathematics for indices. Then, as several others have noticed, conventions from mathematics had a strong influence on early programming conventions, and "α, β, γ" weren't available in many early character sets. - Agreed. Although, a, b, c is a fairly commonly used sequence despite a having multiple meanings... –  Stobor Nov 17 '10 at 5:25 I found another possible answer that could be that i, j, and k come from Hamilton's Quaternions. Euler picked i for the imaginary unit. Hamilton needed two more square roots of -1: ii = jj = kk = ijk = -1 Hamilton was really influential, and quaternions were the standard way to do 3D analysis before 1900. By then, mathematicians were used to thinking of (ijk) as a matched set. Vector calculus replaced quaternionic analysis in the 1890s because it was a better way to write Maxwell's equations. But people tended to write vector quantities as like this: (3i-2j+k) instead of (3,-2,1). So (ijk) became the standard basis vectors in R^3. Finally, physicists started using group theory to describe symmetries in systems of differential equations. So (ijk) started to connote "vectors that get swapped around by permutation groups," then drifted towards "index-like things that take on all possible values in some specified set," which is basically what they mean in a for loop. - at last a different approach to the question, interesting point +1 –  Fabian Dec 5 '10 at 17:20 a seems an array b seems another array c seems a language name d seems another language name e seems exception f looks bad in combination with "for" (for f, a pickup?) g seems g force h seems height i seems an index j seems i (another index) k seems a constant k l seems a number one (1) m seems a matrix n seems a node o seems an output p sounds like a pointer q seems a queue r seems a return value s seems a string t looks like time u reserved for UVW mapping or electic phase v reserved for UVW mapping or electic phase or a vector w reserved for UVW mapping or electic phase or a weight x seems an axis (or an unknown variable) y seems an axis z seems a third axis - I see n as number, usually the number of elements in a set. –  Tom Leys Dec 5 '10 at 19:30 o seems an object actually –  bluesmoon Dec 5 '10 at 21:40 Oh men, and what XXX seem to be? )) +1 for the creativity ;) –  Hovhannes Grigoryan Mar 12 '11 at 13:54 One sunny afternoon, Archimedes what pondering (as was usual for sunny afternoons) and ran into his buddy Eratosthenes. Archimedes said, "Archimedes to Eratosthenes greeting! I'm trying to come up with a solution to the ratio of several spherical rigid bodies in equilibrium. I wish to iterate over these bodies multiple times, but I'm having a frightful time keeping track of how many iterations I've done!" Eratosthenes said, "Why Archimedes, you ripe plum of a kidder, you could merely mark successive rows of lines in the sand, each keeping track of the number of iterations you've done within iteration!" Archimedes cried out to the world that his great friend was undeniably a shining beacon of intelligence for coming up with such a simple solution. But Archimedes remarked that he likes to walk in circles around his sand pit while he ponders. Thus, there was risk of losing track of which row was on top, and which was on bottom. "Perhaps I should mark these rows with a letter of the alphabet just off to the side so that I will always know which row is which! What think you of that?" he asked, then added, "But Eratosthenes... whatever letters shall I use?" Eratosthenes was sure he didn't know which letters would be best, and said as much to Archimedes. But Archimedes was unsatisfied and continued to prod the poor librarian to choose, at least, the two letters that he would require for his current sphere equilibrium solution. Eratosthenes, finally tired of the incessant request for two letters, yelled, "I JUST DON'T KNOW!!!" So Archimedes chose the first two letters in Eratosthenes' exclamatory sentence, and thanked his friend for the contribution. These symbols were quickly adopted by ancient Greek Java developers, and the rest is, well... history. - ...and thankfully the ancient Greeks spoke English... –  Gerrat Nov 18 '10 at 19:08 ... and had the letter j. –  Andrew Grimm Nov 22 '10 at 12:27 hooo, you have some imagination. but no points :) –  alvin Dec 9 '10 at 20:51 i think it's because a lot of loops use an Int type variable to do the counting, like for (int i = 0; etc and when you type, you actually speak it out in your head (like when you read), so in your mind, you say 'int....' and when you have to make up a letter right after that 'int....' , you say / type the 'i' because that is the first letter you think of when you've just said 'int' like you spell a word to kids who start learning reading you spell words for them by using names, like this: WORD spells William W, Ok O, Ruby R, Done D So you say Int I, Double d, Float f, string s etc. based on the first letter. And j is used because when you have done int I, J follows right after it. - i predates this syntax. –  SLaks Nov 18 '10 at 2:55 That's a great way to confuse the crap out of a kid; you really teach yours to spell like that?! –  Lightness Races in Orbit Apr 30 '11 at 12:02 I think it's a combination of the other mentioned reasons : For starters, 'i' was commonly used by mathematicians in their notation, and in the early days of computing with languages that weren't binary (ie had to be parsed and lexed in some fashion), the vast majority of users of computers were also mathematicians (... and scientists and engineers) so the notation fell into use in computer languages for programming loops, and has kind of just stuck around ever since. Combine this with the fact that screen space in those very early days was very limited, as was memory, it made sense to keep shorter variable names. - Possibly historical ? FORTRAN, aurguably the first high level language, defined i,j,k,l,m as Integer datatypes by default, and loops could only be controlled by integer variable, the convention continues ? eg: do 100 i= j,100,5 .... 100 continue .... - i = iterator, i = index, i = integer Which ever you figure "i" stands for it still "fits the bill". Also, unless you have only a single line of code within that loop, you should probably be naming the iterator/index/integer variable to something more meaningful. Like: employeeIndex BTW, I usually use "i" in my simple iterator loops; unless of course it contains multiple lines of code. - i = iota, j = jot; both small changes. iota is the smallest letter in the greek alphabet; in the English language it's meaning is linked to small changes, as in "not one iota" (from a phrase in the New Testament: "until heaven and earth pass away, not an iota, not a dot, will pass from the Law" (Mt 5:18)). A counter represents a small change in a value. And from iota comes jot (iot), which is also a synonym for a small change. - Well from Mathematics: (for latin letters) a,b: used as constants or as integers for a rational number c: a constant d: derivative e: Euler's number f,g,h: functions i,j,k: are indexes (also unit vectors and the quaternions) l: generally not used. looks like 1 m,n: are rows and columns of matrices or as integers for rational numbers o: also not used (unless you're in little o notation) p,q: often used as primes r: sometimes a spatial change of variable other times related to prime numbers s,t: spatial and temporal variables or s is used as a change of variable for t u,v,w: change of variable x,y,z: variables - Many possible main reasons, I guess: • mathematicians use i and j for Natural Numbers in formulas (the ones that use Complex Numbers rarely, at least), so this carried over to programming • from C, i hints to int. And if you need another int then i2 is just way too long, so you decide to use j. • there are languages where the first letter decides the type, and i is then an integer. - It comes from Fortran, where i,j,k,l,m,n are implicitly integers. - I commonly see the variables ii, jj, kk, mm, nn etc. used as counters in DSP code. The variables i and j left on their own are too easily confused with complex number notation. Counter variables l and ll are not commonly used because they are easily confused with the digit 1. - TI-83+ Z-80 Basic. ;-) –  Tim Gostony Feb 22 '12 at 2:34 It definitely comes from mathematics, which long preceded computer programming. So, where did if come from in math? My completely uneducated guess is that it's as one fellow said, mathematicians like to use alphabetic clusters for similar things -- f, g, h for functions; x, y, z for numeric variables; p, q, r for logical variables; u, v, w for other sets of variables, especially in calculus; a, b, c for a lot of things. i, j, k comes in handy for iterative variables, and that about exhausts the possibilities. Why not m, n? Well, they are used for integers, but more often the end points of iterations rather than the iterative variables themselves. Someone should ask a historian of mathematics. - See everyone speaks the same language. No matter even if it is a programming language. :-) - Counters are so common in programs, and in the early days of computing, everything was at a premium... Programmers naturally tried to conserve pixels, and the 'i' required fewer pixels than any other letter to represent. (Mathematicians, being lazy, picked it for the same reason - as the smallest glyph). As stated previously, 'j' just naturally followed... :) - In the early days of computing, pixels didn't exist. –  SLaks Nov 18 '10 at 2:55 @Slaks, that is one winning comment. Just see the grin on my face reading it, and the votes. Nice! –  ProfK Dec 5 '10 at 14:24 ...and thus, premature optimization was born! –  Gerrat Feb 14 '11 at 14:53 It's funny how everyone has a different take on this. I always assumed that it stood for 'index'. The fact that everyone immediately realizes what it means is enough for me. - i is for index and integer, and was in use in mathematics for sum/sigma notation long before COBOL and FORTRAN were invented. The next is j, k, l - in alphabetical order. Greek does not come into it. It is that simple: Why does this question have a bounty? - because i putted it. And the reason for that is that I did want to hear other opinions, why, is that a problem? –  Carlos Nov 18 '10 at 16:18 No problem. it is a question worth asking, but I was surprised at it having a bounty. –  winwaed Nov 18 '10 at 16:27 I use it for a number of reasons. • Usually my loops are int based, so you make a complete triangle on the keyboard typing "int i" with the exception of the space I handle with my thumb. This is a very fast sequence to type. • The "i" could stand for iterator, integer, increment, or index, each of which makes logical sense. With my personal uses set aside, the theory of it being derived from FORTRAN is correct, where integer vars used letters I - N. - Why i and j? Because i comes in Summation.. (from Zack) Why? (from SLaks) i stands for Index (from SLaks) ... watch this - I learned FORTRAN on a Control Data Corp. 3100 in 1965. Variables starting with 'I' through 'N' were implied to be integers. Ex: 'IGGY' and 'NORB' were integers, 'XMAX' and 'ALPHA' were floating-point. However, you could override this through explicit declaration. - It's interesting that so many people point to summation formulas in math. Certainly i and j are common, but I would say n is as common as i (and m as j if using n instead of i). This makes me think the Fortran answer is also onto something. Some earlier programmers chose the i,j,k over n,m,l and now it's just convention in programming. It seems stickier than summation conventions in math or physics. - In math, m and n are more often used as bounds (as in, 0 <= i < m, sigma notation, or dimensions of a matrix / vector space; I'll give you series as an exception). Also look at David's comment to Zack re Lagrange. –  Tobu Dec 7 '10 at 18:54

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# Questions Asked onNovember 8, 2009 1. ## Honors Chemistry "How many grams of NH3 can be produced from the reaction of 28 g of N2 and 25 g of H2? N2 + 3H2 ---> 2NH3 ==> 28 g N2 x (1 mol N2/14.0 g N2) x (2 mol NH3/1 mol N2) x ( 17.0 g NH3/ 1 mol NH3) = 68 g NH3 25 g H2 x ( 1mol H2/2.0 g H2) x (2 mol NH3/3 mol H2) x 2. ## Math Find the variance for the given data. Round your answer to one more decimal place than the original data. {8.5, 4.5, 8.8, 6.9, 5.3} 3. ## Physics Piano tuners tune pianos by listening to the beats between the harmonics of two different strings. When properly tuned, the note A should have the frequency 440 Hz} and the note E should be at 659 Hz}. The tuner can determine this by listening to the beats 4. ## Calc A sample of a radioactive substance decayed to 93.5% of its original amount after a year. a) What is the half-life of the substance? ? years (b) How long would it take the sample to decay to 10% of its original amount? ? years 5. ## Language Arts What follows a linking or action verb? 6. ## Chemistry Which pair of molecules has the strongest dipole-dipole interactions? a- CO2 and CO2 b- CO2 and CH4 c- NH3 and NH3 d- NH3 and CH4 e- CH4 and CH4 Would it be C? Prove that: 2sinxsiny = cos(x-y) - cos(x+y) 8. ## chemistry Which one of the following is NOT a Lewis acid-base reaction? 1. ) Ca + S --> Ca2+ + S2- 2. ) BeF2 + 2 F- --> BeF42- 3. ) H+ + -O-H --> H-O-H 4. ) NH3 + BF3 --> H3N-BF3 i thought it was 1...but im not sure...but i know that 3 & 4 are definatly right. 9. ## Marketing (Help Check) 24.Which of the following is characteristic of the organizational buying process? A)Multiple parties participate in purchase decisions. B)Negotiation between buyers and sellers is commonplace. C)Online buying over the Internet is widespread. D)Buying 10. ## Physics A 1.5 kg block is connected by a rope across a 50-cm-diameter, 2.0 kg, frictionless pulley. A constant 10 N tension is applied to the other end of the rope. Starting from rest, how long does it take the block to move 30 cm? 11. ## math The Moon orbits Earth every 27.3 days. Determine the angular velocity of the Moon, in degrees per day and in radians per day. The radius of the orbit of the Moon is about 384 400 km. How far does the Moon move along an arc of it's orbit every? 12. ## Economics/Algebra A monopolist has a constant marginal and average cost of \$10 and faces a demand curve of QD = 100 - 10P. Marginal revenue is given by MR=100-.20P. a. Calculate the monopolist's profit maximizing quantity, price, and profit. b. Now suppose that the 13. ## Math The table below provides a frequency distribution for the winner of the Davis Cup during the period 1977-1994. Winner of Davis Cup Frequency United States 6 Germany 3 Czechoslovakia 1 Australia 3 France 1 Sweden 4 Which measure of center, the mean, the 14. ## Physics A 2.2 m-long string is fixed at both ends and tightened until the wave speed is 50 m/s.What is the frequency of the standing wave shown in the figure? picture has 6 waves 15. ## Calc A plane flying horizontally at an altitude of 1 mi and a speed of 510 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 6 mi away from the station. (Round to the nearest 16. ## Math Angle x is in the second quadrant and angle y is in the first quadrant such that sinx=5/13 and cosy=3/5, determine and exact value for cos (x+y). I have no idea how to even start this question. Could someone please help me? 17. ## chemistry Which represents the largest pressure? A)five mmHg B)one atmosphere C)one millimeter of mercury D)one hundred pascals E)five pounds per square inch I tried converting them all to mmHg and I think the answer is B, but I just want to make sure. 18. ## Physic The back wall of an auditorium is 29.0 m from the stage. If you are seated in the middle row, how much time elapses between a sound from the stage reaching your ear directly and the same sound reaching your ear after reflecting from the back wall? 19. ## calculus P /|\ / | \ / | \ on this side there is an / | \ arc with A(θ) in the / | \ middle. the B(θ) /θ | B(θ)\ triangle is not equal O -------------- R to the θ triangle. Q the figure shows a setor of a circle with central angle theta. Let A(θ) be the area 20. ## Psychology Can anyone tell me if I answered this correctly? Please help. 2. Assignment: Erikson’s Timeline • Write a 350- to 700-word paper that explains in which of Erikson’s eight stages of life you believe you are currently. • • Explain why you think you 21. ## Social Studies 11 Why did the british fight against the turks in 1915? 22. ## Chemistry on heating the hydrate CaSO4*2H2O, how many moles of water should be driven off per mole of hydrate? 1 mole? 23. ## Chemistry (physical) At room temperature (25 degrees C) butane is a mixture of 72% anti and 28% gauche conformations. Calculate the difference in energy between the gauche and anti confromations. This is how I calculated it but I am not sure I am right: Boltzmann equation: write a spelling word that fits each clue 4.a furnace could provide this. 25. ## excretion Question: which is an example of excretion? a) release of sweat from the sweat glands b) removal of carbondioxide from the lungs Please tell me what is the answer. I thought both urea(from the sweat) and CO2 are products of excretion? In fact, my textbook 26. ## AP Chemistry What acid and what strong base would react in aqueous solution to produce the following salts in the formula equation? Write the balanced formula equation for each reaction. a. potassium perchlorate b. cesium nitrate c. calcium iodide 27. ## chemistry Perform each of the following conversions, being sure to set up clearly the appropriate conversion factor in each case. 2.23 m to yards Am I supposed to round the answer? I don't think I am, but the answer I get is insanely large. 28. ## Clinical Calculations What weight of NaOH would be required to prepare 3000 ml of a 2.5M solution? 29. ## Physics Sound is detected when a sound wave causes the eardrum to vibrate. Typically, the diameter of the eardrum is about 8.4 mm in humans. How much energy is delivered to your eardrum each second when someone whispers 20dB a secret in your ear? 30. ## social studies Why was the Bill of Rights added to the Constitution? 31. ## English Help R for run on sentence, CS for comma splice, F for fragment, and C for correct sentence. Some correct sentences can be punctuated more effectively, however. Check over my anwers if i get it wrong please correct me. Thanks! 1. Carlos took the job and he was 32. ## Chemistry Is the reaction involved in dissolving ammonium chloride in water an endothermic reaction or exothermic reaction? Why? I am pretty sure it is endothermic, but I am just not sure why ? 33. ## Physics121 The back wall of an auditorium is 29.0 m from the stage. If you are seated in the middle row, how much time elapses between a sound from the stage reaching your ear directly and the same sound reaching your ear after reflecting from the back wall? 34. ## algebra I am real stuck, if i am collecting like terms would 19z+z+10/19z be 10/19+21z 35. ## Social Studies Which of the following was not a radical social movement in the nineteenth century? A) Utopian socialism B) Transcendentalism C) Spiritualism D) Naturalism 36. ## Social Studies Which of the following was not a radical social movement in the nineteenth century? A) Utopian socialism B) Transcendentalism C) Spiritualism D) Naturalism 37. ## calculus A fence 4 feet tall runs parallel to a tall building at a distance of 5 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building? 38. ## biology skin cells seem to fit together like pieces of a jigsaw puzzle how is this arrangement of cells helpful to an organism? 39. ## Calc If x2 + y2 = 100 and dy/dt = 3, find dx/dt when y = 8. 40. ## Honors Chemistry On the same subject as before with the limiting/excess reagent stuff -- can someone please check my answer to make sure I'm doing it right? Thanks sooooo much!! :DD 3. Mg + 2HCl ==> MgCl2 + H2 -- What mass of hydrogen at STP is produced from the reaction 41. ## chemistry What is formed at the anode and cathode when the following solutions are electrolysed? sodium iodide copper II chloride sodium sulphate NaOH HCl magnesium nitrate also is this true: if the metal in the compound is higher in the reactivity series than 42. ## Payroll Accounting Help with my Payroll Accounting Final Project. Class AC122-05. Please. I am so lost. 43. ## Chemistry what is the lewis structure for CH3? 44. ## geometry What is the area of a trapezoidal piece of land if the shorter parallel side is 52 ft long, the other parallel side is 130 ft and the altitude of the trapezoid is 75 ft ? 45. ## chemistry sodium iodide copper II chloride sodium sulphate NaOH HCl magnesium nitrate also is this true: if the metal in the compound is higher in the reactivity series than hydrogen then hydrogen is produced instead of the metal at the positive electrode. 46. ## Calculus Suppose f(x)= e^(-1/x). Graph this function in the window -5( 47. ## Enthalpy of a Phase Change How many grams of ice at -20.1C can be completely converted to liquid at 9.9C if the available heat for this process is 4.58×103 kJ? For ice, use a specific heat of 2.01 J/(g*C) and Heat of Fusion is = 6.01 kJ/mol. 48. ## Physics A 72 kg bungee jumper jumps from a bridge. She is tied to a bungee cord whose unstretched length is 13 m, and falls a total of 38 m. Calculate the spring stiffness constant "k" of the bungee cord, assuming Hooke's law applies. Calculate the maximum 49. ## Economics for Global Manager If the current exchange rate is US\$1 equals € .70, how much did you win in US dollars? Suppose that the interest rate in Irish banks is 2% for a one year CD. In the USA, the rate is 4% for a one year CD. If you left your winnings in Ireland, how many 50. ## checking answers 4 algerbra 1. simplify by removing the parenthses and collecting like terms. 83q - (39q-38)=44q+38? 2. solve for y---z=ym answer y=z/m? 3. divide if possible -6/"over" 17 divided by (-5/"over"17)=undefined? 4. translate to algerbirc expression the sum of c and n= Rita won \$60 million lottery. She is to receive \$1 million a year for the next 50 years plus an additional lump sum of \$10 million after the 50th year. The discount rate is 10%. What is the present value of her winnings? you owe \$30,000 payable at the end of five years, what amount should your creditor accept in payment immediately if he could earn 11% on the money? 53. ## Ap english I have to answer a few questions about the essay Ralph Waldo Emerson From Education. (a copy of it is provided on google when you type in -what does emerson mean when he says "nature loves analogies, but not repetitions"?- ) If you have read it or can read 54. ## chemistry What is formed at the anode and cathode when the following solutions are electrolysed? sodium iodide copper II chloride sodium sulphate NaOH HCl magnesium nitrate also is this true: if the metal in the compound is higher in the reactivity series than 55. ## AP Chemistry When hydrochloric acid reacts with magnesium metal, hydrogen gas and aqueous magnesium chloride are produced. What volume of 5.0 M HCI is required to react completely with 3.00 g of magnesium? 56. ## English 1. I have not broken my leg. 2. I have broken my leg. (result) 3. I have never broken my leg. #2 is result. What about #1 and #3? Are #1 and #3 result in the present perfect tense? Or are both 'experience'? 57. ## Chemistry I don't understand how to answer this questions. I thought molecular weight was adding up the atomic weight of each element in a molecule...? If a 0.614g sample of a gas maintains a pressure of 238 mmHg when contained in a 1.0L flask at 0.0 degree Celcius, 58. ## Chemistry Which pair of molecules has the strongest dipole-dipole interactions? a- CO2 and CO2 b- CO2 and CH4 c- NH3 and NH3 d- NH3 and CH4 e- CH4 and CH4 how do you figure out the answer to this question? A hospital has 30 labor rooms, 15 combination labor and delivery rooms, 3 delivery rooms, and 1 special delivery room reserved for complicated births. All rooms operate around the clock. Time spent in labor rooms varies from hours to days, with an average 60. ## algebra 2 Solve the given system of linear inequalities by graphing: x+y>4 x-y 61. ## English 1. Is Eminem a male name or a femalee name? How do you pronounce "Eminem." 2. When you give birth to the baby, you will feel painful. 3. When you deliever the baby, you will feel painful. 4. When you are delivered of the baby, you will feel painful. (Which what is the velocity of someone running if he takes 120 seconds to run 200m 63. ## Math Use linear approximation, i.e. the tangent line, to approximate sqrt[3] { 8.4 } as follows: Let f(x) = sqrt[3] x. The equation of the tangent line to f(x) at x = 8 can be written as y=mx+c where m=1/12 b=4/3 find the approximation for sqrt[3] {8.4} 64. ## Socials-Ms. Sue Ms. Sue this is the memo: Sorry, but I had a tough time on it, I tried to come up with alot, but the ones I did, I don't think they're right. I really need your help Ms. Sue, this is pretty hard. To: Napoleon Bonaparte From: Sara, Senior Advisor Subject: 65. ## grammar Label each clause subordinate or independent. 1. If you visit the city of Chicago.subordinate 2.the Art Institute of Chicago is quite famous independent 3.While the Chicago White Sox play in Comiskey Park. subordinate 4.after the sears Tower was built 66. ## History Currently, Who is the USA president? 67. ## algebra does 13x^2+13y+8x^2 collect like terms =21x^2+13y 68. ## Algebra solve each inequality algebraically and give the answer by using interval notation. 5-9y 69. ## Scoial Studies What were the effects of The Trojan War in its time and today? Does anyone know any websties with this info? Thanks so much!:) 70. ## Algebra Why is television called a communications medium? 71. ## SCIENCE 10 EXAMPLE OF SOLUTION AND COLLOIDS 72. ## math using the commutative law the equivalent expression for k+ts would be ts +k am I right? 73. ## maths if f(x)=(x^2)(e^x) prove by induction that the nth derivative is (x^2 +2nx +n(n-1)(e^x) thanks 74. ## chemistry if you heat 15.00g of the hydrate CaSO4*2H20, and drive off the water, what is the weight of the anhydrous salt remaining? How do I go about solving this? 75. ## alison How do i find the points of inflection for: f(x)= (1/12)x^4 -2x^2 +15 The answers are (2, 25/3) and (-2, 25/3) but i don't know how to get the answers. Can someone show me step by step? 76. ## math an extremely volatile substance, Ofnetite, has a half-life of 25 minutes. Find the percentage decrease of this substance in the first two hours. 77. ## math a train left podunk and traveled west 70 km/h. two hours later, another train left podunk and traveled east at 90km/h. how many hours had the first train traveled when they were 1420 km apart? 78. ## calculus f(x)=2x+8x^-1.For this function there are four important intervals: (-infinity,A],[A,B),(B,C), and [C,infinity) where A,B and C are either critical numbers or points at which f(x) is undefined.Find A,B and C. 79. ## algerbra 1. -1+1=0? 2. 2x(-4)x(-4)x(-2)=-64 3. multiply (-16)(-10)=160? 4. determine if -6 is a soultion of the equation 3x=-18? yes -6 is the soultion? 80. ## English How are the family 81. ## History Can you please explain to me what this means. Chief Justice John Marshall, in Cherokee Nation vs. Georgia held that the court had no juisdiction, under the U.S. Constitution, to deal with this issue because the Cherokees were a domestic, dependent nation- 82. ## physics A toy car runs off the edge of a table that is 1.683 m high. The car lands 0.3309 m from the base of the table. The acceleration of gravity is 9.8 m/s2 . How long does it take for the car to fall? Answer in units of s. - What is the horizontal velocity of 83. ## science why doesn't solute added to a saturated solution dissolve 84. ## chemistry Stelco has been recently legislated to reduce total SO2 emissions from iron smelting operations. Select the most effective chemical reagent to desulfurize Stelco’s gas emissions as a strategy to minimize the environmental impact of acid rain in eastern 85. ## Texas History I need help trying to write my own declaration of independence 86. ## ACCOUNTING Deer Valley Lodge, a ski resort in the Wasatch Mountains of Utah, has plans to eventually add five new chairlifts. Suppose that one lift costs \$2 million, and preparing the slope and installing the lift costs another \$1.3 million. The lift will allow 300 87. ## chemistry Consider three one-liter flasks labeled A, B, and C filled with the gases NO, NO2, and N2O, respectively, each at STP. Which flask contains 1.0 mole of gas? 88. ## Math For a box and whisker plot, if you have an even amount of numbers which number would the mean be. 3,4,4,5,5,6,8,10,10,12,15,18 Is it 6 or 8 Thank you 89. ## Math/algebra The question is 9xy --- 15x I answered 3y --- 5 is this right? 90. ## Math By what percentage does the average price increase from 1994 to 1995? Obtain a truncated version of the graph by sliding a piece of paper over the bottom of the graph so that the bars start In the truncated graph, by what percentage does the price appear 91. ## Calculus R(x)= { ax^2, from A to B { bx+c, from B to C B is 1000 feet horizontally from A and 100 feet higher. Since the road is smooth, R'(x) is continuous. What is the value of b? 92. ## English I have to write a discursive essay on how junkfood leads to obesity and my views about eating well and keeping fit. i just need a few hints about how i should start. 93. ## chemistry A gaseous mixture of and contains 35.8 nitrogen by mass. What is the partial pressure of oxygen in the mixture if the total pressure is 565 ? 94. ## Math What is the difference between the range and the interquartile range? I can't find a difference 95. ## Math Use a centimeter ruler and separate sheet of paper to draw am 8 cm. by 6 cm. rectangle. List its perimeter on the table below. Then cut out the rectangle and also cut along the diagonal as shown below in the picture. Use the your two pieces to create 4 new 96. ## CMC220 how each new medium affected news content and delivery, including how people engaged with news and how the media that preceded it adapted their content and delivery. Be sure to discuss newspapers, magazines, radio, TV, and satellite and Internet services. 97. ## Calc A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 59 cells. (The tolerance is 1% unless your 98. ## Calculus A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 1.5 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building? 99. ## Math can you please check my answers evaluate (-5a)^2 and -5a^2 when a =5 625 for both 1-12.64=-11.64 (-14)/(-7)=2 using multiplying by 1to find an expression equvialnt to 18/19 with a denomanator of 171z?dont simplfy type a fraction one day the temperture 100. ## math a nutrition center sells two types of health foods to mountain-climbing teams, Trailblazer Mix and Frontier Mix. Each package of the Trailblazer Mix sells for \$9.75. Each package of the Frontier Mix sells for \$9.50. The center wishes to maximize its 101. ## chemistry A gaseous mixture of O2 and N2 contains 35.8% nitrogen by mass. What is the partial pressure of oxygen in the mixture if the total pressure is 565 mmHg? I want to send path help an actual photo I took that's attached onto the e-mail. I can't do that on that website. Is there another website where I can e-mail a teacher a photo? 103. ## Algebra Consider the algebraic expression E=(2x+y) (5a-b)^3 104. ## economics apples cost £2 and pears cost £4. For John the marginal Utility (MU) of the last apple consumed was 4 and MU of pears was 12. For Paul MU of last apple was 3 and MU of last pear was 6. Which person is not maximising utility and how can you tell? What 105. ## antiderivatives find the equation of f(x) f''(x)= 2 + x^3 + x^6 106. ## Math determine weather 10 is the solution of the equation x+10=36 is 10 the solution no use multiplcation principle 10x=-90 -9 3[7-9{6-2)]= -87 find -x when x=-62/83*= 62/83 107. ## physics A ball is thrown from the top of a building upward at an angle of 66 ◦ to the horizontal and with an initial speed of 16 m/s. The ball is thrown at a height of 53 m above the ground and hits the ground 33.2074 m from the base of the building. The 108. ## checking answers 4 algerbra 1. What percent of 120 is 48? 57.6%? 2. collect like terms. 17T + T + 15/13T= 249/13T? 3. solve using the principles together. 3x-6=12 i am solving for x=6? 4. solve using the addition principle. -37+n=19 i am solving for n= -18? 5. solve using the 109. ## science8 intergeted what is lubricant and orbital motion 110. ## definition what word is similar to the definition "to make significant" or "to make unique" ? 111. ## social studies How are the counties of Santa Rose and Escambia the same? 112. ## Algebra Consider the algebraic expression E=(2x+y) (5a-b)^3 113. ## Grammar What's wrong with the following sentence? He was in trouble for acting like a tomfoolery. 114. ## Economics/Math Airline pricing is a good example of price discrimination. Airlines set different prices for first-class and excursion. Suppose the economics division of a major airline company estimates the demand and marginal revenue functions for first-class and 115. ## algerbra 1. use a commutative law to find an equivlant expression f+sr? sr+f? 2. determine which real number corresponds to the situation. The record high tempature for a date is 97.8 above zero. The cooresponding number for this sentence is 97.8? 3.Translate to an 116. ## algebra solve the inequality (x-3)/10 >_ (greater or equal to) (x-2)/3 how would you do this? I don't understand how to do the fractions 117. ## geometry A large, circular building has a diameter of 126 feet. Correct to the nearest whole foot, what is the circumference of the building? 118. ## antiderivates find f(x) f'(x) = (x^2-1)/x^(-1) 119. ## health care I am doing a essay and am haivng a hard time finding in goggle search just when computerized pharmacy came about. Any Idea were to go for this? 120. ## geometry A large, irrigated crop circle is 600 meters in radius. Correct to the nearest tenth of a hectare, how many hectares of land are contained in this circle. 121. ## social studies what are coordinates for the point marked j 122. ## Accounts on july 25 Hamilton company accountatn prepared a check for august rent. the landlord received the check on the 31 of july and cashes iton the 2 of august. when should the rent transaction be recorded 123. ## geometry A football field is 130 yards long and 70 yards wide. If sod costs \$0.80 per square foot to lay, how much will the owners have to pay for sodding the entire field? 124. ## geometry A propane tank is in the form of a cylinder with two half-spheres, one on each end. The radius of the cylinder is the same as the radius of each half-sphere. What is the volume of a propane tank of cylindrical length 12 ft and radius 5 ft, correct to the 125. ## visual I can't seem to describe the placement of my objects in my stilllife arrangement. The objects are placed at an angle, which is almost horizontal. Does it relate to the principles of art? 126. ## calculus 1 pt) Find the length of the curve defined by y=1/8(x^2−8ln(x)) from x=3 to x=5 127. ## geometry A rectangular trench is to be dug which is to be 240 ft long, 90 ft wide and 9 ft deep. A large dump truck can carry 20 cubic yards in a load. How many truck loads will be required to remove the dirt from this trench? 128. ## geometry Using 3.14 for p, find the volume, correct to two decimal places, of a sphere which is 4.5 ft in radius. 129. ## geometry Using 3.14 for p, find the volume, correct to two decimal places, of a cylinder which is 4 ft in radius and 10 ft high. 130. ## geometry Using 3.14 for p, find the volume, correct to two decimal places, of a cone which is 4 ft in radius and 24 ft high. 131. ## Algebra I have to find the vertex, axis of symmetry, and x intercepts of x^2-x+(5/4). I put it in standard form as -(x+-.5)^2+1.5. Thus, the vertex would be .5, 1.5. But the book's answer is 1/2, 1. How did they get this? 132. ## geometry Which of the following angles is the supplement of 132o ? 133. ## geometry The measures of two of the angles of a triangle are 47o and 51o. Then the measure of the third angle of the triangle is 134. ## physics Judy, by chance, spots a potted plant falling outside the window at 3.84 m/s . Further down the same building, Judy boyfriend clocks the pot at 61 m/s .The acceleration of gravity is 9.8 m/s2 .How far apart are the friends? Answer in units of m. 135. ## geometry If the lengths of two sides of a right triangle are 33 ft and 56 ft, then the length of the hypotenuse must be 136. ## calculus find f(x) f'(x) = (x^2-1)/x^(-1) 137. ## geometry If the length of the hypotenuse of a right triangle is 65 cm and the length of one side is 56 cm, then the length of the other side must be 138. ## geometry A piece of property is in the form of a right triangle with sides which are 300 meters and 1200 meters in length. What is the area of this triangle in hectares, correct to the nearest whole hectare? 139. ## geometry If there are 7.5 gallons to the cubic foot, and a spherical storage tank has a radius of 19.5 ft, then using 3.14159 for p ,how many gallons, correct to the nearest whole gallon, will the full storage tank hold? 140. ## Accounting Information related to Hermesch Company for 2010 is summarized below. 141. ## geometry A trapezoid has a lower base which is twice as long as its parallel upper base. The upper base is 21 cm long. One non-parallel side is 20 cm long and the other non-parallel side is 6 cm longer than the shorter non-parallel side. What is the perimeter of 142. ## Algebra 27-f(x)=1/4x^2-2x-12. Can you show me how to find the vertex and x intercepts, step-by-step? I tried to put it in standard form, with (1/2x-1)^2-13, but my book said that's not the answer. Thanks! 143. ## geometry If there are 7.5 gallons to the cubic foot, and a cylindrical storage tank has a radius of 21 ft and an altitude of 28 ft, then using 3.14159 for p ,how many gallons, correct to the nearest whole gallon, will the full storage tank hold? 144. ## science need to write 5 liquid and 5 solids for grade 2 145. ## Algebra When using -b/2a with functions, should I ignore the negative, figure out b/2a and then put a negative around it? Or should I turn 2a into -2a? Or should I go -b/-2(-a)? Thanks for clearing this up!!! 146. ## history Garlic- To where did this food product spread from its point of origin? Be sure to include time periods. HELP!! I CANT FIND ANYWHERE 147. ## English Why is Babylon Revisited called that if it takes place in Paris? 148. ## physics A 150 kg crate, starting from rest, is pulled across a floor with a constant horizontal force of 420 N. For the first 21 m the floor is frictionless, and for the next 21 m the coefficient of friction is 0.30. What is the final speed of the crate? 149. ## algebra The tep[erture drpped from -4degree f to -12 degrees f how many degrees did it drop -8 degrees? 150. ## Math determine weather 10 is the solution of the equation x+10=36 is 10 the solution no use multiplcation principle 10x=-90 -9 3[7-9{6-2)]= -87 find -x when x=-62/83*= 62/83 151. ## Math can you please check my answers evaluate (-5a)^2 and -5a^2 when a =5 625 for both 1-12.64=-11.64 (-14)/(-7)=2 using multiplying by 1to find an expression equvialnt to 18/19 with a denomanator of 171z?dont simplfy type a fraction one day the temperture 152. ## visual How do the principles of movement and harmony relate to the placement of my objects in my still life? 153. ## Math -2/13/(-3/13)=undefined 4(x-6)+2=6(x+2)-6= -14 7x+9x=96 x=6 154. ## Trigonometry What is the arcsin of (pi/2)? 155. ## geometry What's another way to write 8 3/4? 156. ## Math Prove that cos2x=(1-tan^2x)/(1+tan^2x) I can't find any identities that can help me with this. I'm really confused 157. ## checking answers 4 algerbra 1. use a commutative law to find an equivlant expression f+sr? sr+f? 2. determine which real number corresponds to the situation. The record high tempature for a date is 97.8 above zero. The cooresponding number for this sentence is 97.8? 3.Translate to an 158. ## Algebra How come there are no x intercepts for x^2-x+(5/4)? Can you show me why, please? 159. ## chemistry a pure compound is put in a polarimeter and the optical activity is measured to be 0 º. what do you know about the compound? 160. ## chemistry a pure compound is put in a polarimeter and the optical activity is measured to be 0 º. what do you know about the compound? 161. ## spelling 6.To make a hole in something/You do this. 162. ## thca 230 what types of reform effort is being implented to improve caregivers socialization skills 163. ## art Am I right with this statement? "The way the shadows created by the coat hangers look very realistic is part of the design quality of my still-life composition." 164. ## science what is orbital motion and lubricant 165. ## algebra solve the compund inequality. 6>-4x+5 or 7≤-2x+4 166. ## health care are health care companies and medical companies the same? 167. ## Science Explain why air as the incident medium allows us to find the unknown indexx of refraction of the medium. (If the incident medium is NOT air, nR will be impossible to determine) 168. ## CHN WHAT DOES CHN STAND FOR? 169. ## Science Compare the angle of refraction with the angle of incidence for all angle of incidences greatter than 0 degrees. what relationships do you notice between the angle of incidence and the angle of refraction? explain why you expect this relationship to be 170. ## Socials-Ms. Sue To: Napoleon Bonaparte From: Sara, Senior Advisor Subject: Continental System 1. Advantage for Britain: None Disadvantages for Britain: Loses money because of trade embargo from Europe *will not be able to trade with other countries *Won't be in debt 171. ## Math for educators Help please! What is the domain and range for the following numbers 2.68, 2.58, 2.38? Thank you The manufacturer of a propeller for a small aircraft mandates a maximum operating angular velocity of 300 rad/s. Determine whether it is safe to install this propeller on an aircraft whose engine is expected to run at a maximum of 2800 rpm. 173. ## science what do you notice about the ratio (sin θi/ sin θR) for all angle of incidences greater than 0 degrees? explain why you would expect this to be true? 174. ## ELA what could you say if you want to give a little intro about the book 175. ## hhs265 The following two financial statements—a statement of activities (profit and loss summary) and a statement of financial position (balance sheet)—are for the Council on Social Work Education for fiscal year 1998. (See Tables 5.3 and 5.4.) Review these 176. ## maths of 50 students, 40 are in the football team and 30are in the cricket team. how many are in both if six do not play either. 177. ## science Explain why the index of refraction of an object is a physical property? 178. ## checking answers 4 algerbra 1. What percent of 120 is 48? 57.6%? 2. collect like terms. 17T + T + 15/13T= 249/13T? 3. solve using the principles together. 3x-6=12 i am solving for x=6? 4. solve using the addition principle. -37+n=19 i am solving for n= -18? 5. solve using the 179. ## spelling 5.you might get one if you return a valuable lost item 180. ## visual do you have an e-mail account bobpursley, so that i can e-mail you a picture of my art? It's a good idea. I'll send it to you. 181. ## Math -2/13/(-3/13)=undefined 4(x-6)+2=6(x+2)-6= -14 7x+9x=96 x=6 Well, then what's the best homework website for tutors who work via e-mail, so that they can take a look at my art and help me? 183. ## Math can you please check my answers evaluate (-5a)^2 and -5a^2 when a =5 625 for both 1-12.64=-11.64 (-14)/(-7)=2 using multiplying by 1to find an expression equvialnt to 18/19 with a denomanator of 171z?dont simplfy type a fraction one day the temperture 184. ## visual What does the art term expressiveness mean? 185. ## physics A car is parked near a cliff overlooking the ocean on an incline that makes an angle of 29.1◦ with the horizontal. The negligent driver leaves the car in neutral, and the emergency brakes are defective. The car rolls from rest down the incline and has a 186. ## Math determine weather 10 is the solution of the equation x+10=36 is 10 the solution no use multiplcation principle 10x=-90 -9 3[7-9{6-2)]= -87 find -x when x=-62/83*= 62/83 187. ## ALGEBRA 1 A Would someone check my answer please? Thank you. A bank offer two checking plans. the anywhere plan charges 30 cent per check, the accucheck plan cost \$0.64 a month, plus 22cent per check, for what number of checks will the accucheck plan cost less than 188. ## trigonometry What is the exact value for sin5pi / 12 ? 189. ## calculus f'(x) = (x^2-1)/x does anyone have an e-mail account, so that i can e-mail a picture of my art? 191. ## English 1. You have smelled my cakes. 2. I haven't stolen your cakes. (What does each present perfect tense mean? Does each mean 'experience' or 'result' or 'accomplishment'?) 192. ## math On his 10th birthday, Tom's allowance was doubled. When he turned 12, his allowance increased by \$10 to \$34 per month. What was Tom's allowance before his tenth birthday? 193. ## algebra does y=11-x ,for x makje x=y+11? -8-14=6 7.4=x-13 answer 6.1 m/m for m =72 and n =9 m/n=72/9=8 -4x+7=39 4x/4x=32/4x 4/32=x8 -10 is greater than -18 -4*(-9)= 36 194. ## Math BLIND BATS AT HALLOWEEN There were number of bats in a cave. Two bats can see out of right eye, Three bats can see out of left eye, Four can't see out of left eye, and Five can't see out of right eye. What is the least number of bats in the cave & what 195. ## English In the sentence below, I'm confused about the word 'about'. I'm not sure whether it's a preposition or an adverb. The theater seats 'about' four thousand people. 196. ## chemistry The following redox reaction occurs in basic aqueous solution. When balanced with the smallest whole number coefficients, what is the coefficient for OH-(aq)? Mn(OH)2(s) + MnO4-(aq) = MnO42-(aq). 1. ) 2 2. ) 3 3. ) 4 4. ) 6 5. ) 8 the answer i got was 197. ## Lord Of The Flies- English What is implied at the end of the novel? Is this truly a happy ending? 198. ## chemistry What is formed at the anode and cathode when the following solutions are electrolysed? sodium iodide copper II chloride sodium sulphate NaOH HCl magnesium nitrate also is this true: if the metal in the compound is higher in the reactivity series than 199. ## nuclear projects what are nuclear projects? 200. ## english i need a really quick summary of chapter 2 in lord of the flies. 201. ## social studies What could I write in an editirial from 1773 about the Tea Act and the Boston Tea Party? 202. ## physics Janet jumps off a high diving platform with a horizontal velocity of 2.22 m/s and lands in the water 1.5 s later. The acceleration of gravity is 9.8 m/s2 . a) How high is the platform? Answer in units of m. 203. ## chemistry What is formed at the anode and cathode when the following solutions are electrolysed? sodium iodide copper II chloride sodium sulphate NaOH HCl magnesium nitrate also is this true: if the metal in the compound is higher in the reactivity series than 204. ## math A bacteria culture starts with 260 bacteria and grows at a rate proportional to its size. After 4 hours there will be 1040 bacteria. (a) Express the population after t hours as a function of t. this is what i put as my answer but i guess its not right do i 205. ## math sorry people i have to post this what happened to my psp 2000? what should i do? okay my little cousin threw my psp at the wall then the battery fell out then i put it back in then it wont turn on. what do i do 206. ## American History Why did the Pilgrims not encounter much Native American resistance upon settling in Plymouth? Is it because of the harsh winter, and the fact that many of the Pilgrims died on the trip? Thanks, Ashley 207. ## algebra The problem I have is (-14)/(-7) divide if possible or n if undefined -2 -9.5+(3.8)=36.1 208. ## algebra Marcella and Rupert bought party stuff. Marcella bought 3 packs of ballooons and 4 packs of favors for a total of \$14.63. Rupert bought 2 packs of balloons and 5 packs of favors for a total or \$16.03. Find the price of each and write a system of equations 209. ## Math Directions: Write an expression for each of the following. Use n for the unknown number Questions: four less than a number a number increased by the same number I am confused, thanks! 210. ## American History How were the slaves brought to America? I think the slave were brought to America by boat from Africa, is this correct? 211. ## Math Thanks Ms. Sue, that's what I thought but I was not sure. 212. ## Physics An airplane traveling 1001 m above the ocean at 125 km/h is going to drop a box of supplies to shipwrecked victims above. a. How many seconds before the plane is directly overhead should the box be dropped? b. What is the horizontal distance between the 213. ## Physics You row a boat, perpendicular to the shore of a river that flows at 3.0 m/s. The velocity of your boat is 4.0 m/s relative to the water. a. What is the velocity of your boat relative to the shore? b. What is the component of your velocity parallel to the 214. ## Organic Chemistry Would it be possible to separate hexane (b.p. 68.95 degrees Celsius) from toluene (b.p. 110.6 degrees Celsius) by simple distillation? 215. ## Math Are these correct? two more than a number and four = 2 + n + 4 ten more than a number plus 3 = n + 10 + 3 three increased by a number minus 5 = n + 3 - 5 six and a number decreased by 7 = n+6-7 216. ## algebra The problem I have is (-14)/(-7) divide if possible or n if undefined -2 -9.5+(3.8)=36.1 217. ## math solve the linear equation -10.8x + 1.4 = -47.6 - 1.0x 218. ## Math does y=11-x ,for x makje x=y+11? -8-14=6 7.4=x-13 answer 6.1 m/m for m =72 and n =9 m/n=72/9=8 -4x+7=39 4x/4x=32/4x 4/32=x8 -10 is greater than -18 -4*(-9)= 36 219. ## Travel and Tourism I'm going to New York City for a school trip next April. Do you think that when you're in NYC, you'll hear the songs, "Empire State of Mind" and "New York, New York" very often? Empire State of Mind is a really good song to hear, especially when you're in 220. ## Maths Determine the exact expression for the following. - cos(pi/4)=(x/60) I got x=60/√2 Is that correct? Also, I had a lot of trouble with this one: cos(pi/6)=(z/60) I got z=(√3 (60/√2))/2 That doesn't seem right, but I don'r know what I', doing wrong. 221. ## Ms. Sue Thanks so much for your help MS. Sue 222. ## math Put into slope intercept form: (2,5) m=3 I have a quiz tomorow, and i need to make sure im doing the steps right, so then do you do..: ? 2=15+b -13=b y=3x-13 ??? 223. ## American history What parts did the government consist of in the colonies? Who could vote? Does this pertain to the Parlimentary rule? And that only male, land owners were permitted to vote in the colonies? 224. ## grammar Tell if the sentences, are phrase write phrase if it is a clause, write independent or subordinate. 9 Before settlers arrived .(phrase) 10 In 1794 .(phrase) 11 When it became a city .(subordinate) 12 Chicago had its first railroad.(independent) 13 Before 225. ## earth science Describe the change in duration of insolation from the Equator to the North Pole A) In the winter b) In the summer c) on the Equinox 226. ## earth science Describe the change in duration of insolation from the Equator to the North Pole A) In the winter b) In the summer c) on the Equinox 227. ## checking answers 4 algerbra 1. use a commutative law to find an equivlant expression f+sr? sr+f? 2. determine which real number corresponds to the situation. The record high tempature for a date is 97.8 above zero. The cooresponding number for this sentence is 97.8? 3.Translate to an 228. ## macroecon If the MPC equals.7 and the MPI equals .1 then the varible net export spending multiplier equals? 229. ## math I was given a problem 9x --- 15x I was told to simplify, I got 3y -- 5 I was told that was wrong. Is it and why? x2/3=125 231. ## Math Thanks Ms. Sue! 232. ## science what is the system of grouping things based on properties? 233. ## childhood By providing shelves low enough for children to select materials, you encourage the development of A Social skills B solitary play C Cleanliness D Independence I believe that A is the correct answer Which of these factors is most likely to determine the 235. ## Math does y=11-x ,for x makje x=y+11? 236. ## grammar/Ms Sue 14 during the great fire (independent 15 After industries were rebuilt(subordinate 237. ## 9th Chemistry Why is there a big space in the periodic table between the 2nd & 3rd periods? The activity of the electrons is related somehow. Show that tanx = sinx / cosx can be written as tan(x+y) = (tanx + tany) / (1 - tanxtany) 239. ## chemistry when water is added to anhydrous copper (II) sulfate, what can be observed? pentahydrate forms and it turns blue is that correct? 240. ## college algebra rectangular region of lenght x and width y has an area of 520 square meters. write the width y as a function of x 241. ## Physic What are the three longest wavelengths for standing sound waves in a 124-cm-long tube that is (a) open at both ends and (b) open at one end, closed at the other? 242. ## history In the movie 'Matewan', who wrote the letter to the company? also, who is telling the story in the movie? 243. ## algebra does x/8=-6 =x=-48? 244. ## Grammar and Composition I have to write a speech and record it on a tape. Pet Peeve Speec You will create a "Pet Peeve" Speech. A "Pet Peeve" is one of those little every day occurrences that bugs you, upsets you, or frustrates you. You will use the extemporaneous delivery for 245. ## language arts I am writing an essay for l.a and was wondering what a conclusion needs to have. 246. ## Social Studies What did the Confederation Congress do to strenghten the United States ? 247. ## social studies Which document or institution do you think had the greatest influence on the development of the United States? Why? 248. ## Bus 210 write a 200-300 word scenario that depicts joint-stcok company, limited liability company, partnership,sole proprietorship 249. ## algerbra 42 more than n? 250. ## social studies what was the general attitude of foreign nations toward the new government of the United States? why? 251. ## social studies Of the problems experienced by the Confederation Congress, which do you think was the most harmful? why? 252. ## math Use the discriminant to determine how many real-number solutions the equation has. v^2 - 7v + 5 = 0 253. ## Family life Can you name a short-term health goal 254. ## Algebra I have to find the standard form of a quadratic function with the vertex of -1,4 and x intercepts of -3,0 and 1,0. What do I do when I have two x intercepts like this? 255. ## social studies In what ways did the Constitution strenghthen the central government? 256. ## algerbra Multiply (-16)(-10)? Would it be -26? 257. ## Math does y=11-x ,for x makje x=y+11? 258. ## Economics/Math The demand curve for a monopolist is Qd = 500 - P and the marginal revenue function is MR = 500 - 2P. The monoploist has a constant marginal and average total cost of \$50 per unit. a. Find the monopolist's profit maximizing output and price b.Calculate the 259. ## Chemistry How do you know if a molecule is polar? Would CH2Cl2 be polar or non-polar? 260. ## chemistry calculate percent water in the following hydrates BaCl2*2H20 14.7%? CaCo3*6H20 51.9% Correct? 261. ## algebra does x/8=-6 =x=-48? 262. ## Chemistry given a 10.0g sample of MgCO3*5H2O, what weight of anhydrous magnesium carbonate can be obtained after driving off the water? 48.4%? I wasn't sure how to go about finding the answer to this.. 263. ## social studies How did the two compromises reached during the Constitutional Convention satisfy competing groups? 264. ## Chemistry a student found the percent water in CaCl2*6H2O to be 45.5%. What's the experimental error? Is it 7.7%? 265. ## social studies were there any weaknesses in the Constitution? Explain. 266. ## algebra -(d-45) would that be d+45 267. ## Chemistry A student recorded the following data for copper sulfate pentahydrate. Weight of crucible and cover (after heating to constant weight), 28.120g Weight of covered crucible plus sample, 31.020g Weight of covered crucible plus sample after heating to constant 268. ## algerbra 1. -1+1=0? 2. 2x(-4)x(-4)x(-2)=-8 or 64 on this one i am not sure if i multiply the absolute value or multiply as is 269. ## Family life How to set up a short-term health goal. 270. ## social studies Why were some Americans opposed to the Constitution? What is the decision facing amazon (the website) and what factors are important in understanding this decision situation? 272. ## Literature I had to write an essay analyzing a short story. I wrote about The Birds: Daphne du Maurier’s short story The Birds is a story of an old war veteran, his family, and how they battle fierce birds. It starts out on the third of December on the Cornish 273. ## Family Life how to create a step-by-step action plan. solve a perfect square trinomial equation. (4x+1)(x+4)=49 275. ## Vista Laptop Help Okay so I'd do this myself but I only have a desktop with Windows Vista and not a laptop so if anyone with a laptop that has Vista on it could please help me: 1. Open Windows Mobility Center and then mute the speakers. 2. Change the plan settings for the 276. ## Calculus The circumference of a sphere was measured to be 74.000 cm with a possible error of 0.50000 cm. Use linear approximation to estimate the maximum error in the calculated surface area? Also Estimate the relative error in the calculated surface area. 277. ## math In math what comes after Tera. 278. ## Algebra 2 Solve By graphing 2x+y=2 2x+y=6 279. ## trig How do I find the "exact value" for the arcsin of -pi/3 radians? 280. ## algebra 2 Solve by graphing 3x+y=15 3x+y=6 281. ## family life One more thing Can you give me an example of a goal . Thanks. 282. ## algebra 2 Solve the system by graphing 2x+y=4 2x+y=2 283. ## Grammar and Composition ok, now that i have my pet peeve, i have to fill out this sheet. (please read my earlier post for more info on the assignment) Pet Peeve--Organizational Sheet Audience: Who will be your audience? You must indicate an audience that your delivery is geared

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ads/auto.txt Definition Of Density Height • adidasshoesoutletwholesale.com The delta image signifies a change in a given variable. ρ m v. Stats4stem ### Which one if both is appropriate. Definition of density peak. Subsequently density will even lower exponentially with peak from a sea degree worth of ρ 0 roughly equal to 12 kg m 3. Pascals Regulation explicitly determines the stress distinction between two completely different heights or depths inside a static liquid. And this one proper over right here discover as a substitute of the peak being 4 for 4 knowledge factors its now 25. P is stress ρ is density g is acceleration of gravity and. It may be measured in a number of methods. The gauge stress at a given depth relies upon solely upon the density of the liquid the acceleration of gravity and the gap under the floor of the liquid. A John is appropriate however Linda is unsuitable. Density is the mass per unit quantity. At heights over 100 km an environment might now not be properly combined. A lifelong lack of calcium performs a job within the improvement of osteoporosis. John and Linda are arguing in regards to the definition of density. John says the density of an object is proportional to its mass. Low calcium consumption contributes to diminished bone density early bone loss and an elevated threat of fractures. The place p 1 is the exterior utilized stress ρ is the density of the fluid Δh is the distinction in peak of the static liquid and g is the acceleration attributable to gravity. C They’re each unsuitable. The quantity {that a} factor weighs. Going upward from the floor it’s the level the place air ceases to chill with peak and turns into virtually fully dry. The SI unit of density is kilogram per cubic meter kgm 3. Following is the precise definition utilized by the World Meteorological Group. This definition based mostly on constructing densities is in keeping with the idea of city economics and implies that town border is. D P d h ρ g displaystyle frac dP dh-rho g and. DH PH 13000 10x 120 13000 1200 14200. For every 1 o C in extra of ISA at a given stress peak the density peak shall be roughly 120 ft greater than the stress peak. The peak of an object or construction above a reference degree normally above sea degree or the Earths floor. 216 is eighteen which is 125. In keeping with the Worldwide Commonplace Ambiance ISA the density of dry air is 1225 kgm³ or 00765 lbft³. The Worldwide Union of Pure and Utilized Chemistry IUPAC defines the air density in a different way. As a result of two of the 16 knowledge factors fall into this class. Decide the density peak at stress peak 13000 ft Flight Degree 130 ISA 10. Density is said to stress by the best fuel legal guidelines. The usual or established quantity {that a} factor ought to weigh. Enter the precise station stress not the altimeter setting and select a unit. The density altitude is the altitude relative to straightforward atmospheric situations at which the air density could be equal to the indicated air density on the place of commentary. It is usually regularly represented within the cgs unit of grams per cubic centimeter gcm 3. Density Altitude in meters. A extra common definition of metropolis boundaries is that town ends the place the agricultural space begins which will be recognized by the imaginary line at which the constructing density decreases to a degree frequent in rural areas. B John is unsuitable however Linda is appropriate. Severely proscribing meals consumption and being underweight weakens bone in each women and men. Poundage required to be carried by a horse in a handicap race. If the fluid density is ρ gmcm 3 kgm 3 and the column peak is h m x 10 m h ft then the stress distinction is ΔP kPa ΔP lbin 2 ΔP mmHg inches Hg ΔP atmos ΔP inches water cm water. However in that first class as a substitute of the bar peak being two the bar peak is now 125. Density Altitude in toes. One of many courses into which contestants in a sports activities occasion are divided based on physique weight. In of mercury mm of mercury millibars hPA m. Enter the dewpoint and select a unit. At commonplace temperature and stress STP the worth for the air density relies on the usual you utilize. R rho is the density of the fluid g is the acceleration of gravity h is the peak of the fluid above the thing The stress because of the liquid alone ie. So discover that is representing the identical knowledge. To calculate the density normally represented by the Greek letter ρ of an object take the mass m and divide by the quantity v. Then every chemical species has its personal scale peak. The equation is as follows. Probably the most correct option to calculate the density of any strong liquid or fuel is to divide its mass in kilograms by its quantity. Extra formally the tropopause is the area of the ambiance the place the environmental lapse charge adjustments from constructive because it behaves within the troposphere to the stratospheric damaging one. In different phrases the density altitude is the air density given as a peak above imply sea levelThe density altitude will also be thought of to be the stress altitude adjusted for a non-standard temperature. Linda says the objects mass is proportional to its density and to its quantity. What Is Density Altitude Aviation Stack Change Drive And Movement Science Domino Overview Exercise This Interactive And Partaking Exercise Focuses On Vital Voc Drive And Movement Science Center College Science Density Method Models Study How To Measure The Density Of A Stable And Liquid The Unit What Is Meant Physics Gayle Responsive Electronic mail Template Responsive Electronic mail Template Responsive Electronic mail Electronic mail Templates Does Density Altitude Have an effect on Precise Altitude Aviation Stack Change Air Altitude Density And Particular Quantity Pace Of Sound Lab Ap Physics Physics Pace Of Sound The Innovation Of Tv Additionally Led To Extra Improved Know-how In 1981 Nhk Japan Broadcasting Company Engineers Demons Digital Cinema Television Gives Hdtv Pin By Cindy Schortgen Cody On High Instructing Math Science Anchor Charts Quantity Math Instructing Math Change In The Ambiance With Altitude Ucar Heart For Science Training Density Is A Measure Used By Physics And Chemistry To Decide The Quantity Of Mass Contained In A Given Vol Calculating Density Density Measurement Conversions Calculating Strain And Density Peak Chapter 11 Click on On The Picture To View The Excessive Definition Model Create Infographics At Http Venngage Com How To Create Infographics Human Sources Free Infographic Customized Photograph Wallpaper 3d Stereo Underwater World Of Marine Fish Dwelling Kids S Room Television Background 3d Mural Giant Wall Murals Mural Wallpaper Trendy Mural Sizzling And Excessive Wikipedia Density For Children Data Examples Definition Method Density Instructor Life Science For Children Pin On Lolo The Tallest Buildings In The World Constructing Structure Structure Scholar

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# X−4 (3 − 4x−5) - Mathematics x4 (3 − 4x−5) #### Solution $\text{ Let } u = x^{- 4} ; v = 3 - 4 x^{- 5}$ $\text{ Then }, u' = - 4 x^{- 5} ; v' = 20 x^{- 6}$ $\text{ Using the product rule }:$ $\frac{d}{dx}\left( uv \right) = uv' + vu'$ $\frac{d}{dx}\left[ x^{- 4} \left( 3 - 4 x^{- 5} \right) \right] = x^{- 4} \left( 20 x^{- 6} \right) + \left( 3 - 4 x^{- 5} \right)\left( - 4 x^{- 5} \right)$ $= 20 x^{- 10} - 12 x^{- 5} + 16 x^{- 10}$ $= - 12 x^{- 5} + 36 x^{- 10}$ Concept: The Concept of Derivative - Algebra of Derivative of Functions Is there an error in this question or solution? #### APPEARS IN RD Sharma Class 11 Mathematics Textbook Chapter 30 Derivatives Exercise 30.4 | Q 23 | Page 39

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Cody # Problem 933. Ordinal numbers Solution 263463 Submitted on 19 Jun 2013 by Dan This solution is locked. To view this solution, you need to provide a solution of the same size or smaller. ### Test Suite Test Status Code Input and Output 1   Pass %% assert(isequal(ord(1),'1st')) ``` ans = 1st ``` 2   Pass %% assert(isequal(ord(2),'2nd')) ``` ans = 2nd ``` 3   Pass %% assert(isequal(ord(3),'3rd')) ``` ans = 3rd ``` 4   Pass %% assert(isequal(ord(4),'4th')) ``` ans = 4th ``` 5   Pass %% assert(isequal(ord(5),'5th')) ``` ans = 5th ``` 6   Pass %% assert(isequal(ord(10),'10th')) ``` ans = 10th ``` 7   Pass %% assert(isequal(ord(11),'11th')) ``` ans = 11th ``` 8   Pass %% assert(isequal(ord(12),'12th')) ``` ans = 12th ``` 9   Pass %% assert(isequal(ord(13),'13th')) ``` ans = 13th ``` 10   Pass %% assert(isequal(ord(14),'14th')) ``` ans = 14th ``` 11   Pass %% assert(isequal(ord(15),'15th')) ``` ans = 15th ``` 12   Pass %% assert(isequal(ord(82),'82nd')) ``` ans = 82nd ``` 13   Pass %% assert(isequal(ord(126),'126th')) ``` ans = 126th ``` 14   Pass %% assert(isequal(ord(911),'911th')) ``` ans = 911th ``` 15   Pass %% assert(isequal(ord(2012),'2012th')) ``` ans = 2012th ``` 16   Pass %% assert(isequal(ord(4077),'4077th')) ``` ans = 4077th ``` 17   Pass %% assert(isequal(ord(0),'0th')) ``` ans = 0th ``` 18   Pass %% assert(isequal(ord(-101),'-101st')) ``` ans = -101st ```

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henryforever14 Reputation 676 Top tag Next privilege 1,000 Rep. Create tags Feb11 accepted Approximate continuous mapping by smooth mappings on manifold(Bott, Tu book) Feb10 comment Approximate continuous mapping by smooth mappings on manifold(Bott, Tu book) I've actually been looking at this proof at a more careful level. And I realized Tubular Neighborhood and Retraction are exactly the tools that Lee used to solve the question I have. I guess I will choose @Potato as the best answer if nobody gives a better answer in the following couple of days! Thanks man, @Potato! Feb9 comment Approximate continuous mapping by smooth mappings on manifold(Bott, Tu book) I saw this proof before. But since I am not aware of Whitney approximation theorem or the smooth retraction mentioned in the proof, I skipped it. Bott, Tu's book's proof requires less background knowledge. But as I explained, I found I can't get around that point. I still wish that someone might be able to tell me how it is possible. Feb9 asked Approximate continuous mapping by smooth mappings on manifold(Bott, Tu book) Nov20 awarded Critic Nov20 awarded Supporter Nov15 accepted Confused at the definition for integration of differential form over manifold Nov14 asked Confused at the definition for integration of differential form over manifold Nov13 comment How to prove this formula for Lie derivative for differential forms @FlybyNight I believe $\phi_t$ in my notation is the $f$ in your notation. And $\phi_t^* w$, viewed as a whole thing, is exactly the $w^*$ in your notation. $\phi_t^*$ is the mapping that takes $w$ to $w^*$. But never mind, I know how to prove this thing now. It's only a simple computation once you know what all those mappings really are. Thanks anyway. Nov13 revised How to prove this formula for Lie derivative for differential forms edited body Nov13 comment How to prove this formula for Lie derivative for differential forms @FlybyNight huh? $w$ here is a differential form. Nov12 asked How to prove this formula for Lie derivative for differential forms Sep26 accepted How do I see that the tangent bundle of torus is trivial Sep26 comment How do I see that the tangent bundle of torus is trivial Thanks, @Neal, for providing so many ways of seeing it Sep26 comment How do I see that the tangent bundle of torus is trivial @RyanBudney Thanks! I guess that's one way of doing it. Sep26 comment How do I see that the tangent bundle of torus is trivial what do you mean by taking one vector field in the direction of each "factor"? Sep26 asked How do I see that the tangent bundle of torus is trivial Sep10 accepted How to show the height function of a torus has 4 critical points Sep10 comment How to show the height function of a torus has 4 critical points Thank you. I wasn't aware of this form before. Sep10 comment How to show the height function of a torus has 4 critical points Thanks, @t.b.! I will take a look.

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# 1-dimensional hard rods Hard Rods, 1-dimensional system with hard sphere interactions. The statistical mechanics of this system can be solved exactly (see Ref. 1). ## Canonical Ensemble: Configuration Integral Consider a system of length $\left. L \right.$ defined in the range $\left[ 0, L \right]$. Our aim is to compute the partition function of a system of $\left. N \right.$ hard rods of length $\left. \sigma \right.$. Model: • External Potential; the whole length of the rod must be inside the range: $V_{0}(x_i) = \left\{ \begin{array}{lll} 0 & ; & \sigma/2 < x < L - \sigma/2 \\ \infty &; & elsewhere. \end{array} \right.$ • Pair Potential: $V (x_i,x_j) = \left\{ \begin{array}{lll} 0 & ; & |x_i-x_j| > \sigma \\ \infty &; & |x_i-x_j| < \sigma \end{array} \right.$ where $\left. x_k \right.$ is the position of the center of the k-th rod. Consider that the particles are ordered according to their label: $x_0 < x_1 < x_2 < \cdots < x_{N-1}$; taking into account the pair potential we can write the canonical parttion function (configuration integral) of a system of $N$ particles as: $\frac{ Z \left( N,L \right)}{N!} = \int_{\sigma/2}^{L+\sigma/2-N\sigma} d x_0 \int_{x_0+\sigma}^{L+\sigma/2-N\sigma+\sigma} d x_1 \cdots \int_{x_{i-1}+\sigma}^{L+\sigma/2-N\sigma+i \sigma} d x_i \cdots \int_{x_{N-2}+\sigma}^{L+\sigma/2-N\sigma+(N-1)\sigma} d x_{N-1}.$ Variable change: $\left. \omega_k = x_k - (k+\frac{1}{2}) \sigma \right.$ ; we get: $\frac{ Z \left( N,L \right)}{N!} = \int_{0}^{L-N\sigma} d \omega_0 \int_{\omega_0}^{L-N\sigma} d \omega_1 \cdots \int_{\omega_{i-1}}^{L-N\sigma} d \omega_i \cdots \int_{\omega_{N-2}}^{L-N\sigma} d \omega_{N-1}.$ Therefore: $\frac{ Z \left( N,L \right)}{N!} = \frac{ (V-N)^{N} }{N!}.$ $Q(N,L) = \frac{ (V-N)^N}{\Lambda^N N!}.$ ## References 1. Lewi Tonks "The Complete Equation of State of One, Two and Three-Dimensional Gases of Hard Elastic Spheres", Physical Review 50 pp. 955- (1936)

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# How to find x and y if xy=20 and y=x=+8 1 by kat2nag 2 and 10. Yes I know the answer but I can't explain the solution and we really need it Yup. I know how to get the roots but it appears as -10 and 2. ohh, im so sorry :( • Brainly User 2016-06-18T18:57:15+08:00 Problem:  A number is 8 more than another number if the product of the two numbers is 20.  Find the numbers. First number: x Second Number: y (or x + 8) First Equation:  xy = 20 Second Equation: y = x+8 In terms of one variable "x", substitute the x+8 of second equation in y in Equation 2: x (x + 8) = 20 x² + 8x = 20 Arrange in standard form of quadratic equation: x² + 8x - 20 = 0 Check if this can be factored by finding the discriminant: a = 1    b = 8    c = -20 Discriminant:  b² - 4ac = (8)² - 4(1)(-20) = 64 + 80 = 144 Since discriminant is more than 0, that is, 144>0, we can use factoring to solve the equation instead of other method. x² + 8x - 20 = 0 Factor: (x + 10) (x - 2) = 0 x + 10 = 0            x - 2 = 0 x = -10                 x = 2 Check: First number: 2 Second Number: 2 + 8 = 10 ANSWER:  The numbers are 2 and 10. Note: I include the explanation so you can recite and defend your answer with solution.  Good luck! Thank you so much!!!! You're welcome :-)

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AS tudy on the Development of the Concept of a Line W Shared by: Categories Tags - Stats views: 0 posted: 2/8/2012 language: pages: 27 Document Sample ``` CALPASS SAN DIEGO CENTRAL MATHEMATICS COUNCIL The Concept of a Line A study of its development through Judy Ross, Laura Stevens, and Terrie Teegarden 4/1/2011 This study originated from the realization that many community college students have significant difficulties with the concepts related to linear functions and their graphs even though these topics are included in the mathematics curriculum from about third grade onward. It is an attempt to identify possible gaps in the math standards in this area, as well as possible oversights in emphasis in classroom practice at various levels. Linear functions and their graphs are important in their own right as models of practical situations. They are also used as regression lines in statistics and modeling, as simple first examples of various concepts in economics, and as a means of finding linear approximations. Working with linear functions and graphs is also a critical part of meeting all three of the “essential areas of focus for all entering college students” in the 2010 Intersegmental Committee of the Academic Senates document. Note especially that the second of these states that “Emphasis should be placed on various representations of functions – using graphs, tables, variables, and words – and on the interplay among the graphical and other representations…” Students who are able to move seamlessly between a linear equation, a table of values, slope and intercepts and a graph will be prepared to do the same with other types of functions. Students who must rely exclusively on plotting points to produce a line will be ill-prepared to interpret the graphs of quadratic, exponential and other functions. Several of the continuing difficulties that students have with linear functions and graphs overlap with their misconceptions about fractions. One of these is the unspoken assumption that the only numbers on the number lines are the integers. Therefore the act of connecting several points on the graph of a line is merely demonstrating that they all lie on the line, implying nothing about function values for non-integer inputs. Another misconception lies in seeing slope exclusively as a ratio of two numbers (rise over run) and not as a unit rate (a single number). These misconceptions can have consequences for future difficulties even with calculus. In the following document we have quoted standards pulled from several sources including California State Standards (1999) (CSS), the California Common Core Standards for Mathematics (CCCSM), Statement on Competencies in Mathematics Expected of Entering College Students, and the National Common Core Standards for Mathematics (CCSM). In addition, the Cal-PASS deconstruction documents for Algebra I through Precalculus and the San Diego County Department of Education's backward mapping project for algebra supplied the example problems throughout the document. For the grades 3 – 7, the examples are taken from the Backwards Mapping project from the San Diego County of Education Department. Those items marked AF are from the Algebra and Functions component. Those marked MG are from the Measurement and Geometry component. The first box indicates the actual state standard, and the second is a benchmark and the last box is an example created by the backwards mapping project participants. For the Algebra 1, Algebra 2, Geometry, Mathematical Analysis and Linear Algebra standards, the examples are taken from the Cal-PASS deconstructed standards. Those standards with a * preceding them are referenced as key in the Statement on Competencies in Mathematics Expected of Entering College Students by the Intersegmental Committee of the Academic Senates of the California Community Colleges, the California State University and the University of California. (2010) Notes refer to resources outside of the California State Standards, and comments refer to the opinions of the writers. California Grade Level Standards Algebra and Functions (AF) 2.0 Students represent simple functional relationships: 2.1 Solve simple problems involving a functional relationship between two quantities (e.g., find the total cost of multiple items given the cost per unit). 2.2 Extend and recognize a linear pattern by its rules (e.g., the number of legs on a given number of horses may be calculated by counting by 4s or by multiplying the number of horses by 4). Note: The Common Core Standards for Mathematics (CCSM) includes the ability to represent unit fractions on a number line. “Students … use fractions to represent parts of a whole or distances on a number line that begins with zero.” AF 1.0 Students use and interpret variables, mathematical symbols, and properties to write and simplify expressions and sentences: 1.1 Use letters, boxes, or other symbols to stand for any number in simple expressions or equations (e.g., demonstrate an understanding and the use of the concept of a variable). 1.4 Use and interpret formulas (e.g., area = length × width or A = lw) to answer questions about quantities and their relationships. 1.5 Understand that an equation such as y = 3x + 5 is a prescription for determining a second number when a first number is given. California State Standard Benchmark sample problem AF 1.5 AF 1.5 AF 1.5 Understand that an equation such as y In an equation in two Complete the table using the = 3x + 5 is a prescription for variables, find the value Rule: determining a second number when a of the first variable first number is given. when given the value of y = 2x + 4 the second variable. Input (x) Output (y) CST (2) 0 1 2 3 4 Comment: This is the first time students see a number and a variable next to each other with no operation symbol. They need to understand that the implied operation is multiplication. AF 2.0 Students know how to manipulate equations: 2.1 Know and understand that equals added to equals are equal. 2.2 Know and understand that equals multiplied by equals are equal. Measurement and Geometry (MG) 2.0 Students use two-dimensional coordinate grids to represent points and graph lines and simple figures: 2.1 Draw the points corresponding to linear relationships on graph paper (e.g., draw 10 points on the graph of the equation y = 3x and connect them by using a straight line). California State Standard Benchmark sample problem 2.2 Understand that the length of a horizontal line segment equals the difference of the x- coordinates. 2.3 Understand that the length of a vertical line segment equals the difference of the y- coordinates. MG 3.0 Students demonstrate an understanding of plane and solid geometric objects and use this knowledge to show relationships and solve problems: 3.1 Identify lines that are parallel and perpendicular. Number Sense (NS) 1.9 Identify on a number line the relative position of positive fractions, positive mixed numbers, and positive decimals to two decimal places. California State Standard Benchmark sample problem NS 1.9 NS 1.9 NS 1.9 Identify on a number line the Plot decimals and What value is represented by the point relative position of positive mixed numbers on a P on this number line? fractions, positive mixed number line. numbers, and positive decimals to two decimal 0 1 P places. Note: The CCSM states that students “understand that the length of a number line (interval from 0 to 1) can be divided into parts of equal fractional length.” AF 1.0 Students use variables in simple expressions, compute the value of the expression for specific values of the variable, and plot and interpret the results: 1.1 Use information taken from a graph or equation to answer questions about a problem situation. 1.2 Use a letter to represent an unknown number; write and evaluate simple algebraic expressions in one variable by substitution. 1.3 Know and use the distributive property in equations and expressions with variables. 1.4 Identify and graph ordered integer pairs in the four quadrants of the coordinate plane. 1.5 Solve problems involving linear functions with integer values; write the equation; and graph the resulting ordered pairs of integers on a grid. California State Standard Benchmark sample problem NS 1.5 NS 1.5 NS 1.5 Identify and represent on Graph decimals Graph the following numbers on a number line decimals fractions, mixed the number line: -5, 1, 5, fractions, mixed numbers numbers and 1 3 1 and positive and negative positive and , ,4 , 2.75, -3.5. 5 4 4 integers. negative integers. Note: The CCSM includes the ability recognize that “equivalent fractions correspond to the same point on a number line.” Comment: Does this standard mean no negative decimals or fractions even though the example includes them? AF 1.0 Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic expressions, solve simple linear equations, and graph and interpret their results: 1.1 Write and solve one-step linear equations in one variable. 1.2 Write and evaluate an algebraic expression for a given situation, using up to three variables. 1.3 Apply algebraic order of operations and the commutative, associative, and distributive properties to evaluate expressions; and justify each step in the process. 1.4 Solve problems manually by using the correct order of operations or by using a scientific calculator. Comment: Solving an equation is not directly related to the concept of a line, however for the student to understand what they are doing, a linear model is helpful. California State Standard Benchmark sample problem AF 1.1 AF 1.1a AF. 1.1 a Write and solve one-step Write one-step linear Which algebraic equation best linear equations in one equations in one variable. describes the total growth (T) variable. in height of pine trees over a three-year period, if g equals the rate of growth in centimeters per year? A) T = 3g B) T = 3 + g g C) T = 3 3 D) T = g AF 1.1b AF 1.b Solve one-step linear Write an equation for the equations in one variable following problem and solve. The number of players on the football team increased by 3 equals 21. How many players were on the original team? Note: The CCSM states that students “understand that for a ratio a:b, the corresponding unit rate is a/b.” This concept is basic to the understanding of the slope of a line as a unit rate. *AF 1.0 Students express quantitative relationships by using algebraic terminology, expressions, equations, inequalities, and graphs: 1.5 Represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in the situation represented by the graph. AF 3.0 Students graph and interpret linear and some nonlinear functions: 2 3 3.1 Graph functions of the form y = nx and y = nx and use in solving problems. 3.2 Plot the values from the volumes of three-dimensional shapes for various values of the edge lengths (e.g., cubes with varying edge lengths or a triangle prism with a fixed height and an equilateral triangle base of varying lengths). 3.3 Graph linear functions, noting that the vertical change (change in y-value) per unit of horizontal change (change in x-value) is always the same and know that the ratio (“rise over run”) is called the slope of a graph. Comment: Students need to understand that slope refers to more than just the ‘rise over the run’. Other applications include unit rate and the relationship between the changes in the dependent and independent variables. Sometimes one is interested in considering a change in x prior to the change in y. 3.4 Plot the values of quantities whose ratios are always the same (e.g., cost to the number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of the line equals the ratio of quantities. Comment: The ratio of circumference to diameter is an irrational number. Note: According to the CCSM, by grade 7 students should understand that “fractions and their opposites form a system of numbers called the rational numbers, represented by points on a number line.” In addition they “prove that various configurations of lines give rise to similar triangles because of the angles created when a transversal cuts parallel lines.” It is in grade 7 that students “plot proportional relationships on a coordinate plane where each axis represents one of the two quantities involved, observe that the graph is a straight line through the origin, and find unit rates from a graph. Explain what a point (x, y) means in terms of the situation, with special attention to the points (0,0) and (1, r) where r is the unit rate.” Note: The State of California has deemed that all students will take algebra in Grade 8, and hence the Algebra I standards are reflective of what is taught. The CCSM separates Grade 8 from the High School curriculum. For grade 8 the following concepts are included as core:  “Students use linear equations … to represent, analyze and solve a variety of problems. … they understand that the slope (m) of a line is a constant rate of change.”  “Understand that the slope of a non-vertical line in the coordinate plane has the same value for any two distinct points used to compute it.” (Linear equations in two variables #3)  “Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship; from two (x, y) values, including reading these from a table; or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.” (Functional relationships between quantities #6)  “Understand that a straight line is a widely used model for exploring relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line…” (Statistics and Probability #3)  “Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.” (Statistics and Probability #4) Algebra I standards: 4.0 Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x-5) + 4(x-2) = 12. Computational and Procedural Skills 1. Simplify the following expressions: 5 1 c.  (2x - 5) 3 a.  x - 6 + x - 5  2 4 d.  2 (3x - 1)- 2 (5x - 4 )  b.  (3x - 4 ) 5 *5.0 Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step. 1. Solve the following equations and inequalities: a. 2 x315 f. 3x9 1 b. x38 g. 4 x75x3 4 c. 4m6 36 h. 5x1 x 5 4 x8 d. 32 i. 82 y4 y 4 e. 5 x21x 22 x1 x 8 j. Solve  3  2 and justify each step. 4 k. The length of a rectangle is six less than twice the width. Its perimeter is 36 inches. Find the dimensions of the rectangle. l. The sum of 32 and twice a number is at most 118. Determine all numbers with this property? m. Jennifer’s cell phone plan charges \$32.99 per month plus \$0.14 for each text message. Write a linear inequality and solve it to find how many text messages she can send per month and still keep her bill under \$50. Comment: This last question was added because it was determined that a real world application was needed. Algebra I standards: 6.0 Students graph a linear equation and compute the x- and y-intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4). Computational and Procedural Skills 1. Find the “x” and “y”-intercepts for the line defined by the following equation: 2x + 3y = 9 2. Use the “x” and “y”-intercepts to graph the line given by the equation above: 2x + 3y = 9 3. Graph the following lines using the method of your choice. Identify and label the “x” and “y” intercepts for each graph if they exist: a) 3x – 5y = 10 d) x = 3.5 2 e) 2x + 4y = 3 b) y  x4 3 1 3 f) x y 2 c) y = 2 2 4 4. Graph the solution set for the following inequalities: 3 1 2 5 a) 2x – 3y < 6 b) y  x  2 c) x y  4 2 3 6 Conceptual Understanding 1. Sketch the graph of a line that has no x-intercept. 2. Identify the “x” and “y”- intercepts from the graph of the given line. 3. Can a line have more than one x-intercept? Explain your answer using a diagram. Algebra I standards: 4. The solution to an inequality has been graphed correctly below. Insert the correct inequality symbol in the inequality below to match the graph of the solution. (Everything else about the inequality is correct – it just needs the correct symbol). Y -3x + 5 Insert correct symbol in box. 5. When is it advantageous to use the x and y-intercepts to graph the equation of a line? When would it perhaps be easier or better to use another graphing method? Give an example to illustrate your answers to both of these questions. Problem Solving/Application 1. The graph displayed below is the graph of the following equation: , where “x” represents the amount of time that has passed since a 5 gallon fish tank sprung a leak, and “y” represents the number of gallons of water in the tank after the leak. a) What is the significance of the “x-intercept” in this situation? What information is given to us by this point? b) What is the significance of the “y-intercept” in this situation? What information is given to us by this point? c) What is the rate of leaking in gallons per minute? Note: This question was added by the authors as an example of unit rate. Leaking Fish Tank 6 Number of Gallons 5 4 3 2 1 0 0 10 20 30 40 50 Tim e (Minutes) Algebra I standards: 2. The cost of a trash pickup service is given by the following formula: y = 1.50x + 11, where “x” represents the number of bags of trash the company picks up, and “y” represents the total cost to the customer for picking up the trash. a) What is the “y-intercept” for this equation? b) What is the significance of the “y-intercept” in this situation? What does c) Draw a sketch of the graph which represents this trash pickup service. 7.0 Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula. Computational and Procedural Skills 3 1. Given the equation of a line, y  x  1 determine whether or not the 2 following points lie on the line: (4.7), (-6, -10) and (1/3, -1/2). 2. Write the equation of the line with slope 2/3 and y-intercept of –2 3. Write the equation of the line with a slope of 4 and passing through the point (-2, 5) 4. Write the equation of the line passing through the points (-3, 7) and (4, -7) 5. Write the equation of the line graphed below. Conceptual Understanding Consider the table of values below. Episode Number of Number Survivors 1 25 2 23 3 21 a) Identify the input and output variables b) Determine whether or not the data could be linear. c) If the data is linear find and interpret the slope. Algebra I standards: Problem Solving/Application A taxi driver charges a \$2.00 pick up fee plus \$3 for each mile traveled. If you are interested in calculating the cost of your trip, what quantities would be of interest? d) Identify the input and output quantities. e) Make a table for inputs 0, 1, and 2. f) Identify and interpret the meaning of the slope. g) Identify and interpret the meaning of the vertical axis intercept. h) Write an equation describing the output as a function of the input. i) Use your equation to determine the cost of a 12-mile taxi ride. *8.0 Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point. a) Recognize parallel lines as having the same slope and different y-intercepts graphically. Graph: y  2 x  4 and y  2 x  1 on the same rectangular coordinate system. Does it appear the two lines are parallel? Explain! b) Recognize parallel lines as having the same slope and different y-intercepts algebraically. Algebraically, demonstrate the two lines whose equations are given by: 2 y  4 x  9 and y  2 x  5 are parallel. c) Recognize perpendicular lines algebraically by intersecting at 90 angles. Graph: y  x  5 and y  x  0 on the same rectangular coordinate system. Does it appear the two lines are perpendicular? Explain! d) Recognize perpendicular lines algebraically as having slopes whose product is -1. Comment: According to the CCSM, a geometric proof is included in geometry. Could an exercise that looks at it heuristically be included in the curriculum at this time? For example, comparing the graphs of a pair of perpendicular lines will show that one slope is positive and one negative and one has a steep (> 45o) slope while the other is more shallow. Algebraically, demonstrate the two lines whose equations are given by: 4 y  3x  7 and 3 y  4 x  15 are perpendicular. Algebra I standards: e) Understand the relationship between the slopes of parallel lines. See a above f) Determine the equation of a line parallel to a given line and passing through a point not on the line. g) Find an equation of a line, in slope-intercept form, through point P(3,2) that is parallel to 3 y  5 x  7. h) Determine the equation of a line perpendicular to a given line and passing through a point not on the line. Find an equation of a line, in slope-intercept form, through point P(12,4) that is perpendicular to y  6 x  3. *9.0 Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets. Computational and Procedural Skills 3. Identify the intersection of two shaded areas created by the graphs of linear inequalities in two variables as the solution to the system: x  y  7 4. Solve the system of inequalities  graphically. 2 x  3 y  12 Conceptual Understanding 1. Interpret the solution as representing the intersection of two lines or the same line: Suppose a system of two linear equations in two variables has a solution, (3,5). When graphing these two equations on the same Cartesian coordinate system, what would you expect the graph of the two lines to look like? Suppose a system of two linear equations in two variables has infinite solutions in the form (x,y). When graphing these two equations on the same Cartesian coordinate system, what would you expect the graph of the two lines to look like?  y  3x  3 Solve the system:  by graphical method. 3x  2 y  12 Algebra I standards:  y  3x  6 Solve the system:  by graphical method.  6 x  2 y  12 *16.0 Students understand the concepts of a relation and a function, determine whether a given relation defines a function, and give pertinent information about given relations and functions. Conceptual Understanding 1. Given the following sets of ordered pairs, give the domain and range of the relation; determine whether the relation is or is not a function: a. {(-4,3), (-2,1), (0,5), (-2,-8)} b. {(3,7), (1,4), (0,-2), (-1,-1), (-2,5)} 2. Given the following figures, give the domain and range of the relation; determine whether the relation is or is not a function: Domain Range 4 -1 2 -2 8 -3 6 -6 10 -8 a. b. 3. Define relation and function. Compare the two definitions. How are they alike? How are they different? *17.0 Students determine the domain of independent variables and the range of dependent variables defined by a graph, a set of ordered pairs, or a symbolic expression. Computational and Procedural Skills 1. Complete each ordered pair so that it is a solution to 3x + y = 10. Then identify the domain and range of the resulting set of ordered pairs. a. (1, ?) c. (?, 4) e. (0, ?) b. (2, ?) d. (3, ?) Algebra I standards: Conceptual Understanding 1. State the domain and range of the relation: { (2,4), (2,5), (4,6), (7,2), (5,10), (8,4), (3,6) } 2. Express the relation in each mapping, table, or graph as a set of ordered pairs and then state the domain and range of each: a. 1 X y 7 3 4 2 5 6 6 7 8 7 6 5 4 3 3 3 5 c. 4 4 5 3 Problem Solving/Application 1. The table below shows the amount that a company charges for a bike rental. Identify the domain and range. Write a set of ordered pairs for the function. Assuming the cost of the bike rental is a linear function of the number of hours the bike was rented, find a formula for the function. Time (hrs) 1 2 3 4 5 6 Cost (\$) 20 24 28 32 36 40 Algebra I standards: 2. The table below shows the per-minute rate for a cell phone. Identify the domain and range. Write a set of ordered pairs for the function.. Assuming the cost is a linear function of the number of minutes, find a formula for the function. Minutes 1 2 3 4 5 6 Cost (\$) 2.00 2..25 2.50 2.75 3.00 3.25 3. The table below shows the distance that a car travels over time. Identify the domain and range. Write a set of ordered pairs for the function. Use the table to write an equation for this function (Comment: Assume the function is linear). Time (hrs) 1 2 3 4 5 6 Distance 50 100 150 200 250 300 (miles) *18.0 Students determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the conclusion. Computational and Procedural Skills 1. Determine whether or not the below relations are functions. Justify your answer. a. (4, 5), ( - 3, 6), (5, 6 ), (- 2, 4)} { b. (7, - 3), (- 3, 6), (7, - 3 ), (- 6, 5)} { y c.  = 3x - 1 Conceptual Understanding 1. If you are looking at a graph, how do you determine whether or not it is the graph of a function? 2. Write a set consisting of three ordered pairs that is a relation, but not a function. Explain why the set of ordered pairs you wrote is not a function. 3. Draw a graph that is both a relation and a function. Write a sentence that states why the graph you drew represents both a relation and a function. Geometry: *7.0 Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles. Algebra II: 2.0 Students solve systems of linear equations and inequalities (in two or three variables) by substitution, with graphs, or with matrices. Computational and Procedural Skills 1. Solve the system by graphing. 3x  2 y  6 x  0 a.  y  0 2 x  y  4  b.    x  y  5  2 x  3 y  3  2. Solve the system by substitution:  x  2 y  11  x  3 y  2 a.  b.  3x  2 y  13 3x  9 y  9 Conceptual Understanding a. If you graph two lines in the same coordinate plane, what are the possible outcomes? b. A system of linear equations may have infinitely many solutions. Explain how this is possible. c. Does every system of linear equations have a solution? Explain. d. After a solution of a system of linear equations is found, why should the solution be checked algebraically? e. If the solution exists, what is the solution of a system of linear inequalities? f. When is it advantageous to use the substitution method? The matrix method? Give an example to illustrate your answers to both parts of this question. g. Write the system of linear inequalities which describes the shaded region below (Inside the triangle is shaded): Algebra II: Problem Solving/Application 1. Your family receives basic television and two movie channels for \$32.30 a month. Your neighbor receives basic cable and four movie channels for \$43.30 a month. What is the monthly charge for just the basic cable? (Assume that the movie channels have the same monthly cost.) What is the monthly charge for one movie channel? 2. The senior class has a carnival to raise money for a senior trip. Student tickets are \$6 and adult tickets are \$11. Since 324 people were in attendance, the senior class raised \$2,359. How many of the people in attendance were adults? 24.0 Students solve problems involving functional concepts, such as composition, defining the inverse function and performing arithmetic operations on functions. Computational and Procedural Skills 1. Let f (x)  3x  2 and g(x)  4x ; find g( f (2)): 2. What is the inverse of f (x)  4x  6 ?  Conceptual Understanding   x 9 1. Show that (x)  4x  9 and g(x)  f are inverse functions. 4 Comment: An extension to this problem might be to ask, graphically what is the relationship between the two functions?  Problem Solving/Application  1. A department store is having a 20%-off-everything sale. You also have a \$10 coupon for any purchase. a. Write the function M that represents the sale price of an item after the 20% discount, and a function K that represents the price of an item after the \$10 coupon: Determine which is the best deal for you, discount then coupon, or coupon then discount, when buying an item costing \$25. Algebra II: 25.0 Students use properties from number systems to justify steps in combining and simplifying functions. Computational and Procedural Skills x 2  3x  2 1. What property of real numbers enables you to simplify to x + 2 for all x 1 values of x not equal to -1? x 2  3 x  18 2. What properties of real numbers enable you to simplify to x + 6 for x3 all values of x not equal to 3? Comment: How does the graph of the original function differ from the graph of the simplified form? Trigonometry 7.0 Students know that the tangent of the angle that a line makes with the x-axis is equal to the slope of the line. Comment: Here is another example of a possibly irrational slope. Students will need more than ‘rise over run’ in order to interpret this. Linear Algebra 6.0 Students demonstrate an understanding that linear systems are inconsistent (have no solutions), have exactly one solution, or have infinitely many solutions. Computational and Procedural Skills Determine if the following systems are consistent or inconsistent. Identify consistent systems as dependent or independent. 2 x  y  4 x  y  5 x  y  z  6 1.  2.   4 x  2 y  8 x  y  1 3. 2 x  y  z  3 x  2 y  2z  0  Conceptual Understanding 1. Given the following matrices, determine if the corresponding systems are consistent or inconsistent. Identify consistent systems as dependent or independent. Where appropriate, give the solution. 1 0 0 3 1 0 0 3 1 0 0 3 a) 0 1 0 0   b) 0 1 0 5   c) 0 1 0 0   0 0 0 4    0 0 2 4    0 0 0 0    2. If you solve a system of linear equations without using matrices, how do you know if the system is consistent or inconsistent? If consistent, how do you know if the system is dependent or independent. 8.0 Students interpret geometrically the solution sets of systems of equations. For example, the solution set of a single linear equation in two variables is interpreted as a line in the plane, and the solution set of a two-by-two system is interpreted as the intersection of a pair of lines in the plane. Calculus: 4.0 Students demonstrate an understanding of the formal definition of the derivative of a function at a point and the notion of differentiability: 4.1 Students demonstrate an understanding of the derivative of a function as the slope of the tangent line to the graph of the function. 4.2 Students demonstrate an understanding of the interpretation of the derivative as an instantaneous rate of change. Students can use derivatives to solve a variety of problems from physics, chemistry, economics, and so forth that involve the rate of change of a function. From the National Common Core Mathematics Standards for High School, the following standards reflect the linear understanding expected beginning with the understanding that “linear functions with a constant term of zero, describe proportional relationships. In addition, the following are from the linear, quadratic and exponential models standards:  “Understand that a linear function defined by f(x) = mx + b for some constants m and b, models a situation in which a quantity changes at a constant rate, m relative to another.” (1)1  “Understand that linear functions grow by equal differences over equal intervals…” (4)  “Arithmetic sequences can be seen as linear functions.” (5)  “Construct a function to describe a linear relationship between two quantities. Determine the rate of change and constant term f a linear function from a graph, a description of a relationship, or from two (x, y) values (including reading from a table).” (10)  “Interpret the rate of change and constant term of a linear function or sequence in terms of the situation it models, and in terms of its graph or table of values.” (13) The following are from the Statistics and Probability standards:  “Functional models may be used to approximate data; if the data approximately linear, the relationship may be modeled with a regression line.” (Introduction) The following are from Geometric Properties with Equations standards:  “Understand that two lines with well-defined slopes are perpendicular if and only if the product of their slopes is –1.” (1)  “Use the slope criteria for parallel and perpendicular lines to solve geometric problems.” (7) 1 - The number in () identifies the corresponding standard in the CCSM document. Mathematically Mature Concept of Line as envisioned by the authors A line (or straight line) is the graph of the set of all solutions of a linear equation ax + by = c or y = mx + b. (By ALL solutions, we mean that x and y can take on fractional and even irrational values unless a particular application requires only integer or rational values.) A complete understanding of line includes the ability to move seamlessly between the equation, a table of values, a graph, and a verbal description. Graphing techniques should include making a table, finding the x and y intercepts, and using the slope and y intercept. Geometric terminology and descriptions of lines are a part of this understanding. An understanding of slope includes the interpretation of positive and negative slopes, as well as zero and undefined slopes. The concept of slope should gradually expand from the formula and “rise over run” to include unit rates, rational and even irrational numbers. Unit rates are relevant in application and proportion problems. Rational and irrational slopes can arise in regression lines and derivatives. A line, particularly in the form y = mx + b, is used in statistics and other applications to model a relationship if the data suggest that the relationship is linear. In addition it is used to approximate function values if the rate of change (slope, derivative) of the function is known. A line can also be the boundary for the solution set of a linear inequality in two variables. Lines are also important as asymptotes when describing the graph or behavior of functions. For a complete development of the concept of a line, students should learn (not necessarily in this order) that:  the integers can be represented as points at uniform intervals on a number line  the absolute value of a number represents its distance from zero  on the number line, the numbers increase as one moves from left to  the values between integers can be represented on a number line (rational fractions first then irrational values)  two points determine a line  plotting input/output values yields a line given that a linear relation exists  all lines are straight and continue infinitely in both directions  the graph of a linear function results in a line  the change in outputs for a change in inputs is constant for a linear function (slope, rate of change)  the graph of a line represents all values for which the linear relationship holds and there are an infinite number of such values  for some real world models a linear function only applies for specific values (ex. positive integers)  the sign of the slope determines whether the linear function increases or decreases  the graph of a line is read from left to right when determining whether the graph increases or decreases  a slope of zero represents a horizontal line while an undefined slope represent a vertical line  parallel and perpendicular lines can be defined both algebraically and geometrically  both algebraic and geometric concepts of a line are complementary ``` Related docs Other docs by HC120208203331 Lecture 10 3 CreditRebuildingLetters template

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I am very confused by this tough question. I hope some experts of Gauss's Law can help me out! Any help is greatly appreciated! 1) A long thin straight wire with linear charge ensity lambda runs down the centre of a thin hollow metal cylinder of radius R. The cylinder has a net linear charge density (2*lambda). Take lambda as positive. Find the electric field (strengh & direction) a) inside the cylinder (r<R) b) outside the cylinder (r>R) For part b (r>R), I picked a coaxial cylinder with a radius r>R and of lengt L as the Gaussian surface E=(Q_enclosed)/(A)(epsilon_o) E=(lambda)L+2(lambda)L/(A)(epsilon_o) E=3(lambda)L/(2pi*r*L)(epsilon_o) Is this the correct answer Note that the radius of the hollow cylinder "R" is not used in any part of my calculation...did I do something wrong? For part a, I got the electric field strength for r<R as [lambda/(2pi*epsilon_o*r)], and when I try to substitute r=R into the answers from part a & b, the electric fields DON'T match at the boundary....which further lowers my confidence of being right. But which part did I do it wrong? I can't find my error...Does anyone know how to solve this problem? By the way, how come they use the term LINEAR charge density for a 3-dimensional hollow cylinder? Say, for example, if a certain hollow cylinder has a linear charge density of 2 C/m, what does it actually mean? A cylinder is definitely NOT a line... Thank you again! Last edited: One more question, for part a, will the electric field also be pointing radially OUTWARD? There are many positive charges surrounding, so wouldn't the electric field be pointing IN? Dick Homework Helper There is no error. You did use R in the calculation. It tells you where one solution begins and another ends. There is a surface charge on the cylinder, so you shouldn't expect the electric field to be continuous across it. The phrase 'linear charge density' just means that they are giving charge per length rather than the charge per area. That's all. Dick

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This website uses cookies to ensure you have the best experience. Analysis Of The Johns Hopkins Hospital 1166 words - 5 pages Ratio Analysis Organizations use financial statements and ratio analysis assess financial performance viability. The ratio analysis are used to identify trends and to perform organizational comparison (financial) with other companies within same industry. Ratio analysis, using data reported on the financial statements, are divided into five major categories: common size, liquidity, solvency, efficiency, and profitability. This paper will assess the financial stability of John Hopkins Hospital (JHH) using the five ratio analysis. Overview: Johns Hopkins Hospital Johns Hopkins Hospital is a teaching and biomedical research health care facility located in Baltimore, Maryland. Founded in 1889, JHH is named after the renowned philanthropist and visionary enthusiast Johns Hopkins, who provided the initial funds for construction. JHH was the first hospital to incorporated teaching, learning, patient care, and research into the health care model. Today, JHH is billion-dollar health care system and is known (nationally and internationally) for distinction in health care excellence, teaching, and research. Ratio Analysis The financial statements from Johns Hopkins Hospital (JHH) were used to calculate and analyze the meaning of the financial health of the organization from the years 2010-2012 (Appendix A). The following five major types of ratios were used: common size, liquidity, solvency, efficiency, and profitability Common size ratios. According to Finkler, Kover, and Jones (2007), “The goal of common sizing is to make an organization comparable to other organizations of different sizes… by putting everything into perspective based on organizational size,” (p. 117). These ratios alson can be used used by the organization to compare trends over time. The following ratios are reviewed: A. Cash to total assets = Cash/Total assets B. Total expenses to total revenues = Total expenses/Total revenues Cash to total assets in three years’ time indicates a significant downward trend reflecting JHH has less cash on hand in relationship to their total assets, form 10.81% to 1.48% (Figure 1). The total expenses to total revenues ratio has a moderately flat trend that indicates a stable financial environment for the organization. Figure 1. JHH Financial Ratios Liquidity ratios. Current ratios and quick ratios determine the organization’s short-term financial solvency. The is to determine if JHH has enough cash and other liquid resources to meet their current obligations (Finkler et al., 2007). The following liquidity ratios are examined: A. Current ratio = Current assets/Current Liabilities B. Quick ratio = Cash + Market securities (short-term investments) + Accounts receivable/Current liabilities According to Finkler et al. (2007), the “current ratio of 2.0 has become widely accepted” (p. 118). JHH shows a downward trend of current ratio over three years’ time that is concerning in such a short period. The quick ratio also follows this... Find Another Essay On Analysis of the Johns Hopkins Hospital Organizational Analysis of Hospital Z 1468 words - 6 pages analysis of the problems and the related literature, conflicts resulting from differentiation and task relationships, and the operational plan of Hospital Z give insight into the complexities of this organization. One of the problems plaguing Hospital Z is the organizational culture, which, according to Robbins and Judge (2013) includes the common characteristics of (1) innovation and risk taking, which allows members of the organization the Ethical and legal analysis of the Ann Hopkins v. Price Waterhouse discrimination law suit. Focuses on case law and ethics 3145 words - 13 pages "LEGAL ANALYSIS MODEL"1. IDENTIFICATION OF THE "CRITICAL OR RELEVANT FACTS" FROM THE CASE.Ann Hopkins came to Price Waterhouse in August of 1978 following a short stint at American Management Systems after the realization that she preferred a multi-project environment that Price Waterhouse offered. Prior to American Management Systems she worked at Touche Ross for close to 2 years. She left Touche Ross because her husband made partner at the Allusions to God in the Poetry of Gerard Manley Hopkins 1765 words - 7 pages Gerard Manley Hopkins was a Victorian poet who frequently utilized symbols to demonstrate how God is evident in all living things. His allusions to God are evident in such works as: “Pied Beauty”, “Spring”, “The Windhover”, and “God’s Grandeur”. The purpose of this research is to examine the way in which Hopkins uses his terms inscape and instress to illustrate these allusions to God. Hopkins’s poetry demonstrates to the readers that seeing Grigson and Ward on the Poetry of Gerald Manley Hopkins 2956 words - 12 pages Explore the views of Grigson and Ward and with close attention to at least three poems. Develop your own view of Hopkins' poetry. Gerard Manley Hopkins was born in 1844. He was born in London of Welsh ancestry, whose family were devout anglicans. He was the eldest of eight children. He was an actively artistic child, especially in music, drawing and poetry. This was encouraged in many Victorian households. He was educated at Balliol Faith and Doubt in the Poetry of Gerard Manley Hopkins 1621 words - 6 pages Gerard Manley Hopkins had eight siblings and was born of Manley and Catherine Smith Hopkins. His parents were Anglicans that followed the Catholic tradition in sacraments and papacy. By instilling the theological values, faith and morals into Gerard, he became heavily influenced by his family. His parents taught him, as well as their other children to love God. Gerard guaranteed his mother that he would strengthen his connection with God and SWOT analysis of Shouldice Hospital Limited 3430 words - 14 pages specialist areas offering similar opportunities like eye surgery etc.4. Changing the scheduling of doctors.The way, the surgeries are carried out at Souldice, any patient needs to stay at hospital for at least 3 days. Appendix 'B' shows weekly maximum achievable throughput of 149 patients under the current operating cycle. Surgeon Capacity Analysis: In general, a typical first time surgery requires 45 minutes of surgeon time. Surgeon requi ... 1 Analysis of “Hard Rock Returns to Prison from the Hospital for the Criminal Insane” 822 words - 4 pages Etheridge Knight’s “Hard Rock Returns to Prison from the Hospital for the Criminal Insane” is an interesting poem spurred from his own experiences, that explores a variety of things from basic human emotions to controversial medical treatments. Knight was incarcerated for 8 years for robbery, during which he began to develop his skill as a poet, and this stint in prison influenced the settings and styles of his poetry. Knight’s poem is unique in Did the CFO have a responsibility to inform Johns of the errors 9274 words - 37 pages for firms to hire this service is to help control the conflict of interests among firm managers, shareholders, and bond- holders. Firm characteristics which affect the severity of this conflict or the marginal cost of external auditing are expected to influence a firm's demand for this service. Based on this analysis, leverage, firm size, and number of accounting-based debt covenants are predicted to increase the probability that a firm will Care In and Out of the Hospital 1566 words - 6 pages Imagine watching an elderly loved one move back and forth between their own home and a hospital, all because they did not have adequate home care. The hospital, in turn, did not provide enough rehospitalization time. This happens to many elderly folks who can no longer take care of themselves and neither can their spouses. Mrs. Gerlach, age 82, suffered from a disease is called Giant Cell Arthritis and is very common for older people to Attitude and Appreciation of the Natural World in Gerard Manley Hopkins and Henry Wadsworth Longfellow's Poetry 1822 words - 7 pages Attitude and Appreciation of the Natural World in Gerard Manley Hopkins and Henry Wadsworth Longfellow's Poetry The simple beauty of nature is an aspect many of us take for granted in our everyday lives - the endearing sounds of birds welcoming another day and the powerful gush of a waterfall being some examples of these. But there are those individuals who have endeavoured to fully comprehend the marvellous complexity of Compare and Contrast of‘‘Binsey Poplars’’ by Gerard Manley Hopkins and ‘‘The Trees’’ by Philip Larkin 2136 words - 9 pages Choose two of the poems given in the handout . Compare and contrast these two poems (‘‘Binsey Poplars’’ by Gerard Manley Hopkins and ‘‘The Trees’’ by Philip Larkin), paying close attention to their language and form. In a recent article in The Guardian, Billy Mills writes, ‘Trees have been putting down roots in poetry for centuries’, and indeed there are as many poems about trees as there are species of trees themselves. As someone who grew Similar Essays The Case Of Enso Martinez And Rebecca Fielding Vs. John Hopkins Hospital 903 words - 4 pages choice, with whom they have developed trusting relationships, are no longer available to care for them. It is certain that the system requires sensible reform (p.525). In what is known as the largest malpractice case in Maryland is the case of Enso Martinez and Rebecca Fielding against John Hopkins Hospital. In this situation, Ms. Fielding was taken to the hospital for an emergency caesarean section. Granted the story does mention if Ms Analysis Of The Poem The Wreck Of Deutschland By Gerard Manley Hopkins 2349 words - 9 pages , legislative bills enacted in the German Kingdom of Prussia during the Kulturkampf conflict with the Catholic Church. The Franciscan nuns’ death inspired Gerard Manley Hopkins to compose his longest Christian theme poem, “The Wreck of the Deutschland,” dedicated to their memory. In this lyrical poem, dedicated to the Franciscan nuns’ lives, Hopkins expresses his reactions to the wreck of the Deutschland , which sparked powerful emotions in him Analysis Of The Poem The Wreck Of Deutschland By Gerald Manley Hopkins 868 words - 3 pages , legislative bills enacted in the German Kingdom of Prussia during the Kulturkampf conflict with the Catholic Church. The Franciscan nuns’ death inspired Gerard Manley Hopkins to compose his longest Christian theme poem, “The Wreck of the Deutschland,” dedicated to their memory. In this lyrical poem, dedicated to the Franciscan nuns’ lives, Hopkins expresses his reactions to the wreck of the Deutschland , which sparked powerful emotions in him The Start Of Banfield Pet Hospital: Swot Analysis 1100 words - 4 pages Corporate name, founding date, founding leaders Banfield Pet Hospital was founded in Portland, Oregon in 1955 by Warren J. Wegert (Banfield Pet Hospital, 2013). The start of Banfield Pet Hospital The hospital was founded with a vision to provide high quality veterinary medicine. In 1987, Scott Campbell purchased Banfield with \$2 million in revenues already invested (Banfield Pet Hospital, 2013). In 1994, the pet store chain PetSmart, teamed up

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Explore BrainMass # The Effect on Net Income of a Special Order This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here! A company manufactures a product. The company can manufacture 1,200,000 units a year at a variable cost of \$3,000,000 and a fixed cost of \$1,800,000. Based on projections for next year, 960,000 units will be sold at the regular price of \$20.00 each. A special order has been received for 240,000 units to be sold at a 70% discount off the regular price. Total fixed costs would be unaffected by this order. By what amount would the company's net operating income be increased as a result of the special order? #### Solution Preview The basic cost-volume-profit formula is Sales revenue-Total variable costs-Total fixed costs=Net profit. Further, Sales revenue-Total variable costs=Contribution Margin, or (sales volume*unit selling price)-(sales volume*unit variable cost)=contribution margin. Factoring out sales volume, we find that Unit selling price-Unit variable costs=Unit ... #### Solution Summary A company manufactures a product. The company can manufacture 1,200,000 units a year at a variable cost of \$3,000,000 and a fixed cost of \$1,800,000. Based on projections for next year, 960,000 units will be sold at the regular price of \$20.00 each. A special order has been received for 240,000 units to be sold at a 70% discount off the regular price. Total fixed costs would be unaffected by this order. By what amount would the company's net operating income be increased as a result of the special order? \$2.19

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× hypot() function with example in C++ C++ hypot() function: Here, we are going to learn about the hypot() function with example of cmath header in C++ programming language? Submitted by IncludeHelp, on April 26, 2019 C++ hypot() function hypot() function is a library function of cmath header, it is used to find the hypotenuse of the given numbers, it accepts two numbers and returns the calculated result of hypotenuse i.e. sqrt(x*x + y*y). Syntax Syntax of hypot() function: ```hypot(x, y); ``` Parameter(s) x, y – numbers to be calculated hypotenuse (or sqrt(x*x + y*y)) Return value double – it returns double value that is the result of the expression sqrt(x*x + y*y). Sample Input and Output ```Input: float x = 10.23; float y = 2.3; Function call: hypot(x, y); Output: 10.4854 ``` Example ```// C++ code to demonstrate the example of // hypot() function #include <iostream> #include <cmath> using namespace std; // main code section int main() { float x = 10.23; float y = 2.3; // calculate the hypotenuse float result = hypot(x, y); cout<<"hypotenuse of "<<x<<" and "<<y<<" is = "<<result; cout<<endl; //using sqrt() function result = sqrt((x*x + y*y)); cout<<"hypotenuse of "<<x<<" and "<<y<<" is = "<<result; cout<<endl; return 0; } ``` Output ```hypotenuse of 10.23 and 2.3 is = 10.4854 hypotenuse of 10.23 and 2.3 is = 10.4854 ```

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