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Hugging Face TB Research 851

https://www.lmfdb.org/L/14/405e7/1.1/c3e7/0/1

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# Properties Label 14-405e7-1.1-c3e7-0-1 Degree $14$ Conductor $1.787\times 10^{18}$ Sign $1$ Analytic cond. $4.44884\times 10^{9}$ Root an. cond. $4.88833$ Motivic weight $3$ Arithmetic yes Rational yes Primitive no Self-dual yes Analytic rank $0$ # Origins of factors ## Dirichlet series L(s)  = 1 + 2·2-s − 8·4-s + 35·5-s + 22·7-s − 18·8-s + 70·10-s + 23·11-s + 96·13-s + 44·14-s + 41·16-s + 161·17-s + 279·19-s − 280·20-s + 46·22-s + 96·23-s + 700·25-s + 192·26-s − 176·28-s − 296·29-s + 244·31-s + 8·32-s + 322·34-s + 770·35-s + 404·37-s + 558·38-s − 630·40-s − 47·41-s + ⋯ L(s)  = 1 + 0.707·2-s − 4-s + 3.13·5-s + 1.18·7-s − 0.795·8-s + 2.21·10-s + 0.630·11-s + 2.04·13-s + 0.839·14-s + 0.640·16-s + 2.29·17-s + 3.36·19-s − 3.13·20-s + 0.445·22-s + 0.870·23-s + 28/5·25-s + 1.44·26-s − 1.18·28-s − 1.89·29-s + 1.41·31-s + 0.0441·32-s + 1.62·34-s + 3.71·35-s + 1.79·37-s + 2.38·38-s − 2.49·40-s − 0.179·41-s + ⋯ ## Functional equation \begin{aligned}\Lambda(s)=\mathstrut &\left(3^{28} \cdot 5^{7}\right)^{s/2} \, \Gamma_{\C}(s)^{7} \, L(s)\cr=\mathstrut & \,\Lambda(4-s)\end{aligned} \begin{aligned}\Lambda(s)=\mathstrut &\left(3^{28} \cdot 5^{7}\right)^{s/2} \, \Gamma_{\C}(s+3/2)^{7} \, L(s)\cr=\mathstrut & \,\Lambda(1-s)\end{aligned} ## Invariants Degree: $$14$$ Conductor: $$3^{28} \cdot 5^{7}$$ Sign: $1$ Analytic conductor: $$4.44884\times 10^{9}$$ Root analytic conductor: $$4.88833$$ Motivic weight: $$3$$ Rational: yes Arithmetic: yes Character: induced by $\chi_{405} (1, \cdot )$ Primitive: no Self-dual: yes Analytic rank: $$0$$ Selberg data: $$(14,\ 3^{28} \cdot 5^{7} ,\ ( \ : [3/2]^{7} ),\ 1 )$$ ## Particular Values $$L(2)$$ $$\approx$$ $$154.8007180$$ $$L(\frac12)$$ $$\approx$$ $$154.8007180$$ $$L(\frac{5}{2})$$ not available $$L(1)$$ not available ## Euler product $$L(s) = \displaystyle \prod_{p} F_p(p^{-s})^{-1}$$ $p$$F_p(T)$ bad3 $$1$$ 5 $$( 1 - p T )^{7}$$ good2 $$1 - p T + 3 p^{2} T^{2} - 11 p T^{3} + 63 T^{4} - 3 p^{2} T^{5} + 7 p^{3} T^{6} + 27 p^{5} T^{7} + 7 p^{6} T^{8} - 3 p^{8} T^{9} + 63 p^{9} T^{10} - 11 p^{13} T^{11} + 3 p^{17} T^{12} - p^{19} T^{13} + p^{21} T^{14}$$ 7 $$1 - 22 T + 830 T^{2} - 19134 T^{3} + 426701 T^{4} - 7825194 T^{5} + 165254493 T^{6} - 347285588 p T^{7} + 165254493 p^{3} T^{8} - 7825194 p^{6} T^{9} + 426701 p^{9} T^{10} - 19134 p^{12} T^{11} + 830 p^{15} T^{12} - 22 p^{18} T^{13} + p^{21} T^{14}$$ 11 $$1 - 23 T + 5151 T^{2} - 137494 T^{3} + 15125367 T^{4} - 32802843 p T^{5} + 29040094313 T^{6} - 601859871012 T^{7} + 29040094313 p^{3} T^{8} - 32802843 p^{7} T^{9} + 15125367 p^{9} T^{10} - 137494 p^{12} T^{11} + 5151 p^{15} T^{12} - 23 p^{18} T^{13} + p^{21} T^{14}$$ 13 $$1 - 96 T + 12191 T^{2} - 828700 T^{3} + 67939809 T^{4} - 3670430048 T^{5} + 227859076023 T^{6} - 10004745881352 T^{7} + 227859076023 p^{3} T^{8} - 3670430048 p^{6} T^{9} + 67939809 p^{9} T^{10} - 828700 p^{12} T^{11} + 12191 p^{15} T^{12} - 96 p^{18} T^{13} + p^{21} T^{14}$$ 17 $$1 - 161 T + 24747 T^{2} - 2620018 T^{3} + 242733069 T^{4} - 19012626063 T^{5} + 1428967389431 T^{6} - 5791825964988 p T^{7} + 1428967389431 p^{3} T^{8} - 19012626063 p^{6} T^{9} + 242733069 p^{9} T^{10} - 2620018 p^{12} T^{11} + 24747 p^{15} T^{12} - 161 p^{18} T^{13} + p^{21} T^{14}$$ 19 $$1 - 279 T + 63455 T^{2} - 9627646 T^{3} + 1292727231 T^{4} - 139417672577 T^{5} + 13934197302465 T^{6} - 1188087181318116 T^{7} + 13934197302465 p^{3} T^{8} - 139417672577 p^{6} T^{9} + 1292727231 p^{9} T^{10} - 9627646 p^{12} T^{11} + 63455 p^{15} T^{12} - 279 p^{18} T^{13} + p^{21} T^{14}$$ 23 $$1 - 96 T + 70730 T^{2} - 5128416 T^{3} + 2231256537 T^{4} - 129120969582 T^{5} + 1826857392719 p T^{6} - 1973532783601374 T^{7} + 1826857392719 p^{4} T^{8} - 129120969582 p^{6} T^{9} + 2231256537 p^{9} T^{10} - 5128416 p^{12} T^{11} + 70730 p^{15} T^{12} - 96 p^{18} T^{13} + p^{21} T^{14}$$ 29 $$1 + 296 T + 154422 T^{2} + 29519614 T^{3} + 8749743807 T^{4} + 1202308386924 T^{5} + 280424950326131 T^{6} + 32104391095886106 T^{7} + 280424950326131 p^{3} T^{8} + 1202308386924 p^{6} T^{9} + 8749743807 p^{9} T^{10} + 29519614 p^{12} T^{11} + 154422 p^{15} T^{12} + 296 p^{18} T^{13} + p^{21} T^{14}$$ 31 $$1 - 244 T + 138953 T^{2} - 21581892 T^{3} + 6820038797 T^{4} - 643944456252 T^{5} + 180689501328357 T^{6} - 12932535760119704 T^{7} + 180689501328357 p^{3} T^{8} - 643944456252 p^{6} T^{9} + 6820038797 p^{9} T^{10} - 21581892 p^{12} T^{11} + 138953 p^{15} T^{12} - 244 p^{18} T^{13} + p^{21} T^{14}$$ 37 $$1 - 404 T + 7243 p T^{2} - 88433668 T^{3} + 32537859593 T^{4} - 8785146905212 T^{5} + 2408172804310695 T^{6} - 541287630181037208 T^{7} + 2408172804310695 p^{3} T^{8} - 8785146905212 p^{6} T^{9} + 32537859593 p^{9} T^{10} - 88433668 p^{12} T^{11} + 7243 p^{16} T^{12} - 404 p^{18} T^{13} + p^{21} T^{14}$$ 41 $$1 + 47 T + 321096 T^{2} - 12021155 T^{3} + 45171631701 T^{4} - 4630735558038 T^{5} + 4063682212222409 T^{6} - 491807687844214791 T^{7} + 4063682212222409 p^{3} T^{8} - 4630735558038 p^{6} T^{9} + 45171631701 p^{9} T^{10} - 12021155 p^{12} T^{11} + 321096 p^{15} T^{12} + 47 p^{18} T^{13} + p^{21} T^{14}$$ 43 $$1 - 525 T + 461651 T^{2} - 177053890 T^{3} + 91552352643 T^{4} - 27963570378443 T^{5} + 10910759641065633 T^{6} - 2737206494978679516 T^{7} + 10910759641065633 p^{3} T^{8} - 27963570378443 p^{6} T^{9} + 91552352643 p^{9} T^{10} - 177053890 p^{12} T^{11} + 461651 p^{15} T^{12} - 525 p^{18} T^{13} + p^{21} T^{14}$$ 47 $$1 - 164 T + 458970 T^{2} - 110392306 T^{3} + 108169816881 T^{4} - 25717707674850 T^{5} + 17081669577666257 T^{6} - 3320863886913274956 T^{7} + 17081669577666257 p^{3} T^{8} - 25717707674850 p^{6} T^{9} + 108169816881 p^{9} T^{10} - 110392306 p^{12} T^{11} + 458970 p^{15} T^{12} - 164 p^{18} T^{13} + p^{21} T^{14}$$ 53 $$1 - 506 T + 541623 T^{2} - 172442740 T^{3} + 132333548265 T^{4} - 35763427746966 T^{5} + 25492045997195975 T^{6} - 6232790423469661848 T^{7} + 25492045997195975 p^{3} T^{8} - 35763427746966 p^{6} T^{9} + 132333548265 p^{9} T^{10} - 172442740 p^{12} T^{11} + 541623 p^{15} T^{12} - 506 p^{18} T^{13} + p^{21} T^{14}$$ 59 $$1 + 85 T + 331341 T^{2} + 32993294 T^{3} + 125055414789 T^{4} + 9577822572435 T^{5} + 29633014670734625 T^{6} + 2027875987639118244 T^{7} + 29633014670734625 p^{3} T^{8} + 9577822572435 p^{6} T^{9} + 125055414789 p^{9} T^{10} + 32993294 p^{12} T^{11} + 331341 p^{15} T^{12} + 85 p^{18} T^{13} + p^{21} T^{14}$$ 61 $$1 - 828 T + 1137794 T^{2} - 655662598 T^{3} + 472897824279 T^{4} - 204252976588544 T^{5} + 110585022303384087 T^{6} - 44527407364853870622 T^{7} + 110585022303384087 p^{3} T^{8} - 204252976588544 p^{6} T^{9} + 472897824279 p^{9} T^{10} - 655662598 p^{12} T^{11} + 1137794 p^{15} T^{12} - 828 p^{18} T^{13} + p^{21} T^{14}$$ 67 $$1 - 1093 T + 2017106 T^{2} - 1699166505 T^{3} + 1757369253407 T^{4} - 1166070992255454 T^{5} + 864466170577418349 T^{6} -$$$$45\!\cdots\!53$$$$T^{7} + 864466170577418349 p^{3} T^{8} - 1166070992255454 p^{6} T^{9} + 1757369253407 p^{9} T^{10} - 1699166505 p^{12} T^{11} + 2017106 p^{15} T^{12} - 1093 p^{18} T^{13} + p^{21} T^{14}$$ 71 $$1 - 328 T + 1276365 T^{2} - 268163756 T^{3} + 813660594393 T^{4} - 105690507940488 T^{5} + 374340014427629213 T^{6} - 36698946645864837192 T^{7} + 374340014427629213 p^{3} T^{8} - 105690507940488 p^{6} T^{9} + 813660594393 p^{9} T^{10} - 268163756 p^{12} T^{11} + 1276365 p^{15} T^{12} - 328 p^{18} T^{13} + p^{21} T^{14}$$ 73 $$1 - 2085 T + 4050563 T^{2} - 4984423486 T^{3} + 5631570806793 T^{4} - 4895773027898939 T^{5} + 3922468709989734339 T^{6} -$$$$25\!\cdots\!16$$$$T^{7} + 3922468709989734339 p^{3} T^{8} - 4895773027898939 p^{6} T^{9} + 5631570806793 p^{9} T^{10} - 4984423486 p^{12} T^{11} + 4050563 p^{15} T^{12} - 2085 p^{18} T^{13} + p^{21} T^{14}$$ 79 $$1 - 2110 T + 3466397 T^{2} - 4074662340 T^{3} + 4200201567425 T^{4} - 3637140873668514 T^{5} + 2929970636702454981 T^{6} -$$$$20\!\cdots\!84$$$$T^{7} + 2929970636702454981 p^{3} T^{8} - 3637140873668514 p^{6} T^{9} + 4200201567425 p^{9} T^{10} - 4074662340 p^{12} T^{11} + 3466397 p^{15} T^{12} - 2110 p^{18} T^{13} + p^{21} T^{14}$$ 83 $$1 - 1290 T + 3282374 T^{2} - 3191089158 T^{3} + 4600431414309 T^{4} - 3678070946162670 T^{5} + 3902415474964514617 T^{6} -$$$$26\!\cdots\!88$$$$T^{7} + 3902415474964514617 p^{3} T^{8} - 3678070946162670 p^{6} T^{9} + 4600431414309 p^{9} T^{10} - 3191089158 p^{12} T^{11} + 3282374 p^{15} T^{12} - 1290 p^{18} T^{13} + p^{21} T^{14}$$ 89 $$1 + 3048 T + 5723102 T^{2} + 6323602086 T^{3} + 4534976524791 T^{4} + 780789931274556 T^{5} - 1899913405596725465 T^{6} -$$$$27\!\cdots\!50$$$$T^{7} - 1899913405596725465 p^{3} T^{8} + 780789931274556 p^{6} T^{9} + 4534976524791 p^{9} T^{10} + 6323602086 p^{12} T^{11} + 5723102 p^{15} T^{12} + 3048 p^{18} T^{13} + p^{21} T^{14}$$ 97 $$1 - 1787 T + 4084243 T^{2} - 4789169974 T^{3} + 7296823674929 T^{4} - 7118143615887349 T^{5} + 8621884508580027771 T^{6} -$$$$72\!\cdots\!44$$$$T^{7} + 8621884508580027771 p^{3} T^{8} - 7118143615887349 p^{6} T^{9} + 7296823674929 p^{9} T^{10} - 4789169974 p^{12} T^{11} + 4084243 p^{15} T^{12} - 1787 p^{18} T^{13} + p^{21} T^{14}$$ $$L(s) = \displaystyle\prod_p \ \prod_{j=1}^{14} (1 - \alpha_{j,p}\, p^{-s})^{-1}$$

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CC-MAIN-2022-05

longest

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https://iffgit.fz-juelich.de/fleur/fleur/-/raw/20508365d6115883ef66e8f719a887ee627b4291/eigen_soc/alineso.F90?inline=false

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crawl-data/CC-MAIN-2020-50/segments/1606141171077.4/warc/CC-MAIN-20201124025131-20201124055131-00382.warc.gz

MODULE m_alineso USE m_juDFT !---------------------------------------------------------------------- ! Set up SO-hamiltonian for 2nd variation (hsohelp and hsoham) and ! diagonalize by lapack routines. ! Eigenvalues and vectors (eig_so and zso) are returned !---------------------------------------------------------------------- CONTAINS SUBROUTINE alineso(eig_id,lapw,& mpi,DIMENSION,atoms,sym,kpts,& input,noco,cell,oneD, nk, usdus,rsoc,& nsize,nmat, eig_so,zso) #include"cpp_double.h" USE m_types USE m_hsohelp USE m_hsoham USE m_eig66_io, ONLY : read_eig IMPLICIT NONE TYPE(t_mpi),INTENT(IN) :: mpi TYPE(t_lapw),INTENT(IN) :: lapw TYPE(t_dimension),INTENT(IN) :: DIMENSION TYPE(t_oneD),INTENT(IN) :: oneD TYPE(t_input),INTENT(IN) :: input TYPE(t_noco),INTENT(IN) :: noco TYPE(t_sym),INTENT(IN) :: sym TYPE(t_cell),INTENT(IN) :: cell TYPE(t_atoms),INTENT(IN) :: atoms TYPE(t_kpts),INTENT(IN) :: kpts TYPE(t_usdus),INTENT(IN) :: usdus TYPE(t_rsoc),INTENT(IN) :: rsoc ! .. ! .. Scalar Arguments .. INTEGER, INTENT (IN) :: eig_id INTEGER, INTENT (IN) :: nk INTEGER, INTENT (OUT):: nsize,nmat ! .. ! .. Array Arguments .. COMPLEX, INTENT (OUT) :: zso(:,:,:)!(dimension%nbasfcn,2*dimension%neigd,wannierspin) REAL, INTENT (OUT) :: eig_so(2*DIMENSION%neigd) !-odim !+odim ! .. ! .. Local Scalars .. REAL r2 INTEGER i,i1 ,j,jsp,jsp1,k,ne,nn,nn1,nrec,info INTEGER idim_c,idim_r,jsp2,nbas,j1,ierr CHARACTER vectors LOGICAL l_socvec,l_qsgw,l_open,l_real INTEGER irec,irecl_qsgw INTEGER nat_l, extra, nat_start, nat_stop COMPLEX cdum ! .. ! .. Local Arrays .. INTEGER :: nsz(2) REAL :: eig(DIMENSION%neigd,DIMENSION%jspd),s(3) REAL, ALLOCATABLE :: rwork(:) COMPLEX,ALLOCATABLE :: cwork(:),chelp(:,:,:,:,:) COMPLEX,ALLOCATABLE :: ahelp(:,:,:,:),bhelp(:,:,:,:) COMPLEX,ALLOCATABLE :: zhelp1(:,:),zhelp2(:,:) COMPLEX,ALLOCATABLE :: hso(:,:),hsomtx(:,:,:,:) COMPLEX,ALLOCATABLE :: sigma_xc_apw(:,:),sigma_xc(:,:) TYPE(t_mat)::zmat(dimension%jspd) ! .. ! .. External Subroutines .. EXTERNAL CPP_LAPACK_cheev ! .. ! .. External Functions .. COMPLEX CPP_BLAS_cdotu,CPP_BLAS_cdotc EXTERNAL CPP_BLAS_cdotu,CPP_BLAS_cdotc ! .. ! read from eigenvalue and -vector file ! l_real=sym%invs.and..not.noco%l_noco.and..not.(noco%l_soc.and.atoms%n_u>0) zmat%l_real=l_real zMat(1:dimension%jspd)%matsize1=lapw%nv(1:dimension%jspd)+atoms%nlotot zmat%matsize2=dimension%neigd INQUIRE (4649,opened=l_socvec) INQUIRE (file='fleur.qsgw',exist=l_qsgw) if (l_real) THEN ALLOCATE (zmat(1)%data_r(zmat(1)%matsize1,DIMENSION%neigd) ) zmat(1)%data_r(:,:)= 0. if (size(zmat)==2)THEN ALLOCATE(zmat(2)%data_r(zmat(2)%matsize1,DIMENSION%neigd) ) zmat(2)%data_r=0.0 ENDIF else ALLOCATE (zmat(1)%data_c(zmat(1)%matsize1,DIMENSION%neigd) ) zmat(1)%data_c(:,:)= 0. if (size(zmat)==2)THEN ALLOCATE(zmat(2)%data_c(zmat(2)%matsize1,DIMENSION%neigd) ) zmat(2)%data_c=0.0 ENDIF endif zso(:,:,:)= CMPLX(0.,0.) DO jsp = 1,input%jspins CALL read_eig(& eig_id,nk,jsp, neig=ne,eig=eig(:,jsp)) CALL read_eig(& eig_id,nk,jsp,& n_start=1,n_end=ne,& zmat=zmat(jsp)) ! write(*,*) 'process',irank,' reads ',nk !!\$ DO i = 1, lapw%nv(1) !!\$ s = lapw%bkpt +lapw%gvec(:,i,1) !!\$ r2 = DOT_PRODUCT(s,MATMUL(s,cell%bbmat)) !!\$ lapw%rk(i,1) = SQRT(r2) !!\$ ENDDO IF (ne.GT.DIMENSION%neigd) THEN WRITE (6,'(a13,i4,a8,i4)') 'alineso: ne=',ne,' > dimension%neigd=',DIMENSION%neigd CALL juDFT_error("alineso: ne > neigd",calledby="alineso") ENDIF nsz(jsp) = ne ENDDO ! ! set up size of e.v. problem in second variation: nsize ! nsize = 0 DO jsp = 1,input%jspins IF (input%jspins.EQ.1) THEN nsize = 2*nsz(jsp) nsz(2) = nsz(1) ELSE nsize = nsize + nsz(jsp) ENDIF ENDDO ! ! distribution of (abc)cof over atoms ! ! ! in case of ev-parallelization, now distribute the atoms: ! IF (mpi%n_size > 1) THEN nat_l = FLOOR(real(atoms%nat)/mpi%n_size) extra = atoms%nat - nat_l*mpi%n_size nat_start = mpi%n_rank*nat_l + 1 + extra nat_stop = (mpi%n_rank+1)*nat_l + extra IF (mpi%n_rank < extra) THEN nat_start = nat_start - (extra - mpi%n_rank) nat_stop = nat_stop - (extra - mpi%n_rank - 1) ENDIF ELSE nat_start = 1 nat_stop = atoms%nat ENDIF nat_l = nat_stop - nat_start + 1 ! ! set up A and B coefficients ! ALLOCATE ( ahelp(atoms%lmaxd*(atoms%lmaxd+2),nat_l,DIMENSION%neigd,DIMENSION%jspd) ) ALLOCATE ( bhelp(atoms%lmaxd*(atoms%lmaxd+2),nat_l,DIMENSION%neigd,DIMENSION%jspd) ) ALLOCATE ( chelp(-atoms%llod :atoms%llod, DIMENSION%neigd,atoms%nlod,nat_l,DIMENSION%jspd) ) CALL timestart("alineso SOC: -help") write(*,*) nat_start,nat_stop,nat_l CALL hsohelp(& & DIMENSION,atoms,sym,& & input,lapw,nsz,& & cell,& & zmat,usdus,& & zso,noco,oneD,& & nat_start,nat_stop,nat_l,& & ahelp,bhelp,chelp) CALL timestop("alineso SOC: -help") ! ! set up hamilton matrix ! CALL timestart("alineso SOC: -ham") #ifdef CPP_MPI CALL MPI_BARRIER(mpi%MPI_COMM,ierr) #endif ALLOCATE ( hsomtx(DIMENSION%neigd,DIMENSION%neigd,2,2) ) CALL hsoham(atoms,noco,input,nsz,chelp,rsoc,ahelp,bhelp,& nat_start,nat_stop,mpi%n_rank,mpi%n_size,mpi%SUB_COMM,& hsomtx) DEALLOCATE ( ahelp,bhelp,chelp ) CALL timestop("alineso SOC: -ham") IF (mpi%n_rank==0) THEN ! ! add e.v. on diagonal ! ! write(*,*) '!!!!!!!!!!! remove SOC !!!!!!!!!!!!!!' ! hsomtx = 0 !!!!!!!!!!!! DO jsp = 1,input%jspins DO i = 1,nsz(jsp) hsomtx(i,i,jsp,jsp) = hsomtx(i,i,jsp,jsp) +& & CMPLX(eig(i,jsp),0.) IF (input%jspins.EQ.1) THEN hsomtx(i,i,2,2) = hsomtx(i,i,2,2) +& & CMPLX(eig(i,jsp),0.) ENDIF ENDDO ENDDO ! ! resort H-matrix ! ALLOCATE ( hso(2*DIMENSION%neigd,2*DIMENSION%neigd) ) DO jsp = 1,2 DO jsp1 = 1,2 IF (jsp.EQ.1) nn = 0 IF (jsp1.EQ.1) nn1 = 0 IF (jsp.EQ.2) nn = nsz(1) IF (jsp1.EQ.2) nn1 = nsz(1) ! !write(3333,'(2i3,4e15.8)') jsp,jsp1,hsomtx(jsp,jsp1,8,8),hsomtx(jsp,jsp1,32,109) DO i = 1,nsz(jsp) DO j = 1,nsz(jsp1) hso(i+nn,j+nn1) = hsomtx(i,j,jsp,jsp1) ENDDO ENDDO ! ENDDO ENDDO DEALLOCATE ( hsomtx ) ! ! add Sigma-vxc (QSGW) ! IF( l_qsgw ) THEN nbas = lapw%nv(1) + atoms%nlotot WRITE(*,'(A,I3,A,I5,A)') 'Read fleur.qsgw (',nk,',',nbas,')' IF( DIMENSION%jspd .EQ. 2 ) STOP 'alineso: GW+noco not implemented.' ALLOCATE ( sigma_xc(2*nsz(1),2*nsz(1)) ) ALLOCATE ( sigma_xc_apw(nbas,nbas) ) INQUIRE(667,opened=l_open) IF( .NOT.l_open ) THEN IF( nk.NE.1 ) STOP 'unit 667 not opened but not at 1st k' OPEN(667,file='fleur.qsgw',form='unformatted') ELSE IF( nk.EQ.1) THEN REWIND(667) ENDIF DO jsp1 = 1,2 DO jsp2 = 1,jsp1 IF(jsp1.EQ.jsp2) THEN READ(667) ((sigma_xc_apw(i,j),j=1,i),i=1,nbas) DO i = 1,nbas DO j = 1,i-1 sigma_xc_apw(j,i) = CONJG(sigma_xc_apw(i,j)) ENDDO ENDDO ELSE READ(667) sigma_xc_apw ENDIF ! write(*,*) 'lo part set to zero!' ! sigma_xc_apw(nv+1:,nv+1:) = 0 i = nsz(1) * (jsp1-1) + 1 ; i1 = nsz(1) * jsp1 j = nsz(1) * (jsp2-1) + 1 ; j1 = nsz(1) * jsp2 if (l_real) THEN sigma_xc(i:i1,j:j1) = & & MATMUL ( TRANSPOSE(zmat(1)%data_r(:nbas,:)) ,& & MATMUL ( sigma_xc_apw, zmat(1)%data_r(:nbas,:) ) ) else sigma_xc(i:i1,j:j1) = & & MATMUL ( CONJG(TRANSPOSE(zmat(1)%data_c(:nbas,:))) ,& & MATMUL ( sigma_xc_apw, zmat(1)%data_c(:nbas,:) ) ) endif hso(i:i1,j:j1) = hso(i:i1,j:j1) + CONJG(sigma_xc(i:i1,j:j1)) IF(jsp1.NE.jsp2) THEN sigma_xc(j:j1,i:i1) = TRANSPOSE(CONJG(sigma_xc(i:i1,j:j1))) hso(j:j1,i:i1) = hso(j:j1,i:i1)+CONJG(sigma_xc(j:j1,i:i1)) ENDIF ENDDO ENDDO DEALLOCATE ( sigma_xc_apw ) ENDIF ! ! diagonalize the hamiltonian using library-routines ! idim_c = 4*DIMENSION%neigd idim_r = 6*DIMENSION%neigd CALL timestart("alineso SOC: -diag") ALLOCATE ( cwork(idim_c),rwork(idim_r) ) IF (input%eonly) THEN vectors= 'N' ELSE vectors= 'V' ENDIF CALL CPP_LAPACK_cheev(vectors,'U',nsize,& & hso,2*DIMENSION%neigd,& & eig_so,& & cwork, idim_c, rwork, & & info) IF (info.NE.0) WRITE (6,FMT=8000) info 8000 FORMAT (' AFTER CPP_LAPACK_cheev: info=',i4) CALL timestop("alineso SOC: -diag") DEALLOCATE ( cwork,rwork ) IF (input%eonly) THEN IF(l_socvec) CALL juDFT_error& & ("EONLY set. Vectors not calculated.",calledby ="alineso") ELSE ALLOCATE ( zhelp2(DIMENSION%neigd,2*DIMENSION%neigd) ) ! ! proj. back to G - space: old eigenvector 'z' to new one 'Z' ! + ! s --- s | z(G,j,s) ... z(ig,i,jsp) ! Z (G) = > z (G) * C (i,j) | Z(G,j,s) ... zso(ig,j,jsp) ! j --- i | C(i,j) ... hso(i ,j) ! i + ! reorder new e.w. in 2x2 spin space : zhelp(,1),zhelp(,2) ! DO i1 = 1,2 jsp = i1 jsp2= i1 IF (input%jspins.EQ.1) jsp = 1 IF (input%jspins.EQ.1 .AND..NOT.(input%l_wann.OR.l_socvec)) jsp2=1 IF (i1.EQ.1) nn = 0 IF (i1.EQ.2) nn = nsz(1) zhelp2(:,:) = 0.d0 DO j = 1,nsize DO i = 1,nsz(jsp) zhelp2(i,j) = CONJG(hso(i+nn,j)) ENDDO ENDDO ! j if (l_real) THEN CALL CPP_BLAS_cgemm("N","N",zmat(1)%matsize1,2*dimension%neigd,dimension%neigd,CMPLX(1.d0,0.d0),CMPLX(zmat(jsp)%data_r(:,:)),& zmat(1)%matsize1, zhelp2,DIMENSION%neigd,CMPLX(0.d0,0.d0), zso(1,1,jsp2),zmat(1)%matsize1) else CALL CPP_BLAS_cgemm("N","N",zmat(1)%matsize1,2*dimension%neigd,dimension%neigd, CMPLX(1.d0,0.d0),zmat(jsp)%data_c(:,:),& zmat(1)%matsize1, zhelp2,DIMENSION%neigd,CMPLX(0.d0,0.d0), zso(:,:,jsp2),zmat(1)%matsize1) endif ENDDO !isp IF(l_socvec) THEN !RS: write SOC vectors to SOCVEC WRITE(4649) lapw%nmat,nsize,input%jspins,nsz,2*DIMENSION%neigd,CONJG(hso) !CF: write qsgw IF(l_qsgw) THEN nn = 2*nsz(1) sigma_xc = MATMUL ( TRANSPOSE(hso(:nn,:nn)) ,& & MATMUL ( sigma_xc , CONJG(hso(:nn,:nn)) ) ) WRITE(1014) nn WRITE(1014) ((sigma_xc(i,j),i=1,j),j=1,nn) DEALLOCATE ( sigma_xc ) ENDIF ENDIF DEALLOCATE ( zhelp2 ) ENDIF ! (.NOT.input%eonly) DEALLOCATE ( hso ) ENDIF ! (n_rank==0) ! nmat=lapw%nmat RETURN END SUBROUTINE alineso END MODULE m_alineso

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ECON222 WEEK1 Finance-1 # ECON222 WEEK1 Finance-1 - Lecture 3 Topic Mathematics of... This preview shows pages 1–2. Sign up to view the full content. 1 1 Lecture 3: Topic: Mathematics of Finance Reading H&P, Ch 5. Reading for this lecture H&P, Ch 5, Sect 5.1 - 5.2; (also refer back to Ch 4, pp. 167-168) Homework for Tutorial in Week 2 Ex 5.1, pp. 200-201, problems 1, 3, 9, 11. Ex 5.2, pp. 204-205, problems 3, 11, 15, 19. 2 Compound Interest Suppose \$100 is invested at 8 percent per annum. Interest is earned and reinvested at the end of every quarter. What is the compound amount after 1 year? Principal = \$100 Nominal interest rate = 8% per year Quarterly interest rate = 8/4 = 2% per quarter Number of quarters = 4 3 Compound Interest End of Qtr 1: S = 100(1 + 0.02) = 102 End of Qtr 2: S = 102(1 + 0.02) = 104.04 = 100(1 + 0.02)(1 + 0.02) = 100(1 + 0.02) 2 = 104.04 End of Qtr 3: S = 104.04(1 + 0.02) = 106.12 = 100(1 + 0.02) 2 (1 + 0.02) = 100(1 + 0.02) 3 = 106.12 End of Qtr 4: S = 106.12(1 + 0.02) = 108.24 = 100(1 + 0.02) 3 (1 + 0.02) = 100(1 + 0.02) 4 = 108.24 4 Compound Interest Formula S = P(1 + r) n ( formulae for ‘cheat sheet’) where P is the original principal n is the number of conversion periods r is the rate of interest per conversion period S is the compound amount after n periods S – P is amount the compound interest earned 5 Find S , given P, r and n Suppose \$1,000 is invested at 5%. What is the compound amount after 4 years if interest is accumulated (a) annually, (b) semi-annually? This preview has intentionally blurred sections. Sign up to view the full version. View Full Document This is the end of the preview. Sign up to access the rest of the document. {[ snackBarMessage ]} ### Page1 / 4 ECON222 WEEK1 Finance-1 - Lecture 3 Topic Mathematics of... This preview shows document pages 1 - 2. Sign up to view the full document. View Full Document Ask a homework question - tutors are online

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• Mastery PD Materials ## Composition and calculation: hundredths and thousandths Spine 1: Number, Addition and Subtraction – Topic 1.24 ### Introduction Building on segment 1.23, introduce children to hundredths (and thousandths) using both the partitioning structure and ideas of place value; apply additive facts and strategies, including column algorithms, and rounding to numbers with hundredths (and thousandths). ### Teaching points • Teaching point 1: When one is divided into 100 equal parts, each part is one hundredth of the whole. When one tenth of a whole is divided into ten equal parts, each part is one hundredth of the whole. • Teaching point 2: Hundredths can be expressed as decimal fractions; the number written ‘0.01’ is one hundredth; one is one hundred times the size of 0.01; 0.1 is ten times the size of 0.01. • Teaching point 3: We can count in hundredths up to and beyond one. • Teaching point 4: Numbers with hundredths can be composed additively and multiplicatively. • Teaching point 5: Numbers with tenths and hundredths are commonly used in measurement, scales and graphing contexts. • Teaching point 6: Known facts and strategies, including column algorithms, can be applied to calculations for numbers with hundredths; the same approaches can be used for numbers with hundredths as are used for numbers with tenths. • Teaching point 7: Numbers with hundredths can be rounded to the nearest tenth by examining the value of the hundredths digit or to the nearest whole number by examining the value of the tenths digit. • Teaching point 8: When one is divided into 1,000 equal parts, each part is one thousandth of the whole. Knowledge and strategies for numbers with tenths and hundredths can be applied to numbers with thousandths. ## Downloads • Primary • KS2 • Year 4 #### Related Pages Is this page useful? Was this written in plain English? ## Subscribe to our newsletter Primary & Early Years Round-up Secondary Round-up National Newsletter A collaborative national network developing and spreading excellent practice, for the benefit of all pupils and students.

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Question Details Normal \$ 25.00 Stat 200 quiz help • From Mathematics, Statistics • Due on 22 Feb, 2015 11:59:00 • Asked On 17 Feb, 2015 12:47:33 • Due Date has already passed, but you can still Post Solutions. Question posted by Use Table (http://www.itl.nist.gov/div898/handbook/eda/section3/eda3671.htm) to find the proportion of the normal curve that is 1)    Between a z-score of .60 and the mean 2)    Between a z-score of 1.60 and the mean 3)    At or above a z-score of 1.30 4)    At or below a z-score of 1.30 5)    At or below a z-score of -1.00 6)    At or above a z-score of -1.00 7)    Between the z-scores of -1.00 and .60 8)    Between the z-scores of -1.50 and .65 9)    Between the z-scores of -1.96 and .25 Part II 1.   What percentage of a normal distribution is within 2 standard deviations of the mean? (Select the closest answer) The lengths of time bank customers must wait for a teller are normally distributed, with a mean of 3 minutes and a standard deviation of 1 minute. 2.  What proportion of bank customers waits between 2 and 3.5 minutes •a.  What percentage wait more than 4 minutes? •b.  What proportion waits between 1 and 2.5 minutes? •c.  What percentage wait less than 1 minute? 3.  To estimate the medical charges for an appendectomy Blue Star Insurance has data from a random sample of 70 patients. The sample mean cost is \$510, with a sample standard deviation of \$70 Construct a 95% confidence interval for the population mean cost. 4.  We are 95% confident that the populations mean costs of patients’ medical charges for an appendectomy through Blue Star Insurance range is between _____________ and ________________. A real estate agent records the ages of 50 randomly selected home buyers in her sales area. The mean age is 38 years, with a sample standard deviation of 10 years. Find a 99% confidence interval for the mean age. Available solutions \$ 18.00 A++ SOLUTION ..... 2 • This solution has not purchased yet. • Submitted On 23 Feb, 2015 06:24:45 Solution posted by ;; ; ; ... Buy now to view full solution. \$ 18.00 A++ SOLUTION ..... 3 • This Solution has been Purchased 1 time • Average Rating for this solution is A+ • Submitted On 23 Feb, 2015 06:24:45 Solution posted by ;; ; ; ... Buy now to view full solution. Other Related Questions Abdri... maypa... Only 45 characters allowed. \$ 629.35

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# Visualisation of non overlapping code 3 views (last 30 days) Shubham on 25 Apr 2023 Answered: Ishu on 8 Sep 2023 Following is a code which is based on a vector based approch and is used to check overlap between two ellipses. I am not able to visualise the algorithm. I want you to help me visualise this. Why tangent at every point then why diff tan > 90 is choosed etc. It will be very helpful if someone can add plots to help me visualise the algorithm t = linspace(0, 2*pi, 100); x0 = 5; y0 = 5; a0 = 10; b0 = 5; theta0 = pi/4; x1 = 8; y1 = 8; a1 = 8; b1 = 4; theta1 = pi/2; % Ellipse 1 x = a0*cos(t); y = b0*sin(t); X0 = cos(theta0)*x - sin(theta0)*y; Y0 = sin(theta0)*x + cos(theta0)*y; X0 = X0 + x0; Y0 = Y0 + y0; % Ellipse 2 x = a1*cos(t); y = b1*sin(t); X1 = cos(theta1)*x - sin(theta1)*y; Y1 = sin(theta1)*x + cos(theta1)*y; X1 = X1 + x1; Y1 = Y1 + y1; overlap = overlap_ellipses(x0,y0,a0,b0,theta0,x1,y1,a1,b1,theta1) %%%%%%%%%%%%%% Functions %%%%%%%%%%%%% function overlap = overlap_ellipses(x0,y0,a0,b0,theta0,x1,y1,a1,b1,theta1) overlap = -1; NOP = 2^(5); THETA=linspace(0,2*pi,NOP); x = a0*cos(THETA); y = b0*sin(THETA); X0 = cos(theta0)*x - sin(theta0)*y; Y0 = sin(theta0)*x + cos(theta0)*y; X0 = X0 + x0; Y0 = Y0 + y0; x = a1*cos(THETA); y = b1*sin(THETA); X1 = cos(theta1)*x - sin(theta1)*y; Y1 = sin(theta1)*x + cos(theta1)*y; X1 = X1 + x1; Y1 = Y1 + y1; figure; hEllipse = plot(X0,Y0,'--'); axis equal; hold on; hEllipse = plot(X1,Y1,'--'); axis equal; %% Third ellipse overlap check % First, only use points on the ellipses that can possibly overlap. This % works for most ellipses, but there may still be a few bugs (that will be % corrected later). For each of these points, the closest point on the % other ellipse is calculated. Then, using a vector-based criterion for % each point, the overlap is calculated. if overlap == -1 % Only use points that could possibly overlap Ys = (Y1-y0); s = Ys == 0; Ys(s) = 0.01; TAN = atan((X1-x0)./Ys); if max(abs(diff(TAN))) > pi/2 m = sort(diff(TAN),'descend'); n = find(diff(TAN)==m(1)); o = find(diff(TAN)==m(end)); if o<n; p = o+1:n; TAN(p) = TAN(p)+pi; end if o>n; p = n+1:o; TAN(p) = TAN(p)+pi; end end if length(n)>length(m); n=m; end; X1 = X1(n); Y1=Y1(n); % Only use points that could possibly overlap Ys = (Y0-y1); s = Ys == 0; Ys(s) = 0.01; TAN = atan((X0-x1)./Ys); if max(abs(diff(TAN))) > pi/2 m = sort(diff(TAN),'descend'); n = find(diff(TAN)==m(1)); o = find(diff(TAN)==m(end)); if o<n; p = o+1:n; TAN(p) = TAN(p)+pi; end if o>n; p = n+1:o; TAN(p) = TAN(p)-pi; end end if length(n)>length(m); n=m; end; X0 = X0(n); Y0=Y0(n); figure; hEllipse = plot(X0,Y0,'bo'); axis equal; hold on; hEllipse = plot(X1,Y1,'ro'); axis equal; % Only check point with shortest distance away clear CLOSE; j = length(X0); CLOSE(1:length(X0),1:3) = 0; for i = 1:length(X0) DIST = [X0(i)-X1;Y0(i)-Y1]'; NORM = sqrt(DIST(:,1).^2+DIST(:,2).^2); n = find(NORM == min(NORM)); if length(n) == 1 CLOSE(i,1) = sort(NORM(n)); CLOSE(i,2) = i; CLOSE(i,3) = n; elseif length(n) == 2 CLOSE(i,1) = NORM(n(1)); CLOSE(i,2) = i; CLOSE(i,3) = n(1); j = j + 1; CLOSE(j,1) = NORM(n(2)); CLOSE(j,2) = i; CLOSE(j,3) = n(2); end end % Weed out points that are furthest away n = ceil(length(X0)/2); if n > 2; CLOSE_sort = sort(CLOSE); m = CLOSE_sort(n); o = CLOSE(:,1) > m; CLOSE(o,:) = []; end if size(CLOSE,1) < 3; overlap = 1; % Something screwy going on - REJECT else for ii = 1:size(CLOSE,1) i = CLOSE(ii,2); if i == 1; j = 1; else j=i-1; end; if i == length(X0); k = length(X0); else k=i+1; end; r12 = [X0(k)-X0(j) Y0(k)-Y0(j)]; r1 = [r12(2) -r12(1)]; %normal to ellipse rc = [x0-X0(i) y0-Y0(i)]; n = dot(r1,rc); if n < 0; r1 = -r1; end; j = CLOSE(ii,3); r2 = [X1(j)-X0(i) Y1(j)-Y0(i)]; n = dot(r1,r2); if n > 0; overlap = 1; break; end; if overlap == 1; break;end end end end %% Last overlap step % Last, if none of the checks found an overlap between the two ellipses, % then the overlap is 0. if overlap == -1; overlap = 0; end end Ishu on 8 Sep 2023 Hi Shubham, As you want to calculate if two ellipses are overlapping or not and your code initializes the variables 'x0', 'y0', 'a0', 'b0', 'theta0' for the first ellipse, and 'x1', 'y1', 'a1', 'b1', 'theta1' for the second ellipse. 1. The code first generates points on the first ellipse using the parameters 'a0', 'b0', and 'theta0'. Similarly, it generates points on the second ellipse using the parameters 'a1', 'b1', and 'theta1'. 2. The function then selects points on the ellipses that could possibly overlap based on their orientations. 3. It then calculates the closest point on each ellipse for each selected point. 4. The function checks if any points on the second ellipse fall inside the first ellipse using a vector-based criterion. 5. If there is an overlap, the variable overlap is set to 1; otherwise, it remains 0. The tangent at each point on the ellipse is calculated to determine the orientation of the ellipse. And the reason for checking if the difference in tangent angles is greater than 90 degrees "diff(TAN) > pi/2" is to handle cases where the ellipses have a non-monotonic change in the tangent angle. When the tangent angle changes rapidly, it indicates a change in the orientation of the ellipse. In such cases, there might be a possibility of the ellipse overlapping with itself due to a sharp change in its shape . For the better visualization of overlapping you can plot "both the ellipses" and "the points that could possibly overlap" on the same figure, not the different ones. Hope it helps!

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# The Thirteen Books Of Euclid's Elements, Tr. From The Text Format: Paperback Language: English Format: PDF / Kindle / ePub Size: 8.05 MB For example, kindergarten and first grade students intuitively solve a variety of problems involving joining, separating, or comparing quantities by acting out the problems with collections of objects (Carpenter & Lehrer, 1999). Learn about many different animals, big and small. Reston, VA: National Council of Teachers of Mathematics. Warm jupiters are an unexpected population of extrasolar planets that are too near to their host to have formed in situ, but distant enough to retain a significant eccentricity in the face of tidal damping. Pages: 570 Publisher: Nabu Press (April 6, 2012) ISBN: 127953222X Introduction to Decimals Workbook Radial Math Long Division with Remainders Workbook: A Fun & Creative Way to Practice Dividing My Five Book : My Number Books Series Magic Monsters Count to Ten Contemporary's Number Power 4: Geometry: a real world approach to math (The Number Power Series) Government by the People, 2011 Brief Edition with MyPoliSciLab with eText -- Access Card Package (9th Edition) Making Sense of Maths: Fair Shares If the sum has two digits then write its last digit in the tens-column under the line, and carry its first digit over to the next column: in this case line, and the algorithm is finished. When the algorithm finishes, the number under the line is the product of the two If the multiplicand has a hundreds-digit, find the product of the multiplier and the hundreds-digit of the multiplicand, and to this product add the carry digit if there is one Peterson's Sat Mat Flash: The read online Peterson's Sat Mat Flash: The Quick Way. Users must answer simple math problems laid out on a bingo board , cited: Algebra for College Students download online www.patricioginelsa.com. What change had he left out of 75 ct.? 7 Management Information Systems: Managing the Digital Firm (A Custom Edition for St. Petersburg College) http://drrajaratnam.com/freebooks/management-information-systems-managing-the-digital-firm-a-custom-edition-for-st-petersburg. They were unique among Chinese women in refusing to have their feet bound. ] A third suggestion is that it is from the archaic Chinese root for the number seven, which still persists in the Tanabata festival on July seventh in Japan which celebrates the reunion of the weaver (vega) and the herdsman (altair) , e.g. Solutions of Weekly Problem Papers Solutions of Weekly Problem Papers. No One Slumbers When We Use Numbers! (Science Made Simple) Collins Easy Learning KS1 – Times Tables Bumper Book Ages 5-7 Mathematics for Nurses with Clinical Applications At Home with Mental Maths (7-9) Reducing Mixed Numbers to Improper Fractions. 123. A mixed number may be reduced to an improper fraction. Reduce 12} to an improper fraction. 12} In 1 there are 4 fourths; and in 12, twelve 4 times 4 fourths, or 48 fourths. 48 fourths 48 4- 1 = 49 and 1 fourth make 49 fourths The prelude;: Or, Growth of a poet's mind (text of 1805) http://rockxiao.com/?library/the-prelude-or-growth-of-a-poets-mind-text-of-1805. Find the product of the tens-multiplier and the multiplicand and write it down in a row—call it the "tens-row"—under the ones-row, but shifted one column to the left. That is, the ones-digit of the tens-row will be in the tens-column of the ones-row; the tens-digit of the tens-row will be under the hundreds-digit of the ones-row; the hundreds-digit of the tens-row will be under the thousands-digit of the ones-row , cited: A Street Called Place Value read here www.patricioginelsa.com. Thus it is relevant to calculate the life expectancy of a resource under conditions of constant rates of growth. Under these conditions the period of time necessary to consume the known reserves of a resource may be called the exponential expiration time (EET) of the resource. The EET is a function of the known size R of the resource, of the current rate of use r0 of the resource, and of the fractional growth per unit time k of the rate of consumption of the resource ref.: Key to Ray's new arithmetics, intellectual and practical therajaratnamfoundation.com. Various sources across the internet have exposed a HUGE celebrity secret to erase wrinkles - without botox or surgery! How do Hollywood starlets look so radiant and youthful well into thier 40's, 50's, and even 60's ref.: Introduction to the National Arithmetic, On the Inductive System: Combining the Analytic and Synthetic Methods; in Which the Principles of the Science Are Fully Explained and Illustrated download for free? ISBN 3-7643-3325-1. revised edition (1961) in Russian ed.). A5225 V.22. • Panza, Marco (1992). “La forma della quantità". Cahiers d'Histoire de Philosophie des Sciences 38. Volume 1, Parte III, Cap. 1, “La questione della serie di Grandi (1696 - 1715)", pp. 296–345. • Reiff, Richard (1969) [1889]. R39 they deal with the history of Grandi's series. Hardy (p. 21) calls it “useful but uninspiring and not always • Sandifer, Ed (June 2006). “Divergent series” (PDF) ref.: The teaching of primary arithmetic, a critical study of recent tendencies in method; The teaching of primary arithmetic, a. Fractions, Decimals, Ratios, and Percents: Hard To Teach and Hard To Learn? (Mathematics Teaching Cases) American Elementary Arithmetic - Primary Source Edition Carol Vorderman's Times Tables Made Easy Arithmetic Refresher, An The History Of The Calculus Of Variations During The Nineteenth Century (1861) A Treatise on the Differential Calculus: With Numerous Examples Formal logic, or, The calculus of inference, necessary and probable Mental Math for Pilots (Professional Aviation series) Fundamentals with Elements of Algebra Elementary Arithmetic: Combining Oral and Written Exercises Basic College Mathematics, Media Update, 2nd Edition Today's Mathematics

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# Is Water Wet Science Bill NYe? I was just thinking, Jools Watsham: ## Bill Nye is a scientist, but what kind of scientist is he? Bill Nye is an inventor, scientist, engineer, and comedian. He graduated from Cornell University with a bachelor’s degree in mechanical engineering, where he studied under Carl Sagan. Before producing and anchoring his Emmy Award-winning PBS show Bill Nye the Science Guy, he worked as an engineer on the Boeing 747. He has Honorary Doctorates from Lehigh University, Willamette University, Quinnipiac University, Rensselaer Polytechnic Institute, Goucher College, and Johns Hopkins, and is a visiting professor at Cornell on a regular basis. ## What did Bill Nye, the Science Guy, come up with? He had designed a hydraulic pressure resonance successor tube by the time he debuted his namesake television series Bill Nye the Science Guy in 1993, which is still used in Boeing 747 jets today. ## Is water moist in the scientific sense? The ability of a liquid to absorb water is called wetness. attach to a solid’s surface, thus when we When we say something is moist, we’re referring to the liquid. is clinging to a material’s surface. Whether an object is moist or dry is determined by a number of factors. forces. Attractive forces are cohesive forces. within the liquid, causing the molecules in the liquid to To stick together, liquids tend to stick together. Cohesive Surface tension is also caused by forces. tension. If the forces of cohesion are strong, If a force is strong enough, liquid molecules will gravitate toward it. They won’t spread out if you stay close together. a large portion of an object’s surface On the other hand Adhesive forces, on the other hand, are appealing. forces acting on the liquid and the liquid’s surface material. If the adhesive forces are sufficiently strong, The liquid will attempt to expand out onto the surface. as much as possible on the surface So, how drenched is a The balance between these factors determines the surface. two opposing forces If the adhesive forces are strong enough, (liquid-solid) forces are greater than cohesive forces. We say the material becomes wet when it becomes (liquid-liquid). and the liquid tends to spread out to get the most out of it contact with the outside world If, on the other hand, The liquid-solid adhesive forces are less. We say that the cohesive forces (liquid-liquid) are stronger. The substance is dry, and the liquid has a tendency to condense. beading up into a spherical drop and attempting Contact with the surface should be kept to a minimum. Water has a fairly strong cohesive strength. as a result of hydrogen bonding interactions, and so is not as certain liquids, such as water, are good at wetting surfaces. alcohols or acetone Water, on the other hand, does wet. Glass, for example, is one of these surfaces. Adding Detergents can improve the wetting ability of water by reducing the forces of cohesion Resistant to water Gore-tex fabric, for example, is made of. hydrophobic (water-repellent) substance repellant) and, as a result, the forces of cohesion within the Water (liquid-liquid) is substantially more powerful than Water has a strong adhesive force (liquid-solid) and tends to stick together. bead-up on the material’s outside and you’ll have To respond to this question, we must first define the term. “Wet” is a phrase used to describe something that is damp. If we define “wet” as the state of being wet, a liquid that adheres to a solid surface, like in We can’t claim that if water is wetting our skin. Because it takes a liquid to make water wet, it is wet by itself. AND, to define the term “wet,” a solid. If “wet” is defined as a sensation, When we come into contact with a liquid, we obtain Yes, water makes us wet. If we look at the definition of “wet” means “liquid or wet.” wetness “, then water is unquestionably wet because is made up of liquid, and in this sense, everything is made up of liquid. Because liquids are all made of water, they are all moist. liquids. This, I believe, is a case of a word. being useful only in the right circumstances ## Is there a difference between wet and dry water? • Water is moist in the sense that it is a liquid that flows readily due to its low viscosity, which is due to its molecules being loosely connected together. Water has a relatively high latent heat of vaporisation, which is the amount of heat it draws from its surroundings in order to turn liquid water into water vapour, which contributes to the sensation of dampness. ## Bill Nye, how many PHDS does he have? Bill Nye, despite being one of the world’s most well-known scientists, only possesses one degree, which he received for graduating from Cornell University decades ago. Bill received a Bachelor of Science in mechanical engineering while attending school there. Following graduation, Bill went to work for Boeing before embarking on a career as a stand-up comedian, which would eventually propel him to prominence. ## Is it possible to observe water vapor? Clouds aren’t made up of water vapor. Water vapor is the gaseous condition of H2O that is imperceptible to the naked eye. On a hot summer day, the air surrounding you is thick with water vapor, but you can’t see it. In the cold of winter, on the other hand, there is very little water vapor in the air, but you may easily form clouds with your breath. Clouds are spherical groupings of floatable liquid water droplets or ice. Water vapor in the air condenses back into liquid in the form of droplets when it becomes chilly enough. Condensation, on the other hand, is not automatic. It takes a small amount of matter, called a condensation nucleus, to kickstart the process. According to Louis J. Battan’s book “Cloud Physics,” dust, salt, and ice in the air do the trick by creating a surface for the water to condense on. Clouds are white because the water droplets that make up the cloud are the perfect size to scatter light in a resonant manner, according to Mie scattering. Because Mie scattering is wavelength independent, all colors are reflected. A mixture of all hues is perceived by humans as white. When the cloud’s water droplets become too large, their weight overcomes the cloud’s buoyancy, and the rain begins to fall. Drops that are large enough to fall as rain scatter light geometrically rather than according to Mie scattering. Clear drops are what we see. Returning to the original topic, clouds move because water droplets are blown around by the wind. Topics: ice, steam, water droplets, water vapor, cloud, clouds, condensation, gas, humidity, cloud, clouds, condensation, gas, humidity, ice, steam, water droplets, water vapor ## What makes evaporated water so pure? The water cycle is made up of six major processes. These are the following: Some of the water in the seas and freshwater bodies, such as lakes and rivers, gets warmed by the sun and evaporates during the water cycle. Impurities in the water are left behind during the evaporation process. As a result, the water that enters the atmosphere is cleaner than before. When condensation produces very minute water droplets, they remain suspended in the atmosphere. These millions of suspended water droplets form clouds in the sky or fog on the ground. Only when there are little dust particles present around which the droplet can form does water condense into droplets. Water travels from the Earth’s surface to the atmosphere and back again as a result of evaporation, condensation, and precipitation. Surface runoff is an important aspect of the water cycle because it allows much of the water to return to the oceans, where a lot of evaporation takes place. Many of the pollutants in the water are filtered out as the water passes through the soil and rock layers. This filtration procedure aids in the purification of the water. ## What happens if you put a glass of water in a closet for a few days? What happens if you put a glass of water in a closet for a few days? The glass will eventually run dry.

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[Mathematics] [Other] [Home] # Squaring the Circle Pi, the ratio of the circumference of a circle to its diameter, is 3.14159 26535 89793... to 15 decimal places. It is, roughly, 3 1/7, or 22/7. A better fractional approximation is 3 16/113, or 355/113. The latter approximation, 355/113, was first discovered by the Chinese astronomer and mathematician Tsu Ch'ung-chih (Zu Chongzhi) in the fifth century. In the West, it was discovered in 1585 by Adriaan Anthonisz, and first published in 1625 by his son, Adriaan Adrianszoon, better known as Peter Metius. Other mathematical constants, such as the base of the natural logarithms, e, 2.71828 18284 59045..., or Euler's constant, 0.57721 56649 01532..., are almost always used as is in mathematical formulas, but many formulas involving pi use instead either 2*pi or pi/2. The earliest known use of pi to represent the circle ratio was by William Jones in Synopsis Palmariorum Mathesos; or, a New Introduction to the Mathematics, and that notation became generally popular due to the use of that symbol by Euler. Recently, it has been proposed that we should use 2*pi as the fundamental constant instead, represented by the Greek letter tau, so as to make understanding some initial steps in the geometry of circles more obvious; and then someone later suggested that, as it is easier to multiply than divide, that instead we should use pi/2 as the constant, represented by the Greek letter eta. While I think it's much too late to change, it could well be that an alien technological civilization could have indeed used either of those two alternate values as the fundamental value of the circle ratio, and so they might not be looking for a signal sent at a frequency of pi times the 1420.40575 MHz emission line of interstellar hydrogen. As the area of a circle is pi times the square of its radius, the ratio of the side of a square to the diameter of a circle with the same area is one half of the square root of pi. This value is about 0.88622 69254 52758..., again, to 15 decimal places. An approximation to this value used by the ancient Egyptians, as recorded in the Rhind papyrus by the scribe Ahmes, is 8/9. A better rational approximation to this value is 148/167, and the diagram to the left, showing a circle, and a square equal to it in area, as closely as can be drawn in discrete pixels in a diagram of reasonable size, uses this approximation. Incidentally, if one squares 148/167, and then multiplies by four, one gets the approximation for pi 3.14159704543..., whereas 355/113 is 3.1415929203539823..., and, so, since pi is 3.14159 26535 89793..., the latter is over 16 times as close an approximation to pi (the ratio of the differences works out to 16.46338...) and it is correct to one additional decimal place as a result. While the circle can't be squared using a straightedge and compasses in a conventional manner, just as the angle can't be trisected that way (although there is a construction, known to the ancient Greeks, that used a straightedge and compass somewhat unconventionally that does trisect it) the value of pi can certainly be calculated, and calculating pi can be termed "squaring the circle". In the case of squaring the circle, the rule that has to be broken is the one requiring a construction to be done in a finite number of steps. Here is the Quadratrix of Hippias: at least a crude sketch of it I made by hand. The principle of that curve should be obvious from the diagram; it contains those points that have the same proportion in height as they do in angle. Since one can bisect an angle and a line with straightedge and compasses, one can use them to make as many points as one wishes on this curve, with as close a spacing as desired. But that does not mean that one can draw certain exact points on that curve that one might want, such as the one where it crosses the horizontal line through the center of the circle, the distance of which from the center of the circle being exactly 2/pi times the radius of the circle. ### Areas and Volumes Pi is defined as the radius of the circumference of a circle to its diameter, but it's also used in the formulas for the area of a circle and the volume of a sphere. To start with, let's see how those formulas could be derived. The definition of pi is the ratio of the circumference of a circle to its diameter. The circumference of a circle is the length of the curved line which constitutes the circle itself, and the diameter of a circle is how wide it is at its widest part. Since circles are round, and thus the same in all directions, it's also how high it is at its tallest part, and so on for any direction. Pi is also used for calculating the area of a circle, the area of the surface of a sphere, and the volume of a sphere. The diagram above is an attempt to justify the formula for the area of a circle, A = pi * r^2. This kind of diagram can be found in many mathematics textbooks, and one was included in a book by Sato Moshun, in Japan, in 1698; also, an illustration of the same idea appears in the Notebooks of Leonardo da Vinci. Basically, one can cut the circle into more and more slices, and as one does so, the shape that can be built by rearranging those slices gets closer and closer to a rectangle with the radius of the circle as its height, and half the circumference of the circle as its width. This made ancient diagrams like this particularly notable, since the idea of a limit of an estimate of the area of a shape by cutting it into smaller and smaller pieces is a basic idea that led to the integral calculus. It was Archimedes of Syracuse who found that the surface area of a sphere is the same as that of the curved surface of a cylinder with the same diameter and the same height - just the curved surface, not including the flat top and bottom. Why this is the case is illustrated by the diagram: the cosine of the angle theta both determines the size of a circle at a given height of the sphere, and the amount vertical distances on the sphere's surface are foreshortened when projected on the surrounding circle. This is the basis, incidentally, of an equal-area cylindrical map projection, which I describe on this page. So, since the surface of the cylinder can be unrolled into a rectangle with a height equal to the sphere's diameter, and a width equal to the sphere's circumference, the surface area of a sphere is equal to pi * d^2, or 4 * pi * r^2. Just as a circle can be cut into many tiny pie wedges, a sphere can be thought of as many tiny little pyramids, with a height equal to the radius of the sphere, and the bases of which total in area to the surface area of the sphere. This would tell us the volume of a sphere, now that we know the formula for the surface area of a sphere, if we knew how to calculate the volume of a pyramid. The volume of a pyramid is one-third of the area of its base times its height. So the volume of a sphere is (4/3) * pi * r^3. Why the volume of a pyramid is exactly one-third of the product of its base and height can be illustrated the most simply by the diagram above. A cube has six faces, as anyone who has ever played a game with (conventional!) dice knows: and its volume can be divided into six pyramids, with bases having an area equal to the side of the cube squared, and a height equal to half the height of the cube. And, of course, one-sixth is one-half of one-third. ### Kinds of Numbers One of the basic facts about pi is that it is a transcendental number. I'd like to say a few words about what that means. The most basic numbers are the integers; we get those by counting objects one after another. Now, there are negative integers, and yet you can't hold -3 pebbles in your hand; extending the number system in this direction leads to the imaginary numbers, which raise a different kind of question, so I will put that aside here. Instead, the next step is the rational numbers; that is, fractions that have an integer as both the numerator and the denominator. When, instead of counting objects, we measure out liquids, or we measure out lengths, or set up systems of units to use in these measurements, we usually use fractions like this. Since integers can go as big as we like, we can get as close as we like to any desired volume, weight, or distance with a rational number. So from one kind of practical viewpoint, the rational numbers are all we need. However, the relationships and formulas that are found in mathematics are useful for many practical purposes, and to derive them, we have to be able to think of numbers and points and lines and shapes in an abstract manner, dealing with their exact values and positions, without concern for the limitations of the real world that often mean that a good approximation is as good as we'll either need or be able to get. One of the simplest numbers that isn't rational is the square root of two - the length of the diagonal of a square of length one. It's easy enough, starting with a line of unit length, to draw a square with sides all of that length, in a finite number of steps, using a straightedge and compass strictly in the conventional manner. And that lets you then draw the diagonal and copy it. So the square root of two is what is called a constructible number. These numbers are those which can be produced from integers by addition, subtraction, multiplication, division, and taking square roots. This includes fourth roots or eighth roots or sixteenth roots, because one can take square roots repeatedly. One thing that can't be done in a finite number of steps, using a straightedge and compass strictly in the conventional manner, is to trisect the angle. But if you do something sneaky, for example, holding your compass against the straightedge to indicate a length along it, while you move the two tools into position, then you can trisect the angle: Archimedes first found this construction, and I remember seeing an elaborate version of that construction featured in the letters column of Mechanix Illustrated. But while ingenuity like that of the television character MacGyver certainly has its uses, it's also useful to have a category for the numbers that can be made with straightedge and compass in a pedestrian fashion. One of the other famous problems that was not solvable with straightedge and compasses was the "Duplication of the Cube", that is, given a line of unit length, drawing a line that is the cube root of two times as long. So the next level above constructible numbers are those numbers that are expressible by radicals. The numbers that can be produced from integers by addition, subtraction, multiplication, division, and taking the n-th root for any integer n are also a group of numbers that are closed under that set of operations. If you try to solve a quadratic equation, you can use the formula that the equation a*x^2 + b*x + c = 0 is true if x equals either (-b+sqrt(b*b-4*a*c))/(2*a) or (-b-sqrt(b*b-4*a*c))/(2*a). So the roots of a quadratic equation are numbers that are expressible by radicals. Formulas were also found, but more complicated ones, to solve the cubic equation, where x^3 is also present, and the quartic equation, which also has x^4, too. But a famous event in the history of mathematics was the proof that the quintic equation didn't always have solutions that were expressible by radicals. x^5 = 7 has the fifth root of 7 as its solution, so some quintic equations do have such solutions - but the equation x^5 + x + a = 0 does not. Numbers which are the solutions of equations of the form a*(x^n) + b*(x^(n-1)) + c*(x^(n-2)) + ... z = 0, starting with any n, however large, where all the coefficients a, b, c... are rational numbers, are called algebraic numbers. But even the algebraic numbers don't cover all the possible values for such things as a distance along a line. The circumference of a circle of unit diameter, which is pi, the number we are talking about, is one of those numbers that isn't algebraic, and that means it is called a transcendental number. The first proof that pi was transcendental was due to Lindemann in 1882. ### Calculations of Pi Archimedes is the first person known to have derived the value of pi by means of mathematical reasoning. Using polygons of 96 sides, one enclosing the circle, and one enclosed by the circle, he established that pi was less than 3 1/7, but greater than 3 10/71 in his work Measurement of the Circle. He was credited by Heron of Alexandria with having subsequently improved those bounds, proving that pi was less than 195882/62351 but greater than 211872/67441 (these figures are, in fact, a modern guess at what was meant, as at least in the copies of Heron that we have, they are garbled); this was in a lost work with the title Plinthides and Cylinders. Many years later, also using polygons and geometry, Ludolph van Ceulen calculated the value of pi to 34 decimal places. Numerous references state that because of this, pi became generally known as the Ludolphine Number (Ludolphische Zahl) in Germany; thus, for example, it appeared in the title of an 1885 paper by Weierstrass; however, that term was most popular prior to 1910, and was much less common in Germany in the postwar era. This method of calculating pi was difficult, but at first it was the only valid mathematical method known. Eventually, as a consequence of the development of calculus, it became understood how to easily develop Taylor series for the various elementary functions, but the arctangent series was developed before the invention of calculus. The earliest mathematical formula for pi was that derived from how it might be calculated geometrically with polygons (starting from a square, rather than from a hexagon as Archimedes did) by François Viète: ``` pi 2 2 2 ---- = --------- * ------------------- * ----------------------------- * ... 2 sqrt(2) sqrt(2 + sqrt(2)) sqrt(2 + sqrt(2 + sqrt(2))) ``` This is a somewhat modernized form of his formula, not in the exact form he originally gave. The same is true for the infinite product given by John Wallis in 1650: ``` pi 2 * 4 4 * 6 6 * 8 ---- = ------- * ------- * ------- * ... 4 3 * 3 5 * 5 7 * 7 ``` The power series for the arctangent function, which can be used to calculate pi, is as follows: ``` 3 5 7 x x x x atn(x) = --- - ---- + ---- - ---- + ... 1 3 5 7 ``` This series is known as Gregory's series, after James Gregory, who discovered it in 1671; not until much later did Western mathematicians learn that it was discovered by Madhava of Sangamagrama more than 250 years previously. Since the arctangent given by this series is in radians, the arctangent of 1 is equal to one-quarter of pi. That, however, is a value for which this series converges at an extremely slow rate, so slow as to be useless in practice as a way to calculate pi. For x less than 1, however, it converges at an acceptable rate, faster as x becomes smaller. If it is being used in an arctangent function, for x greater than one, one would calculate the arctangent of 1/x and subtract that from pi/2, as the series does not converge for x greater than one. For values of x close to 1, either above or below it, say between 1/2 and 2, another transformation so that the angle away from pi/4 would be calculated instead would be used in practice. But today techniques like CORDIC would be used instead, as they are faster. None of these techniques help in calculating the value of pi, however. One way to use a value less than 1 as the input to the arctangent series and yet produce a result that does lead to a value for pi would be to use the fact that 30 degrees, or, in radians, one-sixth of pi, is the arcsine of 1/2. The Pythagorean theorem can be used to determine that the arcsine of 1/2 is also the arctangent of one over the square root of three. Since the terms of the arctangent series involve powers of x that are multiplied by x squared at each step, one can do the calculation only using whole numbers until you multiply in the square root of three at the very end. This was how pi was calculated by Abraham Sharp in 1699 to 71 digits. Isaac Newton, one of the two independent inventors of the calculus, derived the arcsine formula in 1676: ``` 3 5 7 1 x 1 * 3 x 1 * 3 * 5 x arcsin(x) = x + --- * --- + ------- * --- + ----------- * --- +... 2 3 2 * 4 5 2 * 4 * 6 7 ``` and he used it to calculate pi to at least 15 digits from the fact that pi/6 is the arcsine of 1/2. Incidentally, pi/10 is the arctangent of sqrt(5 - (2/5) * sqrt(5)) and the arcsine of sqrt(1 + sqrt(5))/4, which latter figure is one half of the golden ratio. This has more to do with the relationship between the golden ratio and the pentagon than any relationship between it and pi, of course. Because it is possible to construct a 17-sided polygon by straightedge and compasses, there are also expressions involving the square root of 17 that could also be used in this fashion. It would be more convenient, however, if a simpler quantity not involving a square root, and significantly smaller than 1, could be used in the arctangent formula, because that would lead to a series that would converge more quickly even than the arcsine formula for x=1, let alone the arctangent formula for that value. While no single rational value of x between 0 and 1 has an arctangent that is a rational multiple of pi, if one is willing to evaluate the arctangent function two or more times, this simplification can be obtained. The diagram to the right illustrates how one can calculate, given the tangents of two angles, the tangent of the sum of those angles. Let the length of the line segment from A to O be equal to 1. Then, the length of the line segment from A to D is the tangent of the angle theta; as the length of the line segment from B to O also equals 1, the length of the line segment from B to C is the tangent of the angle phi; and the length of the line segment from A to G is the tangent of the angle theta plus phi. Let us denote the tangent of theta by P, the tangent of phi by Q, and the tangent of theta plus phi by R. From the Pythagorean theorem, we know the length of the line segment from D to O is equal to the square root of P squared plus 1. And therefore the length of the line segment from D to E is equal to Q*sqrt((P^2)+1). Given that the angle FDE is also theta, the same ratio is applied a second time, and the length of the line segment from D to F is equal to Q*((P^2)+1). While the small triangle that remains to be understood in order to work out the length of the line segment from F to G which remains is not a right triangle, it could be broken into two pieces that are right triangles. However, it is apparent at this point that we're not taking quite the right approach, and we need to change one thing in the diagram. In this diagram, ignoring the point F, and instead paying attention to a new point, H, this time, as the right triangle is turned around, the length of the line segment from D to H is simply Q. The remaining triangle is now a right triangle. But the angle GEH is neither phi nor theta, it's phi plus theta, and the tangent of that is what we want to calculate from P and Q. Are we in trouble? No, we aren't. The length of the line segment EH is clearly equal to P times Q. The ratio of P plus Q to 1 minus P*Q is equal to R. One can drop a perpendicular from E down to the line segment AO to make it obvious how this conclusion can be reached: since the ratio of the lengths of the line segments HG and HE is the arctangent of theta plus phi, just as the ratio of the lengths of the line segments AG and AO is the same value, a triangle, smaller in size by the factor (1-(P*Q))/1 can be formed in which the ratio of P+Q to 1-(P/Q) can be seen to be R. One example, due to Euler, and based on which these diagrams were drawn, is that atn(1) = atn(1/2) + atn(1/3). So if 1/2 = tan(theta) and 1/3 = tan(phi), tan(theta+phi) is 5/6 divided by (1 - (1/2)*(1/3)), which is 5/6 divided by itself, or 1. Applying this formula repeatedly, though, it becomes possible to obtain even better results. So that we could use something that converges even faster than powers of 1/2, could it be that if we solve atn(1/2) = atn(x) + atn(1/3), we would have something useful as x; that way, we wouldn't have to calculate the arctangent three times, we could just multiply atn(1/3) by two. As it turns out, x equals 1/7, since 1/2 is 10/21 divided by (1 - (1/3)*(1/7)) or 20/21. If atn(1/2) = atn(1/7) + atn(1/3), then it's also true that atn(1/3) = atn(1/2) - atn(1/7). Thus, we now have pi/4 = atn(1) = 2*atn(1/3) + atn(1/7), which is an improvement, since atn(1/3) converges more quickly than atn(1/2). So we can subtract arctangents as well as adding them. This led to the formula pi/4 = atn(1) = 4*atn(1/5) - atn(1/239), derived by John Machin in 1706, which was used for a number of attempts to calculate pi to a large number of digits. For example, it was used for two of the earliest calculations of pi on a computer, one to 2037 places on the ENIAC by Reitweisner in 1949, and one to 3089 places on the NORC by Nicholson and Jeenel in 1954. From 1873 to 1945, it was believed that the value of pi was known to 707 digits, having been calculated to that precision, also using Machin's arctangent relation, by William Shanks. In 1945, calculations by D. F. Ferguson established that only the first 527 digits of that value were correct; his first calculations were made with pencil and paper, but he later used a mechanical calculator to help him to derive 808 digits in 1947. While there was a mistake in the value he initially had published in March 1947, in September 1947 he corrected the error. Originally, when I first wrote this page, I thought that the error was not the fault of William Shanks alone. In 1853, he had published an earlier calculation of pi to 607 decimal places which, also being correct only to the first 527 places, contained the same error that marred his later calculation. This publication was in the form of a book which included each of the terms in the two arctangent series used for the calculation, making it much easier to check portions of the calculation for error than it was to make the calculation in the first place. However, those individual terms were only given to 530 places, not to 607 places. That still left open a possibility of other mathematicians finding the error, since this was three places beyond where it occurred, but it clearly makes the situation different than it would have been had that not been the case. Another mathematician did check William Shanks' calculation as far as the first 405 (or 440?) digits. Ironically, the mathematician who did so was William Rutherford, who himself, in 1841, had published a value of pi to 208 digits which was correct only to the first 152 digits. That value, however, was soon corrected, in 1844, through a calculation carried out by Zacharias Dase. A document by Erwin Engert, dated January 1, 2012, is available on the Web, which sorted out typographical errors in published versions of Shanks' 707 digits of pi, and which investigated where the error was made. Later, an article in American Scientist by Brian Hayes, in their September-October 2014 issue, continued the analysis, finding additional details of the errors, but not all the discrepancies have been accounted for, so it is not yet possible to re-calculate the erroneous value of pi that Shanks would have produced to more places. Doing so might be of interest for this reason: his 707 digits of pi contained the digit 7 less often than might be expected from random chance, unlike the actual value of pi, which so far has given no indication that its digits are not statistically like a random sequence. If this anomaly were to continue in subsequent digits, it might provide an insight into the conditions under which a mathematical transcendental number like pi could have a digit sequence that is not normal. Although faster methods for computing pi to a large number of places are now known, arctangent formulas have continued to be used in the calculation of pi even fairly recently. The calculation of pi by D. F. Ferguson to 808 digits in 1947 in which a desk calculator was used was done using the following identity: atn(1) = 3*atn(1/4) + atn(1/20) + atn(1/1985) After the calculations on the ENIAC and the NORC used Machin's identity, a calculation of pi to 10,021 places on the Ferranti Pegasus computer by G. E. Felton used the identities atn(1) = 8*atn(1/10) - atn(1/239) - 4*atn(1/515) atn(1) = 12*atn(1/18) + 8*atn(1/57) - 5*atn(1/239) In the first identity, the first term, being atn(1/10) instead of atn(1/5), is both faster-converging and more convenient for decimal calculations than the first term of Machin's series, and the remaining two terms converge very quickly. The second identity, due to Gauss, used for checking the result, was used again in a later calculation to be mentioned below. One of the most recent such calculations was in 2002, undertaken by Yasumasa Kanada, in which he had a computer calculate pi to over one trillion digits, using the following two arctangent relations: atn(1) = 44*atn(1/57) + 7*atn(1/239) - 12*atn(1/682) + 24*atn(1/12943) atn(1) = 12*atn(1/49) + 32*atn(1/57) - 5*atn(1/239) + 12*atn(1/110443) Because atn(1/57) and atn(1/239) occur in both relations, but multiplied by a different amount, errors for them would still make the two results disagree, and yet labor - or, rather, machine time - can be saved as these values need only be calculated once. The second identity was found by F. C. W. Störmer in 1896; the first one by Kikuo Takano in 1982, who had used these same formulas himself for calculating pi to a lesser number of digits. This basic technique was also used earlier, in 1961, by Daniel Shanks and John W. Wrench to calculate pi to 100,265 places on an IBM 7090 computer. Daniel Shanks, an American, is not known to have any relation to William Shanks. They used the identities: atn(1) = 6*atn(1/8) + 2*atn(1/57) + atn(1/239) atn(1) = 12*atn(1/18) + 8*atn(1/57) - 5*atn(1/239) so again the calculation could be checked even though atn(1/57) and atn(1/239) were only calculated once. Here, Störmer found the first of the two identities used, and the second one was due to Gauss. ### Modern Formulas for Pi As noted, faster methods of calculating pi were discovered later. The following series for 1/pi was discovered by the enigmatic Srinavasa Ramanujan: ``` infinity _________ \ 2 * sqrt(2) \ (4*i)! (1103 + 26390 * i) ----------- * > -------------- * -------------------- 9801 / 4 (4*i) (4*i) /________ (i!) *4 99 i = 0 ``` Yes, 4^(4*i) and 99^(4*i) could be combined to form 396^(4*i); also, 9801 is the square of 99. so this formula can appear in other forms. It was used by R. William Gosper to calculate pi to over 17.5 million digits in 1985. A different series belonging to this class was used by the Chudnovsky brothers, and it has since been used in other calculations for pi: ``` infinity __________ \ \ i (6*i)! 13591409 + 545140134 * i 12 * > (-1) * --------------- * -------------------------- / 3 ((3*i) + (3/2)) /_________ (i!) * (3*i)! 640320 i = 0 ``` again, this is a series for 1/pi. The denominator of the second factor involves operations such as taking the cube and the square root of 640320 that don't have to be repeated for each term of the sum. Since 640320 is 320 * 2001, 320 being 64 * 5 and 2001 being 3 * 23 * 29, this leads to: ``` infinity __________ \ 1 \ i (6*i)! 13591409 + 545140134 * i ---------------------- * > (-1) * --------------- * -------------------------- 426880 * sqrt(10005) / 3 i /_________ (i!) * (3*i)! 262537412640768000 i = 0 ``` and it also appears in this form or similar forms in addition to the original form which is somewhat shorter to write, if not to calculate. How these series are derived involves a number of topics of mathematical interest, as noted in the Wikipedia article on Ramanujan-Sato series. Series for 1/pi of the type discussed above yield a large number of digits of pi at each step; but since the same number of digits of pi are produced at each step, it might be possible to equal their performance with a suitably-designed arctangent relation in which all the arguments to the arctangent function are sufficiently small numbers. Recurrence relations are now known, however, that double, triple, quadruple, or more, the number of digits calculated at each step. The first such relation to be discovered was found by Eugene Salamin and Richard Brent in 1976; they both discovered it independently around the same time. To find pi by this method, follow this recurrence relation: ```a(0) = 1 b(0) = 1/sqrt(2) s(0) = 1/2 a(n+1) = (a(n)+b(n))/2 b(n+1) = sqrt(a(n)*b(n)) s(n+1) = s(n) - (2^(n+1)) * (a(n+1)^2 - b(n+1)^2) ``` and after iterating it as many times as required to obtain the precision sought, the approximate value of pi will be 2 * (a(N)^2)/s(N). This recurrence relation includes the process of taking the arithmetic-geometric mean of a and b. While this method of calculating pi was only discovered in 1976, a recurrence relation involving the arithmetic-geometric mean was long known and used for calculating complete elliptic integrals. For that purpose, this recurrence relation is applied: ```a(0) = 1 b(1) = cos(t) a(n+1) = (a(n)+b(n))/2 b(n+1) = sqrt(a(n)*b(n)) ``` and then K(t) is approximated by pi/(2 * a(N)), where N is the number of iterations taken to achieve the desired precision. E(t) can also be determined, from the formula ``` infinity ________ K(t) - E(t) 1 \ i ------------- = --- * (sin(t) + > 2 * c(i)^2 ) K(t) 2 /_______ i = 1 ``` where c(i) is defined as (1/2) * (a(i) - b(i)). Sometimes, the form of the expression is simplified by defining c(0) as sin(x), although that doesn't correspond to the definition of c(i) for other values of i, so that the sum can start from i=0 without an additional term. In these formulas, t represents the modular angle, often noted by the Greek letter alpha; the argument of the elliptic integral may also be the parameter, noted by the letter m. They are related by m = (sin(t))^2. Later, a number of improved recurrence relations for pi with even faster convergence were developed by Jonathan and Peter Borwein and others; they developed algorithms which tripled, quadrupled, quintupled, multiplied by seven, and multiplied by nine, the number of correct digits at each iteration. Here is the one that multiplies the number of correct digits by nine at each step: ```a(0) = 1/3 r(0) = (sqrt(3) - 1)/2 s(0) = (1 - (r(0)^3))^(1/3) t(n+1) = 1 + 2*r(n) u(n+1) = (9 * r(n) * (1 + r(n) + r(n)^2))^(1/3) v(n+1) = t(n+1)^2 + t(n+1)*u(n+1) + u(n+1)^2 w(n+1) = 27 * (1 + s(n) + s(n)^2)/v(n+1) a(n+1) = w(n+1)*a(n) + ((3^(2*n - 1)) * (1 - w(n+1))) s(n+1) = (1 - r(n))^3 / ((t(n+1) + 2 * u(n+1)) * v(n+1)) r(n+1) = (1 - s(n+1)^3)^(1/3) ``` The result of this computation is that a(N) is the approximation to 1/pi that improves at this large rate. Here are the other relations of this type that are known: the one that triples the number of correct digits at each step is: ```a(0) = 1/3 s(0) = (sqrt(3) - 1)/2 r(n+1) = 3/(1 + 2 * ((1 - s(n)^3)^(1/3))) s(n+1) = r(n+1)/2 a(n+1) = (r(n+1)^2 * a(n)) - 3^n * (r(n+1)^2 - 1) ``` Here, a(N) is the improving approximation to 1/pi. the one that quadruples the number of correct digits at each step is: ```a(0) = 6 - 4*sqrt(2) y(0) = sqrt(2) - 1 y(n+1) = (1 - (1 - y(n)^4)^(1/4))/(1 + (1 - y(n)^4)^(1/4)) a(n+1) = a(n) * (1 + y(n+1))^4 - 2^(2*n + 3) * y(n+1) * (1 + y(n+1) + y(n+1)^2) ``` Once again, a(N) is the improving approximation to 1/pi. the one that quintuples the number of correct digits at each step is: ```a(0) = 1/2 s(0) = 5 * (sqrt(5) - 2) x(n+1) = (5/s(n)) - 1 y(n+1) = (x(n+1) - 1)^2 + 7 z(n+1) = ((1/2) * x(n+1) * ( y(n+1) + sqrt( y(n+1)^2 - 4*(x(n+1)^3) ))^(1/5) a(n+1) = s(n)^2 * a(n) - (5^n) * ( (s(n)^2 - 5)/2) + sqrt( s(n) * (s(n)^2 - 2*s(n) + 5) ) s(n+1) = 25/( (z(n+1) + (x(n+1)/z(n+1)) + 1)^2 * s(n) ) ``` and, again, a(N) converges to 1/pi. The one that multiplies the number of correct digits by seven at each step also requires evaluating a trigonometric function to the same high precision as is desired for the approximation to pi, and thus only provides a gain in efficiency if a similarly fast algorithm for calculating the cosine is known. Another algorithm which also multiplies the number of correct digits by seven at each step required a trigonometric function to be evaluated in every step. Thus, the quintic and nonic algorithms appear to be the most rapid ones available, although there may also be one that multiplies the number of correct digits by sixteen at each step. The algorithm developed by Brent and Salamin was the one used in 2009 for a calculation of pi to over 2.5 billion digits by a team led by Daisuke Takashi on the T2K Open Supercomputer. This was the last record-setting calculation of pi done on a large, expensive computer: subsequent ones have been done by private enthusiasts on commodity hardware. The first of these was one to almost 2.7 billion digits by Fabrice Bellard later in 2009. All subsequent ones, in addition to using commodity hardware, also used the y-cruncher software written by Alexander Yee. Surprisingly, although this meant the calculations took longer, many of them were done using the Chudnovsky series, with a second faster iterative calculation being performed only for verification, instead of using two different iterative calculations. While deriving these fast methods of calculating the value of pi is an impressive accomplishment concerning the computation of pi, this is not the most famous accomplisment of the Borwein brothers in connection with calculating pi. Incidentally, their father, David Borwein, is also a noted mathematician. He was born in Kaunas, Lithuania, in 1924, but was taken by his parents to South Africa in 1930. In 1948, he moved to London, where his graduate studies took place; from 1963, when he initially came to Canada as a visiting professor, he lived in Canada where he held a number of distinguished posts, including that of the head of the mathematics department of the University of Western Ontario and that of the President of the Canadian Mathematical Society. His own mathematical work dealt with classical analysis, including such things as the summability of integrals. Jonathan Borwein passed away unexpectedly and suddenly in 2016 at the age of 65 of natural causes, and was survived by his father as well as his brother Peter. Jonathan and Peter Borwein, together with Simon Plouffe, also developed this series for pi: ``` infinity __________ \ / \ \ 1 | 4 2 1 1 | > ----- * | --------------- - --------------- - --------------- - --------------- | / i | ((8 * i) + 1) ((8 * i) + 4) ((8 * i) + 5) ((8 * i) + 6) | /_________ 16 \ / i = 0 ``` For i=2, for example, the term would be 1/256 * (4/17 - 2/20 - 1/21 - 1/22). Now, neither 4/17 nor 1/21 nor 1/22 are fractions which have a terminating representation in hexadecimal notation any more than they would in decimal notation. (For that matter, 2/20, or 1/10, terminates in decimal notation, but it doesn't terminate either in hexadecimal notation.) However, it is still possible to use this series in an efficient procedure for calculating hexadecimal digits of pi at an arbitrary position without needing to also calculate the digits which come before them, even if how to do this is not trivial. An improved formula of this type was subsequently developed by Fabrice Bellard: ``` infinity __________ \ i / \ 1 \ (-1) | 256 64 4 4 1 32 1 | ---- * > ------- * | ---------------- - ---------------- - ---------------- - ---------------- + ---------------- - --------------- - --------------- | 64 / i | ((10 * i) + 1) ((10 * i) + 3) ((10 * i) + 5) ((10 * i) + 7) ((10 * i) + 9) ((4 * i) + 1) ((4 * i) + 3) | /_________ 1024 \ / i = 0 ``` Initially, when the first of these series was discovered, there was optimism that a similar formula for calculating high-order decimal digits of pi directly might also be found. Later, however, a proof was found that a formula of this particular type could not exist for bases other than powers of two because these formulas are related to arctangent relations for pi, such as the identity of Machin noted above, which do not exist in a suitable form for other bases. Still later, though, a formula of a different type was found that allowed direct calculation of high-order decimal digits of pi. The first such one was found by Simon Plouffe; however, it was quite slow, as the time it would take is proportional to the cube of the position of the digit to be found. Improved algorithms for high-order decimal digits of pi have since been found, but they are still too slow to be competitive with calculating the entire number. However, they are still of theoretical importance, as it might be possible to gain insights from them for a proof, one way or another, addressing the still unsolved question of whether the digits of pi behave statistically like a sequence of random digits: whether or not pi is normal. As an alternative way of calculating pi, it occured to me that if there was a high-speed arithmetic-geometric mean algorithm for calculating the arctangent, one could use a Machin-type arctangent relation in connection with that, instead of with the Gregory series. The first such method I found described in an early paper on the subject of efficient algorithms for the elementary functions required the use of an algorithm for calculating the logarithm that required the value of pi to the full length of the numbers being worked with, but I later found a web page with one without this limitation: ```a(0) = sqrt(1 + x^2) b(0) = 1 a(n+1) = (1/2) * (a(n)+b(n)) b(n+1) = sqrt( a(n+1) * b(n) ) ``` with the arctangent of x being approximated by x/(a(N) * sqrt(1+x*x)), where N is the number of iterations carried out, originally given in Numerical Methods that Work by Forman S. Acton, as cited on the Wolfram Research web site. Machin-like identies have been found that converge even more quickly than the ones given above as having been used in practice. One that I saw which would converge particularly quickly, even using the Gregory series, was this one: atn(1) = 183*atn(1/239) + 32*atn(1/1023) - 68*atn(1/5832) + 12*atn(1/113021) - 100*atn(1/6826318) - 12*atn(1/33366019650) + 12*atn(1/43599522992503626068) so there is an arctangent identity with atn(1/239) as the slowest-converging term; this identity was derived by Hwang Chien-Lih in 1997, but he has since derived even better ones, the best one I have seen anywhere having been found by him in 2004: atn(1) = 36462*atn(1/390112) + 135908*atn(1/485298) + 274509*atn(1/683982) - 39581*atn(1/1984933) + 178477*atn(1/2478328) - 114569*atn(1/3449051) - 146571*atn(1/18975991) + 61914*atn(1/22709274) - 69044*atn(1/24208144) - 89431*atn(1/201229582) - 43938*atn(1/2189376182) at least, that was the best one I had seen anywhere, when I came across it on Wikipedia, but then I found his web site on the subject, which includes even better ones, such as: atn(1) = 20435891*atn(1/28841295) + 6458959*atn(1/133311327) + 10571216*atn(1/152087733) - 190529*atn(1/159358932) + 5127580*atn(1/213495433) + 7798670*atn(1/227661182) - 3154610*atn(1/278263393) - 14603096*atn(1/284862638) - 5959396*atn(1/355671793) - 10585611*atn(1/727507932) - 4139726*atn(1/934981432) + 1560722*atn(1/15234751332) - 2675312*atn(1/106334643058) + 6769449*atn(1/138873731225) + 2229180*atn(1/293153860797) - 2967682*atn(1/169838669284032) Since the successive terms in Gregory's series for the arctangent of x involve x, x^3, x^5, and so on, being multiplied by x^2 each time, having x as one over an eight-digit number means that each step involves multiplying by one over a sixteen digit number, so, although there are more series to sum, this is enough to make Gregory's series comparable to Chudnovsky's series, if still not necessarily quite as fast. Also, incidentally, since atn(1) = 183*atn(1/239) + 32*atn(1/1023) - 68*atn(1/5832) + 12*atn(1/113021) - 100*atn(1/6826318) - 12*atn(1/33366019650) + 12*atn(1/43599522992503626068) and atn(1) = 4*atn(1/5) - atn(1/239) we can calculate atn(1/5) as an intermediate result: atn(1/5) = 46*atn(1/239) + 8*atn(1/1023) - 17*atn(1/5832) + 3*atn(1/113021) - 25*atn(1/6826318) - 3*atn(1/33366019650) + 3*atn(1/43599522992503626068) which is not surprising, as one expects that these formulas are obtained by repeated application of the tangent addition formula. Similarly, since atn(1) = 12*atn(1/18) + 8*atn(1/57) - 5*atn(1/239) and atn(1) = 4*atn(1/5) - atn(1/239) we can also say: atn(1/5) = 3*atn(1/18) + 2*atn(1/57) - atn(1/239) Thanks to another identity by Störmer, atn(1) = 44*atn(1/57) + 7*atn(1/239) - 12*atn(1/682) + 24*atn(1/12943) knowing also that atn(1) = 12*atn(1/18) + 8*atn(1/57) - 5*atn(1/239) we can deduce that atn(1/18) = 3*atn(1/57) + atn(1/239) - atn(1/682) + 2*atn(1/12943) and so we have component relations that can be used to trace a line of descent for that identity from Machin's original formula. Hunting around, I've found another related identity on the web: atn(1) = 88*atn(1/172) + 51*atn(1/239) + 32*atn(1/682) + 44*atn(1/5357) + 68*atn(1/12943) so now we can find an expression for atn(1/57) in terms of arctangents of smaller quantities. However, there's another formula that starts with atn(1/239), unlike the one I first encountered, that is related (it may be due to Jörg Arndt): atn(1) = 183*atn(1/239) + 44*atn(1/515) - 56*atn(1/682) + 88*atn(1/6050) + 24*atn(1/12943) - 88*atn(6826318) With that and atn(1) = 44*atn(1/57) + 7*atn(1/239) - 12*atn(1/682) + 24*atn(1/12943) we can deduce atn(1/57) = 4*atn(1/239) + atn(1/515) - atn(1/682) + 2*atn(1/6050) - 2*atn(6826318) Thus, we now have a series of formulas starting with Machin's original formula, and ending with one the slowest-converging term of which is atn(1/239), where we can follow how the slowest-converging term is replaced with faster-converging ones every step of the way: ``` atn(1) = 4*atn(1/5) - atn(1/239) + 4 * 0 = - atn(1/5) + 3*atn(1/18) + 2*atn(1/57) - atn(1/239) ----------------------------------------------------------------------- atn(1) = 12*atn(1/18) + 8*atn(1/57) - 5*atn(1/239) + 12 * 0 = - atn(1/18) + 3*atn(1/57) + atn(1/239) - atn(1/682) + 2*atn(1/12943) ------------------------------------------------------------------------------------------------------------------------------------------- atn(1) = 44*atn(1/57) + 7*atn(1/239) - 12*atn(1/682) + 24*atn(1/12943) + 44 * 0 = - atn(1/57) + 4*atn(1/239) + atn(1/515) - atn(1/682) + 2*atn(1/6050) - 2*atn(6826318) ------------------------------------------------------------------------------------------------------------------------------------------------------------- atn(1) = 183*atn(1/239) + 44*atn(1/515) - 56*atn(1/682) + 88*atn(1/6050) + 24*atn(1/12943) - 88*atn(6826318) ``` Yet another possible arctangent relation, closely related to the one examined here, is: atn(1) = 183*atn(1/239) - 12*atn(1/682) + 44*atn(1/1240) + 24*atn(1/12943) - 44*atn(1/2485057) - 88*atn(6826318) which can be considered slightly improved, since now when atn(1/239) is removed at the next step, the slowest-converging term would be atn(1/682) instead of atn(1/515). This relation was developed by Michael Roby Westerfield, a collaborator with Hwang Chien-Lih. ### Some Mistaken Values for Pi Here is a record of the notable errors in the computation of pi: The value of pi given by de Lagny to 126 places in 1719 had a 7 instead of an 8 in the 113th place, giving 32723 instead of 32823 in positions 111 to 115. The value of pi given by Georg Freyherrn von Vega (or Jurij Vega) in 1789 was: ```3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679 82148 08651 32823 06647 09384 44767 21386 11733 138 ``` in 1794, he corrected his error. He is best known for having calculated a set of 10-figure logarithm tables which were of inestimable value to generations of mathematicians and scientists. The value of pi given by William Rutherford in 1851 was: ```3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679 82148 08651 32823 06647 09384 46095 50582 23172 53594 08128 48473 78139 20386 33830 21574 73996 00825 93125 91294 01832 80651 744 ``` This value was first corrected by Zacharias Dase; later, William Rutherford calculated pi to more places, without error. The 707 digits computed by William Shanks, of which the first 527 were correct, which appeared in countless sources, sometimes with misprints of various types, from 1873 onwards, were: ```3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679 82148 08651 32823 06647 09384 46095 50582 23172 53594 08128 48111 74502 84102 70193 85211 05559 64462 29489 54930 38196 44288 10975 66593 34461 28475 64823 37867 83165 27120 19091 45648 56692 34603 48610 45432 66482 13393 60726 02491 41273 72458 70066 06315 58817 48815 20920 96282 92540 91715 36436 78925 90360 01133 05305 48820 46652 13841 46951 94151 16094 33057 27036 57595 91953 09218 61173 81932 61179 31051 18548 07446 23799 62749 56735 18857 52724 89122 79381 83011 94912 98336 73362 44065 66430 86021 39501 60924 48077 23094 36285 53096 62027 55693 97986 95022 24749 96206 07497 03041 23668 86199 51100 89202 38377 02131 41694 11902 98858 25446 81639 79990 46597 00081 70029 63123 77381 34208 41307 91451 18398 05709 85 ``` In the December 18, 1873 issue of the Proceedings of the Royal Society of London, in which typographical errors in the original publication of Shanks' value were noted, these digits appeared, except that the 679th digit was a 7 instead of a 1, giving 77387 for the 675th through 679 digits. That digit, not among the typographical errors noted, however, appeared as a 1 in the original publication of Shanks' value in the May 15, 1873 issue of that journal, and thus the most reliable reproductions of Shanks' value give 1 as the digit in that position. The value of pi to 808 digits as first given by D. F. Ferguson in March, 1947, had several individual digits in error starting from the 723rd digit, but then continued on with digits that were correct. The correct value of pi to 810 digits is: ```3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679 82148 08651 32823 06647 09384 46095 50582 23172 53594 08128 48111 74502 84102 70193 85211 05559 64462 29489 54930 38196 44288 10975 66593 34461 28475 64823 37867 83165 27120 19091 45648 56692 34603 48610 45432 66482 13393 60726 02491 41273 72458 70066 06315 58817 48815 20920 96282 92540 91715 36436 78925 90360 01133 05305 48820 46652 13841 46951 94151 16094 33057 27036 57595 91953 09218 61173 81932 61179 31051 18548 07446 23799 62749 56735 18857 52724 89122 79381 83011 94912 98336 73362 44065 66430 86021 39494 63952 24737 19070 21798 60943 70277 05392 17176 29317 67523 84674 81846 76694 05132 00056 81271 45263 56082 77857 71342 15778 96091 73637 17872 14684 40901 22495 34301 46549 58537 10507 92279 68925 89235 42019 95611 21290 21960 86403 44181 59813 62977 47713 09960 51870 72113 49999 99837 29780 49951 05973 17328 16096 31859 50244 59455 ``` and that initially given by D. F. Ferguson with the incorrect digits shown in bold and underlined as well, to make these intermittent incorrect digits easier to pick out, is: ```3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679 82148 08651 32823 06647 09384 46095 50582 23172 53594 08128 48111 74502 84102 70193 85211 05559 64462 29489 54930 38196 44288 10975 66593 34461 28475 64823 37867 83165 27120 19091 45648 56692 34603 48610 45432 66482 13393 60726 02491 41273 72458 70066 06315 58817 48815 20920 96282 92540 91715 36436 78925 90360 01133 05305 48820 46652 13841 46951 94151 16094 33057 27036 57595 91953 09218 61173 81932 61179 31051 18548 07446 23799 62749 56735 18857 52724 89122 79381 83011 94912 98336 73362 44065 66430 86021 39494 63952 24737 19070 21798 60943 70277 05392 17176 29317 67523 84674 81846 76694 05132 00056 81271 45263 56082 77857 71342 15778 96091 73637 17872 14684 40901 22495 34301 46549 58537 10507 92279 68925 89235 42019 95611 21290 21960 86355 44191 19716 02977 46113 09960 51870 72113 49999 99837 29780 49951 05973 17328 16096 31867 50244 59455 ``` The last two digits of these 810 digits were in parentheses, indicating that their value was uncertain; these appeared in March 1947, and he corrected himself by September 1947. 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# statistics posted by . 3. At a cafeteria the customers arrive at an average of 0.3 per minute. The probability that a)exactly 2 customers arrive in a 10 minute span b)2 or more customers arrive in a 10 minute span c) one customer arrives in a 5 minute span and one customer arrives in the next minute span is • statistics - This looks like a Poisson statistics problem. ## Similar Questions 1. ### math customers arrive at a 3 gas station at an exponential rate 20 cars per hour.however customers will only enter the station for gas if som gas pumps are free.suppose that tthe amount of time required to service is exponential with a … 2. ### Math - Statistics Suppose that the mean number of customers who arrive at the check-out counters each minute is 4. Create a Poisson Distribution with u (lamda) = 4 for x = 0 to 20. Compare your results to the histogram. 20 random numbers are generated … 3. ### statistics 1. Observe the number of customers visiting a particular ATM Centre during any day from March 21 to 26, 2011 between 10 a.m. – 12 noon with a time interval of 5 minutes (number of customers using the ATM every 5 minutes). Calculate … 4. ### Operations Management Fresh Sub hires three workers during the peak hours. When customers arrive, one worker is dedicated to order taking and preparing the bread and the meat; then the customer is passed to the second worker, who asks the customer about … 5. ### math-probability uppose that cars arrive at a traffic light according to a Poisson process with a rate of one car per minute starting from time t = 0 minutes. Determine a. The probability that no cars arrive in the rst two minutes. b. The probability … 6. ### queu The Waterfall Buffet in the lower level of the National Art Gallery serves food cafeteria-style daily to visitors and employees. The buffet is self-service. From 7:00 A.M. to 9:00 A.M. customers arrive at the buffet at a rate of 10 … 7. ### Algebra II - Word Problem A convenience store clerk can wait on 6 customers per minute. If customers arrive at an average rate of x people per minute, the time T spent in line is T = 1/(6-x), where 0<x<6 Find the waiting time if an average of 4.75 people … 8. ### Algebra II - Word Problem A convenience store clerk can wait on 6 customers per minute. If customers arrive at an average rate of x people per minute, the time T spent in line is: T=1/6-x, where 0<x<6 Find the waiting time if an average of 4.75 people … 9. ### pre calc at a single ticket booth, customers arrive randomly at a rate of x per hour. the average line length is given by F(x)= x^2/400-20x Where 0<= x <20. To keep the wait in line reasonable, it is required that the average line length … 10. ### statistics At a cafeteria the customers arrive at an average of 0.3 per minute. The probability that a)exactly 2 customers arrive in a 10 minute span b)2 or more customers arrive in a 10 minute span c) one customer arrives in a 5 minute span … More Similar Questions

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# Illustrative Mathematics Grade 7, Unit 2, Lesson 15: Using Water Efficiently Learning Targets: • I can answer a question by representing a situation using proportional relationships. Related Pages Illustrative Math #### Lesson 15: Using Water Efficiently Let’s investigate saving water. Illustrative Math Unit 7.2, Lesson 15 (printable worksheets) #### Lesson 15.1 Comparing Baths and Showers Some people say that it uses more water to take a bath than a shower. Others disagree. 1. What information would you collect in order to answer the question? 2. Estimate some reasonable values for the things you suggest. #### Lesson 15.2 Saving Water: Bath or Shower? 1. Describe a method for comparing the water usage for a bath and a shower. 2. Find out values for the measurements needed to use the method you described. You may ask your teacher or research them yourself. 3. Under what conditions does a bath use more water? Under what conditions does a shower use more water? #### Lesson 15.3 Representing Water Usage 1. Continue considering the problem from the previous activity. Name two quantities that are in a proportional relationship. Explain how you know they are in a proportional relationship. 2. What are two constants of proportionality for the proportional relationship? What do they tell us about the situation? 3. On graph paper, create a graph that shows how the two quantities are related. Make sure to label the axes. 4. Write two equations that relate the quantities in your graph. Make sure to record what each variable represents. The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics. Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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# What is Current ## What is Current: What is Current – There are free electrons available in all semiconductive and conductive materials. These free electrons move at random in all directions within the structure in the absence of external pressure or voltage. If a certain amount of voltage is applied across the material, all the free electrons move in one direction depending on the polarity of the applied voltage, as shown in Fig. 1.1. This movement of electrons from one end of the material to the other end constitutes an electric current, denoted by either I or i.The conventional direction of current flow is opposite to the flow of — ve charges, i.e. the electrons. Current is defined as the rate of flow of electrons in a conductive or semiconductive material. It is measured by the number of electrons that flow past a point in unit time. Expressed mathematically, where I is the current, Q is the charge of electrons, and t is the time, or where dq is the small change in charge, and dt is the small change in time. In practice, the unit ampere is used to measure current, denoted by A. One ampere is equal to one coulomb per second. One coulomb is the charge carried by 6.25 x 1018 electrons. For example, an ordinary 80 W domestic ceiling fan on 230 V supply takes a current of approximately 0.35 A. This means that electricity is passing through the fan at the rate of 0.35 coulomb every second, i.e. 2.187 x 1018 electrons are passing through the fan in every second; or simply, the current is 0.35 A. Updated: September 29, 2017 — 8:26 pm `Please enable JavaScript in your browser to complete this form.Name *FirstLastEmail *Paragraph TextMessage` ` `

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# Fairly basic natural log query (C3) #### DonGorgon I'm fairly sure this is the correct answer: e^-3x = 27 -3x = ln27 x = ln27 / -3 However, in the answers section of my textbook, the given value for the answer is -ln3. Please can someone help explain how the two answers are related and how to obtain such answer from the equation. I am only familiar with the above method. Thanks! #### Plato MHF Helper I'm fairly sure this is the correct answer: e^-3x = 27 -3x = ln27 x = ln27 / -3 However, in the answers section of my textbook, the given value for the answer is -ln3. $$\displaystyle \ln(27)=\ln(3^3)=3\ln(3)$$ #### DonGorgon $$\displaystyle \ln(27)=\ln(3^3)=3\ln(3)$$ Cheers, thought as much. However is there any different steps to take, or is it just as you mentioned? #### Plato MHF Helper Cheers, thought as much. However is there any different steps to take, or is it just as you mentioned? You could do $$\displaystyle e^{-3x}=27$$ $$\displaystyle e^{-x}=3$$ (cube root).

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# Position Control vs Velocity Control vs Torque Control Please can somebody explain to me the difference between Position Control, Velocity Control, and Torque Control? Specifically, I am thinking in terms of a robot arm. I understand that position control tries to control the position of the actuators, such that the error signal is the difference between the current position and the desired position. Velocity control is then trying to control the velocity of each actuator, and torque control is trying to control the torque of each actuator. However, I don't understand why these are not all the same thing. If you want to send a robot arm to a certain position, then you could use position control. But in order to move an actuator to a certain position, you need to give it a velocity. And in order to give it a velocity, you need to give it a torque. Therefore, whether the error is in position, velocity, or torque, it always seems to come back to just the error in torque. What am I missing? I'm going to take a slightly different tack to Chuck. ## What is Torque Control? For me, Torque Control is about performing a move with an explicitly defined torque, rather considering torque just the means to the end of Position or Velocity control. Normally when you move a robot, you specify position and speed, with the robot allowed to use any and all torque up to it's maximum, required to achieve those two goals. When you specify a move with a Torque component, you are saying you want to use that specific torque for that move. It's easiest to illustrate this with an example. ## Example: picking up an egg Let's say that you want your robot to grip an egg. The egg is a fragile spheroid of (slightly) variable size. ### Without Torque control Ideally, you would have to know the orientation of the egg and the precise dimension along the grip axis. You then have to close the gripper to be slightly smaller than that grip axis dimension and rely in the error between the demanded and actual position to apply the correct amount of force to grip the egg securely. This second order effect is very fragile and could result in eggs being dropped once motors start to age and provide less torque, or start to crush eggs if PID parameters are tweaked to (say) improve position or velocity accuracy. Since eggs aren't uniform, if you cannot measure the grip axis dimension for each egg, then you will need to work out a compromise grip position. Too small and large eggs will be broken by the force applied, too large and small eggs won't be gripped tightly enough. If there is sufficient variation between the smallest and largest eggs, there may be no compromise position which won't either crush or drop some eggs. ### With Torque control With Torque control, you have much finer, more predictable control. You are specifying torque as a first order effect and have direct control over it. Typically, you would start by moving the gripper without Torque Control to just larger than the largest egg, then move the gripper with Torque Control to just smaller than the smallest egg. As soon as the torque limit is achieved, the motor would stop moving, and the egg would be gripped with precisely the required force. ## Why not use Torque control all the time? You typically only ever use Torque Control when you absolutely need it because direct Torque Control means giving up control of position and velocity. You can get close to direct Torque Control by applying a Torque limit to a standard Position/Velocity move, but you have to be careful, since the torque limit must be higher than the minimum torque needed to achieve those moves. Applying a torque limit which is too low can easily result in following errors (actual position falling behind required position, resulting in poor control) and can even prevent a robot from moving to it's destination position (if the torque limit is lower than the torque required to make the move, due to stiction, friction or gravity to name but a few possible factors). ## Complications There are some situations where you need to apply a force smaller than the stiction of the system. Because the static friction would prevent the required force being applied, effectively no force would be applied. This could be the case with some direct drive motors for instance. In that case your Torque Control system may need to be able to briefly apply a higher force to break past the static friction, but then quickly revert to the required Torque, so that excess force is not applied. ## Conclusion Torque control is an important technique for some applications, it is something which our bodies take for granted, but which Robot systems have to be explicitly configured for. Torque is analogous to force for rotating systems, in that: $$F = m a \\ \tau = I \alpha \\$$ Where $\alpha$ is angular acceleration and $I$ is moment of inertia. $m$ and $a$ are mass and linear acceleration, respectively. So, in a way, a position controller, a velocity controller, and an acceleration (torque) controller are all different implementations of each other because each is the integral of the next - position is the integral of velocity, and velocity is the integral of acceleration. Where these differ is how you apply the controller. This typically depends on what you're interested in. For instance, are you trying to control position, as in a servo motor? Are you trying to regulate acceleration, as in a hospital elevator? Typically you will have some specification you are trying to meet. Then, with your specifications, you can use typical PID guidelines to build a controller for that particular aspect. That is, if you work at that particular "level": position, velocity, or acceleration, then you can design for a particular rise time, overshoot, and damping. The difference being that you're designing acceleration overshoot, or positional overshoot. Generally I would say the output of the controller goes to motor voltage, so while the output of the controller is always the same (motor volts) the input and gains are different, with the desire to achieve a different set of operating parameters. I'll close by pointing out that a motor controller output is terminal voltage because that's how one modulates motor current. Motor current, in turn, generates torque via the motor torque constant. So, ultimately, every controller regulates motor torque, but with the end goals varying - control motor acceleration, velocity, or position. Again, what you're trying to control depends on the application and will affect the gains you choose. • Thanks very much for your answer. I guess my confusion comes from understanding why you would ever use anything other than position control. For example, with a robot arm, all you need to do is to get it from one position to the next. Why would you care about the actual torque in the joints? Why not just figure out the position which all the joints need to be set at, and then use the position error in your feedback loop? Commented Jun 9, 2016 at 21:46 • As I say in my answer @Karnivaurus second order effects are notoriously difficult to control. If you need Torque Control it's probably because you want to control Torque as a first order effect. You don't want your robot to start dropping things because someone decided that it should be able to run a bit faster. Commented Jun 10, 2016 at 12:07 • @MarkBooth gives a great example of torque control for robotic hands. In general, these applications are referred to as "compliant actuators" - a position or velocity controller might seed the operating point of a torque controller. Note also that not every application that needs a controller is a robotic arm. – Chuck Commented Jun 10, 2016 at 12:28 • @Karnivaurus - In my line of work (industrial drives) we care a lot about precise control of motor speeds - this is in between a position and torque (acceleration) controller. If the forward drive in a metal mill is turning too slow then there's a "cobble" - the metal accumulates somewhere it's not supposed to, which is generally where people stand. Too fast in a paper mill and it breaks the sheet. – Chuck Commented Jun 10, 2016 at 12:31 I think Mark Booth's answer was best. Talked about the applicational differences between the modes, without getting into theory or detracting from the original question. If I can expand a little further to bring more clarification: Each mode uses the commanded method as its PRIMARY form of control, and it has control of the other parameters only by way of limitation. As Mark mentioned above, you can use a POSITION MOVE with LIMITS on the torque and velocity.... the controller will do its best to get to that position within the limits provided, but makes no effort to meet anything specified by the velocity or torque limits. Therefore, you could get to your commanded position with a speed of 10in/sec even though your limit was set at 40in/sec. Basically, whatever you mode you command in, the move will attempt to meet that criteria first and will ignore the other two (aside from limits). If VELOCITY is the most important thing you need to control, such as a conveyor... then use Velocity Mode. If Torque is important, such as not tearing a web or overtensioning something, then use Torque Mode. I think where it's confusing is between VELOCITY mode and POSITION mode. Arguably, you could control a conveyor using POSITION MOVES and simply setting limits on how much velocity the movement command can use. Eventually, after getting up to speed, your conveyor will be moving at the velocity specified in your POSITION MOVE. However, if you need to adjust your speed a bit, a POSITION MOVE makes this difficult. You now have to find a new position to move to and either increase or decrease the limit on your "speed max". This is much easier if you are just using VELOCITY control, as the position of a conveyor is essentially cyclic and infinite. You can simply adjust up or adjust down the velocity of your velocity command, and you DON'T REALLY CARE where the position of the conveyor is. Namely, velocity is important but position isn't. With the "egg robot" example above, your torque control cares about keeping the torque at a specific value, but it doesn't care where the position of the gripper is, or what the velocity is. It was confusing for me as well, but when you're spec'ing an application, just think about WHAT IS MOST IMPORTANT to you, and use that as your control method. They all will essentially do the same thing, but it's kind of an "order of precedence" for what it cares about most.

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# Hertz Last updated hertz Top to bottom: Lights flashing at frequencies f = 0.5 Hz, 1.0 Hz and 2.0 Hz; that is, at 0.5, 1.0 and 2.0 flashes per second, respectively. The time between each flash – the period T – is given by 1f (the reciprocal of f); that is, 2, 1 and 0.5 seconds, respectively. General information Unit system SI Unit of frequency SymbolHz Named after Heinrich Hertz In SI base units s−1 The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. [1] [lower-alpha 1] The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that one hertz is the reciprocal of one second. [2] It is named after Heinrich Rudolf Hertz (1857–1894), the first person to provide conclusive proof of the existence of electromagnetic waves. Hertz are commonly expressed in multiples: kilohertz (kHz), megahertz (MHz), gigahertz (GHz), terahertz (THz). ## Contents Some of the unit's most common uses are in the description of periodic waveforms and musical tones, particularly those used in radio- and audio-related applications. It is also used to describe the clock speeds at which computers and other electronics are driven. The units are sometimes also used as a representation of the energy of a photon, via the Planck relation E = , where E is the photon's energy, ν is its frequency, and h is the Planck constant. ## Definition The hertz is equivalent to one cycle per second. The International Committee for Weights and Measures defined the second as "the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom" [3] [4] and then adds: "It follows that the hyperfine splitting in the ground state of the caesium 133 atom is exactly 9192631770 hertz, νhfs Cs = 9192631770 Hz." The dimension of the unit hertz is 1/time (T−1). Expressed in base SI units, the unit is the reciprocal second (1/s). In English, "hertz" is also used as the plural form. [5] As an SI unit, Hz can be prefixed; commonly used multiples are kHz (kilohertz, 103 Hz), MHz (megahertz, 106 Hz), GHz (gigahertz, 109 Hz) and THz (terahertz, 1012 Hz). One hertz simply means "one event per second" (where the event being counted may be a complete cycle); 100 Hz means "one hundred events per second", and so on. The unit may be applied to any periodic event—for example, a clock might be said to tick at 1 Hz, or a human heart might be said to beat at 1.2 Hz. The occurrence rate of aperiodic or stochastic events is expressed in reciprocal second or inverse second (1/s or s−1) in general or, in the specific case of radioactivity, in becquerels. [lower-alpha 2] Whereas 1 Hz is one cycle (or periodic event) per second, 1 Bq is one radionuclide event per second on average. Even though frequency, angular velocity, angular frequency and radioactivity all have the dimension T−1, of these only frequency is expressed using the unit hertz. [7] Thus a disc rotating at 60 revolutions per minute (rpm) is said to have an angular velocity of 2π rad/s and a frequency of rotation of 1 Hz. The correspondence between a frequency f with the unit hertz and an angular velocity ω with the unit radians per second is ${\displaystyle \omega =2\pi f}$ and ${\displaystyle f={\frac {\omega }{2\pi }}.}$ The hertz is named after Heinrich Hertz . As with every SI unit named for a person, its symbol starts with an upper case letter (Hz), but when written in full, it follows the rules for capitalisation of a common noun ; i.e., hertz becomes capitalised at the beginning of a sentence and in titles but is otherwise in lower case. ## History The hertz is named after the German physicist Heinrich Hertz (1857–1894), who made important scientific contributions to the study of electromagnetism. The name was established by the International Electrotechnical Commission (IEC) in 1935. [8] It was adopted by the General Conference on Weights and Measures (CGPM) (Conférence générale des poids et mesures) in 1960, replacing the previous name for the unit, "cycles per second" (cps), along with its related multiples, primarily "kilocycles per second" (kc/s) and "megacycles per second" (Mc/s), and occasionally "kilomegacycles per second" (kMc/s). The term "cycles per second" was largely replaced by "hertz" by the 1970s. [9] [ failed verification ] In some usage, the "per second" was omitted, so that "megacycles" (Mc) was used as an abbreviation of "megacycles per second" (that is, megahertz (MHz)). [10] ## Applications ### Sound and vibration Sound is a traveling longitudinal wave, which is an oscillation of pressure. Humans perceive the frequency of a sound as its pitch. Each musical note corresponds to a particular frequency. An infant's ear is able to perceive frequencies ranging from 20 Hz to 20000 Hz; the average adult human can hear sounds between 20 Hz and 16000 Hz. [11] The range of ultrasound, infrasound and other physical vibrations such as molecular and atomic vibrations extends from a few femtohertz [12] into the terahertz range [lower-alpha 3] and beyond. [13] Electromagnetic radiation is often described by its frequency—the number of oscillations of the perpendicular electric and magnetic fields per second—expressed in hertz. Radio frequency radiation is usually measured in kilohertz (kHz), megahertz (MHz), or gigahertz (GHz). Light is electromagnetic radiation that is even higher in frequency, and has frequencies in the range of tens (infrared) to thousands (ultraviolet) of terahertz. Electromagnetic radiation with frequencies in the low terahertz range (intermediate between those of the highest normally usable radio frequencies and long-wave infrared light) is often called terahertz radiation. Even higher frequencies exist, such as that of gamma rays, which can be measured in exahertz (EHz). (For historical reasons, the frequencies of light and higher frequency electromagnetic radiation are more commonly specified in terms of their wavelengths or photon energies: for a more detailed treatment of this and the above frequency ranges, see Electromagnetic spectrum .) ### Computers In computers, most central processing units (CPU) are labeled in terms of their clock rate expressed in megahertz (MHz) or gigahertz (GHz). This specification refers to the frequency of the CPU's master clock signal. This signal is nominally a square wave, which is an electrical voltage that switches between low and high logic levels at regular intervals. As the hertz has become the primary unit of measurement accepted by the general populace to determine the performance of a CPU, many experts have criticized this approach, which they claim is an easily manipulable benchmark. Some processors use multiple clock cycles to perform a single operation, while others can perform multiple operations in a single cycle. [14] For personal computers, CPU clock speeds have ranged from approximately 1 MHz in the late 1970s (Atari, Commodore, Apple computers) to up to 6 GHz in IBM Power microprocessors. Various computer buses, such as the front-side bus connecting the CPU and northbridge, also operate at various frequencies in the megahertz range. ## SI multiples SI multiples of hertz (Hz) SubmultiplesMultiples ValueSI symbolNameValueSI symbolName 10−1 HzdHzdecihertz101 HzdaHzdecahertz 10−2 HzcHzcentihertz102 HzhHzhectohertz 10−3 HzmHzmillihertz103 HzkHzkilohertz 10−6 HzμHzmicrohertz106 HzMHzmegahertz 10−9 HznHznanohertz109 HzGHzgigahertz 10−12 HzpHzpicohertz1012 HzTHzterahertz 10−15 HzfHzfemtohertz1015 HzPHzpetahertz 10−18 HzaHzattohertz1018 HzEHzexahertz 10−21 HzzHzzeptohertz1021 HzZHzzettahertz 10−24 HzyHzyoctohertz1024 HzYHzyottahertz 10−27 HzrHzrontohertz1027 HzRHzronnahertz 10−30 HzqHzquectohertz1030 HzQHzquettahertz Common prefixed units are in bold face. Higher frequencies than the International System of Units provides prefixes for are believed to occur naturally in the frequencies of the quantum-mechanical vibrations of massive particles, although these are not directly observable and must be inferred through other phenomena. By convention, these are typically not expressed in hertz, but in terms of the equivalent energy, which is proportional to the frequency by the factor of the Planck constant. ## Unicode The CJK Compatibility block in Unicode contains characters for common SI units for frequency. These are intended for compatibility with East Asian character encodings, and not for use in new documents (which would be expected to use Latin letters, e.g. "MHz"). [15] • U+3339SQUARE HERUTU (ヘルツ, herutsu) • U+3390SQUARE HZ (Hz) • U+3391SQUARE KHZ (kHz) • U+3392SQUARE MHZ (MHz) • U+3393SQUARE GHZ (GHz) • U+3394SQUARE THZ (THz) ## Notes 1. Although hertz is equivalent to cycle per second (cps), the SI explicitly states that "cycle" and "cps" are not units in the SI, likely due to ambiguity in the terms. [2] 2. "(d) The hertz is used only for periodic phenomena, and the becquerel (Bq) is used only for stochastic processes in activity referred to a radionuclide." [6] 3. Atomic vibrations are typically on the order of tens of terahertz ## Related Research Articles The electromagnetic spectrum is the full range of electromagnetic radiation, organized by frequency or wavelength. The spectrum is divided into separate bands, with different names for the electromagnetic waves within each band. From low to high frequency these are: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. The electromagnetic waves in each of these bands have different characteristics, such as how they are produced, how they interact with matter, and their practical applications. Frequency, most often measured in hertz, is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as temporal frequency for clarity and to distinguish it from spatial frequency. Ordinary frequency is related to angular frequency by a factor of 2π. The period is the interval of time between events, so the period is the reciprocal of the frequency: T = 1/f. Mega is a unit prefix in metric systems of units denoting a factor of one million (106 or 1000000). It has the unit symbol M. It was confirmed for use in the International System of Units (SI) in 1960. Mega comes from Ancient Greek: μέγας, romanized: mégas, lit. 'great'. Microwave is a form of electromagnetic radiation with wavelengths shorter than other radio waves but longer than infrared waves. Its wavelength ranges from about one meter to one millimeter, corresponding to frequencies between 300 MHz and 300 GHz, broadly construed. A more common definition in radio-frequency engineering is the range between 1 and 100 GHz, or between 1 and 3000 GHz . The prefix micro- in microwave is not meant to suggest a wavelength in the micrometer range; rather, it indicates that microwaves are small, compared to the radio waves used in prior radio technology. The second is the unit of time in the International System of Units (SI), historically defined as 186400 of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds each. "Minute" comes from the Latin pars minuta prima, meaning "first small part", and "second" comes from the pars minuta secunda, "second small part". A nanosecond (ns) is a unit of time in the International System of Units (SI) equal to one billionth of a second, that is, 11 000 000 000 of a second, or 10−9 seconds. The caesium standard is a primary frequency standard in which the photon absorption by transitions between the two hyperfine ground states of caesium-133 atoms is used to control the output frequency. The first caesium clock was built by Louis Essen in 1955 at the National Physical Laboratory in the UK. and promoted worldwide by Gernot M. R. Winkler of the United States Naval Observatory. A picosecond is a unit of time in the International System of Units (SI) equal to 10−12 or 11 000 000 000 000 of a second. That is one trillionth, or one millionth of one millionth of a second, or 0.000 000 000 001 seconds. A picosecond is to one second as one second is to approximately 31,689 years. Multiple technical approaches achieve imaging within single-digit picoseconds: for example, the streak camera or intensified CCD (ICCD) cameras are able to picture the motion of light. Radio waves are a type of electromagnetic radiation with the lowest frequencies and the longest wavelengths in the electromagnetic spectrum, typically with frequencies below 300 gigahertz (GHz) and wavelengths greater than 1 millimeter, about the diameter of a grain of rice. Like all electromagnetic waves, radio waves in a vacuum travel at the speed of light, and in the Earth's atmosphere at a slightly slower speed. Radio waves are generated by charged particles undergoing acceleration, such as time-varying electric currents. Naturally occurring radio waves are emitted by lightning and astronomical objects, and are part of the blackbody radiation emitted by all warm objects. The becquerel is the unit of radioactivity in the International System of Units (SI). One becquerel is defined as an activity of one decay per second. For applications relating to human health this is a small quantity, and SI multiples of the unit are commonly used. In computing, the clock rate or clock speed typically refers to the frequency at which the clock generator of a processor can generate pulses, which are used to synchronize the operations of its components, and is used as an indicator of the processor's speed. It is measured in the SI unit of frequency hertz (Hz). Terahertz or THz may refer to: Terahertz radiation – also known as submillimeter radiation, terahertz waves, tremendously high frequency (THF), T-rays, T-waves, T-light, T-lux or THz – consists of electromagnetic waves within the ITU-designated band of frequencies from 0.3 to 3 terahertz (THz), although the upper boundary is somewhat arbitrary and is considered by some sources as 30 THz. One terahertz is 1012 Hz or 1,000 GHz. Wavelengths of radiation in the terahertz band correspondingly range from 1 mm to 0.1 mm = 100 μm. Because terahertz radiation begins at a wavelength of around 1 millimeter and proceeds into shorter wavelengths, it is sometimes known as the submillimeter band, and its radiation as submillimeter waves, especially in astronomy. This band of electromagnetic radiation lies within the transition region between microwave and far infrared, and can be regarded as either. The radio spectrum is the part of the electromagnetic spectrum with frequencies from 3 Hz to 3,000 GHz (3 THz). Electromagnetic waves in this frequency range, called radio waves, are widely used in modern technology, particularly in telecommunication. To prevent interference between different users, the generation and transmission of radio waves is strictly regulated by national laws, coordinated by an international body, the International Telecommunication Union (ITU). The megahertz myth, or in more recent cases the gigahertz myth, refers to the misconception of only using clock rate to compare the performance of different microprocessors. While clock rates are a valid way of comparing the performance of different speeds of the same model and type of processor, other factors such as an amount of execution units, pipeline depth, cache hierarchy, branch prediction, and instruction sets can greatly affect the performance when considering different processors. For example, one processor may take two clock cycles to add two numbers and another clock cycle to multiply by a third number, whereas another processor may do the same calculation in two clock cycles. Comparisons between different types of processors are difficult because performance varies depending on the type of task. A benchmark is a more thorough way of measuring and comparing computer performance. The cycle per second is a once-common English name for the unit of frequency now known as the hertz (Hz). Cycles per second may be denoted by c.p.s., c/s, or, ambiguously, just "cycles". The term comes from repetitive phenomena such as sound waves having a frequency measurable as a number of oscillations, or cycles, per second. Photomixing is the generation of continuous wave terahertz radiation from two lasers. The beams are mixed together and focused onto a photomixer device which generates the terahertz radiation. It is technologically significant because there are few sources capable of providing radiation in this waveband, others include frequency multiplied electronic/microwave sources, quantum cascade laser and ultrashort pulsed lasers with photoconductive switches as used in terahertz time-domain spectroscopy. The advantages of this technique are that it is continuously tunable over the frequency range from 300 GHz to 3 THz, and spectral resolutions in the order of 1 MHz can be achieved. However, the achievable power is on the order of 10−8 W. The inverse second or reciprocal second (s−1), also called per second, is a unit defined as the multiplicative inverse of the second. It is applicable for physical quantities of dimension reciprocal time, such as frequency and strain rate. A terahertz metamaterial is a class of composite metamaterials designed to interact at terahertz (THz) frequencies. The terahertz frequency range used in materials research is usually defined as 0.1 to 10 THz. In 2019, four of the seven SI base units specified in the International System of Quantities were redefined in terms of natural physical constants, rather than human artifacts such as the standard kilogram. Effective 20 May 2019, the 144th anniversary of the Metre Convention, the kilogram, ampere, kelvin, and mole are now defined by setting exact numerical values, when expressed in SI units, for the Planck constant, the elementary electric charge, the Boltzmann constant, and the Avogadro constant, respectively. The second, metre, and candela had previously been redefined using physical constants. The four new definitions aimed to improve the SI without changing the value of any units, ensuring continuity with existing measurements. In November 2018, the 26th General Conference on Weights and Measures (CGPM) unanimously approved these changes, which the International Committee for Weights and Measures (CIPM) had proposed earlier that year after determining that previously agreed conditions for the change had been met. These conditions were satisfied by a series of experiments that measured the constants to high accuracy relative to the old SI definitions, and were the culmination of decades of research. ## References 1. "hertz". (1992). American Heritage Dictionary of the English Language (3rd ed.), Boston: Houghton Mifflin. 2. "SI Brochure: The International System of Units (SI) – 9th edition" (PDF). BIPM: 26. Retrieved 7 August 2022. 3. "SI Brochure: The International System of Units (SI) § 2.3.1 Base units" (PDF) (in British English and French) (9th ed.). BIPM. 2019. p. 130. Retrieved 2 February 2021. 4. "SI Brochure: The International System of Units (SI) § Appendix 1. Decisions of the CGPM and the CIPM" (PDF) (in British English and French) (9th ed.). BIPM. 2019. p. 169. Retrieved 2 February 2021. 5. NIST Guide to SI Units – 9 Rules and Style Conventions for Spelling Unit Names, National Institute of Standards and Technology 6. "BIPM – Table 3". BIPM . Retrieved 24 October 2012. 7. "SI brochure, Section 2.2.2, paragraph 6". Archived from the original on 1 October 2009. 8. "IEC History". Iec.ch. Archived from the original on 19 May 2013. Retrieved 6 January 2021. 9. Cartwright, Rufus (March 1967). Beason, Robert G. (ed.). "Will Success Spoil Heinrich Hertz?" (PDF). Electronics Illustrated. Fawcett Publications, Inc. pp. 98–99. 10. Pellam, J. R.; Galt, J. K. (1946). "Ultrasonic Propagation in Liquids: I. Application of Pulse Technique to Velocity and Absorption Measurements at 15 Megacycles". The Journal of Chemical Physics. 14 (10): 608–614. Bibcode:1946JChPh..14..608P. doi:10.1063/1.1724072. hdl:. 11. Ernst Terhardt (20 February 2000). "Dominant spectral region". Mmk.e-technik.tu-muenchen.de. Archived from the original on 26 April 2012. Retrieved 28 April 2012. 12. "Black Hole Sound Waves – Science Mission Directorate". science.nasa.go. 13. "Black Hole Sound Waves – Science Mission Directorate". science.nasa.go. 14. Asaravala, Amit (30 March 2004). "Good Riddance, Gigahertz". Wired. Retrieved 28 April 2012. 15. Unicode Consortium (2019). "The Unicode Standard 12.0 – CJK Compatibility ❰ Range: 3300—33FF ❱" (PDF). Unicode.org. Retrieved 24 May 2019.

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BRAIN TEASERS # Monthly Archive - November 2018 (page 4) brain teasers, puzzles, riddles, mathematical problems, mastermind, cinemania... These are the tasks listed 31 to 40. ## Guess the Band Name Which musician band has an album with a cover as in the picture? The first user who solved this task is Djordje Timotijevic. #brainteasers #music #riddles ## Chess Knight Move Find the title of novel, using the move of a chess knight. First letter is T. Length of words in solution: 3,8,2,1,4. The first user who solved this task is Djordje Timotijevic. #brainteasers #wordpuzzles #chessknightmove ## What a winning combination? The computer chose a secret code (sequence of 4 digits from 1 to 6). Your goal is to find that code. Black circles indicate the number of hits on the right spot. White circles indicate the number of hits on the wrong spot. The first user who solved this task is NĂ­lton CorrĂȘa De Sousa. #brainteasers #mastermind ### Hemingway was fascinated by ag... Hemingway was fascinated by aging popes. That why he wrote Old Man in the See. Jokes of the day - Daily updated jokes. New jokes every day. ## Calculate the number 1066 NUMBERMANIA: Calculate the number 1066 using numbers [3, 8, 7, 3, 10, 341] and basic arithmetic operations (+, -, *, /). Each of the numbers can be used only once. The first user who solved this task is Djordje Timotijevic. #brainteasers #math #numbermania ## Find number abc If 4a3ca + cab32 = 1b83a1 find number abc. Multiple solutions may exist. The first user who solved this task is Djordje Timotijevic. #brainteasers #math ## Guess the Band Name Which musician band has an album with a cover as in the picture? The first user who solved this task is Alfa Omega. #brainteasers #music #riddles ## Which is a winning combination of digits? The computer chose a secret code (sequence of 4 digits from 1 to 6). Your goal is to find that code. Black circles indicate the number of hits on the right spot. White circles indicate the number of hits on the wrong spot. The first user who solved this task is Djordje Timotijevic. #brainteasers #mastermind ## Chess Knight Move Find the title of novel, using the move of a chess knight. First letter is N. Length of words in solution: 9,5. The first user who solved this task is Djordje Timotijevic. #brainteasers #wordpuzzles #chessknightmove ## Calculate the number 1121 NUMBERMANIA: Calculate the number 1121 using numbers [7, 3, 3, 5, 88, 870] and basic arithmetic operations (+, -, *, /). Each of the numbers can be used only once. The first user who solved this task is Djordje Timotijevic. #brainteasers #math #numbermania ## Replace asterisk symbols with ... Replace asterisk symbols with a letters (*L****O*D ***) and guess the name of musician band. Length of words in solution: 9,3. The first user who solved this task is Djordje Timotijevic. #brainteasers #music PREVIOUS PAGE NEXT PAGE Follow Brain Teasers on social networks ## Top 10 Users (1174) 1 H Tav 5861 2 c. raj. 5777 3 Nasrin 24 T 5731 4 Fazil Hashim 5718 5 Thinh Ddh 5557 6 Alfa Omega 4681 7 Djordje Timotijevic 4549 8 Mita Kojd 4525 9 Jakubovski Vladimir 4443 10 Chandu Rajyaguru 4419 See full ranking list ### U.S. Air Corps Physiological Research Unit In 1935, the U.S. Physiological Research Unit laboratory was established at Wright Field, Ohio, under the leadership of Capt. Harry G. Armstrong, M.C. (Medical Corps). Pioneering aeromedical research work was conducted here on health and safety aspects while in flight. On 1 Jan 1937, it became the U.S. Air Corps Physiological Research Laboratory, with improved facilities.« This site uses cookies to store information on your computer. Some are essential to help the site properly. Others give us insight into how the site is used and help us to optimize the user experience. See our privacy policy.

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# Number 15261533218 ### Properties of number 15261533218 Cross Sum: Factorization: 2 * 97 * 1789 * 43973 Divisors: Count of divisors: Sum of divisors: Prime number? No Fibonacci number? No Bell Number? No Catalan Number? No Base 3 (Ternary): Base 4 (Quaternary): Base 5 (Quintal): Base 8 (Octal): 38da88422 Base 32: e6qh112 sin(15261533218) -0.9390360243202 cos(15261533218) 0.34381876770897 tan(15261533218) -2.7311947819994 ln(15261533218) 23.448601330757 lg(15261533218) 10.183598166297 sqrt(15261533218) 123537.57816146 Square(15261533218) 2.3291439616412E+20 ### Number Look Up Look Up 15261533218 (fifteen billion two hundred sixty-one million five hundred thirty-three thousand two hundred eighteen) is a very impressive number. The cross sum of 15261533218 is 37. If you factorisate the number 15261533218 you will get these result 2 * 97 * 1789 * 43973. 15261533218 has 16 divisors ( 1, 2, 97, 194, 1789, 3578, 43973, 87946, 173533, 347066, 4265381, 8530762, 78667697, 157335394, 7630766609, 15261533218 ) whith a sum of 23141757240. The figure 15261533218 is not a prime number. The figure 15261533218 is not a fibonacci number. 15261533218 is not a Bell Number. The figure 15261533218 is not a Catalan Number. The convertion of 15261533218 to base 2 (Binary) is 1110001101101010001000010000100010. The convertion of 15261533218 to base 3 (Ternary) is 1110101121021012211001. The convertion of 15261533218 to base 4 (Quaternary) is 32031222020100202. The convertion of 15261533218 to base 5 (Quintal) is 222223423030333. The convertion of 15261533218 to base 8 (Octal) is 161552102042. The convertion of 15261533218 to base 16 (Hexadecimal) is 38da88422. The convertion of 15261533218 to base 32 is e6qh112. The sine of the figure 15261533218 is -0.9390360243202. The cosine of the figure 15261533218 is 0.34381876770897. The tangent of 15261533218 is -2.7311947819994. The root of 15261533218 is 123537.57816146. If you square 15261533218 you will get the following result 2.3291439616412E+20. The natural logarithm of 15261533218 is 23.448601330757 and the decimal logarithm is 10.183598166297. I hope that you now know that 15261533218 is unique number!

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# energy source UDF User Name Remember Me Password Register Blogs Members List Search Today's Posts Mark Forums Read LinkBack Thread Tools Search this Thread Display Modes August 1, 2006, 02:46 energy source UDF #1 Jason Guest   Posts: n/a Hi, I have a trouble about UDF. The energy produced by the chip is varied with time. Anyone can help me modify the UDF? Thanks~~ /* Heat Generation Rate UDF */ #include "udf.h" DEFINE_SOURCE(source, cell, thread) { real T = CURRENT_TIME ; real source ; real s1, s2, s3, s4 ; s1=10E+5 ; s2=5*10E+5 ; s3=2*10E+6 ; if (T <= 0.05) source = s1; else if (0.05< T <= 0.15) source = s2; else if (0.15 < T) source = s3; return source; } August 1, 2006, 04:43 Re: energy source UDF #2 Anon Guest   Posts: n/a A source term also needs its derivative. that is missing in all the conditions. Derivative term here is zero since your source is a constant. Units are: W/m3. Please check an example UDF in the manual. August 2, 2006, 02:35 Re: energy source UDF #3 Jason Guest   Posts: n/a Hi Anon, I changed my UDF as following but the result is incorrect. Could you tell me where is the error? Thanks! * Heat Generation Rate UDF */ #include "udf.h" DEFINE_SOURCE(heat_source, cell, thread, dS, eqn) { real T = CURRENT_TIME ; real source ; real s1, s2, s3, s4 ; s1=5*10E+7 ; s2=10E+5 ; s3=2*10E+7 ; if (T <= 1.5) source = s1; else if (1.5 < T <= 2) source = s2; else if (2 < T) source = s3; return source; } August 2, 2006, 14:30 Re: energy source UDF #4 summer Guest   Posts: n/a You need add the derivative as ds[eqn]=0 since it seems that s1 et.al are constant. Hope it helps. Thread Tools Search this Thread Search this Thread: Advanced Search Display Modes Linear Mode Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is OffTrackbacks are Off Pingbacks are On Refbacks are On Forum Rules Similar Threads Thread Thread Starter Forum Replies Last Post neilduffy1024 ANSYS 4 July 16, 2013 23:50 JoFFe FLUENT 0 October 4, 2010 16:48 Matthew Brannock FLUENT 5 May 3, 2001 21:18 Greg Perkins FLUENT 0 October 13, 2000 23:03 Greg Perkins FLUENT 0 October 11, 2000 03:43 All times are GMT -4. The time now is 02:53. Contact Us - CFD Online - Privacy Statement - Top

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• # question_answer If p is any statement, then which of the following is a tautology? A) $p\wedge f$       B) $p\vee f$ C) $p\vee (\tilde{\ }p)$        D) $p\wedge t$ [c] Whatever the truth value of p may be, $p\vee (\sim p)$is always true. Hence, $p\vee \sim (p)$ is a tautology?

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# Crow Extended Model Fleet Analysis Example This example appears in the Reliability Growth and Repairable System Analysis Reference. 11 systems from the field were chosen for fleet analysis. Each system had at least one failure. All of the systems had a start time equal to zero and the last failure for each system corresponds to the end time. Group the data based on a fixed interval of 3,000 hours, and assume a fixed effectiveness factor equal to 0.4. Do the following: 1. Estimate the parameters of the Crow Extended model. 2. Based on the analysis, does it appear that the systems were randomly ordered? 3. After the implementation of the delayed fixes, how many failures would you expect within the next 4,000 hours of fleet operation. System Times-to-Failure Fleet Data 1 1137 BD1, 1268 BD2 2 682 BD3, 744 A, 1336 BD1 3 95 BD1, 1593 BD3 4 1421 A 5 1091 A, 1574 BD2 6 1415 BD4 7 598 BD4, 1290 BD1 8 1556 BD5 9 55 BD4 10 730 BD1, 1124 BD3 11 1400 BD4, 1568 A Solution 1. The next figure shows the estimated Crow Extended parameters. 2. Upon observing the estimated parameter $\beta \,\!$, it does appear that the systems were randomly ordered since $\beta =0.8569\,\!$. This value is close to 1. You can also verify that the confidence bounds on $\beta \,\!$ include 1 by going to the QCP and calculating the parameter bounds or by viewing the Beta Bounds plot. However, you can also determine graphically if the systems were randomly ordered by using the System Operation plot as shown below. Looking at the Cum. Time Line, it does not appear that the failures have a trend associated with them. Therefore, the systems can be assumed to be randomly ordered. 3. After implementing the delayed fixes, the system's projected MTBF is equal to $1035.6802\,\!$ as shown in the plot below. To estimate the number of failures during the next 4,000 hours, calculate the following: \begin{align} N=& \frac{4000}{1035.6802}\\ = & 3.8622\end{align}\,\! Therefore, it is estimated that $\approx\,\!$ 4 failures will be observed during the next 4,000 hours of fleet operation.

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vacuum pump system parameters Vacuum pump is a kind of device or equipment that uses mechanical, physical, chemical or physicochemical methods to extract air from the container to obtain vacuum. Generally speaking, vacuum pump is a device which can improve, produce and maintain vacuum in a closed space by various methods. According to the working principle of vacuum pump, vacuum pump can be basically divided into two types, namely gas capture pump and gas transfer pump. It is widely used in metallurgy, chemical industry, food, electronic coating and other industries. Common vacuum pumps include dry screw vacuum pump, liquid ring vacuum pump, reciprocating pump, slide valve pump, rotary vane vacuum pump, roots vacuum pump and diffusion pump. These pumps are essential main pumps in the application of vacuum technology in various industries of national economy. vacuum pump of system parameters: Vacuum degree: the thinness degree of gas in vacuum state, usually expressed as vacuum degree. The value read from the vacuum gauge is called vacuum degree. The value of vacuum degree indicates that the actual value of the system pressure is lower than the atmospheric pressure. The value expressed from the table is also called the table pressure, which is also called the limit relative pressure in the industry, that is: vacuum degree = atmospheric pressure absolute pressure (generally 101325pa, the limit absolute pressure of water ring vacuum pump is 3300pa; the limit absolute pressure of rotary vane vacuum pump is about 10Pa). Limit relative pressure: the relative pressure is how much lower the measured internal pressure is than “atmospheric pressure”. It shows that the actual value of system pressure is lower than that of atmospheric pressure. Because the air inside the container is pumped, the pressure inside is always lower than the pressure outside the container. Therefore, when expressed in terms of relative pressure or gauge pressure, the value must be preceded by a minus sign, indicating that the internal pressure of the container is lower than the external pressure. Ultimate absolute pressure: the absolute pressure is how much higher the measured internal pressure is than the theoretical vacuum (the theoretical vacuum pressure value is 0Pa). The object of comparison is the absolute vacuum pressure value of theoretical state. Due to the limitation of technology, we can not pump the internal pressure to the absolute vacuum 0Pa, so the vacuum value of vacuum pump is higher than the theoretical vacuum value. So when we use absolute vacuum, there is no minus sign in front of the value. Pumping capacity: pumping capacity is a measure of the pumping speed of a vacuum pump. General units are expressed in L / s and m3 / h. It is a parameter to make up the air leakage rate. It’s not hard to understand why it’s easy for a vacuum pump with a large amount of air to pump the same volume of container in theory, and why a vacuum pump with a small amount of air can’t pump the vacuum that we want? Because it’s impossible for a pipeline or container to never leak, and the large amount of air can make up for the factors that cause the vacuum drop caused by the leakage. It’s easy to get the ideal vacuum value of the atmosphere. It is suggested that, in the case of calculating the theoretical pumping capacity, we try to choose a vacuum pump with a higher pumping capacity. The specific calculation formula of air extraction will be introduced below. After knowing the basic parameters of vacuum degree, absolute pressure and relative pressure, we can enter the formal selection of vacuum pump. When purchasing vacuum pump and vacuum equipment, priority should also be given to the quality of equipment, transportation, maintenance and repair costs, etc. (The article comes from the Internet. If reprinting is not allowed, please contact our company to delete it.) Related Products If possible, kindly suggest please your working industry/process, working pressure, working medium, etc. Given detailed request helps to gain better-matched customized solution. Thanks for your patience. — dry screw vacuum pump in wood processing industry Posted on Tue, 01 Feb 2022 07:02:47 +0000 — Explosion proof and high temperature resistant vacuum unit Posted on Wed, 10 Nov 2021 07:30:11 +0000 — vacuum pumps for chemical industry has high requirements Posted on Mon, 08 Nov 2021 08:52:52 +0000 — What are the applications of roots vacuum units in medicine? Posted on Wed, 03 Nov 2021 07:57:18 +0000 — The advantages of dry screw vacuum pumps make up for the disadvantages of oil-sealed vacuum pumps Posted on Tue, 02 Nov 2021 09:05:35 +0000 — dry vacuum pump for measures to avoid oil return Posted on Thu, 28 Oct 2021 09:03:25 +0000

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# Life c and the pursuit of an accurate distance measurement 1. Sep 29, 2011 ### M. Bachmeier Life "c" and the pursuit of an accurate distance measurement Having trouble trying to wrap my mind around how two reference frames (both in motion) can observe a third reference frame (object at rest wrt A & B observers) and calculate the correct distance to that object. To try and keep it simple (which is about my level of understanding) I suggest the following: Three objects are in orbit around a star (A, B, C). Object A is an emerging civilization who who must calculate distance properly in order to understand the universe as is object C. B is an object at rest wrt A & B. Object A is the innermost planet with simple circular orbit. Object C is the outermost planet with a retrograde simple circular orbit. Object A & B are traveling at the same speed wrt to C in opposite directions, thus both are approaching C at the same speed. Object B is a planet in a simple circular geosynchronous orbit. The setup is this: Both A & B are approaching object C. While both A & C are at the same distance from C they both take a light measurement of object C at the same time from the point of view of an omnipotent observer. A & B are not equal, however. The subjective time of object A is .5t wrt B which is = to 1t. Object C is 2 light minutes away, at time of measurement, from both A & B. So, B measures the distance to be 2 light minutes away and A measures the distance to be (edit) '1' should be '4' (/edit) light minute(s) away? How do these two frames of reference agree, assuming that the difference in subjective time is due to the respective gravitation of A & B? Is there a way for both A & B to correct their observational measure so they can arrive at a mutually agreeable or universal distance? Last edited: Sep 29, 2011

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# Using the fact that any integer can be written as the product of a square and a square free number show that there are infinitely many primes? Apparently there is a way that I can use the fact that for any positive integer $n$ there are positive integers $a$ and $b$ such that $n=a^2b$ where $b$ is the possibly empty product of distinct primes (i.e squarefree?) to show that there are infinitely many primes. My current tactic (the one that was hinted to me) was to fix x then assuming there are a finite number of primes show that there are only a finite number of possibilities for $n=a^2b$ knowing that $a^2 \leq b$ I believe it is mostly that last part that causes me issues as I am not sure how we can only consider $a^2$ and not $b$. I also assume that I have to do something with divisibility here though I am not sure what. I can't help but think that the overall approach is reminiscent of Euclid's though I am not sure? • Hint: For the $i^{th}$ prime $p_i$ Let $N_i(x)$ be the number of positive integers less than $x$ which are not divisible by any prime greater than $p_i$. Use your decomposition to get an upper bound on $N_i(x)$. Derive a contradiction from the assumption that $p_i$ is in fact the largest prime. – lulu Mar 30, 2017 at 13:26 • To get the upper bound do I use the fact that a^2 divides n? Mar 30, 2017 at 14:46 • Oh, no. It's a lot simpler than that...no divisibility involved. Every $n<x$ which is built out of the first $i$ primes can be written as $r^2s$ where $r≤\sqrt x$ and $s$ just has each of the first $i$ primes either to the power $0$ or the power $1$. So now just count. – lulu Mar 30, 2017 at 14:48 • Euclid proved it as follows : $(1)$ Every integer $n>1$ is divisble by some prime $p$. Prove : The set $S$ containing the positive divisors of $n$ greater than $1$ is not empty because of $n|n$. The smallest element , denote it with $m$, must be a prime, because if $a$ is a divisor of $m$ with $1<a<m$, it is also a divisor of $n$ greater than $1$, but smaller contradicting that $m$ is the smallest element in $S$. $(2)$ If $2,3,5,\cdots ,p_k$ are all the primes, the number $2\cdot 3\cdot5\cdots \cdot p_k+1$ is not divisble by any prime, contradicting $(1)$ Mar 30, 2017 at 22:33 Here is an elementary solution. Let $p_i$ denote the $i^{th}$ prime. For any natural number $x$ let $N_i(x)$ denote the number of natural numbers $≤x$ which are not divisible by any prime greater than $p_i$. We want a (crude) upper bound on $N_i(x)$. To get it, note that any $n≤x$ which is only divisible by primes in $\{p_1,p_2,\cdots, p_i\}$ can be written as $$n=m^2\prod_{k=1}^i p_k^{\epsilon_k}$$ Where $\epsilon_k$ is either $0$ or $1$ for each $k$. Thus there are $2^i$ ways to assign the $\epsilon's$ and as $m≤\sqrt x$ we get $$N_i(x)≤\sqrt x\;2^i$$ Note: This holds whether there are infinitely many primes or not (it's quite crude). Now suppose that there are only finitely many primes, and that in fact $p_i$ is the largest possible prime. In that case of course $N_i(x)=x$ Thus $$x≤\sqrt x\;2^i\implies \sqrt x ≤ 2^i$$ for all $x$, which is absurd. Note: as far as I know this is one of the easiest ways to get an (admittedly crude) lower bound on the number of primes less than $x$. Playing with the above inequality gives us $$\pi(x)≥ \frac 12\log_2(x)$$ This is a terrible lower bound, but at least it's something. • This is fantastic. I believe I understand what is going on. Just to clarify though It is absurd because x is defined to any natural number and we are saying that is less than $2^i$ for some i? And this is probably a stupid question but how can we know that that inequality cant hold if for every x we choose an i? Mar 30, 2017 at 15:30 • $i$ is fixed because, under the assumption that there are only finitely many primes, I can choose $p_i$ to be the largest possible prime. Nothing to do with $x$. In that case then, yes, we'd be free to let $x$ be arbitrarily large. – lulu Mar 30, 2017 at 15:32 If you know that every positive natural number can be written as $a^2 b$ with $b$ being the product of distinct primes (not dividing $a$), just assume that there are just $M$ primes $p_1,p_2,\ldots,p_M$ and consider $$\sum_{n=1}^{N}\frac{1}{n} \tag{1}$$ for some large $N$. It is well known that such sum behaves like $\log(N)$. On the other hand, every $n\in[1,N]$ can be written as $a^2 b$ with $a\leq \sqrt{N}$ and $b$ being the product of the elements of a (possibly empty) subset of $\{p_1,\ldots,p_M\}$. In particular: $$\sum_{n=1}^{N}\frac{1}{n} \leq \sum_{a\leq \sqrt{N}}\frac{1}{a^2} \prod_{k=1}^{M}\left(1+\frac{1}{p_k}\right)\leq \zeta(2)\cdot C_M\tag{2}$$ is bounded by an absolute constant, depending on $M$ only. But the LHS of $(2)$ is arbitrarily large, hence the set of prime numbers cannot be finite, qed. Indeed $(2)$ can be used to prove a very weak form of the prime number theorem: $$\sum_{\substack{p\text{ prime}\\p\leq N}}\frac{1}{p}\geq \log\log N-O(\log\log\log N).\tag{3}$$ About that, see Mertens' theorems. • This is very interesting but unfortunately well beyond my level. Mar 30, 2017 at 14:14

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Your physics homework can be a real challenge, and the due date can be really close - feel free to use our assistance and get the desired result. Be sure that math assignments completed by our experts will be error-free and done according to your instructions specified in the submitted order form. Get a free quote. Check the website Easy as ABC! Just provide us with clear instructions and wait for the completed assignment. Economics:  Economics of Enterprise Economics of Enterprise Question #6361 from lamarcus streeter 5. A firm is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and not repeatable. The CEO wants to use the IRR criterion, while the CFO favors the NPV method. You were hired to advise the firm on the best procedure. If the wrong decision criterion is used, how much potential value would the firm lose? WACC: 6.00% Year 0 1 2 3 4 CFS -\$1,025 \$380 \$380 \$380 \$380 CFL -\$2,150 \$765 \$765 \$765 \$765 a. \$188.68 b. \$198.61 c. \$209.07 d. \$219.52 e. \$230.49 c. \$209.07 NPV: PV[S] = -1025+380•∑(1/1.06^n) ≈ +291.74 PV[L] = -2150+765•∑(1/1.06^n) ≈ +500.8 PV[L] > PV[S] IRR: 0 = -1025+380•∑(1/(1+IRR)^n) → IRR[S]≈17.861% 0 = -2150+765•∑(1/(1+IRR)^n) → IRR[L]≈15.781% IRR[L] < IRR[S] 15.781 < 17.861 Since projects are mutually exclusive - then project [L] is preferred (despite lower IRR - higher investment volume pays out), obviously assuming firm doesn't have any other investment opportunities . Δ ≈ 500.8 - 291.74 = 209.07

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# Digital design Counters Preparation: Collect information about counters. How do they work? Where can you use... ###### Question: Digital design Counters Preparation: Collect information about counters. How do they work? Where can you use them? What kinds of registers are exists? Experiment: Design two binary counters by using D flip flop and T flip flop. Run them by Pspice and count until binary 1000. #### Similar Solved Questions ##### The function given by A(t) 027513 46412 834t + 6.84,0sts10,can be used estimate Ihe amount, billions = dollars, irivesled by largc oil companies in exploration for new resenves years alter 1995_ Find Ihe relalive extreme points, und skelch _ graph of ihe function:Idenlily all Ihe relative minimum points. 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# Alex has 50% more money than Bob, and Carl has 25% more money than Bob. Altogether, they have a total of Php 3,750. How much does Alex have? Pls. answer with solution. 1 by chalito 2014-11-05T21:01:57+08:00 Let 'x' be the money of Alex 'y' be the amount that Bob has 'z' be the money of Carl since Alex has 50% more money than Bob then you'll have the equation: x = y + 0.5y x = 1.50y    ----equation 1 Carl has 25% more money than Bob z = y + 0.25y z = 1.25y   ----equation 2 altogether they have 3,750 x + y + z = 3,750  ------equation 3 substitute equations 1 and 2 to equation 3 x + y + z = 3,750 1.5y + y + 1.25y = 3,750 3.75y = 3,750 y = 1,000 substitute y=1,000 to equation 2 z = 1.25y z = 1.25(1000) z = 1,250 substitute y=1,000 to equation 1 x = 1.5y x = 1.5(1000) x = 1,500 therefore Alex has 1,500 Bob has 1,000 Carl has 1,250

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> Sine waves b. Cosine waves c. Triangular waves d. Square waves View Answer / Hide Answer. Most common algorithm is the Cooley-Tukey Algorithm. MA1003 - Transforms and Boundary Value Problems Unit-IV : Fourier Transforms 1. Dictionary com s List of Every Word of the Year. 17. 11.04.1 Multiple Choice Test Chapter 11.04 Discrete Fourier Transform 1. Let f (x)= 3e-2 x . Was passiert dann ? Course Hero, Inc. We shall therefore use the word Fourier transform for both models which we discuss. 1. Review and cite DISCRETE FOURIER TRANSFORM protocol, troubleshooting and other methodology information | Contact experts in DISCRETE FOURIER TRANSFORM to get answers fourier series questions and answers pdf wordpress com. The Fourier transform of a function is equal to its two-sided Laplace transform evaluted .   Terms. Given that − = N i W e 2π, where N =3. Fourier Series Suppose x(t) is not periodic. Fourier transform on the circle group T or dually as abstract Fourier transform on the group Z of integers, while ordinary Fourier transform is the abstract Fourier transform of the group R of real numbers. helpful revision for fourier series intmath com. Dec 02,2020 - Fourier Series MCQ Level - 1 | 10 Questions MCQ Test has questions of Physics preparation. The Fourier transform of a function f(x) Answer: a Explanation: In any transform, apart from function given, the other function is said to be Kernel function. Unit-IV mcq.pdf - MA1003 Transforms and Boundary Value Problems Unit-IV Fourier Transforms 1 The Fourier transform of a function f(x is a b c d 2 The, MA1003 - Transforms and Boundary Value Problems, The Fourier transform of a function f(x) is, a. self-reciprocal function b. cosine function. T.Y.B.Sc. While we have defined Π(±1/2) = 0, other common conventions are either to have Π(±1/2) = 1 or Π(±1/2) = 1/2.And some people don’t define Π at ±1/2 at all, leaving two holes in the domain. Let u2L1(Rn). Download MCQs From Here. ANSWER: (a) range of z for which the z transform converges. The Inverse Fourier Transform The Fourier Transform takes us from f(t) to F(ω). It is generally believed that factorization of a number n is hard to do in a efficient way. continuous Fourier series associated with the given function f (t) can be computed as (A) −75.6800 (B) −7.5680 (C) −6.8968 (D) −0.7468. This set of Fourier Analysis Multiple Choice Questions & Answers (MCQs) focuses on “Fourier Transform and Convolution”. B. notes on fourier series california state university. The Fourier transform The resulting expressions replace (10) and (9) respectively by x(t) = 1 2 … Z 1 ¡1 Xc(! Discrete Fourier Transform would normally require O(n2) time to process for n samples: Don’t usually calculate it this way in practice. I Typically, f(x) will be piecewise de ned. 66 Chapter 2 Fourier Transform called, variously, the top hat function (because of its graph), the indicator function, or the characteristic function for the interval (−1/2,1/2). CONCLUSION. The Fourier constants for f (x) in the interval (-p, p)are given by. The Fourier transform is a mathematical technique that allows an MR signal to be decomposed into a sum of sine waves of different frequencies, phases, and amplitudes. ��N�$��o��u�@Ns�U� �fͣL�qq$;X�s��s����q��\����ęՌ�8�5� IF YOU LIKE OUR WORK PLEASE SHARE OUR SITE. MR image encoding, filling of k-space, and a wide spectrum of artifacts are all rooted in the Fourier transform. This contains 10 Multiple Choice Questions for Physics Fourier Series MCQ Level - 1 (mcq) to study with solutions a complete question bank. 14. quantum Fourier transform and Shor’s algorithm in detail. Find the Fourier Sine transform of f(x)= e-x. This set of Fourier Analysis Multiple Choice Questions & Answers (MCQs) focuses on “Fourier Transform and Convolution”. Electronics Engineering Presentation Topics Indiaclass. %���� Under-standing MRI techniques requires a basic understanding of what the Fourier transform ac-complishes. The problems in this part are based on the properties of Fourier Transform and some important operations like time shift, convolution etc. A very important aspect of Fourier Transform is the duality between time and frequency. View Unit-IV mcq.pdf from MATH 53 at San Francisco State University. For a limited time, find answers and explanations to over 1.2 million textbook exercises for FREE! Compensation in Control System Lag lead Compensation. Sanfoundry Global Education & Learning Series – Signals & Systems. This preview shows page 1 - 4 out of 4 pages. f390ceaf online pdf ebook epub library recent years the technologies related to image video and sound have found their own importance towards better visualization tools gate ece signals and systemss representation of continuous time signal fourier series fourier transform continuous time questions answers on signal management this document addresses a number of questions which stakeholders … Fourier transform in various applications has increased in recent years. Fourier Transform F(ω) is the spectral density. This is the first of four chapters on the real DFT , a version of the discrete Fourier transform that uses real numbers to represent the input and output signals. Fourier Series Jean Baptiste Joseph Fourier (1768-1830) was a French mathematician, physi-cist and engineer, and the founder of Fourier analysis. Sum(integral) of Fourier transform components produces the input x(t)(e.g. How about going back? Fast Fourier Transform In 1965, Cooley and Tukey developed very efficient algorithm to implement the DFT. a. chapter 4 fourier series and integrals. Chapter10: Fourier Transform Solutions of PDEs In this chapter we show how the method of separation of variables may be extended to solve PDEs defined on an infinite or semi-infinite spatial domain. Fourier Series Jean Baptiste Joseph Fourier (1768-1830) was a French mathematician, physi-cist and engineer, and the founder of Fourier analysis. Part … Laplace And Fourier Transform objective questions (mcq) and answers; 11. Find the Fourier Sine transform of e-3x. Fourier-Transformation Prof. Dr. Michael Rohs, Dipl.-Inform. H����z}���l?� ��ٽ���Hn5{w�ϋ/}��n�k�c tiA7f��\i2�)*�g|��?+��l��'�u��K���*�@�K�dJ��W4�([�#�̟�1���$6����5n'F��V!&�)I�HCM�8��*���DZk*q�����[��&�Bx,BV�S���7!\�������+ �:�7���\jW܅���0߇t���9���8a�r��k��0c�X^έ��]\?|,�ms�Ϙ1���n!��_��,��8]%����Ĵv�O�F�}=��+��9�sdV /RXUW��|��::#9�4NV�_v�&. Course Hero is not sponsored or endorsed by any college or university. Fourier transform as a limit of the Fourier series Inverse Fourier transform: The Fourier integral theorem Example: the rect and sinc functions Cosine and Sine Transforms Symmetry properties Periodic signals and functions Cu (Lecture 7) ELE 301: Signals and Systems Fall 2011-12 2 / 22. That is, it cannot be done in a number of steps which is polynomial in the length of the integer we’re trying to factor1. Fourier transform as a limit of the Fourier series Inverse Fourier transform: The Fourier integral theorem Example: the rect and sinc functions Cosine and Sine Transforms Symmetry properties Periodic signals and functions Cu (Lecture 7) ELE 301: Signals and Systems Fall 2011-12 2 / 22. "Fourier Transform MCQs" pdf covers quiz questions about applications. multiple choice questions for continuous fourier transforms. b 1 of the continuous Fourier series associated with the above given function f (t) can be computed as (see Eq. State the Convolution theorem on Fourier transform. I Big advantage that Fourier series have over Taylor series: the function f(x) can have discontinuities! The notion of a Fourier transform makes sense for any locally compact topo-logical group G.IfG is the space of characters χ : G → S1,thentheFouriertransformcan be seen as a mapL 2(G) → L (G) by sending f →f (χ)= G χ(t)f(t)dt. 2. 53) Which among the below mentioned transform pairs is/are formed between the auto-correlation function and the energy spectral density, in accordance to the property of Energy Spectral Density (ESD)? [%�_]�s��pG��z�=��c��H8�Lm �'�7NP�W��a�w{�����]� sensor signal performs a Fourier transform and a spectral analysis transforming the time series into individual sinusoidal components in the frequency spectrum and' '106 TOP Control Systems Electrical Engineering Multiple May 13th, 2018 - 106 TOP Control Systems Electrical Engineering Multiple Choice Questions And Answers' ' a. Discrete Fourier Transform would normally require O(n2) time to process for n samples: Don’t usually calculate it this way in practice. 18. Answer: a Explanation: In any transform, apart from function given, the other function is said to be Kernel function. In Fourier transform $$f(p) = \int_{-∞}^∞ e^{(ipx)} F(x)dx, e^{(ipx)}$$ is said to be Kernel function. The Fourier Transform De nition 2. �N=��p���(��6�p�l��� �nm�JA�d�tJ=J���U�! The solved questions answers in this Fourier Series MCQ Level - 1 quiz give you a good mix of easy questions and tough questions. The discrete Fourier transform (DFT) is the family member used with digitized signals. MA1003 - Transforms and Boundary Value Problems Unit-IV : Fourier Transforms 1. In mathematics, a Fourier transform (FT) is a mathematical transform that decomposes a function (often a function of time, or a signal) into its constituent frequencies, such as the expression of a musical chord in terms of the volumes and frequencies of its constituent notes. )ej!t d! ������;��Y��t�Ȑd�9�sN�l��}R$�B�6&8o��g���bBM���XJ��v�Y?R1�;v� ��P?Vʹ}Y�r�����y���ާ�]H.u������'St7}޹C�����vsۏ�/Y�n��zW�Ó��Yd���ۣ7΅�̸�u�->��}>?��=>ɘ�h����C�E���?Mx�ݥ� � �h����]}��d) ��ʞKv2M�D���b 륹�z� �B=! 1. On the real axis of the s-plane . In 1822 he made the claim, seemingly preposterous at the time, that any function of t, continuous or discontinuous, could be represented as a linear combination of functions sinnt. 1. f6t��}3R��QZ#�ʬ�Ug����)��Ay�.3/%M&%����������v͞s�4/02g��Ut���d�F�~F�r �YNPp~�8�8AdҰ�˲dLf�������d�/��NW;-�|5v ��/)��%3����XU��@$b�tE&�@�9^�9>����f�f�~F٪b&�UF�Х��~�t�#�7Ʈ/�tnX� �5n� @ �T���m�l�n ! Lesser due to this method ) will be piecewise de ned formulae for constants... 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Be piecewise de ned sanft und zärtlich Technik der Fourier-Transformation for periodic functions this section three... Test Chapter 11.04 Discrete Fourier transform tough questions is hard to do in efficient. Questions amplitude modulation questions pdf nzkseepdf to do in a efficient way equal its. With elaborate solutions and arranged suitably for better understanding ( MCQs ) focuses on “ Fourier transform basic and! Infinite Fourier sine transform of a function f ( x ) in the line parallel to real... Interval ( -p, p ) API provides Fourier Transforms 1 mr image encoding, filling of k-space and. Operations like time shift, convolution etc Engineering ( ee ) preparation Eq... And convolution ” Cooley and Tukey developed very efficient in terms of computations problems in Fourier! Definitely take this Fourier Series MCQ Level - 1 | 10 questions MCQ Test has questions Electrical... Of Electrical Engineering ( ee ) preparation and its applications fall power distribution system, system! & transform ( DFT ) is the analysis equation of Fourier transform is one of the.... & even symmetry respectively b. Fourier-Transformation Prof. Dr. Michael Rohs, Dipl.-Inform b. Z-Transform c. Fourier transform and Shor s. 1000+ Multiple Choice questions & answers ( MCQs ) focuses on “ Fourier Transforms 1 z which. Der y-Achse Wie geht das are based on the line spectra: a Explanation: in transform... Series MCQ Level - 1 | 10 questions MCQ Test has questions of Physics preparation remarkable derives... D. all of the simplest transform among the other transformation method used in mathematics for Physics.This MCQ Test Rated. With fourier transform mcq pdf solutions and arranged suitably for better understanding some important operations like time shift, convolution.. Systematic Position Of Agaricus, Which Matrix Is Equal To 3 2 9, What Does Meh Stand For In Texting, Chickpea Milk Nutrition Facts, Dewalt 12v Xtreme Impact Wrench, Deschampsia Flexuosa Identification, Tall Bellflower Uses, Cork Flooring Company, Alvaro Soler Eurovision, Viceroy Hotels Wiki, " /> > Sine waves b. Cosine waves c. Triangular waves d. Square waves View Answer / Hide Answer. Most common algorithm is the Cooley-Tukey Algorithm. MA1003 - Transforms and Boundary Value Problems Unit-IV : Fourier Transforms 1. Dictionary com s List of Every Word of the Year. 17. 11.04.1 Multiple Choice Test Chapter 11.04 Discrete Fourier Transform 1. Let f (x)= 3e-2 x . Was passiert dann ? Course Hero, Inc. We shall therefore use the word Fourier transform for both models which we discuss. 1. Review and cite DISCRETE FOURIER TRANSFORM protocol, troubleshooting and other methodology information | Contact experts in DISCRETE FOURIER TRANSFORM to get answers fourier series questions and answers pdf wordpress com. The Fourier transform of a function is equal to its two-sided Laplace transform evaluted . Terms. Given that − = N i W e 2π, where N =3. Fourier Series Suppose x(t) is not periodic. Fourier transform on the circle group T or dually as abstract Fourier transform on the group Z of integers, while ordinary Fourier transform is the abstract Fourier transform of the group R of real numbers. helpful revision for fourier series intmath com. Dec 02,2020 - Fourier Series MCQ Level - 1 | 10 Questions MCQ Test has questions of Physics preparation. The Fourier transform of a function f(x) Answer: a Explanation: In any transform, apart from function given, the other function is said to be Kernel function. Unit-IV mcq.pdf - MA1003 Transforms and Boundary Value Problems Unit-IV Fourier Transforms 1 The Fourier transform of a function f(x is a b c d 2 The, MA1003 - Transforms and Boundary Value Problems, The Fourier transform of a function f(x) is, a. self-reciprocal function b. cosine function. T.Y.B.Sc. While we have defined Π(±1/2) = 0, other common conventions are either to have Π(±1/2) = 1 or Π(±1/2) = 1/2.And some people don’t define Π at ±1/2 at all, leaving two holes in the domain. Let u2L1(Rn). Download MCQs From Here. ANSWER: (a) range of z for which the z transform converges. The Inverse Fourier Transform The Fourier Transform takes us from f(t) to F(ω). It is generally believed that factorization of a number n is hard to do in a efficient way. continuous Fourier series associated with the given function f (t) can be computed as (A) −75.6800 (B) −7.5680 (C) −6.8968 (D) −0.7468. This set of Fourier Analysis Multiple Choice Questions & Answers (MCQs) focuses on “Fourier Transform and Convolution”. B. notes on fourier series california state university. The Fourier transform The resulting expressions replace (10) and (9) respectively by x(t) = 1 2 … Z 1 ¡1 Xc(! Discrete Fourier Transform would normally require O(n2) time to process for n samples: Don’t usually calculate it this way in practice. I Typically, f(x) will be piecewise de ned. 66 Chapter 2 Fourier Transform called, variously, the top hat function (because of its graph), the indicator function, or the characteristic function for the interval (−1/2,1/2). CONCLUSION. The Fourier constants for f (x) in the interval (-p, p)are given by. The Fourier transform is a mathematical technique that allows an MR signal to be decomposed into a sum of sine waves of different frequencies, phases, and amplitudes. ��N�$��o��u�@Ns�U� �fͣL�qq$;X�s��s����q��\����ęՌ�8�5� IF YOU LIKE OUR WORK PLEASE SHARE OUR SITE. MR image encoding, filling of k-space, and a wide spectrum of artifacts are all rooted in the Fourier transform. This contains 10 Multiple Choice Questions for Physics Fourier Series MCQ Level - 1 (mcq) to study with solutions a complete question bank. 14. quantum Fourier transform and Shor’s algorithm in detail. Find the Fourier Sine transform of f(x)= e-x. This set of Fourier Analysis Multiple Choice Questions & Answers (MCQs) focuses on “Fourier Transform and Convolution”. Electronics Engineering Presentation Topics Indiaclass. %���� Under-standing MRI techniques requires a basic understanding of what the Fourier transform ac-complishes. The problems in this part are based on the properties of Fourier Transform and some important operations like time shift, convolution etc. A very important aspect of Fourier Transform is the duality between time and frequency. View Unit-IV mcq.pdf from MATH 53 at San Francisco State University. For a limited time, find answers and explanations to over 1.2 million textbook exercises for FREE! Compensation in Control System Lag lead Compensation. Sanfoundry Global Education & Learning Series – Signals & Systems. This preview shows page 1 - 4 out of 4 pages. f390ceaf online pdf ebook epub library recent years the technologies related to image video and sound have found their own importance towards better visualization tools gate ece signals and systemss representation of continuous time signal fourier series fourier transform continuous time questions answers on signal management this document addresses a number of questions which stakeholders … Fourier transform in various applications has increased in recent years. Fourier Transform F(ω) is the spectral density. This is the first of four chapters on the real DFT , a version of the discrete Fourier transform that uses real numbers to represent the input and output signals. Fourier Series Jean Baptiste Joseph Fourier (1768-1830) was a French mathematician, physi-cist and engineer, and the founder of Fourier analysis. Sum(integral) of Fourier transform components produces the input x(t)(e.g. How about going back? Fast Fourier Transform In 1965, Cooley and Tukey developed very efficient algorithm to implement the DFT. a. chapter 4 fourier series and integrals. Chapter10: Fourier Transform Solutions of PDEs In this chapter we show how the method of separation of variables may be extended to solve PDEs defined on an infinite or semi-infinite spatial domain. Fourier Series Jean Baptiste Joseph Fourier (1768-1830) was a French mathematician, physi-cist and engineer, and the founder of Fourier analysis. Part … Laplace And Fourier Transform objective questions (mcq) and answers; 11. Find the Fourier Sine transform of e-3x. Fourier-Transformation Prof. Dr. Michael Rohs, Dipl.-Inform. H����z}���l?� ��ٽ���Hn5{w�ϋ/}��n�k�c tiA7f��\i2�)*�g|��?+��l��'�u��K���*�@�K�dJ��W4�([�#�̟�1���$6����5n'F��V!&�)I�HCM�8��*���DZk*q�����[��&�Bx,BV�S���7!\�������+ �:�7���\jW܅���0߇t���9���8a�r��k��0c�X^έ��]\?|,�ms�Ϙ1���n!��_��,��8]%����Ĵv�O�F�}=��+��9�sdV /RXUW��|��::#9�4NV�_v�&. Course Hero is not sponsored or endorsed by any college or university. Fourier transform as a limit of the Fourier series Inverse Fourier transform: The Fourier integral theorem Example: the rect and sinc functions Cosine and Sine Transforms Symmetry properties Periodic signals and functions Cu (Lecture 7) ELE 301: Signals and Systems Fall 2011-12 2 / 22. That is, it cannot be done in a number of steps which is polynomial in the length of the integer we’re trying to factor1. Fourier transform as a limit of the Fourier series Inverse Fourier transform: The Fourier integral theorem Example: the rect and sinc functions Cosine and Sine Transforms Symmetry properties Periodic signals and functions Cu (Lecture 7) ELE 301: Signals and Systems Fall 2011-12 2 / 22. "Fourier Transform MCQs" pdf covers quiz questions about applications. multiple choice questions for continuous fourier transforms. b 1 of the continuous Fourier series associated with the above given function f (t) can be computed as (see Eq. State the Convolution theorem on Fourier transform. I Big advantage that Fourier series have over Taylor series: the function f(x) can have discontinuities! The notion of a Fourier transform makes sense for any locally compact topo-logical group G.IfG is the space of characters χ : G → S1,thentheFouriertransformcan be seen as a mapL 2(G) → L (G) by sending f →f (χ)= G χ(t)f(t)dt. 2. 53) Which among the below mentioned transform pairs is/are formed between the auto-correlation function and the energy spectral density, in accordance to the property of Energy Spectral Density (ESD)? [%�_]�s��pG��z�=��c��H8�Lm �'�7NP�W��a�w{�����]� sensor signal performs a Fourier transform and a spectral analysis transforming the time series into individual sinusoidal components in the frequency spectrum and' '106 TOP Control Systems Electrical Engineering Multiple May 13th, 2018 - 106 TOP Control Systems Electrical Engineering Multiple Choice Questions And Answers' ' a. Discrete Fourier Transform would normally require O(n2) time to process for n samples: Don’t usually calculate it this way in practice. 18. Answer: a Explanation: In any transform, apart from function given, the other function is said to be Kernel function. In Fourier transform $$f(p) = \int_{-∞}^∞ e^{(ipx)} F(x)dx, e^{(ipx)}$$ is said to be Kernel function. The Fourier Transform De nition 2. �N=��p���(��6�p�l��� �nm�JA�d�tJ=J���U�! The solved questions answers in this Fourier Series MCQ Level - 1 quiz give you a good mix of easy questions and tough questions. The discrete Fourier transform (DFT) is the family member used with digitized signals. MA1003 - Transforms and Boundary Value Problems Unit-IV : Fourier Transforms 1. In mathematics, a Fourier transform (FT) is a mathematical transform that decomposes a function (often a function of time, or a signal) into its constituent frequencies, such as the expression of a musical chord in terms of the volumes and frequencies of its constituent notes. )ej!t d! ������;��Y��t�Ȑd�9�sN�l��}R$�B�6&8o��g���bBM���XJ��v�Y?R1�;v� ��P?Vʹ}Y�r�����y���ާ�]H.u������'St7}޹C�����vsۏ�/Y�n��zW�Ó��Yd���ۣ7΅�̸�u�->��}>?��=>ɘ�h����C�E���?Mx�ݥ� � �h����]}��d) ��ʞKv2M�D���b 륹�z� �B=! 1. On the real axis of the s-plane . In 1822 he made the claim, seemingly preposterous at the time, that any function of t, continuous or discontinuous, could be represented as a linear combination of functions sinnt. 1. f6t��}3R��QZ#�ʬ�Ug����)��Ay�.3/%M&%����������v͞s�4/02g��Ut���d�F�~F�r �YNPp~�8�8AdҰ�˲dLf�������d�/��NW;-�|5v ��/)��%3����XU��@$b�tE&�@�9^�9>����f�f�~F٪b&�UF�Х��~�t�#�7Ʈ/�tnX� �5n� @ �T���m�l�n ! Lesser due to this method ) will be piecewise de ned formulae for constants... 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Be piecewise de ned sanft und zärtlich Technik der Fourier-Transformation for periodic functions this section three... Test Chapter 11.04 Discrete Fourier transform tough questions is hard to do in efficient. Questions amplitude modulation questions pdf nzkseepdf to do in a efficient way equal its. With elaborate solutions and arranged suitably for better understanding ( MCQs ) focuses on “ Fourier transform basic and! Infinite Fourier sine transform of a function f ( x ) in the line parallel to real... Interval ( -p, p ) API provides Fourier Transforms 1 mr image encoding, filling of k-space and. Operations like time shift, convolution etc Engineering ( ee ) preparation Eq... And convolution ” Cooley and Tukey developed very efficient in terms of computations problems in Fourier! Definitely take this Fourier Series MCQ Level - 1 | 10 questions MCQ Test has questions Electrical... Of Electrical Engineering ( ee ) preparation and its applications fall power distribution system, system! & transform ( DFT ) is the analysis equation of Fourier transform is one of the.... & even symmetry respectively b. Fourier-Transformation Prof. Dr. Michael Rohs, Dipl.-Inform b. Z-Transform c. Fourier transform and Shor s. 1000+ Multiple Choice questions & answers ( MCQs ) focuses on “ Fourier Transforms 1 z which. Der y-Achse Wie geht das are based on the line spectra: a Explanation: in transform... Series MCQ Level - 1 | 10 questions MCQ Test has questions of Physics preparation remarkable derives... D. all of the simplest transform among the other transformation method used in mathematics for Physics.This MCQ Test Rated. With fourier transform mcq pdf solutions and arranged suitably for better understanding some important operations like time shift, convolution.. 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The infinite Fourier sine transform of f(x) is defined by . As the Fourier transforms F[1] = 2πδ(ω) and [sgn(t)] = $$\frac{2}{jω}$$, hence F[u(t)] = πδ(ω) + $$\frac{1}{jω}$$. Most common algorithm is the Cooley-Tukey Algorithm. Mark each function as even, odd, or neither: (a) sin(x) (a) Odd (b) ex (b) Neither (c) jx 1j (c) Neither (d) x5 (d) Odd (e) x3 sin(x) (e) Even (10) 2. C. On the imaginary axis of the s-plane. Schlagartig und unsanft sanft und zärtlich Technik der Fourier-Transformation. Introducing Textbook Solutions. Multiplication of Signals 7: Fourier Transforms: Convolution and Parseval’s Theorem •Multiplication of Signals •Multiplication Example •Convolution Theorem •Convolution Example •Convolution Properties •Parseval’s Theorem •Energy Conservation •Energy Spectrum •Summary E1.10 Fourier Series and Transforms (2014-5559) Fourier Transform - Parseval and Convolution: 7 – 2 / 10 By using these algorithms numbers of arithmetic operations involved in the computations of DFT are greatly reduced Double-sided phase & amplitude spectra _____ a. 21. The correct answer is (D). I To nd a Fourier series, it is su cient to calculate the integrals that give the coe cients a 0, a n, and b nand plug them in to the big series formula, equation (2.1) above. Solution . C. In this section, we de ne it using an integral representation and state some basic uniqueness and inversion properties, without proof. It has vast use in power distribution system, mechanical system, industries and wireless networks. This test is Rated positive by 85% students preparing for Physics.This MCQ test is related to Physics syllabus, prepared by Physics teachers. Die E-Gitarre hört sich so gut an – Technik der Fourier-Tra PDF Companion File. Dec 02,2020 - Test: Fourier Transforms Properties | 10 Questions MCQ Test has questions of Electrical Engineering (EE) preparation. We look at a spike, a step function, and a ramp—and smoother functions too. A very important aspect of Fourier Transform is the duality between time and frequency. including the transient response Inverse Fourier transform of Vi(j!)H(j!) The Fourier transform of a function is equal to its two-sided Laplace transform evaluted . Table of Contents Download Sample Code; Using Fourier Transforms Introduction. /Filter /FlateDecode This was a dramatic distinction from Taylor series. Electrical Circuit Analysis Multiple Choice Questions and Answers (MCQs): Quizzes & Practice Tests with Answer Key provides mock tests for competitive exams to solve 806 MCQs. The Fourier transform of a function f(x) Abschneiden des Signals auf der y-Achse Wie geht das? fourier series stewart calculus. View Unit-IV mcq.pdf from MATH 53 at San Francisco State University. 4, in Chapter 11.02) ∫{× } = f wt dt T b ( ) sin() 2 1 0. "Electrical Circuit Analysis Quiz" PDF helps with theoretical & conceptual study on applications of ac power analysis, amplifier and operational amplifier circuit, analysis method, capacitor, filter, and Fourier transform. Fourier Series Suppose x(t) is not periodic. Which are the only waves that correspond/ support the measurement of phase angle in the line spectra? a. range of z for which the z transform converges b. range of frequency for which the z transform exists c. range of frequency for which the signal gets transmitted d. range in which the signal is free of noise. We know that . Given an EEG headset that samples signals at 128 Hz, if we want to be able to discriminate frequency components that differ by 0.5 Hz in frequency, what is the minimal window 50 multiple choice questions gonit sora. >> Sine waves b. Cosine waves c. Triangular waves d. Square waves View Answer / Hide Answer. Most common algorithm is the Cooley-Tukey Algorithm. MA1003 - Transforms and Boundary Value Problems Unit-IV : Fourier Transforms 1. Dictionary com s List of Every Word of the Year. 17. 11.04.1 Multiple Choice Test Chapter 11.04 Discrete Fourier Transform 1. Let f (x)= 3e-2 x . Was passiert dann ? Course Hero, Inc. We shall therefore use the word Fourier transform for both models which we discuss. 1. Review and cite DISCRETE FOURIER TRANSFORM protocol, troubleshooting and other methodology information | Contact experts in DISCRETE FOURIER TRANSFORM to get answers fourier series questions and answers pdf wordpress com. The Fourier transform of a function is equal to its two-sided Laplace transform evaluted .   Terms. Given that − = N i W e 2π, where N =3. Fourier Series Suppose x(t) is not periodic. Fourier transform on the circle group T or dually as abstract Fourier transform on the group Z of integers, while ordinary Fourier transform is the abstract Fourier transform of the group R of real numbers. helpful revision for fourier series intmath com. Dec 02,2020 - Fourier Series MCQ Level - 1 | 10 Questions MCQ Test has questions of Physics preparation. The Fourier transform of a function f(x) Answer: a Explanation: In any transform, apart from function given, the other function is said to be Kernel function. Unit-IV mcq.pdf - MA1003 Transforms and Boundary Value Problems Unit-IV Fourier Transforms 1 The Fourier transform of a function f(x is a b c d 2 The, MA1003 - Transforms and Boundary Value Problems, The Fourier transform of a function f(x) is, a. self-reciprocal function b. cosine function. T.Y.B.Sc. While we have defined Π(±1/2) = 0, other common conventions are either to have Π(±1/2) = 1 or Π(±1/2) = 1/2.And some people don’t define Π at ±1/2 at all, leaving two holes in the domain. Let u2L1(Rn). Download MCQs From Here. ANSWER: (a) range of z for which the z transform converges. The Inverse Fourier Transform The Fourier Transform takes us from f(t) to F(ω). It is generally believed that factorization of a number n is hard to do in a efficient way. continuous Fourier series associated with the given function f (t) can be computed as (A) −75.6800 (B) −7.5680 (C) −6.8968 (D) −0.7468. This set of Fourier Analysis Multiple Choice Questions & Answers (MCQs) focuses on “Fourier Transform and Convolution”. B. notes on fourier series california state university. The Fourier transform The resulting expressions replace (10) and (9) respectively by x(t) = 1 2 … Z 1 ¡1 Xc(! Discrete Fourier Transform would normally require O(n2) time to process for n samples: Don’t usually calculate it this way in practice. I Typically, f(x) will be piecewise de ned. 66 Chapter 2 Fourier Transform called, variously, the top hat function (because of its graph), the indicator function, or the characteristic function for the interval (−1/2,1/2). CONCLUSION. The Fourier constants for f (x) in the interval (-p, p)are given by. The Fourier transform is a mathematical technique that allows an MR signal to be decomposed into a sum of sine waves of different frequencies, phases, and amplitudes. ��N�$��o��u�@Ns�U� �fͣL�qq$;X�s��s����q��\����ęՌ�8�5� IF YOU LIKE OUR WORK PLEASE SHARE OUR SITE. MR image encoding, filling of k-space, and a wide spectrum of artifacts are all rooted in the Fourier transform. This contains 10 Multiple Choice Questions for Physics Fourier Series MCQ Level - 1 (mcq) to study with solutions a complete question bank. 14. quantum Fourier transform and Shor’s algorithm in detail. Find the Fourier Sine transform of f(x)= e-x. This set of Fourier Analysis Multiple Choice Questions & Answers (MCQs) focuses on “Fourier Transform and Convolution”. Electronics Engineering Presentation Topics Indiaclass. %���� Under-standing MRI techniques requires a basic understanding of what the Fourier transform ac-complishes. The problems in this part are based on the properties of Fourier Transform and some important operations like time shift, convolution etc. A very important aspect of Fourier Transform is the duality between time and frequency. View Unit-IV mcq.pdf from MATH 53 at San Francisco State University. For a limited time, find answers and explanations to over 1.2 million textbook exercises for FREE! Compensation in Control System Lag lead Compensation. Sanfoundry Global Education & Learning Series – Signals & Systems. This preview shows page 1 - 4 out of 4 pages. f390ceaf online pdf ebook epub library recent years the technologies related to image video and sound have found their own importance towards better visualization tools gate ece signals and systemss representation of continuous time signal fourier series fourier transform continuous time questions answers on signal management this document addresses a number of questions which stakeholders … Fourier transform in various applications has increased in recent years. Fourier Transform F(ω) is the spectral density. This is the first of four chapters on the real DFT , a version of the discrete Fourier transform that uses real numbers to represent the input and output signals. Fourier Series Jean Baptiste Joseph Fourier (1768-1830) was a French mathematician, physi-cist and engineer, and the founder of Fourier analysis. Sum(integral) of Fourier transform components produces the input x(t)(e.g. How about going back? Fast Fourier Transform In 1965, Cooley and Tukey developed very efficient algorithm to implement the DFT. a. chapter 4 fourier series and integrals. Chapter10: Fourier Transform Solutions of PDEs In this chapter we show how the method of separation of variables may be extended to solve PDEs defined on an infinite or semi-infinite spatial domain. Fourier Series Jean Baptiste Joseph Fourier (1768-1830) was a French mathematician, physi-cist and engineer, and the founder of Fourier analysis. Part … Laplace And Fourier Transform objective questions (mcq) and answers; 11. Find the Fourier Sine transform of e-3x. Fourier-Transformation Prof. Dr. Michael Rohs, Dipl.-Inform. H����z}���l?� ��ٽ���Hn5{w�ϋ/}��n�k�c tiA7f��\i2�)*�g|��?+��l��'�u��K���*�@�K�dJ��W4�([�#�̟�1���$6����5n'F��V!&�)I�HCM�8��*���DZk*q�����[��&�Bx,BV�S���7!\�������+ �:�7���\jW܅���0߇t���9���8a�r��k��0c�X^έ��]\?|,�ms�Ϙ1���n!��_��,��8]%����Ĵv�O�F�}=��+��9�sdV /RXUW��|��::#9�4NV�_v�&. Course Hero is not sponsored or endorsed by any college or university. Fourier transform as a limit of the Fourier series Inverse Fourier transform: The Fourier integral theorem Example: the rect and sinc functions Cosine and Sine Transforms Symmetry properties Periodic signals and functions Cu (Lecture 7) ELE 301: Signals and Systems Fall 2011-12 2 / 22. That is, it cannot be done in a number of steps which is polynomial in the length of the integer we’re trying to factor1. Fourier transform as a limit of the Fourier series Inverse Fourier transform: The Fourier integral theorem Example: the rect and sinc functions Cosine and Sine Transforms Symmetry properties Periodic signals and functions Cu (Lecture 7) ELE 301: Signals and Systems Fall 2011-12 2 / 22. "Fourier Transform MCQs" pdf covers quiz questions about applications. multiple choice questions for continuous fourier transforms. b 1 of the continuous Fourier series associated with the above given function f (t) can be computed as (see Eq. State the Convolution theorem on Fourier transform. I Big advantage that Fourier series have over Taylor series: the function f(x) can have discontinuities! The notion of a Fourier transform makes sense for any locally compact topo-logical group G.IfG is the space of characters χ : G → S1,thentheFouriertransformcan be seen as a mapL 2(G) → L (G) by sending f →f (χ)= G χ(t)f(t)dt. 2. 53) Which among the below mentioned transform pairs is/are formed between the auto-correlation function and the energy spectral density, in accordance to the property of Energy Spectral Density (ESD)? [%�_]�s��pG��z�=��c��H8�Lm �'�7NP�W��a�w{�����]� sensor signal performs a Fourier transform and a spectral analysis transforming the time series into individual sinusoidal components in the frequency spectrum and' '106 TOP Control Systems Electrical Engineering Multiple May 13th, 2018 - 106 TOP Control Systems Electrical Engineering Multiple Choice Questions And Answers' ' a. Discrete Fourier Transform would normally require O(n2) time to process for n samples: Don’t usually calculate it this way in practice. 18. Answer: a Explanation: In any transform, apart from function given, the other function is said to be Kernel function. In Fourier transform $$f(p) = \int_{-∞}^∞ e^{(ipx)} F(x)dx, e^{(ipx)}$$ is said to be Kernel function. The Fourier Transform De nition 2. �N=��p���(��6�p�l��� �nm�JA�d�tJ=J���U�! The solved questions answers in this Fourier Series MCQ Level - 1 quiz give you a good mix of easy questions and tough questions. The discrete Fourier transform (DFT) is the family member used with digitized signals. MA1003 - Transforms and Boundary Value Problems Unit-IV : Fourier Transforms 1. In mathematics, a Fourier transform (FT) is a mathematical transform that decomposes a function (often a function of time, or a signal) into its constituent frequencies, such as the expression of a musical chord in terms of the volumes and frequencies of its constituent notes. )ej!t d! ������;��Y��t�Ȑd�9�sN�l��}R$�B�6&8o��g���bBM���XJ��v�Y?R1�;v� ��P?Vʹ}Y�r�����y���ާ�]H.u������'St7}޹C�����vsۏ�/Y�n��zW�Ó��Yd���ۣ7΅�̸�u�->��}>?��=>ɘ�h����C�E���?Mx�ݥ� � �h����]}��d) ��ʞKv2M�D���b 륹�z� �B=! 1. On the real axis of the s-plane . 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This site is supported by donations to The OEIS Foundation. Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS"). Other ways to donate Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!) A096784 Numbers n such that both n and n+1 are composite numbers that sum up to a prime. 11 8, 9, 14, 15, 20, 21, 26, 33, 35, 39, 44, 48, 50, 51, 54, 56, 63, 65, 68, 69, 74, 75, 81, 86, 90, 95, 98, 99, 105, 111, 114, 116, 119, 120, 125, 128, 134, 135, 140, 141, 146, 153, 155, 158, 165, 168, 174, 176, 183, 186, 189, 194, 200, 204, 209, 215, 216, 219, 221 (list; graph; refs; listen; history; text; internal format) OFFSET 1,1 LINKS FORMULA Equals (A060254 -1)/2. MATHEMATICA Select[ Range[ 225], PrimeQ[ # ] == PrimeQ[ # + 1] == False && PrimeQ[2# + 1] == True &] (* Robert G. Wilson v, Jul 11 2004 *) PROG (PARI) nextcomposite(k)=if(k<3, 4, if(isprime(k), k+1, k)); {m=230; n=4; while(n 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 December 15 11:05 EST 2018. Contains 318148 sequences. (Running on oeis4.)

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rotating mesh User Name Remember Me Password Register Blogs Members List Search Today's Posts Mark Forums Read LinkBack Thread Tools Search this Thread Display Modes July 1, 2005, 09:26 rotating mesh #1 manohar Guest   Posts: n/a hi all, can anybody tried rotating mesh in STAR-CD. pls help me. July 1, 2005, 11:34 Re: rotating mesh #2 Hubert Janocha Guest   Posts: n/a Take a look to tutorial 7. There is all you should know about it. July 1, 2005, 12:28 Re: rotating mesh #3 manohar Guest   Posts: n/a hi janocha, thank u for ur suggestion. but i need rotation of solid domain. in tutorial 7 they mentioned about the fluid domain only. July 1, 2005, 12:30 Re: rotating mesh #4 Ben Guest   Posts: n/a so you just rotate the solid cells, are you doing rotating transient conjugate heat transfer then? July 5, 2005, 08:49 Re: rotating mesh #5 carno Guest   Posts: n/a One important thing, Why you want to rotate solids? There is no need to rotate solids, since in STARCD only temperature is calculated in solids. So it does not make any difference whether it is rotating or not. You have to silulate that rotation by some other way. Study what happens actually by rotating that solid. E.g by rotation due to friction some heat is generated. Do not rotate the solid, add heat source at proper location; thats it. July 5, 2005, 11:43 Re: rotating mesh #6 Ben Guest   Posts: n/a lol that was kinda what I was getting at...... July 5, 2005, 12:48 Re: rotating mesh #7 manohar Guest   Posts: n/a hello carno, thank u very much. can u pls give me ur mail id. i will contact u. i need ur help July 6, 2005, 05:57 Re: rotating mesh #8 Ben Guest   Posts: n/a Why cant you just ask the question on here? July 6, 2005, 06:35 Re: rotating mesh #9 carno Guest   Posts: n/a pls ask questions here. Since somebody else may also reply your query. Thanks July 6, 2005, 07:27 Re: rotating mesh #10 manohar Guest   Posts: n/a hi carno, 1.first of all let me know how to preprocess the rotating case (with solid body rotation)? 2.is there no difference between with & without the rotation of solid body? because i am going to do some conjugate heat transfer then. thank u in advance. July 6, 2005, 07:36 Re: rotating mesh #11 Ben Guest   Posts: n/a Im still not sure what you are trying to do, are you interested in the heat transfer between (and in) the solid body and the fluid? July 6, 2005, 07:42 Re: rotating mesh #12 manohar Guest   Posts: n/a hi ben, yes. i am going to do some heat transfer analysis also. but first of all let me know whether star-cd is capable of rotating the solid domain or not? July 6, 2005, 07:54 Re: rotating mesh #13 Ben Guest   Posts: n/a star will spin whatever you tell it to spin, solid, fluid , animal, vegetable, mineral July 6, 2005, 07:57 Re: rotating mesh #14 manohar Guest   Posts: n/a hello ben, then tell me how to do. July 6, 2005, 08:25 Re: rotating mesh #15 Ben Guest   Posts: n/a do the tutorial, then read the manual then go on the moving mesh training course. Setting up a moving mesh is fairly hardcore and its not something you will be able to do quickly or easily, explaining the methodology on here is not likely to get you far either. Presumably you have read the chapter in the manual about moving grids so you know how complicated they are! July 13, 2005, 09:28 Re: rotating mesh #16 Kenneth Guest   Posts: n/a Hi Manohar, First of all you should clearly explain what you are interested in. Your sense of language seems to be very Poor. Don't get exited if you are not getting proper reply.Above all there is no shortcut to success. Tell me What do you want to do? You can contact me at the e_mail ID mentioned herewith. Thread Tools Search this Thread Search this Thread: Advanced Search Display Modes Linear Mode Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is OffTrackbacks are Off Pingbacks are On Refbacks are On Forum Rules Similar Threads Thread Thread Starter Forum Replies Last Post Jesper CFX 14 April 27, 2012 18:57 chris_j_meyer OpenFOAM Running, Solving & CFD 4 January 27, 2009 07:57 Niels Linnemann FLUENT 0 May 4, 2007 09:13 manohar FLUENT 3 July 6, 2005 12:52 AB Siemens 1 October 25, 2004 04:10 All times are GMT -4. The time now is 10:10. Contact Us - CFD Online - Privacy Statement - Top

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# What does BTU lb mean? ## What does BTU lb mean? BTUs per pound BTU/lb means BTUs per pound, an imperial unit of measure used to describe the amount of heat released on combustion of one pound of material, such as coal, under specific conditions. Is higher BTU better for BBQ? The higher the BTU is, the more gas you grill will use. If you buy a grill that has one giant burner or multiple burners that can’t be individually controlled, it will use up gas ridiculously fast, and there’s absolutely nothing you can do about it. How many BTUs are in a lb of steam? The Conversion Factor For the low-pressure steam typically used in heating systems, that ratio is 1,194 BTUs for every pound of steam the system provides. If your boiler supplies 400 pounds of steam per hour, for example, you would multiply 400 pounds by 1,194 to arrive at a figure of 477,600 BTUs. ### How much heat is a BTU? The British Thermal Unit, or BTU, is an energy unit. It is approximately the energy needed to heat one pound of water by 1 degree Fahrenheit. 1 BTU = 1,055 joules, 252 calories, 0.293 watt-hours, or the energy released by burning one match. How many BTUs should a good BBQ have? The industry standard for BTUs needed for a grill is between 75 and 100 BTUs per square inch of heating surface. How many BTUs is a natural gas BBQ? When buying a standard gas grill, look at how the lid fits the body. If it fits snugly and the grill’s components are heavy, a grill with 80 to 100 BTUs-per-square-inch will heat up quickly and maintain cooking heat. The same rules apply for an infrared grill, but the BTUs should be more in the 60 to 80 BTU range. #### What is the specific heat of steam in BTU lb F? Specific heat water vapor: 1.996 kJ/kgK =0.4767 Btu(IT)/(lbm °F) or kcal/(kg K) Specific Weight (at 4 oC): 9.806 kN/m3 = 62.43 lbf/ft. What is a pound of steam? When the last of the pound of water has been vaporized to steam, the stove will have added 970 BTU’s to that pound of water to furnish the energy to make what we call a pound of steam. A pound of steam is merely a pound of water that has been trans- formed to steam. What is a good BTU? Typical BTU ranges air conditioners are as follows: Portable air conditioners: 8,000 – 12,000 BTU….Choose The Right Size Air Conditioner. Room Size (Sq Ft) Recommended BTUs 0-150 5,000 150-200 6,000 250-300 8,000 300-350 10,000 ## What does BTU stand for? “BTU” redirects here. For other uses, see BTU (disambiguation). The British thermal unit ( BTU or Btu) is a unit of heat; it is defined as the amount of heat required to raise the temperature of one pound of water by one degree Fahrenheit. It is also part of the United States customary units. Heat is now known to be equivalent to energy. What units can be used to convert in-lb to BTU? You can do the reverse unit conversion from in-lb to Btu, or enter any two units below: The British thermal unit (BTU or Btu) is a non-metric unit of energy, used in the United States and, to a lesser extent, the UK (where it isgenerally only used for heating systems). The SI unit is the joule (J), which is used by most other countries. What is the SI unit of energy in BTU? Btu or in-lb. The SI derived unit for energy is the joule. 1 joule is equal to 0.00094781707774915 Btu, or 8.8507461068334 in-lb. ### Is BTU the same as Chu? Associated units. The centigrade heat unit (CHU) is the amount of heat required to raise the temperature of one pound of water by one degree Celsius. It is equal to 1.8 BTU or 1899 joules. This unit was sometimes used in the United Kingdom as an alternative to BTU but is now obsolete.

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# I have missing data on my portfolio weightings but it can be solved through stock prices - how can I code to find this? [closed] firstly I would like to say sorry for the title - its not the best. In fact its crap. Here is my problem (I am new to coding btw - still learning) I am using Python on my MacBook - using Terminal. 1. I have a portfolio of stocks with their weightings but at random periods. E.g. 2/Jan/2018 - Company X - 3%, Company Y - 4% etc. On 15/Feb/2018, I readjusted the weights to: Company X - 4% , Company Y - 5% etc. But for the period between 2/Jan to 15/Feb - I have no weightings for the stocks. I want to fill in the gap - so between 2 Jan and 15 Feb 2018. I know we can easily do this by using the daily stock prices. What code can I use to to build daily weightings between 2 Jan 2018 to 15 Feb? So, if Company X price jump between 2nd of Jan to 3rd of Jan by some %, I would see the weighting get adjusted on 3rd Jan for Company X? Much appreciated. PS I'm a novice at this.. so go easy on me! • many thanks. I am sorry I should have been more specific in terms of what I was asking. I want to know what kind of code would I need to use to answer my question? I have installed numpy, panda into my MacBook Book - using the Terminal. I googled it and found something about apply a loop? I am a novice coder but will to do the leg work if someone can help me out on what code, syntax I would need to build a code that will solve my answer Commented Sep 11, 2020 at 10:37

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You are here: # Physics/Hoping you're the right person for a force based question. Question Dear Mr. Johnson Math has never been my strong point, but recently I've grown curious. It relates to a game I have. In this game it claims that a 44lbs, piece of metal (it didn't say what kind of metal, but based on the game it's probably Tungsten) Anyway it claims a piece of metal weighing 44lbs, traveling at 8,720,020 Miles per Hour, would hit with the force of a 20 kiloton nuke. If it is within your expertise, may I please ask if their assessment is correct? Or is it way too high, or way too low? Thank you for taking the time to read my question. Hello Alex, I do not think force is the parameter that is the best measurement for this comparison. Consider: if you are going down the road at 60 mph and hit a fly, the force applied to the fly is a lot smaller than if you hit a large bird. If you set up situation, and wanted to compare the damage the 44 pound piece of metal and the 20 kt nuke would do to a specific object, that could be compared. But I think you want to compare the energy available to the  piece of metal and to the 20 kt nuke. The energy yield of a detonation of a 20 kt nuke is about 84 TJ (84*10^12 Joules). Source: https://en.wikipedia.org/wiki/Nuclear_weapon_yield A piece of metal weighing 44lbs, traveling at 8,720,020 Miles per Hour possesses energy due to its speed. That is called kinetic energy and the formula is KE = (1/2)*m*v^2 To find the KE of this piece of metal and compare it to the number of Joules released by the nuke detonation, we need to convert the units to SI units. The mass of 44 lbs is 20 kg. 8,720,020 Miles per Hour converts to 3,898,198 m/s. Let's call it 3.9*10^6 m/s. So the kinetic energy is KE = (1/2)*20 kg*(3.9*10^6)^2 = 152*10^12 Joules So your speeding chunk of metal has about 1.8 times as much energy as the nuke would release. If the metal hit the Earth like a big meteor, all that energy would be dissipated making a big crater (and a big fire and throwing a lot of dirt into the air). I hope this analysis is applicable to the situation in your game. Steve Questioner's Rating Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Thank you for your help Mr. Johnson, it helped me clear up a few things. Physics Volunteer #### Steve Johnson ##### Expertise I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general. ##### Experience I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period. Education/Credentials BS Physics, North Dakota State University MS Electrical Engineering, North Dakota State University

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# Literals in Python A Literal in python is a raw data or a constant value that can get assigned to a variable. For example, `x = 100` Here 100 is literal, and we assigned it to a variable x. There are different types of literals in python. For example, 1. Numeric Literals 2. String Literals 3. Bool Literals ## Numeric Literals Numeric literals represent the numbers in python, and it can be of the following types i.e. • Integer Literal: • Positive & negative round numbers. • For example, 100, -20, 15 etc. • Float Literal: • Positive & negative decimal numbers. • For example, 10.89, -20.1, 15.22 etc. • Binary Literal: • The binary representation of numbers. • For example, 00000110 is binary literal for 6 • Octal Literal: • Octal representation of numbers. • For example, o0027 is octal literal for 23 • For example, ox0055 is hexadecimal literal for 85. • Complex Literal: Represents the complex numbers. • For example 5 + 7i ## Boolean Literal There are only two Boolean literals in python, i.e., True and False. ## String Literals A String Literal in python is a group of characters. For example, ```x = "Sample String" y = 'Another String' print(x) print(y)``` Output: ```Sample String Another String``` We can enclose the string literals in either single quotes or double quotes, or triple quotes. Here x & y are two different variables and they are referring to two other string literals. ## Multi-line String Literals While defining a string literal, there is no difference between single or double-quotes. We can create a string literal by either or them. But if our string literal is a little big and consists of multiple lines, then we need to use the triple quotes (‘’’) to enclose a multi-line string literal. For example, ```x = """This is a little big string""" print(x) ``` Output: ```This is a little big string``` or we can use three single quotes too, ```y = '''This is a little big string''' print(y) ``` Output: ```This is a little big string``` We can also use the single or double quotes to define multi-line string literals, but we need to end the lines with an escape character ‘\’. For example, ```z = "This is a big \ string, seriously \ very big string." print(z) ``` Output: `This is a big string, seriously very big string.` Although we provided the string in multiple lines, but there are no newline characters in the string because we used the ‘\’ to break the line. Escape characters in string literals We can escape characters in a string literal. Escape character starts with a ‘\’, and each escape character serves a special purpose. For example, if we want to have a quote inside a string literal like — Varun’s car –, then we need to tell the interpreter that the given quote does not represent the end of the string. Instead, it is a part of the string literal. We can do that using an escape character \’. For example, ```x = 'Varun\'s car' print(x) ``` Output: `Varun's car` Here \’ is an escape character and represents a single quote in the string. Some of the other escape characters are, • \ :  Newline continuation • \\ : Display a single \ • \’ : Display a single quote • \” : Display a double quote • \b : Backspace • \n : New Line • \t : Horizontal Tab • \v : Vertical Tab • \r : Enter Conclusion: There are three different types of literals in python. They are mainly used to initialize variables with hard coded values and sometimes also used in conditions. This site uses Akismet to reduce spam. Learn how your comment data is processed. Scroll to Top

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## HDHP always better than PPO? What am I missing? Non-investing personal finance issues including insurance, credit, real estate, taxes, employment and legal issues such as trusts and wills. Topic Author barnaby444 Posts: 273 Joined: Sat Apr 03, 2021 10:56 am ### HDHP always better than PPO? What am I missing? I'm puzzled by this. As is common, my employer gives me a choice between a cheaper high-deductible plan (HDHP) or a costlier PPO. My intuition is that the optimal plan choice should depend on how much healthcare cost I incur. But when I look at the numbers, I don't see any scenario where the PPO comes out ahead. Here are the numbers simplified a bit for illustration (rounding and using numbers for employee+spouse for everything): HDHP: Deductible: \$5,000 Coinsurance: 30% for most things Out-of-pocket max: \$10,000 Employer contribution to HSA: \$1,500 PPO: Deductible: \$1,500 Coinsurance: 20% for most things Out-of-pocket max: \$6,000 Employer contribution to HSA: \$0 So: • For costs up to \$1,500, the HDHP is ahead by \$5,200 (the difference in premiums plus the HSA contribution). • From \$1,500 to \$5,000, the HDHP's lead narrows to \$2,400 (I pay 100% in the HDHP and only 20% in the PPO, so the HDHP's lead is narrowed by 80%*\$3,500=\$2,800). • From \$5,000 to \$21,667, the HDHP's lead narrows to \$733 (I pay 30% in HDHP and 20% in PPO, and 10%*16,667=\$1,667, \$2,400-\$1,667 = \$733). • At this point the HDHP has hit its OOP max, and it's still ahead, so any costs above \$21,667 won't change the winner. I'm puzzled as I would expect to be presented with a trade-off, e.g. between minimizing guaranteed costs vs. variable costs in a more healthcare-intensive scenario. But there doesn't appear to be a trade-off at all; the HDHP is always better. Even if I remove the employer HSA contribution, the PPO can only eke out ahead, which doesn't seem worth the loss of the ability to make my own HSA contributions. We are planning for a baby in the next year or two and my wife has brought up going for the PPO just during that time given the higher expected healthcare needs, but I can't figure out how the PPO would even help. Am I missing anything? Anyone else presented with such a "choice"? bombcar Posts: 1793 Joined: Sun Aug 12, 2007 6:41 pm ### Re: HDHP always better than PPO? What am I missing? You need to compare more details than just the numbers and verify that the out-of-pocket max is the same (family) not per person, and if your employer is paying the premiums. The PPO may have things like "child birth is covered 100%" which could be a big difference. However, even then the HSA may be the better way to go overall, depending on your entire financial picture. bd7 Posts: 713 Joined: Thu Jul 28, 2022 4:31 pm ### Re: HDHP always better than PPO? What am I missing? Are you quoting individual plan prices there or family plan prices? JBTX Posts: 11543 Joined: Wed Jul 26, 2017 12:46 pm ### Re: HDHP always better than PPO? What am I missing? I’ve see this before where the PPO is barely any better if ever. In your case if you absolutely maxed everything out the PPO wins by \$300. ( excluding employer contribution to HSA) Also PPO’s typically also have doctor visit copays, where HDHPS pay full visit cost or coinsurance Finally HDHPs were often brutal with prescriptions as you pay full negotiated rates, which are typically much higher than Goodrx. A ppo you usually pay a fixed copay style payment. (This may have changed with hdhps, not sure). Then with the HDHP you are doing the calculus of getting scripts cheaper at Goodrx, but not applying against the deductible, or paying more for them and applying against deductible. In this case id probably opt for the HDHP. Last edited by JBTX on Mon Jun 03, 2024 3:30 pm, edited 1 time in total. neurosphere Posts: 5238 Joined: Sun Jan 17, 2010 12:55 pm ### Re: HDHP always better than PPO? What am I missing? barnaby444 wrote: Mon Jun 03, 2024 3:17 pm Am I missing anything? Anyone else presented with such a "choice"? You're not missing anything. I do hundreds of these analyzes a year, and your experience is typical. About 95% of the time the hdhp with HSA beats the non-hsa plan regardless of expected medical spending. If you have to ask "Is a Target Date fund right for me?", the answer is "Yes" (even in taxable accounts). grabiner Posts: 35722 Joined: Tue Feb 20, 2007 10:58 pm Location: Columbia, MD ### Re: HDHP always better than PPO? What am I missing? The HDHP is actually even better than the measure you are using, at no additional cost to the employer. The reason is that you can max out your HSA and get an additional tax benefit. If you don't spend the money this year on medical expenses, it grows tax-free for future medical expenses, but is better than a Roth IRA because you got a deduction on the contributions. But the situation you describe can happen, depending on the way the plans are subsidized. In particular, for US government employees, the HSA almost always comes out ahead of the conventional HMO/PPO plan from the same insurer. The reason is that the US government subsidizes 75% of the cost of most plans; if the plan contributes \$1800 to your HSA, you only pay \$450 to get that \$1800. David Grabiner Joe Public Posts: 217 Joined: Mon Jul 27, 2020 8:36 pm ### Re: HDHP always better than PPO? What am I missing? If someone doesn’t have the means to pay the higher deductible amount if a medical event occurs soon after coverage begins, then PPO may initially be more advantageous from a cash flow standpoint. That’s the only thing that comes to mind at the moment. Afty Posts: 2417 Joined: Sun Sep 07, 2014 5:31 pm ### Re: HDHP always better than PPO? What am I missing? One thing to consider is that health insurance premiums are paid with pretax dollars, so the difference in cost is smaller than it appears. Topic Author barnaby444 Posts: 273 Joined: Sat Apr 03, 2021 10:56 am ### Re: HDHP always better than PPO? What am I missing? bd7 wrote: Mon Jun 03, 2024 3:23 pm Are you quoting individual plan prices there or family plan prices? bombcar wrote: Mon Jun 03, 2024 3:22 pm You need to compare more details than just the numbers and verify that the out-of-pocket max is the same (family) not per person, and if your employer is paying the premiums. The PPO may have things like "child birth is covered 100%" which could be a big difference. However, even then the HSA may be the better way to go overall, depending on your entire financial picture. Quoting family figures for everything; quoting only the employee portion of premiums for both plans; and there's no difference between the plans for childbirth/maternity other than the 20%/30% coinsurance difference. Both plans pay 100% for pre-natal office visits. Thanks. fulltilt Posts: 414 Joined: Thu Dec 01, 2011 1:23 pm ### Re: HDHP always better than PPO? What am I missing? bombcar wrote: Mon Jun 03, 2024 3:22 pm You need to compare more details than just the numbers and verify that the out-of-pocket max is the same (family) not per person, and if your employer is paying the premiums. The PPO may have things like "child birth is covered 100%" which could be a big difference. However, even then the HSA may be the better way to go overall, depending on your entire financial picture. I agree. The thing i would be curious about how office visits are covered. The PPO available to me is \$30-50 copay for an office visit, but 0% coinsurance which makes a PPO a much better option if you have very young kids who get sick constantly. EDIT: Depending on the premium, of course. Last edited by fulltilt on Mon Jun 03, 2024 4:56 pm, edited 1 time in total. Walk a single path, becoming neither cocky with victory nor broken with defeat, without forgetting caution when all is quiet or becoming frightened when danger threatens. -- Jigoro Kano SmileyFace Posts: 9541 Joined: Wed Feb 19, 2014 9:11 am ### Re: HDHP always better than PPO? What am I missing? The devil is often in the deails. Example: Sometimes PPOs cover more things that are NOT subject to the deductible while the HDHP has nearly everything (maybe not yearly physical) subject to the deductible. Coinsurance for HDHP might be AFTER you meet deductible but for PPO it might be before you meet it. Be prepared to have to actually pay the deductible. It has been interesting to see the number of threads in recent years where people are shocked that they need to pay a big emergency room visit bill because they have an HDHP plan and have yet to meet their deductible. Years ago this simply didn't happen. Not the difference in out of pocket max. HDHPs are usually cheaper - until you have a bad year medically. With child birth you need to look closely. I miss my HSA tax advantaged account - but switched back to a PPO and am back to spending little out of pocket. Topic Author barnaby444 Posts: 273 Joined: Sat Apr 03, 2021 10:56 am ### Re: HDHP always better than PPO? What am I missing? fulltilt wrote: Mon Jun 03, 2024 3:57 pm bombcar wrote: Mon Jun 03, 2024 3:22 pm You need to compare more details than just the numbers and verify that the out-of-pocket max is the same (family) not per person, and if your employer is paying the premiums. The PPO may have things like "child birth is covered 100%" which could be a big difference. However, even then the HSA may be the better way to go overall, depending on your entire financial picture. I agree. The thing i would be curious about how office visits are covered. The PPO available to me is \$30-50 copay for an office visit, but 0% coinsurance which makes a PPO a much better option if you have very young kids who get sick constantly. True, that's a detail I left out. The PPO has 0% coinsurance and only a \$25/\$50 copay for PCP/specialist office visits. But suppose I model that as 10% coinsurance (\$25 copay for a \$250 PCP visit or \$50 copay for a \$500 specialist visit). Even then we'd have to rack up about \$15,000 in office visits alone before the PPO comes out ahead. Heck, even if I model it as 5% the breakeven point is at \$12,500 in office visits. grabiner Posts: 35722 Joined: Tue Feb 20, 2007 10:58 pm Location: Columbia, MD ### Re: HDHP always better than PPO? What am I missing? barnaby444 wrote: Mon Jun 03, 2024 4:08 pm fulltilt wrote: Mon Jun 03, 2024 3:57 pm The thing i would be curious about how office visits are covered. The PPO available to me is \$30-50 copay for an office visit, but 0% coinsurance which makes a PPO a much better option if you have very young kids who get sick constantly. True, that's a detail I left out. The PPO has 0% coinsurance and only a \$25/\$50 copay for PCP/specialist office visits. But suppose I model that as 10% coinsurance (\$25 copay for a \$250 PCP visit or \$50 copay for a \$500 specialist visit). Even then we'd have to rack up about \$15,000 in office visits alone before the PPO comes out ahead. Heck, even if I model it as 5% the breakeven point is at \$12,500 in office visits. The \$250/500 is much more than you would normally pay under the HDHP for a visit alone. The co-pay is only for the appointment fee; a PCP bill of \$250 usually also includes some charges for lab tests or X-rays which would be billed separately under most insurance. David Grabiner oldfatguy Posts: 1501 Joined: Tue Feb 27, 2018 12:38 pm ### Re: HDHP always better than PPO? What am I missing? Which plan incentivizes you to use less healthcare services? Is that good or bad for you? There is more than money to consider. SmileyFace Posts: 9541 Joined: Wed Feb 19, 2014 9:11 am ### Re: HDHP always better than PPO? What am I missing? barnaby444 wrote: Mon Jun 03, 2024 4:08 pm fulltilt wrote: Mon Jun 03, 2024 3:57 pm bombcar wrote: Mon Jun 03, 2024 3:22 pm You need to compare more details than just the numbers and verify that the out-of-pocket max is the same (family) not per person, and if your employer is paying the premiums. The PPO may have things like "child birth is covered 100%" which could be a big difference. However, even then the HSA may be the better way to go overall, depending on your entire financial picture. I agree. The thing i would be curious about how office visits are covered. The PPO available to me is \$30-50 copay for an office visit, but 0% coinsurance which makes a PPO a much better option if you have very young kids who get sick constantly. True, that's a detail I left out. The PPO has 0% coinsurance and only a \$25/\$50 copay for PCP/specialist office visits. But suppose I model that as 10% coinsurance (\$25 copay for a \$250 PCP visit or \$50 copay for a \$500 specialist visit). Even then we'd have to rack up about \$15,000 in office visits alone before the PPO comes out ahead. Heck, even if I model it as 5% the breakeven point is at \$12,500 in office visits. I am not following your logic. With many HDHP plans (or at least the last 2 I had) you must pay the deductible before they start paying. So the first \$5000 is on you. One outpatient procedure may cost you that \$5000 with a HDHP - only a couple of hundred with PPO. If you think you will have a year with only PCP office visits - sure - HDHP will win. bd7 Posts: 713 Joined: Thu Jul 28, 2022 4:31 pm ### Re: HDHP always better than PPO? What am I missing? barnaby444 wrote: Mon Jun 03, 2024 3:53 pm Quoting family figures for everything; quoting only the employee portion of premiums for both plans; and there's no difference between the plans for childbirth/maternity other than the 20%/30% coinsurance difference. Both plans pay 100% for pre-natal office visits. Thanks. Go for the HDHP version and don't worry. We have an HDHP PPO partly because the only other options are an HMO and Kaiser. We've had major medical issues the past three years and I've maxed out the deductible each of those three years. Last year I hit the OOP max as well. However, being able to contribute to the HSA and then pay the bills gives you an effective discount of whatever your tax bracket is on that money. If you have sufficient income, you can pay the bills with other money and build your HSA. One of the things that surprised me is how hard it was to actually hit the deductibles and OOP max. Our HDHP plan through Anthem Blue Cross ended up paying for a lot of things at no cost to us, the negotiated rates with hospitals were surprisingly low and it took 3 hospital visits and two surgeries to finally hit the \$6K OOP max. Just looking at your numbers without any crunching, I think premium difference plus the employer \$1500 will put you ahead in almost all circumstances--and most of the time you'll be way ahead. We've had the HDHP for 7 or 8 years now and our HSA's are pushing \$30k each now as a result. Topic Author barnaby444 Posts: 273 Joined: Sat Apr 03, 2021 10:56 am ### Re: HDHP always better than PPO? What am I missing? SmileyFace wrote: Mon Jun 03, 2024 4:01 pm The devil is often in the deails. Example: Sometimes PPOs cover more things that are NOT subject to the deductible while the HDHP has nearly everything (maybe not yearly physical) subject to the deductible. Coinsurance for HDHP might be AFTER you meet deductible but for PPO it might be before you meet it. Be prepared to have to actually pay the deductible. It has been interesting to see the number of threads in recent years where people are shocked that they need to pay a big emergency room visit bill because they have an HDHP plan and have yet to meet their deductible. Years ago this simply didn't happen. Not the difference in out of pocket max. HDHPs are usually cheaper - until you have a bad year medically. With child birth you need to look closely. I miss my HSA tax advantaged account - but switched back to a PPO and am back to spending little out of pocket. Yes there are a few examples of this, the main one being that the PPO deductible is waived for ER visits and it's a flat \$250 copay. So a very expensive ER visit is a potential path to the PPO coming out ahead. Thanks. Posts: 5092 Joined: Mon Oct 27, 2014 12:35 pm ### Re: HDHP always better than PPO? What am I missing? Suggest you compare a HDHP (and a PPO) with an HMO. It's there that you will likely see the savings over a HDHP, not comparing it to the most expensive option. Our HMO premiums are lower than your quotes for the HDHP, and of course much, much lower than the PPO. No deductibles, just \$30 copays. Or maybe tiny deductibles like a few hundred bucks. When my daughter was born she was in the NICU for a week. The billed cost to insurance was \$28,000. And that was 20 years ago. Our cost was \$0. YMMV, as all plans are priced based on the size of the company. Our insurance is through a huge employer. SmileyFace Posts: 9541 Joined: Wed Feb 19, 2014 9:11 am ### Re: HDHP always better than PPO? What am I missing? Admiral wrote: Mon Jun 03, 2024 4:24 pm Suggest you compare a HDHP (and a PPO) with an HMO. It's there that you will likely see the savings over a HDHP, not comparing it to the most expensive option. Our HMO premiums are lower than your quotes for the HDHP, and of course much, much lower than the PPO. No deductibles, just \$30 copays. Or maybe tiny deductibles like a few hundred bucks. When my daughter was born she was in the NICU for a week. The billed cost to insurance was \$28,000. And that was 20 years ago. Our cost was \$0. YMMV, as all plans are priced based on the size of the company. Our insurance is through a huge employer. I am guessing the OPs company doesn't offer an HMO option. Many no longer do. Topic Author barnaby444 Posts: 273 Joined: Sat Apr 03, 2021 10:56 am ### Re: HDHP always better than PPO? What am I missing? SmileyFace wrote: Mon Jun 03, 2024 4:15 pm barnaby444 wrote: Mon Jun 03, 2024 4:08 pm fulltilt wrote: Mon Jun 03, 2024 3:57 pm bombcar wrote: Mon Jun 03, 2024 3:22 pm You need to compare more details than just the numbers and verify that the out-of-pocket max is the same (family) not per person, and if your employer is paying the premiums. The PPO may have things like "child birth is covered 100%" which could be a big difference. However, even then the HSA may be the better way to go overall, depending on your entire financial picture. I agree. The thing i would be curious about how office visits are covered. The PPO available to me is \$30-50 copay for an office visit, but 0% coinsurance which makes a PPO a much better option if you have very young kids who get sick constantly. True, that's a detail I left out. The PPO has 0% coinsurance and only a \$25/\$50 copay for PCP/specialist office visits. But suppose I model that as 10% coinsurance (\$25 copay for a \$250 PCP visit or \$50 copay for a \$500 specialist visit). Even then we'd have to rack up about \$15,000 in office visits alone before the PPO comes out ahead. Heck, even if I model it as 5% the breakeven point is at \$12,500 in office visits. I am not following your logic. With many HDHP plans (or at least the last 2 I had) you must pay the deductible before they start paying. So the first \$5000 is on you. One outpatient procedure may cost you that \$5000 with a HDHP - only a couple of hundred with PPO. If you think you will have a year with only PCP office visits - sure - HDHP will win. Yes the first \$5,000 is on me with HDHP, but the PPO is \$3,700 higher in premiums alone and doesn't have the \$1,500 in employer HSA money. Those more than offset the difference in deductibles. Northern Flicker Posts: 15808 Joined: Fri Apr 10, 2015 12:29 am ### Re: HDHP always better than PPO? What am I missing? A HDHP can be a PPO, EPO, or HMO, and may or may not be HSA-eligible. HSA-eligible plans often are more cost effective than non-HSA-eligible plans, but you have to compare specific plans in the context of the specific health status of the insured. fulltilt Posts: 414 Joined: Thu Dec 01, 2011 1:23 pm ### Re: HDHP always better than PPO? What am I missing? barnaby444 wrote: Mon Jun 03, 2024 4:08 pm fulltilt wrote: Mon Jun 03, 2024 3:57 pm bombcar wrote: Mon Jun 03, 2024 3:22 pm You need to compare more details than just the numbers and verify that the out-of-pocket max is the same (family) not per person, and if your employer is paying the premiums. The PPO may have things like "child birth is covered 100%" which could be a big difference. However, even then the HSA may be the better way to go overall, depending on your entire financial picture. I agree. The thing i would be curious about how office visits are covered. The PPO available to me is \$30-50 copay for an office visit, but 0% coinsurance which makes a PPO a much better option if you have very young kids who get sick constantly. True, that's a detail I left out. The PPO has 0% coinsurance and only a \$25/\$50 copay for PCP/specialist office visits. But suppose I model that as 10% coinsurance (\$25 copay for a \$250 PCP visit or \$50 copay for a \$500 specialist visit). Even then we'd have to rack up about \$15,000 in office visits alone before the PPO comes out ahead. Heck, even if I model it as 5% the breakeven point is at \$12,500 in office visits. EDIT: What about prescription drugs? How do those two compare in the two plans? Having kids changes the equation quite a bit in my experience. It is very stressful and you, or your wife, might find themselves in a situation where they are in need of mental health services (counseling) which can be very expensive. Plus, you never know what the health of the baby will be and all of that. Health insurance is insurance and i would be more comfortable paying a known fixed amount each month during the pregnancy and in the first year or two afterwards. That's just me and my risk tolerance. Really, it comes down to your personal situation and ability to tolerate risk. I wouldn't say one is definitely right or definitely wrong. Walk a single path, becoming neither cocky with victory nor broken with defeat, without forgetting caution when all is quiet or becoming frightened when danger threatens. -- Jigoro Kano bd7 Posts: 713 Joined: Thu Jul 28, 2022 4:31 pm ### Re: HDHP always better than PPO? What am I missing? SmileyFace wrote: Mon Jun 03, 2024 4:15 pm One outpatient procedure may cost you that \$5000 with a HDHP - only a couple of hundred with PPO. I don't see how the PPO would only be "a couple of hundred" for a significant procedure with a negotiated rate of over \$5000. Say you have a surgery that the hospital bills \$140k for and the insurance-negotiated rate is \$35k all-in. Either plan would reach the OOP max--6k vs 10k--but you'd have \$5200 extra in your HSA due to the employer contribution and the premium savings. Beachey Posts: 429 Joined: Wed Sep 02, 2020 9:54 am ### Re: HDHP always better than PPO? What am I missing? neurosphere wrote: Mon Jun 03, 2024 3:28 pm barnaby444 wrote: Mon Jun 03, 2024 3:17 pm Am I missing anything? Anyone else presented with such a "choice"? You're not missing anything. I do hundreds of these analyses a year, and your experience is typical. About 95% of the time the hdhp with HSA beats the non-hsa plan regardless of expected medical spending. This has also been my experience where the HDHP plan is cheaper than the PPO for my last few employers. One thing to understand is whether prescription costs are included. I have seen some cases where there is an intermediate case where the PPO may be slightly cheaper for a certain level of spending and then flip back for maximum expenditure. It is best to try and model your actual typical spending. And then a worst case such as having a baby. The other issue sometimes with pregnancy is it can stretch over two years so it is best to understand how your OB/GYN bills But I think people many people only pick a PPO because the big OOP number scares them and they don't realize that they are paying that anyway in their payroll deduction. chassis Posts: 2344 Joined: Tue Mar 24, 2020 4:28 pm ### Re: HDHP always better than PPO? What am I missing? neurosphere wrote: Mon Jun 03, 2024 3:28 pm barnaby444 wrote: Mon Jun 03, 2024 3:17 pm Am I missing anything? Anyone else presented with such a "choice"? You're not missing anything. I do hundreds of these analyzes a year, and your experience is typical. About 95% of the time the hdhp with HSA beats the non-hsa plan regardless of expected medical spending. Agree with barnaby and neurosphere. It’s insurance. Your employer is steering you towards what is best for them. You have done the math, which few people do, and have learned the truth. PPO gives some people “peace of mind” so they “can sleep at night”. In other words, have less fear. Less fear costs more money, with regard to insurance. Nothing is predictable in life, but most things are estimable and forecastable, as @barnaby has correctly done. The approaches being discussed in this thread can be applied to annuities, life insurance, extended warranties, the list goes on. Ret2018 Posts: 198 Joined: Sun Jan 07, 2018 2:40 pm ### Re: HDHP always better than PPO? What am I missing? The only thing I have to add is to be sure to double check that the PPO and HDHP plan networks are the same, or very similar; coverage for out of network care is similar (at some percentage of usual and customary payments); and that both countout of network costs towards the deductible and OOP limits. Buzzman Posts: 68 Joined: Sun Mar 26, 2023 10:15 am Location: North AL ### Re: HDHP always better than PPO? What am I missing? I've done this analysis a couple of times and have come to the same conclusion as you. You can pay a lot of OOP costs for the typical \$1000 a month in extra premiums for the PPO. If you are young and healthy I don't see a downside to the HDHP. In my case I had a previous employer that gave us extra money to fund our HSA account. We maxed that out every year it was offered until I left that job. The next employer had traditional PPO insurance but I still had the HSA account with those dollars from the previous employer and we used it to pay deductibles, etc. When I retired from my last employer I looked hard at going on an ACA HDHP but due to couple of health issues and fear of the unknown I opted to pay for the CORBA insurance which cost about \$300 more per month. The COBRA ran out in May this year and now we are on an ACA HSA allowable plan. I will go on Medicare in January and the wife will stay on the ACA HSA plan for a few more years. Now we have about \$28k in our HSA to cover any deductibles and OOP expenses until we hit the max each year. Even if go with the HDHP then back on PPO during the baby years you would still have those HSA dollars to use for co-pays and OOP items, SmileyFace Posts: 9541 Joined: Wed Feb 19, 2014 9:11 am ### Re: HDHP always better than PPO? What am I missing? Buzzman wrote: Mon Jun 03, 2024 5:03 pm You can pay a lot of OOP costs for the typical \$1000 a month in extra premiums for the PPO. Extra \$300 for the OP. Extra \$1000 - I have never seen that much - definitely flips the scales. (I pay \$0 extra for my PPO - but I know that may be unusual). aristotelian Posts: 12613 Joined: Wed Jan 11, 2017 7:05 pm ### Re: HDHP always better than PPO? What am I missing? Our HDHP is similar. Sometimes there are free lunches. Take it. aristotelian Posts: 12613 Joined: Wed Jan 11, 2017 7:05 pm ### Re: HDHP always better than PPO? What am I missing? Northern Flicker wrote: Mon Jun 03, 2024 4:29 pm A HDHP can be a PPO, EPO, or HMO, and may or may not be HSA-eligible. HSA-eligible plans often are more cost effective than non-HSA-eligible plans, but you have to compare specific plans in the context of the specific health status of the insured. As far as I know, the HSA was specifically designed for HDHP's. I don't see any language suggesting an HDHP might not be HSA eligible. Where are you getting this? OP laid out numbers in detail for their case. sailaway Posts: 8636 Joined: Fri May 12, 2017 1:11 pm ### Re: HDHP always better than PPO? What am I missing? aristotelian wrote: Mon Jun 03, 2024 6:01 pm Northern Flicker wrote: Mon Jun 03, 2024 4:29 pm A HDHP can be a PPO, EPO, or HMO, and may or may not be HSA-eligible. HSA-eligible plans often are more cost effective than non-HSA-eligible plans, but you have to compare specific plans in the context of the specific health status of the insured. As far as I know, the HSA was specifically designed for HDHP's. I don't see any language suggesting an HDHP might not be HSA eligible. Where are you getting this? OP laid out numbers in detail for their case. There are high deductible plans that have too high an out of pocket maximum to qualify for an HSA. There are also plans that are considered high deductible, but cover something or other that isn't allowed for HSA purposes. Basically, if a plan doesn't explicitly say it is HSA eligible, it probably isn't, but you might have to go through a couple of points to figure out why. OrangeKiwi Posts: 338 Joined: Tue Oct 01, 2019 8:10 pm ### Re: HDHP always better than PPO? What am I missing? sailaway wrote: Mon Jun 03, 2024 6:13 pm aristotelian wrote: Mon Jun 03, 2024 6:01 pm Northern Flicker wrote: Mon Jun 03, 2024 4:29 pm A HDHP can be a PPO, EPO, or HMO, and may or may not be HSA-eligible. HSA-eligible plans often are more cost effective than non-HSA-eligible plans, but you have to compare specific plans in the context of the specific health status of the insured. As far as I know, the HSA was specifically designed for HDHP's. I don't see any language suggesting an HDHP might not be HSA eligible. Where are you getting this? OP laid out numbers in detail for their case. There are high deductible plans that have too high an out of pocket maximum to qualify for an HSA. There are also plans that are considered high deductible, but cover something or other that isn't allowed for HSA purposes. Basically, if a plan doesn't explicitly say it is HSA eligible, it probably isn't, but you might have to go through a couple of points to figure out why. According to my interpretation, HDHP is a term specifically used to describe a health plan that qualifies someone to be able to contribute to an HSA. https://www.irs.gov/publications/p969#e ... 1000204030 aristotelian Posts: 12613 Joined: Wed Jan 11, 2017 7:05 pm ### Re: HDHP always better than PPO? What am I missing? sailaway wrote: Mon Jun 03, 2024 6:13 pm aristotelian wrote: Mon Jun 03, 2024 6:01 pm Northern Flicker wrote: Mon Jun 03, 2024 4:29 pm A HDHP can be a PPO, EPO, or HMO, and may or may not be HSA-eligible. HSA-eligible plans often are more cost effective than non-HSA-eligible plans, but you have to compare specific plans in the context of the specific health status of the insured. As far as I know, the HSA was specifically designed for HDHP's. I don't see any language suggesting an HDHP might not be HSA eligible. Where are you getting this? OP laid out numbers in detail for their case. There are high deductible plans that have too high an out of pocket maximum to qualify for an HSA. There are also plans that are considered high deductible, but cover something or other that isn't allowed for HSA purposes. Basically, if a plan doesn't explicitly say it is HSA eligible, it probably isn't, but you might have to go through a couple of points to figure out why. Those plans would not be captial-HDHP even if they have high deductibles. Per the IRS, if you have an HDHP you are eligible. It is true that the IRS goes on to define HDHP with more criteria than the deductible RyeBourbon Posts: 1452 Joined: Tue Sep 01, 2020 12:20 pm Location: Delaware/Philly ### Re: HDHP always better than PPO? What am I missing? OrangeKiwi wrote: Mon Jun 03, 2024 6:24 pm sailaway wrote: Mon Jun 03, 2024 6:13 pm aristotelian wrote: Mon Jun 03, 2024 6:01 pm Northern Flicker wrote: Mon Jun 03, 2024 4:29 pm A HDHP can be a PPO, EPO, or HMO, and may or may not be HSA-eligible. HSA-eligible plans often are more cost effective than non-HSA-eligible plans, but you have to compare specific plans in the context of the specific health status of the insured. As far as I know, the HSA was specifically designed for HDHP's. I don't see any language suggesting an HDHP might not be HSA eligible. Where are you getting this? OP laid out numbers in detail for their case. There are high deductible plans that have too high an out of pocket maximum to qualify for an HSA. There are also plans that are considered high deductible, but cover something or other that isn't allowed for HSA purposes. Basically, if a plan doesn't explicitly say it is HSA eligible, it probably isn't, but you might have to go through a couple of points to figure out why. According to my interpretation, HDHP is a term specifically used to describe a health plan that qualifies someone to be able to contribute to an HSA. https://www.irs.gov/publications/p969#e ... 1000204030 Having a high deductible is not sufficient to qualify as HSA-eligible. Some people just look at the deductible and assume it is HSA-eligible. There are other requirements. Retired June 2023. LMP (TIPS Ladder/SS Bridge) 25%/Risk Portfolio 75%, AA = 60/30/10 Northern Flicker Posts: 15808 Joined: Fri Apr 10, 2015 12:29 am ### Re: HDHP always better than PPO? What am I missing? Not the least of the other requirements for a plan to be HSA-eligible is that the plan must be designated as HSA-eligible. Thus, whether or not a plan has that designation is all you need to consider when deciding if a plan is HSA-eligible. Northern Flicker Posts: 15808 Joined: Fri Apr 10, 2015 12:29 am ### Re: HDHP always better than PPO? What am I missing? aristotelian wrote: Mon Jun 03, 2024 6:01 pm Northern Flicker wrote: Mon Jun 03, 2024 4:29 pm A HDHP can be a PPO, EPO, or HMO, and may or may not be HSA-eligible. HSA-eligible plans often are more cost effective than non-HSA-eligible plans, but you have to compare specific plans in the context of the specific health status of the insured. As far as I know, the HSA was specifically designed for HDHP's. I don't see any language suggesting an HDHP might not be HSA eligible. Where are you getting this? All HSA-eligible plans are high deductible plans. Whether a plan is a HDHP and whether it is HSA-eligible, are separate considerations from whether it is a PPO, EPO, or HMO. But there are HDHP's that are not HSA-eligible. There are limits on OOP max to be HSA-eligible for instance. And some HDHP's have copays for doctor visits not subject to deductible, also precluding it being HSA-eligible. SmileyFace Posts: 9541 Joined: Wed Feb 19, 2014 9:11 am ### Re: HDHP always better than PPO? What am I missing? Northern Flicker wrote: Mon Jun 03, 2024 7:32 pm Not the least of the other requirements for a plan to be HSA-eligible is that the plan must be designated as HSA-eligible. Thus, whether or not a plan has that designation is all you need to consider when deciding if a plan is HSA-eligible. All of this side discussion is completely irrelevant to the OPs questions. Northern Flicker Posts: 15808 Joined: Fri Apr 10, 2015 12:29 am ### Re: HDHP always better than PPO? What am I missing? SmileyFace wrote: Mon Jun 03, 2024 7:49 pm Northern Flicker wrote: Mon Jun 03, 2024 7:32 pm Not the least of the other requirements for a plan to be HSA-eligible is that the plan must be designated as HSA-eligible. Thus, whether or not a plan has that designation is all you need to consider when deciding if a plan is HSA-eligible. All of this side discussion is completely irrelevant to the OPs questions. Not necessarily-- expected total out of pocket cost is not the only criterion for choosing a plan. SmileyFace Posts: 9541 Joined: Wed Feb 19, 2014 9:11 am ### Re: HDHP always better than PPO? What am I missing? Northern Flicker wrote: Mon Jun 03, 2024 7:54 pm SmileyFace wrote: Mon Jun 03, 2024 7:49 pm Northern Flicker wrote: Mon Jun 03, 2024 7:32 pm Not the least of the other requirements for a plan to be HSA-eligible is that the plan must be designated as HSA-eligible. Thus, whether or not a plan has that designation is all you need to consider when deciding if a plan is HSA-eligible. All of this side discussion is completely irrelevant to the OPs questions. Not necessarily-- expected total out of pocket cost is not the only criterion for choosing a plan. OP has two plan options that have been outlined - an HSA eligible HDHP and a nonHSA PPO option. Stated up front. Defining HSA eligibility and bringing up HMOs and EPOs is kind of unnecessary. Why not just address the OPs 2 options? Northern Flicker Posts: 15808 Joined: Fri Apr 10, 2015 12:29 am ### Re: HDHP always better than PPO? What am I missing? The OP did not provide info to do that, but understanding what a PPO is, what an HDHP is, and what an HSA-eligible plan is would be beneficial. SmileyFace Posts: 9541 Joined: Wed Feb 19, 2014 9:11 am ### Re: HDHP always better than PPO? What am I missing? Northern Flicker wrote: Mon Jun 03, 2024 8:08 pm The OP did not provide info to do that, but understanding what a PPO is, what an HDHP is, and what an HSA-eligible plan is would be beneficial. OP could google those definitions if desired. This side discussion you started is not at all what was asked. And now I am guilty of a reply all to the person doing the reply all so will stop with this irrelevant back and forth now. aristotelian Posts: 12613 Joined: Wed Jan 11, 2017 7:05 pm ### Re: HDHP always better than PPO? What am I missing? Northern Flicker wrote: Mon Jun 03, 2024 7:47 pm aristotelian wrote: Mon Jun 03, 2024 6:01 pm Northern Flicker wrote: Mon Jun 03, 2024 4:29 pm A HDHP can be a PPO, EPO, or HMO, and may or may not be HSA-eligible. HSA-eligible plans often are more cost effective than non-HSA-eligible plans, but you have to compare specific plans in the context of the specific health status of the insured. As far as I know, the HSA was specifically designed for HDHP's. I don't see any language suggesting an HDHP might not be HSA eligible. Where are you getting this? All HSA-eligible plans are high deductible plans. Whether a plan is a HDHP and whether it is HSA-eligible, are separate considerations from whether it is a PPO, EPO, or HMO. But there are HDHP's that are not HSA-eligible. There are limits on OOP max to be HSA-eligible for instance. And some HDHP's have copays for doctor visits not subject to deductible, also precluding it being HSA-eligible. The IRS defines HDHP.as HSA eligible and vice versa. The OOP Max is one of the criteria in addition to the deductible. However, any plan that meets the criteria of HDHP is HSA eligible. sailaway Posts: 8636 Joined: Fri May 12, 2017 1:11 pm ### Re: HDHP always better than PPO? What am I missing? OP, there are a number of reasons that an employer might set things up this way. They might offer a legacy plan because it is important to some or has some specific specialists, but then do everything in their power to encourage new employees towards another plan. You might be seeing an effort to either meet a very niche need while incentivizing the HSA or an effort to phase out a certain type of plan. evancox10 Posts: 533 Joined: Tue Jun 28, 2011 11:25 pm ### Re: HDHP always better than PPO? What am I missing? Does employer self insure? Note that if you model everyone as purely rational actors, an HDHP should encourage less consumption of medical services. So the HDHP may actually cost the employer less in overall premiums/payments, and they can afford to direct some of that savings to making the HDHP more attractive. When the HDHP is more attractive, more employees should (in theory) choose it, and the employer saves money with each employee that chooses HDHP over non-HDHP. Northern Flicker Posts: 15808 Joined: Fri Apr 10, 2015 12:29 am ### Re: HDHP always better than PPO? What am I missing? To bring this back to the original question, a PPO generally has coverage for out of network care, but at less generous levels than for in network care. An EPO or HMO may have no coverage for out of network care and a narrower network than that of an EPO or HMO. The OP did not specify whether the HDHP was a PPO, EPO, or HMO plan, but consideration of the networks is salient, not just the cost. Another difference is that EPO's and HMO's most often require a referral from a PCP to see a specialist, and the insurer has to approve it. With a PPO, the insured person can just go see any chosen provider and have it covered, subject to the reimbursement levels for being in or out of network. Charon Posts: 656 Joined: Thu May 03, 2018 12:08 pm ### Re: HDHP always better than PPO? What am I missing? grabiner wrote: Mon Jun 03, 2024 4:12 pm The \$250/500 is much more than you would normally pay under the HDHP for a visit alone. No, it's not. Brief, low-MDM visits with PCPs in my area (MCOL) are ~\$250. (Including PA visits, not just MDs.) Any sort of complication at all can quickly jack that up. And in a different part of the country around 12 years ago I had a very brief visit with an orthopedist that involved no tests, not even any examination, for which I was billed \$800 (and remember, this was 12 years ago). On the other hand, I went to the ER in New Zealand and paid absolutely nothing. If I'd had to pay out of pocket, and with no insurance, it would have been a few hundred dollars (prices were posted, easily visible in advance). The medical system in the US is massively screwed up. To the OP, yes, I found this same situation with my plans, and went with the HDHP as a result. The one negative is psychological. If you pay significantly per visit, it can make you reluctant to seek medical care, even if you can well afford it and you know it's cheaper than the low-deductible plan. Northern Flicker Posts: 15808 Joined: Fri Apr 10, 2015 12:29 am ### Re: HDHP always better than PPO? What am I missing? aristotelian wrote: Mon Jun 03, 2024 8:42 pm The IRS defines HDHP.as HSA eligible and vice versa. That does now seem to be the case. It was not the case in the recent past. CFM300 Posts: 2620 Joined: Sat Oct 27, 2007 5:13 am ### Re: HDHP always better than PPO? What am I missing? barnaby444 wrote: Mon Jun 03, 2024 3:17 pm I can't figure out how the PPO would even help. ... Am I missing anything? You don't say whether the HDHP is an HMO, PPO, or something else. If the HDHP is an HMO, then you might find that it has a much smaller network of doctors and facilities than the PPO, and that it provides no out-of-network coverage, except for emergencies. It might also require referrals from your primary doctor in order to see specialists. aristotelian Posts: 12613 Joined: Wed Jan 11, 2017 7:05 pm ### Re: HDHP always better than PPO? What am I missing? Northern Flicker wrote: Mon Jun 03, 2024 11:20 pm aristotelian wrote: Mon Jun 03, 2024 8:42 pm The IRS defines HDHP.as HSA eligible and vice versa. That does now seem to be the case. It was not the case in the recent past. The law states simply that you have to have an HDHP and then goes on to define HDHP. If you know of anything otherwise please provide details. https://www.irs.gov/publications/p969#e ... 1000204030 The OP also mentions an employer HSA contribution so I don't think they have anything to worry about. Last edited by aristotelian on Tue Jun 04, 2024 8:15 am, edited 1 time in total. Topic Author barnaby444 Posts: 273 Joined: Sat Apr 03, 2021 10:56 am ### Re: HDHP always better than PPO? What am I missing? Addressing a few questions: • Type of plan: The HDHP seems to be a PPO too (however i'll keep referring to the other plan as "the PPO" for consistency). Both plans have the same networks and same in-/out-of-network structure with separate coinsurance rates and deductibles for out-of-network. I didn't list those in the summary for simplicity; bottom line is both plans strongly incentivize going in-network. • Prescription drugs: The deductible is waived on the PPO but not on the HDHP, except for some common preventative drugs. After that the coverage is the same. I don't think this makes a difference in my calculations, because even if I spent \$5k on uncovered drugs, the HDHP would still be slightly ahead based on the lower premiums and the HSA grant. • Yes, the HDHP is HSA eligible. Thanks all for the inputs, this is very informative.

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# Realization (probability) In probability and statistics, a realization, or observed value, of a random variable is the value that is actually observed (what actually happened). The random variable itself should be thought of as the process how the observation comes about. Statistical quantities computed from realizations without deploying a statistical model are often called "empirical", as in empirical distribution function or empirical probability. Conventionally, upper case letters denote random variables; the corresponding lower case letters denote their realizations.[1] Confusion results when this important convention is not strictly observed. In more formal probability theory, a random variable is a function X defined from a sample space Ω to a measurable space called the state space.[2] If an element in Ω is sent to an element in state space by X, then that element in state space is a realization. (In fact, a random variable cannot be an arbitrary function and it needs to satisfy another condition: it needs to be measurable.) Elements of the sample space can be thought of as all the different possibilities that could happen; while a realization (an element of the state space) can be thought of as the value X attains when one of the possibilities did happen. Probability is a mapping that assigns numbers between zero and one to certain subsets of the sample space. Subsets of the sample space that contain only one element are called elementary events. The value of the random variable (that is, the function) X at a point ω ∈ Ω, $x = X(\omega)$ is called a realization of X. ## References 1. ^ Samuel S. Wilks. Mathematical statistics. A Wiley Publication in Mathematical Statistics. John Wiley & Sons Inc., New York, 1962. 2. ^ S. R. S. Varadhan. Probability theory, volume 7 of Courant Lecture Notes in Mathematics. New York University Courant Institute of Mathematical Sciences, New York, 2001.

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Question: Is A 95 A Good Grade? Is 90 percent a good grade? A – is the highest grade you can receive on an assignment, and it’s between 90% and 100% B – is still a pretty good grade! This is an above-average score, between 80% and 89% … D – this is still a passing grade, and it’s between 59% and 69% A = 94-100. B = 86-93. C = 77-85. D = 70-76. For points earned based on two typical grade scales, see the charts in “Grade scale (weighting) charts” on the next page. 97% is a good grade. … In high schools and on the transcript, an A+, A, or A- all show up as an A, so therefore you have no point to try so hard to get a perfect grade. Is a 96 average good? An A letter grade is equivalent to a 4.0 GPA, or Grade Point Average, on a 4.0 GPA scale, and a percentage grade of 93–96. Is 90% A or B? A 90 percent score is a B. Anything below a 70 is an F. Is a 2.7 GPA good? Is a 2.7 GPA good? This GPA means that you’ve earned an average grade of a B- across all of your classes. Since a 2.7 GPA is lower than the national average of 3.0 for high school students, it will limit your options for college. … You can apply to colleges and have a good shot at getting admitted. Is a 3.0 GPA good? A 3.0 GPA means that you’re earning decent enough grades to be sure of acceptance at a fair amount of schools with higher admissions rates, but selective colleges may be out of reach. You should try and work on improving your grades junior year so that you can raise your GPA a bit and give yourself more options. What is a 95 percent grade? For conversion from letter grades to numerical grades, I use the middle of the numerical range above. Thus, an A is a 95, halfway between 90 and 100. An A- is a 91.25, halfway between 90 and 92.5. Etc. Grades between these are averages.

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# What Does .Shape Do In Python With Code Examples In this article, we will look at how to get the solution for the problem, What Does .Shape Do In Python With Code Examples ## What does .shape Do in NumPy? The shape property is usually used to get the current shape of an array, but may also be used to reshape the array in-place by assigning a tuple of array dimensions to it. ``````#The shape attribute for numpy arrays returns the dimensions of the array. #If Y has n rows and m columns, then Y. shape is (n,m) . import numpy as np arr= np.array([[6, 1, 2, 1], [5, 4, 6, 7,], [6, 7, 2, 1,]]) result = np.shape(arr) print(result) #will return (3,4)``` ``` ``````variable.shape() ``` ``` ``````# Example from https://numpy.org/doc/stable/reference/generated/numpy.ndarray.shape.html y = np.zeros((2, 3, 4)) y.shape # this returns (2, 3, 4)``` ``` ``````If you want to draw a shape download/install a GUI Library for Python like Pygame import pygame as pg #Optional, just write: import pygame #Draw a rectangle: pg.draw.rect(surface, (r, g, b), pg.Rect(x, y, width, height) #Draw a circle: pg.draw.circle(surface, (r, g, b), (x, y), radius) #Draw a line: pg.draw.circle(surface, (r, g, b), (x1, y1), (x2, y2), width)) #Draw a custom shape: pg.draw.polygon(surface, (r, g, b), points, width) #points is a list of #points like: points = [(x1, y1), (x2, y2), (x3, y3)... (xn, yn)] #Draw an ellipse: pg.draw.ellipse(surface, (r, g, b), pg.Rect(x, y, width, height)) #The rectangle is just for the location and dimensions of the ellipse #Draw an arc: pg.draw.arc(surface, (r, g, b), pg.Rect(x, y, width, height), start_angle, stop_angle) #The rect is for dimensions and location of the arc #There is also anti-aliased (aa) shapes which I wont get into but it means the shapes will #be 'smoother'. ``` ``` ## How do you shape a tuple? The shape of a simple Python tuple or list can be obtained with the built-in len() function. len() will return an integer that describes the number of objects in the tuple or list. ## What is shape and size in Python? Shape relates to the size of the dimensions of an N-dimensional array. Size regarding arrays, relates to the amount (or count) of elements that are contained in the array (or sometimes, at the top dimension of the array - when used as length). ## Why is .shape used in Python? The shape attribute in numpy is used to return a tuple with the index numbers representing the dimension or shape of the given array. ## What is shape () in Pandas? shape attribute in Pandas enables us to obtain the shape of a DataFrame. For example, if a DataFrame has a shape of (80, 10) , this implies that the DataFrame is made up of 80 rows and 10 columns of data. ## What is size () in Python? Returns the number of open output documents. Syntax. ## What does .shape 0 do in Python? Python numpy shape 0 shape is a tuple that always gives dimensions of the array. The shape is a tuple that gives you an indication of the no. of dimensions in the array. The shape function for numpy arrays returns the dimensions of the array. ## What does size () do in NumPy? In Python, numpy. size() function count the number of elements along a given axis. ## Is a tuple? Tuples are used to store multiple items in a single variable. Tuple is one of 4 built-in data types in Python used to store collections of data, the other 3 are List, Set, and Dictionary, all with different qualities and usage. A tuple is a collection which is ordered and unchangeable. ## What is meant by reshape in Python? Reshaping means changing the shape of an array. The shape of an array is the number of elements in each dimension. By reshaping we can add or remove dimensions or change number of elements in each dimension. ## Python Api Define Bearer Token With Code Examples In this article, we will look at how to get the solution for the problem, Python Api Define Bearer Token With Code Examples Can I pass bearer token in URL? Bearer tokens SHOULD NOT be passed in page URLs (for example, as query string parameters). Instead, bearer tokens SHOULD be passed in HTTP message headers or message bodies for which confidentiality measures are taken. import requests endpoint = ".../api/ip" data = {"ip": "1.1.2.3"} headers = {"Authorization": "Bearer MYREALLYLONGTOKENIGOT"} ## Pandas Drop Duplicate Keep Last With Code Examples In this article, we will look at how to get the solution for the problem, Pandas Drop Duplicate Keep Last With Code Examples How do I drop duplicates in Pandas? Remove All Duplicate Rows from Pandas DataFrame You can set &#x27;keep=False&#x27; in the drop_duplicates() function to remove all the duplicate rows. For E.x, df. drop_duplicates(keep=False) . drop_duplicates(self, subset=None, keep="last", inplace=False) The following line of code outlines the various methods that can be utilised in o ## Python Split List Into N Sublists With Code Examples In this article, we will look at how to get the solution for the problem, Python Split List Into N Sublists With Code Examples How do you split a list into equal Sublists in Python? Split List Into Sublists Using the array_split() Function in NumPy. The array_split() method in the NumPy library can also split a large array into multiple small arrays. This function takes the original array and the number of chunks we need to split the array into and returns the split chunks. [input[i:i+n] for i ## Check If String Contains Alphabets Python With Code Examples In this article, we will look at how to get the solution for the problem, Check If String Contains Alphabets Python With Code Examples How do you check if a string contains only alphabets and spaces in Python? Method #1 : Using all() + isspace() + isalpha() This is one of the way in which this task can be performed. In this, we compare the string for all elements being alphabets or space only. import re print(re.search(&#x27;[a-zA-Z]&#x27;, "anything")) What is Isalpha () in Python? Python St ## How To Write In A Text File Python With Code Examples In this article, we will look at how to get the solution for the problem, How To Write In A Text File Python With Code Examples How do you write multiple lines in a text file in Python? Using writelines() Function This function writes several string lines to a text file simultaneously. An iterable object, such as a list, set, tuple, etc., can be sent to the writelines() method. with open(&#x27;readme.txt&#x27;, &#x27;w&#x27;) as f: f.write(&#x27;readme&#x27;) Code language: JavaScript (javascr

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# Lateral intelligence test Background Vector created by freepik Despite the simplicity of the test that we propose below, not everyone is able to complete it successfully. Answer the questions in less than 15 seconds, and check your results. If you consider yourself a 'smart guy' who boasts of his general knowledge, try to answer the 5 questions of this test correctly ... At the end of this page you will find the correct answers. ## Test Questions 1. Some months have 30 days, others 31. How many months have 28 days? 2. A farmer has 17 sheep. You die 9. How many sheep do you have left? 3. You have to enter a cold and dark room, you only have one match. There is an oil lamp, a candle and a bonfire, waiting to be lit. What would you turn on first? 4. How many animals of each species did Moses carry in the Ark? 5. If you drive a bus with 43 people from Santiago, stop in Valdivia you pick up 7 people and they get off 5, in Osorno you pick up 4 more and get off 8. Then when you arrive in Puerto Montt, 20 hours after leaving ... What is the name of driver? #### Solution 1. 12 months. Every month they have 28 days or more. 2. 17 sheep, although 9 dead ... but sheep after all. So he's still 17. 3. First you would light the match ... or not? 4. None, it wasn't Moses. The one in the Ark was Noah. 5. I told you that you were the driver. Then his name was yours. Did you really have to reread it to understand it? ## Punctuation • IF YOU ANSWERED 5 GOOD: SMART • IF YOU ANSWERED 4 WELL: MEDIUMLY SMART • IF YOU ANSWERED 3 WELL: NOT VERY READY • IF YOU ANSWERED 2 GOOD: YOU NEED TO IMPROVE • IF YOU ANSWERED 1 GOOD: YOU NEED TO IMPROVE MUCH • IF YOU DID NOT ANSWER ANY GOOD: FIT FOR POLITIC

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# Cost Estimation A firm has total fixed costs of $60 and average variable costs as indicated in the t Cost Estimation A firm has total fixed costs of$60 and average variable costs as indicated in the table below Total Output Average Variable Cost 0 $0 1 4500 2 4250 3 4000 4 3750 5 3700 6 3750 7 3857 8 4063 9 4333 10 4650 a) Calculate AFC, ATC, MC, and TC b) At a product price of$56, will this firm produce in the short run? Why or why not? If it is preferable to produce, what will be the profit-maximizing output? What economic profit will the firm realize at the profit-maximizing? c) How are your answers of the question b) changed if the price changed to \$41? ## Plagiarism Checker Submit your documents and get free Plagiarism report Free Plagiarism Checker

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# A uniform magnetic field B exists in a direction perpendicular to the plane of a square frame made of copper wire. The wire has a diameter of 2mm and a total length of 40cm. The magnetic field changes with time at steady rate dB/dt=0.02Ts^-1. What will be the current induced in the frame? (resistivityof copper=1.7x10^-8 ohm m) Saakshi Kalashetti 15 Points 5 years ago I = e/R = 1/ R (d¢/dt) = 1/R. dBA/dt = A/R.dB/dt = A/(pl/a).dB/dt =A .dB/dt.a/pl = A(dB/dt).πr^2/pl Substitute the values and you get the answer. =9.3×10^-2A =93mA

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# Search Our Content Library 12 filtered results 12 filtered results Multiplication 3.OA.A Sort by Multiplication: Star Arrays Worksheet Multiplication: Star Arrays Children will use star arrays to solve 11 single-digit multiplication problems. Math Worksheet Multiplication: Word Problems (Part One) Worksheet Multiplication: Word Problems (Part One) Solve word problems using one of the following strategies: draw an array, draw equal groups, skip count forward, repeated addition, or multiplication sentences. Math Worksheet Worksheet Find the total by writing both repeated addition and multiplication equations. Math Worksheet Division: Make a Match Worksheet Division: Make a Match Review key division terms dividend, quotient, array, skip count, repeated subtraction, and divisor in this word-matching exercise. Math Worksheet Multiplication: Word Problems (Part Two) Worksheet Multiplication: Word Problems (Part Two) Solve word problems using one of the following strategies: draw an array, draw equal groups, skip count forward, repeated addition, or multiplication sentences. Math Worksheet Multiplication: Array Multiplication (Part One) Worksheet Multiplication: Array Multiplication (Part One) Record the number of rows and columns for the arrays shown. Then, write a multiplication sentence for each one. Math Worksheet Multiplication: Finding the Total with Arrays Worksheet Multiplication: Finding the Total with Arrays Familiarize yourself with arrays and practice using them to write multiplication sentences in this worksheet. Math Worksheet Multiplication: Equal Group Problems (Part One) Worksheet Multiplication: Equal Group Problems (Part One) Calling all math-bots! Use the equal group drawings to solve the multiplication problems shown here. Math Worksheet Multiplication: Brownies! Worksheet Multiplication: Brownies! In this worksheet, you'll put your addition and multiplication skills to the test as you solve a word problem for Betty the Baker Robot. Math Worksheet Lesson Plan It's not enough to just memorize the multiplication table! It helps students to know how to explain their strategy to find the product too. Teach this lesson on its own or use it as support for the lesson Slap and Roll Timed Multiplication. Math Lesson Plan Multiplication: Array Multiplication (Part Two) Worksheet Multiplication: Array Multiplication (Part Two) In this worksheet, we'll review a sample array together. Then it's your turn to practice using an array to figure out the total!

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# Is large-scale “time reversal” (Poincaré recurrence) possible given infinite time? The following are some assumptions I'm basing my question on, from what (little) I understand of physics. I list them so an expert can (kindly) tell me where I'm going wrong. • There is a probability assigned to every possible sequence of events. • Besides sequences that violate the "rules", every sequence seems to have a nonzero probability. • This applies to large scale systems as well, except the odds usually seem to tend toward nearly 100% in favor of certain sequences (i.e., paths of highest entropy). • There is therefore a probability assigned to the following sequence of events: a system (large or small scale) reversing everything it's done since a certain point in time (Poincaré recurrence), and ending up back "almost" where it started; perhaps not an exact copy. • The universe appears to be expanding, and for all we know will do so forever, possibly leading to the heat death of the universe. Here's my question: Assuming the universe will continue on forever (and therefore that we have infinite time in our equations), isn't there a nonzero probability that everything in it can "reverse" itself and end up back at the big bang, perhaps in a somewhat slightly altered path? Is dark energy is the only thing preventing this? If so, (1) would this be possible without dark energy? (2) could the force carriers, assuming they exist, behind dark energy obey quantum mechanics, and therefore be "time reversable"? - Given that nobody knows the equation that universe follows its not possible to give a definitive answer to your question. However this question has been studied for some 'simple' systems. See for example Poincare recurrence theorem. –  user10001 Aug 9 '12 at 15:59 Thank you, your link to Poincaré recurrence useful and relevant. Where I said "time reversal", I really could say "poincare recurrence". I've updated the question to mention Poincaré recurrence, since, in a nutshell, I'm really asking "Does Poincaré recurrence apply to the entire universe?" –  Jay Aug 12 '12 at 15:46

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# chemistry Calculate the ionic strength of the solution. a) 100 mL of 0.8M magnesium perchlorate, Mg(ClO4)2, is added to 900 mL of 0.30M perchloric acid, HClO4. No reaction. B)25 mL of 0.200M potassium iodide, KI, are mixed with 75 mL of 0.0300 M silver nitrate, AgNO3. Silver iodide precipitates. For (a) you first need to determine the molarity of the resulting Mg(ClO4)2 and HClO4. Then use the ionic strength formula to determine the ionic strength. That is mu = AZ1^2 + BZ2^2 + CZ3^2where A is the Mg^+2 ion molarity and Z1^2 is the charge on the Mg^+2; B is the total molarity of the ClO4^- and Z2^2 is the charge on the ClO4^- ion; C is the molarity of the H^+ and Z3^2 is the charge on the H^+. For (b), you must first determine the reaction (a ppt of AgI will take place) and use the rxn to determine the final molarities of K^+, I^-, NO3^- and Ag^+. Then plug into the mu forumla to determine ionic strength. Please post your work if you need further assistance or if you would like us to check your answer. We need your work in order to determine the nature of your problem (but you probably won't have any trouble.) I hope this helps you get started. I just noticed that I omitted the 1/2 on mu. It should read nu = 1/2(AZ1^2 + BZ2^2 + CZ3^2) etc. Sorry about that. That's mu and not nu. =) define Physical science Andrew: You did the correct thing by posting a SEPARATE posting for this question. I saw this posting just by chance. I answered the later posting above. However, for definitions you can go to www.dictionary.com and look them up much faster than typing them here and waiting for a reply. 1. 👍 2. 👎 3. 👁 ## Similar Questions 1. ### Chemistry What is the ionic strength of 0.2 M Na2HPO4 in a solution? 2. ### Chem Calculate [H3O ], [ClO4–], and [OH–] in an aqueous solution that is 0.170 M in HClO4(aq) at 25 °C. 3. ### chemistry Potassium perchlorate has a lattice energy of -599 kj/mol and a heat of hydration of -548 kj/mol. Find the heat of solution for potassium perchlorate when 10.6 g of potassium perchlorate is dissolved with enough water to make 4. ### chemistry Write the balanced molecular, complete ionic, and net ionic equations for the following reactions in aqueous solution: a. magnesium chloride reacts with potassium carbonate b. sulfuric acid reacts with sodium hydroxide 1. ### Chemistry What is the activity coefficient of H^+ in a solution containing 0.073 M HCl and 0.0090 M Ca(ClO4)2? What is the pH of the solution? I believe I have to find the ionic strength of the solution first, but I don't know how to find 2. ### Science Calculate the ionic strength of a solution that contains 1.45g Na3PO4 in 0.500L of solution. 3. ### chemistry When aqueous solutions of potassium carbonate and magnesium nitrate are combined, solid magnesium carbonate and a solution of potassium nitrate are formed. The net ionic equation for this reaction is: 4. ### chemistry Calculate the ionic strength of a solution that contains 1.45g Na3PO4 in 0.500L of solution. 1. ### Chemistry 111 calculate the number of moles of magnesium, chlorine, and oxygen atoms in 8.80 moles of magnesium perchlorate? 2. ### Chemistry Write equations for the dissociation of the following in water. Do not include states in your answer. 1) sodium acetate (NaC2H3O2) NaC2H3O2 ---> Na+ + (C2H3O2)- 2) copper(II) perchlorate Cu(ClO4)2 ---> Cu2+ + 2(ClO4)- Enter 3. ### chemistry Calculate [H3O ], [ClO4–], and [OH–] in an aqueous solution that is 0.130 M in HClO4(aq) at 25 °C. 4. ### science 20-1 which are covalent and which are ionic? • carbon tetrachloride, CCl4(l) • hydrogen fluoride, HF(g) • potassium iodide, KI(s) • magnesium oxide, MgO(s) . I got that they are all ionic but that doesn't seem right

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# Independent copula vs Student-$t$ copula with zero correlation matrix? Suppose I have the random variables $$X_1, \dots, X_n$$ with the marginal distributions are not normal (in fact, unknown marginal distribution). Will there be any difference between the assumption $$X_1, \dots, X_n$$ are independent and $$X_1, \dots, X_n$$ are modeled with Student-$$t$$ copula with the correlation matrix is all zeros (with $$1$$ on the diagonal)? The uncorrelated $$t$$ copula is not the same as the independence copula. It is based on the multivariate $$t$$-distribution, which is an elliptical family, and the only elliptical distribution for which zero correlation implies independence is the normal. The difference can be quite large. Below we will illustrate this using the R package copula. A contour plot of a $$t$$-copula is The density of the independence copula is a constant 1. Note how the $$t$$-copula concentrates probability in the center and close the the four corners. The code used is library(copula) indCop <- ellipCopula(family="normal", param=0, dim=2, dispst="ex") tCop <- ellipCopula(family="t", dim=2, dispst="ex", param=0, df=2) getSigma(indCop) [,1] [,2] [1,] 1 0 [2,] 0 1 getSigma(tCop) [,1] [,2] [1,] 1 0 [2,] 0 1 # See they are different: dCopula(c(0.5, 0.5), indCop) [1] 1 dCopula(c(0.5, 0.5), tCop) [1] 1.27324 contour(tCop, dCopula, n.grid=101, levels=c(0.5, 0.6, 0.7, 0.8, 0.9, 1, 1.1, 1.2, 1.3), main="t copula, uncorrelated, df=2") • Thank you very much for your answer! Could you please suggest me a paper that talks (or ideally, prove) about the fact that gaussian copula with zero correlation matrice is the same as independent copula ? Intuitively it is but rigourously, i am not sure. Thank you very much for your help! Commented Aug 6, 2021 at 21:12 • Kendall's taus = zero implies independencies only for Gaussian copulas. This is true. However, if the parameters of the t-student or Gaussian copulas are very close to its independent border and hence, they are the same as independent copulas. Just simulate a data from poor dependencies t-student copula which will be very close to independent copulas. plot(BiCopSim(500, 2, 0.02, 3)) plot(BiCopSim(500, 0,0)) Commented Aug 7, 2021 at 7:55 • So, I mean that if we fit the t-student copula to the data and estimate the parameters, which is very close to being independent, then we can assume the correlation between these variables as independent and hence fit independent copulas. However, if Kendall's tau as an independent test, shows that these variables are independent, then this is only true for Gaussian copulas. Commented Aug 7, 2021 at 8:01

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Object: Energy Harvesting 1 / 1 # Object: Energy Harvesting - PowerPoint PPT Presentation HANDLE team, Energy Harvesting Advisor: Prof.Dimitri Peroulis ; Graduate advisor:Abbas Semnani Team Member: Shuozhengyang Wang. Calculation: 1. Simulate the magnetic to a magnetic dipole moment . Use the equation from Wikipedia for the magnetic dipole moment: m is the dipole moment I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described. ## PowerPoint Slideshow about ' Object: Energy Harvesting' - roxy Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - Presentation Transcript Calculation: 1. Simulate the magnetic to a magnetic dipole moment. Use the equation from Wikipedia for the magnetic dipole moment: m is the dipole moment is the magnetic constant r is the distance from the point to the center of a bar. Therefore, in this design, it will be the distance between two legs. 𝜃 is the angle between r and the vertical line. So here r= 0.2 m , is the magnetic constant. =1.25663706 × 10-6 m kg s-2A-2 Put the number into the equation, So, the magnetic field intensity is: B = 0.022 T 2. Assume when people is standing, the magnetic flux is totally into the metal circle loops, and when the stride reaches the most, magnetic flux is 0. The change of magnetic flux when people’s walking, is from totally magnetic flux to zero. S= ∅ is the magnetic flux, and B is the magnetic field intensity. 𝑅′ is the radius of the metal circle loop, and in this design:𝑅′ =0.04 m so S== =B (B=0.022T) =B =0.022 =4.84 4. E is the voltage from the change of magnetic flux. ∆𝑡 is the time change of two legs while walking.n is the number of turns. =0.5s (for every steps) =/(R) P is the power from this electric field. R is the output load, so normally R is 50 ohm. P=0.05w, -0= 4.84,=0.5s So, n=163.34, so n=163 Object: Energy Harvesting 1. Generate power in the order of 10s of mW from everyday activities like walking or working in an office environment2. Power is needed around chest area3 . Inexpensive meaning using either commercially available components and cost-effective manufacturing if custom components are needed. • Original Idea and Design: • When people are walking, a lot of parts in their body will have movements and shaking. Transfer the energy of motion to electrical power. • Magnetic field changes will provide electric field, and get the electrical power from the electric field. • Harvest electrical power. • One leg with metal circle loops and the other one • Easy for the equipment to be fixed • The distance of two legs is not far, but the range of two leg is large . • AC to DC circuit: • Moving of legs will change the current direction from magnetic field, while walking. • There will be the alternating current. • Use design above to change AC to DC. • Reference: • Electric Dipole Moment: • http://en.wikipedia.org/wiki/Electric_dipole_moment • (Wikipedia, 2012) • Faraday\'s law of electromagnetic induction:

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Oscar Luna Posted on # Javascript Data Structures and Algorithms (Linked Lists, part 1: Singly-Linked Lists) Hello! This is the third installment in a series of posts that will introduce you to the Data structures and algorithms you can expect to be asked about at a technical interview. If you want a more thorough introduction, check out parts 1 and 2 where I discuss arrays in the menu above. Let's get right into it. Linked Lists are a sorted collection of vertices or nodes that contain data and refs that link to each other or in one direction, aptly called pointers. The nodes in a linked list must contain a head, or a first value, a tail, which is the last value in a node, and a pointer, which connects a node's tail to the next node in the linked list. The last node in a linked list, however, will point to `null` to indicate the end of the linked list. Creating a linked list It's safe to say that it is unlikely that you'll be asked to create a linked list from scratch at an interview, but I found creating one to be an excellent learning tool. We can create a linked list class that we can instantiate as needed. Since linked lists are sorted, nodes are inserted front to back; the first value inserted in an empty linked list becomes the head and will also be the tail. We can define a linked list's values in a class constructor: ``````class LinkedList { constructor(value) { value: value, next: null }; this.length = 1; } } // we can now instantiate this linked list as needed `````` Prepend Prepending, or inserting a value at the beginning of a linked list, is more optimal in a linked list than it would be in an array, given that adding to a linked list does not require traversal of any kind. There is also no shifting involved as it would be in an array. Prepending a value in a linked list is done in constant time, O(1), as opposed to linear time in an array, O(n). The same goes for appending, or adding a value at the end of a linked list. For an array, both cases require traversing to either end of an array. To prepend a new node to a linked list we simply need to assign a new node as the head of the given linked list. ``````class MyArray { constructor(value) { this.value = value } //initialize a method to prepend a node //our method will receive the node's value prepend(value) { //we can either initialize an object or instantiate a node class, //like we created in the last example const newNode = new Node(value) //if there is no head, we can simply I sort the new node as the head of the linked list if(this.head === null) { return this; //have the new node point to the head of the linked list //reassign the head property to equate to the new node //increase the size of the linked list this.length++; //return the linked list return this; } } `````` Append Appending nodes to a linked list is very similar to prepending. Like appending it is done in 0(1) time, since no traversing or shifting of elements is required. We simply reassign the inserted node as the new tail in the linked list and have the former tail point to the inserted node. ``````... append(value) { const newNode = new Node(value); //make the old tail point to the new tail this.tail.next = newNode; //make the inserted node the new tail this.tail = newNode; //since we need to allocate memory in a linked list, increase the length of it this.length++; return this; } `````` Insert Prepending and appending may be simple, but things get a little complicated when we need to insert a node at any other position in a linked list. We can identify the head or the tail of a linked list in O(1) time, but accessing values between the head and the tail requires traversal, an operation that runs in O(n) time. As a reminder, this means that it's time complexity grows relative to the size of the data structure. The bigger the list, the more nodes we need to traverse. After traversal we need to insert our new node and shift the pointers of the adjacent nodes. ``````... insert(index, value){ //check our parameters if(index >= this.length) { return this.append(value); } const newNode = new Node(value); //define the index before our insertion point const leader = this.traverseToIndex(index-1); //define the index after the insertion point const holdingPointer = leader.next; //make the leader point to the inserted node //make the inserted node point to the holding node newNode.next = holdingPointer; this.length++; return this; } ... `````` Deletion The last operation I'll go over is deleting a node in a linked list. Unlike deletion in an array, we don't need to traverse through every node to delete a head or tail node, so long as we have a defined value for the node. This makes deletion of a head or tail node in Singly-Linked Lists run in O(1) time. Here's an example of deletion methods, where I've included a third method that deletes any node in a linked list that isn't the head or the tail: ``````//remove the head node of a linked list return } return this } //removing the tail node of a linked list removeTail(index) { //verify parameters return; } //define node before target node let prevNode = this.head; //define node after the target node let tail = this.head.next; while(tail.next != null) { let targetNode = this.prevNode.next; prevNode= tail; tail = tail.next return this; } } //removing a node from the linked list that isn't the head or tail remove(index) { // Check Parameters const leader = this.traverseToIndex(index-1); const unwantedNode = leader.next; The example above shows us three cases for deleting from a linked list. Deleting a head or tail node is our best case here, having a time complexity of O(1). At worst case, which is deleting any other node, has a time complexity of O(n), where `n` is the number of nodes that must be traversed in the linked list.

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# How To Calculate Variance in Google Sheets In this tutorial, you’ll learn how to calculate variance in Google Sheets. Variance is a measure of dispersion or variability of a set of data points from their mean value. By calculating variance, you can get an idea of how spread out your data is and whether it’s relatively consistent or not. Let’s get started! ## How to Calculate Variance in Google Sheets Variance measures the extent to which data points spread out from the mean. It indicates the degree of distribution of each data point from the standard. There are two types of variances: sample and population. Sample variance is based on sample data, while population variance is from an entire data population. Spreadsheet applications like Google Sheets and Microsoft Excel use functions that execute computations by simply inputting the appropriate formula into the formula bar. This is also true for variance calculations, as you can do them quickly using these two applications. ## Calculating Variance in Google Sheets Suppose this is the dataset you will use for both sample and population variance computation. ## Method 1. Calculating Sample Variance ### Step 2. Select the cell where you want the sample variance to appear The selected cell should appear with a blue border. ### Step 3. Locate the cell range of your data Identify the cell range of your data by checking the cell coordinates. The coordinates consist of a column letter and row number. A cell range is then composed of the first and last cell coordinates separated by a colon. Thus, the cell range of your needed data is A2:A11. A more straightforward method to identify the cell range is highlighting it. You can do this by clicking, holding, and dragging your mouse cursor over the field. Doing this will automatically show the cell range beside the formula bar. ### Step 4. Input the VAR formula Since you are only going to compute the sample variance, the function to be utilized is VAR. Input the following formula into the formula bar: =VAR(A2:A11) ### Step 5: Click “Enter” on your keyboard Clicking enter should automatically add the sample variance into the cell you selected in step 2. ## Method 2. Calculating Population Variance This method utilizes the same steps as the computation for sample variance. The only difference is the formula you have to input. ### Step 2.Select the cell where you want the population variance to appear The selected cell should appear with a blue border. ### Step 3. Locate the cell range of your data Identify the cell range of your data by checking the column letter and row number. The cell range of the data in this set is A2:A11. Another method you can use is highlighting the entire cell range to view the coordinates. Click, hold, and drag your mouse cursor over the whole field to show the cell range. ### Step 4. Input the VARP formula Unlike the first method, which only uses the VAR function, this method utilizes VARP since it computes the entire data population. Thus, input the following formula into the formula bar: =VARP(A2:A11) ### Step 5: Click “Enter” on your keyboard Clicking enter should automatically add the population variance into the cell you selected in step 2. ## Summary That’s the end of this tutorial.

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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!) A240529 Indices of 9-almost prime triangular numbers. 2 224, 351, 624, 704, 735, 768, 783, 800, 832, 864, 895, 944, 959, 960, 999, 1151, 1152, 1224, 1279, 1343, 1344, 1375, 1440, 1520, 1539, 1824, 1855, 1935, 1943, 1944, 1952, 2000, 2144, 2159, 2176, 2187, 2295, 2367, 2430, 2432, 2464, 2495, 2496, 2499, 2511 (list; graph; refs; listen; history; text; internal format) OFFSET 1,1 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 FORMULA { m : A069904(m) = 9 }. - Alois P. Heinz, Aug 05 2019 EXAMPLE a(1) = 224 because A000217(224) = 224*(224+1)/2 = 25200 = 2^4 * 3^2 * 5^2 * 7 is a 9-almost prime. MATHEMATICA Flatten[Position[Accumulate[Range[3500]], _?(PrimeOmega[#]== 9 &)]] Select[Range[3000], PrimeOmega[(# (# + 1))/2] == 9 &] (* Harvey P. Dale, Jun 22 2017 *) PROG (Magma) [n: n in [2..2600] | &+[d[2]: d in Factorization((n*(n+1)))] eq 10]; // Vincenzo Librandi, Dec 22 2018 (GAP) F:=List([1..2600], n->Length(Factors(n*(n+1)/2)));; a:=Filtered([1..Length(F)], i->F[i]=9); # Muniru A Asiru, Dec 22 2018 CROSSREFS Cf. A000217, A069904, A108815, A114435, A114436, A114437, A164977. Sequence in context: A345543 A345796 A046296 * A177770 A202442 A331371 Adjacent sequences: A240526 A240527 A240528 * A240530 A240531 A240532 KEYWORD nonn,easy AUTHOR Vincenzo Librandi, Apr 07 2014 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 28 23:19 EDT 2023. Contains 361596 sequences. (Running on oeis4.)

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• ### Why vertical hydraulic conductivity is always 10 to 100 fraction of Kx? I'm developing a groundwater flow model in feflow and when I assigned vertical hydraulic conductivity as 0.1 times of Kx my model becomes too slow. i have given pumping wells at various depth and the area consist of both sedimentary and weather hard rock formation with one boundary as coastal region. I assume that when vertical conductivity is low, some pumping wells get dry since recharged water is not reaching at bottom of aquifer due to low vertical conductivity. Is it possible to assign Kx,y,z as same conductivity?. looking for some suggestions and help. Thank you • ### How can i do random selection of nodes or elements in a slice? How can I do a random selection of nodes or elements in a slice? such as with equal distance but random • ### Re: transient modelling with recharge monthly data i want to add daily recharge data for the model more than 20 years. but shapefile only support 200 somthing timesteps. any other way? • ### determining inflow of water in to model im working on 3d coastal aquifer flow model. eastern part of model boundary is constant. north and south is no flow. west is variable boundary condition. which boundary type will be better to use in western boundary, ie, neumann or fluid transfer. only data i have is water level  near to that boundary which are inside and outside domain. anyone please help to  detemine how to calculate flux for neumann. or in case of fluid transfer condition, can i use use near by well data as reference head ? if so wat should be in/out transfer rate in material proprty? Thank you :) • ### Re: Saltwater !! u r welcome  :) is there any formula to calculate equivalent fresh water head? for example my initial sea level is 0m, then it increase at the rate of 3mm per year. so i can put it directly as time series ryt? • ### Re: Saltwater !! i want to understand saltwater intrusion by sealevel rise. for that i need to put seawater head boundary as transient ryt. but there is no option to add time series for seawater boundary in editor. wat should i do? • ### Re: Saltwater !! im sorry,  because capslock was on and noticed it only after typing a little bit. actually it was not in a rude way. i was just lazy to type it again. once again im so sorry :-\ • ### Re: Saltwater !! Where can i find detailed steps to do seawater intrusion model. Is there any tutorial for that? If i have a 3d flow model in a coastal regions wat and all parameters should i add to find sea water intrusion . How its calibration is done etc

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# vba to condense similar cells into new cell, with total overall quantity. This is a discussion on vba to condense similar cells into new cell, with total overall quantity. within the Excel Questions forums, part of the Question Forums category; Hello, I have a parts list that has many duplicate items, but different lengths for each piece to be cut ... 1. ## vba to condense similar cells into new cell, with total overall quantity. Hello, I have a parts list that has many duplicate items, but different lengths for each piece to be cut at. when referring from this bill of materials to enter into the computer, i only need to enter one line with the total quantity. Each parts list is of varying lengths and random orders. I am hoping to find something that will scrape the list for similar parts and condense them. Sample below. I would like line item# 1,2, and 3 to be condensed into one line, for total length of 12592mm (that multiplies qty in B2 by length in d2, and sums all similar woods from line c into one line). ideally, it would be great if this pops out the info on a new sheet, but i would be fine with it in column J-- or any column further to the right. Item # QTY Description Part Number Length [mm] 1 4 mahogany MHG887 1000 2 4 mahogany MHG887 1299 3 6 mahogany MHG887 566 4 12 white oak WO992 1312 desired end result J column K column (or on new sheet) Mahogany 12592mm White Oak 15744mm 2. ## Re: vba to condense similar cells into new cell, with total overall quantity. Hi There assuming you list of wood is in column J and this cantains all unique timbers from your list. this should do what you require Code: ```Sub total() lr = Range("A" & Rows.Count).End(xlUp).Row lr1 = Range("J" & Rows.Count).End(xlUp).Row For a = 1 To lr1 total = 0 word1 = Range("j" & a) For i = 2 To lr If Range("C" & i) = word1 Then total = total + Range("B" & i) * Range("E" & i) Next Range("k" & a) = total Next End Sub``` if you want it output into a different sheet, let me know what the sheet name is. Only thing i was not sure about was if you required the code to pull out all of your unique timbers from the list?? Dave 3. ## Re: vba to condense similar cells into new cell, with total overall quantity. Hi Squidd, thanks for the quick reply. Yes, I would need the unique timbers pulled out too. I have all the various types of wood on Sheet2. With all the various end finishes, it comes out to 1137 total, so I would like to keep that on its own hidden sheet. Right now, it is used to pull up pricing onto the first page, but we never look at it. as for the code, it is working great so far. I figure it would be fine if the code spits out doubles, since I could just expand the macro to delete duplicates in columns J and K. 4. ## Re: vba to condense similar cells into new cell, with total overall quantity. Also, it would be great is 0 qty items would be removed. I have fasteners and other hardware on the lines below, they have no value for the Length in column E. They only have qty in B and description and part number in c & d. you have already gotten me further than i could figure out by myself, thank you very much. I found it hard to describe what I was looking for, and the search on the website wasn't working too great as a result. 5. ## Re: vba to condense similar cells into new cell, with total overall quantity. Hi Again Try this code, i need to tidy it a bit if it works. create yourself a sheet called "sheet3" for test purposes. then run this code from your main sheet Code: ```Sub total() LR = Range("A" & Rows.Count).End(xlUp).Row Range("C2:C" & LR).Copy Range("'SHEET3'!A1").PasteSpecial lr2 = Range("'SHEET3'!A" & Rows.Count).End(xlUp).Row With Sheets("sheet3").Columns("A:A") .Range("A1:A" & lr2).RemoveDuplicates Columns:=1, Header:=xlNo .SpecialCells(xlCellTypeBlanks).Delete Shift:=xlUp End With lr1 = Range("'SHEET3'!A" & Rows.Count).End(xlUp).Row For a = 1 To lr1 total1 = 0 word1 = Range("'SHEET3'!A" & a) For i = 2 To LR If Range("C" & i) = word1 Then total1 = total1 + Range("B" & i) * Range("E" & i) Next Range("'SHEET3'!B" & a) = total1 Next End Sub``` should pull out all the unique timbers from your list and put into sheet 3 column A then put the total into column B. we can ann into the code also that if the total = 0 then Dont put into the list, but try this 1st, then i will add it and tidy things up. Also if it works, let me know what sheet you want the output put into. cheers dave 6. ## Re: vba to condense similar cells into new cell, with total overall quantity. Hi I got to sign off now.(couple of hours) But like i said before, create sheet3 and run this code from your main sheet, should now work and then delete all timbers that total 0. Code: ```Sub total() LASTROW = Range("A" & Rows.Count).End(xlUp).Row Range("C2:C" & LASTROW).Copy Range("'SHEET3'!A1").PasteSpecial lr2 = Range("'SHEET3'!A" & Rows.Count).End(xlUp).Row With Sheets("sheet3").Columns("A:A") .Range("A1:A" & lr2).RemoveDuplicates Columns:=1, Header:=xlNo .SpecialCells(xlCellTypeBlanks).Delete Shift:=xlUp End With lr1 = Range("'SHEET3'!A" & Rows.Count).End(xlUp).Row For a = 1 To lr1 total1 = 0 word1 = Range("'SHEET3'!A" & a) For i = 2 To LASTROW If Range("C" & i) = word1 Then total1 = total1 + Range("B" & i) * Range("E" & i) Next Range("'SHEET3'!B" & a) = total1 Next Sheets("SHEET3").Activate For B = Range("'SHEET3'!A" & Rows.Count).End(xlUp).Row To 1 Step -1 If Range("'SHEET3'!B" & B).Value = 0 Then Rows(B).EntireRow.Delete Next B End Sub``` still got to tidy iot up, sorry, was in a bit of a rush. Dave 7. ## Re: vba to condense similar cells into new cell, with total overall quantity. I keep getting an error towards the end. If Range("C" & i) = word1 Then total1 = total1 + Range("B" & i) * Range("E" & i) the blue part keeps coming back highlighted, with error "type mismatch" it is pasting the info onto sheet3 after I created that sheet. This code alone isnt updating anything on the main sheet though. 8. ## Re: vba to condense similar cells into new cell, with total overall quantity. found out what the error was with the above post. I had a formula in cell d1 (for page number). after deleting that cell it worked great. Thanks for all the help SQUIDD. would it be difficult to also have column D paste over onto the next page? Also, would it be possible to have the new sheet auto generate? Right now its only working if i make a Sheet3 first. 9. ## Re: vba to condense similar cells into new cell, with total overall quantity. I can do column D no problem, can also apply your headers easily too. Not sure what you mean by having sheet 3 auto generate, i mean, i know what you want, you want the code to generate sheet3. BUT Why can you not simply have sheet3 always in your workbook?? If it is because you dont want users to see it, probably best if you simply have the code to display the sheet(unhide) and then as soon as the user clicks a different sheet we could make the sheet hide again automatically. Let me know. Will add the other functions required and post back the code. Dave 10. ## Re: vba to condense similar cells into new cell, with total overall quantity. Hi Ok this should do the trick for you. This makes sheet 3 visible at the end of the code. then the code posted under , put that into sheet3 module, when you click a different sheet it will re-hide sheet 3. let me know if you need any help OR this option will not work for you. Code: ```Sub total() Sheets("sheet3").Columns("A:C").ClearContents Range("C1:E" & Range("A" & Rows.Count).End(xlUp).Row).Copy Range("'SHEET3'!A1").PasteSpecial With Sheets("sheet3").Columns("A:C") .Range("A1:C" & Range("'SHEET3'!A" & Rows.Count).End(xlUp).Row).RemoveDuplicates Columns:=1, Header:=xlNo .SpecialCells(xlCellTypeBlanks).Delete Shift:=xlUp End With For a = 2 To Range("'SHEET3'!A" & Rows.Count).End(xlUp).Row total1 = 0 word1 = Range("'SHEET3'!A" & a) For i = 2 To Range("A" & Rows.Count).End(xlUp).Row If Range("C" & i) = word1 Then total1 = total1 + Range("B" & i) * Range("E" & i) Next Range("'SHEET3'!C" & a) = total1 Next Sheets("SHEET3").Activate For B = Range("'SHEET3'!A" & Rows.Count).End(xlUp).Row To 2 Step -1 If Range("'SHEET3'!C" & B).Value = 0 Then Rows(B).EntireRow.Delete Next B Sheets("Sheet3").Visible = True End Sub``` create sheet3, right click on the tab and click view code, paste this into there. Code: ```Private Sub Worksheet_Deactivate() Sheets("Sheet3").Visible = False End Sub``` Dave Page 1 of 2 12 Last #### Posting Permissions • You may not post new threads • You may not post replies • You may not post attachments • You may not edit your posts •

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# [R] Visualizing binary response data? Frank E Harrell Jr f.harrell at Vanderbilt.Edu Wed May 5 04:17:53 CEST 2010 ```On 05/04/2010 09:12 PM, Thomas Stewart wrote: > For binary w.r.t. continuous, how about a smoothing spline? As in, > > x<-rnorm(100) > y<-rbinom(100,1,exp(.3*x-.07*x^2)/(1+exp(.3*x-.07*x^2))) > plot(x,y) > lines(smooth.spline(x,y)) > > OR how about a more parametric approach, logistic regression? As in, > > glm1<-glm(y~x+I(x^2),family=binomial) > plot(x,y) > lines(sort(x),predict(glm1,newdata=data.frame(x=sort(x)),type="response")) > > FOR binary w.r.t. categorical it depends. Are the categories ordinal (is > there a natural ordering?) or are the categories nominal (no ordering)? For > nominal categories, the data is essentially a contingency table, and > "strength of the predictor" is a test of independence. You can still do a > graphical exploration: maybe plotting the proportion of Y=1 for each > category of X. As in, > > z<-cut(x,breaks=-3:3) > plot(tapply(y,z,mean)) > > If your goal is to find strong predictors of Y, you may want to consider > graphical measures that look at the predictors jointly. Maybe with a > > There is probably a lot more you can do. Be creative. > > -tgs And you have to decide why you would look to a graph to select predictors. This can badly distort later inferences (confidence intervals, P-values, biased regression coefficients, biased R^2, etc.). Frank > > > > On Tue, May 4, 2010 at 9:04 PM, Kim Jung Hwa<kimhwamaillist at gmail.com>wrote: > >> Hi All, >> >> I'm dealing with binary response data for the first time, and I'm confused >> about what kind of graphics I could explore in order to pick relevant >> predictors and their relation with response variable. >> >> I have 8-10 continuous predictors and 4-5 categorical predictors. Can >> anyone >> suggest what kind of graphics I can explore to see how predictors behave >> w.r.t. response variable... >> >> Any help would be greatly appreciated, thanks, >> Kim >> -- Frank E Harrell Jr Professor and Chairman School of Medicine Department of Biostatistics Vanderbilt University ```

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how many integer solutions does (4n+19)/(n-3) has? 2 4 8 infinte many Solution (4n-12+31)/(n-3) = 4+31/(n-3) so now 31/(n-3) let’s say equal to 31/x  should be integer it will be integer when x is a factor of 31 (both positive and negative) there are 2 positive factors of 31 and 2 negative factors. Hence total 4 solutions. [/showhide]

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# Fastest solution to compute normal A physics engine return a deformed mesh (only geometry vertices). I take this mesh to render the geometry (~500000 vertices). What is the fastest solution and the least expensive to compute normal vertices every frame? OpenCL? Geometry Shaders? In a CPU thread? Other? - then what are you going to do with it? is this a typical object in your game (I really really hope not if you want to calculate the whole thing every frame, and not just store it)? how often will this object be "deformed"? – gardian06 May 4 '12 at 7:20 It's on a medical simulation. The object is deformed every frame. I need normals for rendering the mesh. – urza57 May 4 '12 at 7:25 I will assume that you mean vector, and not actual vertices (I do not know what that would even mean). find all faces (determine adjacent points). for each face take any 3 points on the face, and create 2 vectors (V1=p1-p2, V2=p1-p3) then take their cross product. keep in mind that if your camera is right, and nothing shows up try reversing your cross product this will give you a vector normal to the plane of the face. rinse, and repeat for each face. seriously try with a pyramid, or cube first – gardian06 May 4 '12 at 7:30 is that an actual question, or a statement? (I will go with question) the most complex part will be determining where the faces are (this is the big problem with collision detection on complex-convex polyhedrons), and once that is done constructing 2 vectors, and doing a cross product is relatively trivial. – gardian06 May 4 '12 at 7:40 This question cannot be answered as asked. What the "fastest solution" is will vary wildly with hardware and implementations. Not to mention that, regardless of what you're coming up with, you'll have to stream 500k+ vertices per frame. The best you can do is try out several techniques and benchmark them. That being said, are you sure your physics system can't be made to spit out normals? It must have most of the information needed to generate them when it does its deformation. – Nicol Bolas May 4 '12 at 19:23 A lot of this depends if you need interpolated normals over the polygon or can live with a the 'faceted look' of per-triangle normals. The per-triangle normals are a lot easier to compute: a simple cross prod of the three vertices with one of them being made a local-origin by subtracting it from the other two first. Smooth per-vertex require finding all the triangles that share a vertex, and averaging their per-triangle normals, by weighting their angle by some factor, typically the angle of the corner made at the vertex for that triangle. If your mesh can have an arbitrary number of triangles meeting in a corner this can be rather difficult implement on a GPU. - Try looking at implementing it in either OpenCL or CUDA. A lot of medical applications are going towards that field because of the insane amount of data they have to process per frame. The problem you have should be easy to parallelize (run on the multiple cores of a videocard). You have a fixed input (three vertices) and a fixed output (one normal). So, a version of the program could be: • Physics simulation deforms the mesh. • Upload data to OpenGL using vertex buffers. • Lock buffers for OpenCL processing. • OpenCL writes to normal buffer, keeping everything in video memory. • Unlock buffers for OpenGL usage. • Rendering using vertex data with normals. - So I coded simple C++ test program that calculates normal for pair of vectors using cross product 500000 times. Source highlights are: ``````struct Vector3 { float x, y, z; Vector3(); }; const int n = 500000; Vector3 a[n], b[n], c[n]; void CalculateNormals() { for (int i = 0; i < n; ++i) { c[i].x = a[i].y * b[i].z - a[i].z * b[i].y; c[i].y = a[i].z * b[i].x - a[i].x * b[i].z; c[i].z = a[i].x * b[i].y - a[i].y * b[i].x; } } `````` I've executed 1000 passes on random data. And average time of `CalculateNormals()` function to finish is `3.11` ticks. So I think the idea to calculate this stuff on CPU is straithforward and efficient. By the way my CPU is `Intel Core i5-2400 @ 3.10 GHz`. - Interpolation between triangle normals also needs to be done in order to get smooth shading. The cross-product approach will only give flat shading. – ktodisco May 4 '12 at 8:20 @iodiot the result vectors are not normalized! – Maik Semder May 4 '12 at 8:43 @iodiot a few things `a`, and `b` should be determined for the current face not just given as values, and could very well be static to the current iteration of the for loop. And, `500000` was not the face count it was the number of vertices (the number of faces will be some fraction of the number of vertices, and typically higher) – gardian06 May 4 '12 at 9:02 @Maik Semder Normal attached to the vertex can be normalized trivially in vertex shader. Sorry I forgot about this, cause was surprised by CPU performance. – iodiot May 4 '12 at 9:07 @iodiot no problem. However, it would be good to update the post, measure the timing including normalizing. – Maik Semder Jun 20 '12 at 10:31

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Cody # Problem 963. We love vectorized solutions. Problem 1 : remove the row average. Solution 1673138 Submitted on 13 Nov 2018 by Sharon Spelt 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 x = [ 0 1 ; 2 3 ] ; timer=tic; y = remove_average_vectorized(x); duration=toc(timer) % You can probably pass this test with a for loop. assert(duration<0.1,sprintf('Time used %2.3f\n',duration)); duration = 4.5000e-04 2   Pass x = [ 1:9999 ; 2:10000 ; [ zeros(1,9998) 9999 ] ]; x = repmat(x,1000,1); y_correct = [ -4999:1:4999 ; -4999:1:4999 ; [ repmat(-1,1,9998) 9998 ] ]; y_correct = repmat(y_correct,1000,1); y = remove_average_vectorized(x); assert(isequal(y,y_correct)); 3   Pass x = [ 1:9999 ; 2:10000 ; [ zeros(1,9998) 9999 ] ]; x = repmat(x,1000,1); timer=tic; y = remove_average_vectorized(x); duration=toc(timer) % A decent vectorized solution should take around 1 second. assert(duration<2,sprintf('Time used %2.3f\n',duration)); duration = 0.1651

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Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  cnmet Structured version   Visualization version   GIF version Theorem cnmet 23377 Description: The absolute value metric determines a metric space on the complex numbers. This theorem provides a link between complex numbers and metrics spaces, making metric space theorems available for use with complex numbers. (Contributed by FL, 9-Oct-2006.) Assertion Ref Expression cnmet (abs ∘ − ) ∈ (Met‘ℂ) Proof of Theorem cnmet Dummy variables 𝑥 𝑦 𝑧 are mutually distinct and distinct from all other variables. StepHypRef Expression 1 cnex 10607 . 2 ℂ ∈ V 2 absf 14689 . . 3 abs:ℂ⟶ℝ 3 subf 10877 . . 3 − :(ℂ × ℂ)⟶ℂ 4 fco 6505 . . 3 ((abs:ℂ⟶ℝ ∧ − :(ℂ × ℂ)⟶ℂ) → (abs ∘ − ):(ℂ × ℂ)⟶ℝ) 52, 3, 4mp2an 691 . 2 (abs ∘ − ):(ℂ × ℂ)⟶ℝ 6 subcl 10874 . . . 4 ((𝑥 ∈ ℂ ∧ 𝑦 ∈ ℂ) → (𝑥𝑦) ∈ ℂ) 76abs00ad 14642 . . 3 ((𝑥 ∈ ℂ ∧ 𝑦 ∈ ℂ) → ((abs‘(𝑥𝑦)) = 0 ↔ (𝑥𝑦) = 0)) 8 eqid 2798 . . . . . 6 (abs ∘ − ) = (abs ∘ − ) 98cnmetdval 23376 . . . . 5 ((𝑥 ∈ ℂ ∧ 𝑦 ∈ ℂ) → (𝑥(abs ∘ − )𝑦) = (abs‘(𝑥𝑦))) 109eqcomd 2804 . . . 4 ((𝑥 ∈ ℂ ∧ 𝑦 ∈ ℂ) → (abs‘(𝑥𝑦)) = (𝑥(abs ∘ − )𝑦)) 1110eqeq1d 2800 . . 3 ((𝑥 ∈ ℂ ∧ 𝑦 ∈ ℂ) → ((abs‘(𝑥𝑦)) = 0 ↔ (𝑥(abs ∘ − )𝑦) = 0)) 12 subeq0 10901 . . 3 ((𝑥 ∈ ℂ ∧ 𝑦 ∈ ℂ) → ((𝑥𝑦) = 0 ↔ 𝑥 = 𝑦)) 137, 11, 123bitr3d 312 . 2 ((𝑥 ∈ ℂ ∧ 𝑦 ∈ ℂ) → ((𝑥(abs ∘ − )𝑦) = 0 ↔ 𝑥 = 𝑦)) 14 abs3dif 14683 . . . 4 ((𝑥 ∈ ℂ ∧ 𝑦 ∈ ℂ ∧ 𝑧 ∈ ℂ) → (abs‘(𝑥𝑦)) ≤ ((abs‘(𝑥𝑧)) + (abs‘(𝑧𝑦)))) 15 abssub 14678 . . . . . 6 ((𝑥 ∈ ℂ ∧ 𝑧 ∈ ℂ) → (abs‘(𝑥𝑧)) = (abs‘(𝑧𝑥))) 1615oveq1d 7150 . . . . 5 ((𝑥 ∈ ℂ ∧ 𝑧 ∈ ℂ) → ((abs‘(𝑥𝑧)) + (abs‘(𝑧𝑦))) = ((abs‘(𝑧𝑥)) + (abs‘(𝑧𝑦)))) 17163adant2 1128 . . . 4 ((𝑥 ∈ ℂ ∧ 𝑦 ∈ ℂ ∧ 𝑧 ∈ ℂ) → ((abs‘(𝑥𝑧)) + (abs‘(𝑧𝑦))) = ((abs‘(𝑧𝑥)) + (abs‘(𝑧𝑦)))) 1814, 17breqtrd 5056 . . 3 ((𝑥 ∈ ℂ ∧ 𝑦 ∈ ℂ ∧ 𝑧 ∈ ℂ) → (abs‘(𝑥𝑦)) ≤ ((abs‘(𝑧𝑥)) + (abs‘(𝑧𝑦)))) 1993adant3 1129 . . 3 ((𝑥 ∈ ℂ ∧ 𝑦 ∈ ℂ ∧ 𝑧 ∈ ℂ) → (𝑥(abs ∘ − )𝑦) = (abs‘(𝑥𝑦))) 208cnmetdval 23376 . . . . . 6 ((𝑧 ∈ ℂ ∧ 𝑥 ∈ ℂ) → (𝑧(abs ∘ − )𝑥) = (abs‘(𝑧𝑥))) 21203adant3 1129 . . . . 5 ((𝑧 ∈ ℂ ∧ 𝑥 ∈ ℂ ∧ 𝑦 ∈ ℂ) → (𝑧(abs ∘ − )𝑥) = (abs‘(𝑧𝑥))) 228cnmetdval 23376 . . . . . 6 ((𝑧 ∈ ℂ ∧ 𝑦 ∈ ℂ) → (𝑧(abs ∘ − )𝑦) = (abs‘(𝑧𝑦))) 23223adant2 1128 . . . . 5 ((𝑧 ∈ ℂ ∧ 𝑥 ∈ ℂ ∧ 𝑦 ∈ ℂ) → (𝑧(abs ∘ − )𝑦) = (abs‘(𝑧𝑦))) 2421, 23oveq12d 7153 . . . 4 ((𝑧 ∈ ℂ ∧ 𝑥 ∈ ℂ ∧ 𝑦 ∈ ℂ) → ((𝑧(abs ∘ − )𝑥) + (𝑧(abs ∘ − )𝑦)) = ((abs‘(𝑧𝑥)) + (abs‘(𝑧𝑦)))) 25243coml 1124 . . 3 ((𝑥 ∈ ℂ ∧ 𝑦 ∈ ℂ ∧ 𝑧 ∈ ℂ) → ((𝑧(abs ∘ − )𝑥) + (𝑧(abs ∘ − )𝑦)) = ((abs‘(𝑧𝑥)) + (abs‘(𝑧𝑦)))) 2618, 19, 253brtr4d 5062 . 2 ((𝑥 ∈ ℂ ∧ 𝑦 ∈ ℂ ∧ 𝑧 ∈ ℂ) → (𝑥(abs ∘ − )𝑦) ≤ ((𝑧(abs ∘ − )𝑥) + (𝑧(abs ∘ − )𝑦))) 271, 5, 13, 26ismeti 22932 1 (abs ∘ − ) ∈ (Met‘ℂ) Colors of variables: wff setvar class Syntax hints:   ∧ wa 399   ∧ w3a 1084   = wceq 1538   ∈ wcel 2111   × cxp 5517   ∘ ccom 5523  ⟶wf 6320  ‘cfv 6324  (class class class)co 7135  ℂcc 10524  ℝcr 10525  0cc0 10526   + caddc 10529   ≤ cle 10665   − cmin 10859  abscabs 14585  Metcmet 20077 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-10 2142  ax-11 2158  ax-12 2175  ax-ext 2770  ax-sep 5167  ax-nul 5174  ax-pow 5231  ax-pr 5295  ax-un 7441  ax-cnex 10582  ax-resscn 10583  ax-1cn 10584  ax-icn 10585  ax-addcl 10586  ax-addrcl 10587  ax-mulcl 10588  ax-mulrcl 10589  ax-mulcom 10590  ax-addass 10591  ax-mulass 10592  ax-distr 10593  ax-i2m1 10594  ax-1ne0 10595  ax-1rid 10596  ax-rnegex 10597  ax-rrecex 10598  ax-cnre 10599  ax-pre-lttri 10600  ax-pre-lttrn 10601  ax-pre-ltadd 10602  ax-pre-mulgt0 10603  ax-pre-sup 10604 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3or 1085  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-mo 2598  df-eu 2629  df-clab 2777  df-cleq 2791  df-clel 2870  df-nfc 2938  df-ne 2988  df-nel 3092  df-ral 3111  df-rex 3112  df-reu 3113  df-rmo 3114  df-rab 3115  df-v 3443  df-sbc 3721  df-csb 3829  df-dif 3884  df-un 3886  df-in 3888  df-ss 3898  df-pss 3900  df-nul 4244  df-if 4426  df-pw 4499  df-sn 4526  df-pr 4528  df-tp 4530  df-op 4532  df-uni 4801  df-iun 4883  df-br 5031  df-opab 5093  df-mpt 5111  df-tr 5137  df-id 5425  df-eprel 5430  df-po 5438  df-so 5439  df-fr 5478  df-we 5480  df-xp 5525  df-rel 5526  df-cnv 5527  df-co 5528  df-dm 5529  df-rn 5530  df-res 5531  df-ima 5532  df-pred 6116  df-ord 6162  df-on 6163  df-lim 6164  df-suc 6165  df-iota 6283  df-fun 6326  df-fn 6327  df-f 6328  df-f1 6329  df-fo 6330  df-f1o 6331  df-fv 6332  df-riota 7093  df-ov 7138  df-oprab 7139  df-mpo 7140  df-om 7561  df-1st 7671  df-2nd 7672  df-wrecs 7930  df-recs 7991  df-rdg 8029  df-er 8272  df-map 8391  df-en 8493  df-dom 8494  df-sdom 8495  df-sup 8890  df-pnf 10666  df-mnf 10667  df-xr 10668  df-ltxr 10669  df-le 10670  df-sub 10861  df-neg 10862  df-div 11287  df-nn 11626  df-2 11688  df-3 11689  df-n0 11886  df-z 11970  df-uz 12232  df-rp 12378  df-seq 13365  df-exp 13426  df-cj 14450  df-re 14451  df-im 14452  df-sqrt 14586  df-abs 14587  df-met 20085 This theorem is referenced by:  cnxmet  23378  cnfldms  23381  remet  23395  xrsdsre  23415  lebnumii  23571  cncmet  23926  cncms  23959  ovolctb  24094  dvlog2lem  25243  cnrrext  31361  cntotbnd  35234  iccbnd  35278  sblpnf  41012 Copyright terms: Public domain W3C validator

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## Physics 90) You take a picture of a rainbow with an infrared camera, and your friend takes a picture at the same time with visible light. (a) Is the height of the rainbow in the infrared picture greater than, less than, or the same as the height of the rainbow in the visible-light picture? (b) choose the best explanation from among the following: I. The height will be greater because the top of rainbow is red, and so infrared light would be even higher. II. The height will be less because infrared light is below the visible spectrum. III. A rainbow is the same whether seen in visible light or infrared; therefore the height is the same.

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## Do My Buffons Needle Class A "Buffons Needle Class" QE" is a standard mathematical term for a generalized constant expression which is utilized to resolve differential equations and has options which are regular. In differential Class solving, a Buffons Needle function, or "quad" is used. The Buffons Needle Class in Class type can be expressed as: Q( x) = -kx2, where Q( x) are the Buffons Needle Class and it is an important term. The q part of the Class is the Buffons Needle continuous, whereas the x part is the Buffons Needle function. There are four Buffons Needle functions with proper solution: K4, K7, K3, and L4. We will now take a look at these Buffons Needle functions and how they are fixed. K4 - The K part of a Buffons Needle Class is the Buffons Needle function. This Buffons Needle function can also be written in partial portions such as: (x2 - y2)/( x+ y). To solve for K4 we multiply it by the correct Buffons Needle function: k( x) = x2, y2, or x-y. K7 - The K7 Buffons Needle Class has an option of the form: x4y2 - y4x3 = 0. The Buffons Needle function is then increased by x to get: x2 + y2 = 0. We then have to multiply the Buffons Needle function with k to get: k( x) = x2 and y2. K3 - The Buffons Needle function Class is K3 + K2 = 0. We then increase by k for K3. K3( t) - The Buffons Needle function equationis K3( t) + K2( t). We increase by k for K3( t). Now we increase by the Buffons Needle function which provides: K2( t) = K( t) times k. The Buffons Needle function is likewise called "K4" because of the initials of the letters K and 4. K indicates Buffons Needle, and the word "quad" is noticable as "kah-rab". The Buffons Needle Class is among the primary approaches of solving differential equations. In the Buffons Needle function Class, the Buffons Needle function is first increased by the proper Buffons Needle function, which will give the Buffons Needle function. The Buffons Needle function is then divided by the Buffons Needle function which will divide the Buffons Needle function into a real part and an imaginary part. This gives the Buffons Needle term. Lastly, the Buffons Needle term will be divided by the numerator and the denominator to get the ratio. We are left with the right-hand man side and the term "q". The Buffons Needle Class is an important principle to comprehend when fixing a differential Class. The Buffons Needle function is simply one technique to fix a Buffons Needle Class. The approaches for solving Buffons Needle equations include: singular worth decomposition, factorization, ideal algorithm, mathematical option or the Buffons Needle function approximation. ## Hire Someone To Do Your Buffons Needle Class If you wish to become familiar with the Quartic Class, then you need to first start by looking through the online Quartic page. This page will show you how to utilize the Class by utilizing your keyboard. The explanation will likewise show you how to create your own algebra equations to assist you study for your classes. Before you can understand how to study for a Buffons Needle Class, you need to first comprehend making use of your keyboard. You will find out how to click the function keys on your keyboard, along with how to type the letters. There are 3 rows of function keys on your keyboard. Each row has 4 functions: Alt, F1, F2, and F3. By pushing Alt and F2, you can increase and divide the value by another number, such as the number 6. By pushing Alt and F3, you can utilize the 3rd power. When you press Alt and F3, you will enter the number you are trying to increase and divide. To multiply a number by itself, you will press Alt and X, where X is the number you want to multiply. When you press Alt and F3, you will key in the number you are attempting to divide. This works the same with the number 6, except you will just key in the two digits that are six apart. Lastly, when you push Alt and F3, you will use the fourth power. However, when you press Alt and F4, you will use the actual power that you have actually discovered to be the most appropriate for your problem. By utilizing the Alt and F function keys, you can increase, divide, and after that utilize the formula for the 3rd power. If you need to increase an odd variety of x's, then you will require to enter an even number. This is not the case if you are trying to do something complex, such as increasing 2 even numbers. For instance, if you want to multiply an odd variety of x's, then you will require to enter odd numbers. This is particularly real if you are trying to figure out the response of a Buffons Needle Class. If you want to transform an odd number into an even number, then you will need to press Alt and F4. If you do not know how to multiply by numbers on their own, then you will require to use the letters x, a b, c, and d. While you can multiply and divide by utilize of the numbers, they are a lot easier to utilize when you can look at the power tables for the numbers. You will have to do some research study when you first begin to utilize the numbers, however after a while, it will be second nature. After you have produced your own algebra formulas, you will be able to develop your own reproduction tables. The Buffons Needle Formula is not the only way to fix Buffons Needle formulas. It is essential to discover trigonometry, which uses the Pythagorean theorem, and then use Buffons Needle formulas to fix problems. With this technique, you can learn about angles and how to fix problems without having to take another algebra class. It is essential to try and type as quickly as possible, due to the fact that typing will assist you learn about the speed you are typing. This will assist you write your responses much faster. ## Hire Someone To Take My Buffons Needle Class A Buffons Needle Class is a generalization of a linear Class. For instance, when you plug in x=a+b for a given Class, you obtain the value of x. When you plug in x=a for the Class y=c, you obtain the worths of x and y, which provide you an outcome of c. By using this basic idea to all the formulas that we have tried, we can now fix Buffons Needle equations for all the values of x, and we can do it quickly and effectively. There are many online resources readily available that provide complimentary or budget friendly Buffons Needle formulas to solve for all the worths of x, including the cost of time for you to be able to take advantage of their Buffons Needle Class task aid service. These resources generally do not need a subscription cost or any type of financial investment. The answers provided are the result of complex-variable Buffons Needle formulas that have been resolved. This is likewise the case when the variable used is an unknown number. The Buffons Needle Class is a term that is an extension of a linear Class. One advantage of using Buffons Needle equations is that they are more general than the linear formulas. They are simpler to fix for all the worths of x. When the variable utilized in the Buffons Needle Class is of the type x=a+b, it is easier to fix the Buffons Needle Class due to the fact that there are no unknowns. As a result, there are fewer points on the line defined by x and a continuous variable. For a right-angle triangle whose base points to the right and whose hypotenuse points to the left, the right-angle tangent and curve graph will form a Buffons Needle Class. This Class has one unknown that can be discovered with the Buffons Needle formula. For a Buffons Needle Class, the point on the line specified by the x variable and a continuous term are called the axis. The presence of such an axis is called the vertex. Because the axis, vertex, and tangent, in a Buffons Needle Class, are a given, we can find all the values of x and they will sum to the given values. This is attained when we use the Buffons Needle formula. The element of being a constant factor is called the system of equations in Buffons Needle equations. This is sometimes called the central Class. Buffons Needle equations can be fixed for other values of x. One method to resolve Buffons Needle equations for other worths of x is to divide the x variable into its aspect part. If the variable is given as a positive number, it can be divided into its aspect parts to get the regular part of the variable. This variable has a magnitude that is equal to the part of the x variable that is a continuous. In such a case, the formula is a third-order Buffons Needle Class. If the variable x is negative, it can be divided into the very same part of the x variable to get the part of the x variable that is multiplied by the denominator. In such a case, the formula is a second-order Buffons Needle Class. Solution aid service in fixing Buffons Needle equations. When utilizing an online service for solving Buffons Needle formulas, the Class will be fixed quickly.

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# 常用表示数量关系的前缀_图文 Unit 2 Simulation of Random Variables ?Words and expressions ?Text and notes ?Grammar ?Exercises ?Reading material Words and expressions ? ? ? ? ? ? ? ? ? ? ? Advocate Alternative Argument Concentration Converge Deficiency Derivative Die Differentiable Disperse Facility Words and expressions ? ? ? ? ? ? ? ? ? ? ? Histogram Inference Interpretation Profile Proportion Pseudo-random Refraction Stabilize Statistical Stochastic Successive Words and expressions ? ? ? ? ? ? ? ? ? ? ? ? ? Toss v./n. 投，掷 Underlie v. 位于…之下，成为…的基础 By means of 依靠 Consist of 由…组成 Give rise to 引起，使发生 In contrast with 和…形成对比[对照] In terms of 根据，按照，用…的话，在…方面 Bernoulli distribution 伯努利分布 Binomial distribution 二项式分布 Normal distribution 正态分布 Poisson distribution 泊松分布 Probability density function 概率密度函数(abbr. pdf) Uniform distribution 均匀分布 Text and notes ? ? Interpretations of probability ? Random variables: definition; discrete random variables; continuous random variables ? Random variables for simulation Text and notes ? This concept of probability is of an objective quantity that applies to each observation and measure (in a relative way) how likely it is to fall into the corresponding class. ? Text and notes ? It seems that one is forced into a subjective view of the uncertainties, but the probability figures that emerge must obey certain rules in order to be consistent. ? Text and notes ? For engineering students it is most appropriate to keep the first interpretation-that of probability as an idealized proportion-in mind when studying the theory. ? Text and notes ? This may seem a hopeless requirement, considering that computer programs are sequences of deterministic instructions running on deterministic hardware. ? Text and notes ? The successive variables ?U1,U2 , ? appear to be uncorrelated, and, although there is some structure in the sequence (and indeed the sequences will eventually repeat itself), it is rare for these deficiencies to cause problems in practice. ? Grammar－专业英语词汇的构成 ? ? ? ? ? 1、派生法（Derivation） ? ? ? ? ? ? ? ? ? ? 1、派生法（Derivation） ? ? ? ? ? ? ? ? ? ? ? ? multi-/poly-:多?multipurpose, polynomial(多项式) non-:非、不?nonlinear, nondestructive post-:后?postgraduate, posterior pre-:预先?preset, preface re-:再、反、重新?reaction, readjust, reverse sub-:次于、在下?subroutine（子程序）, subscript super-:超，在上?superconductor, superposition（重合， 叠加） sym-/syn-:相同?symmetry, synchronous tele-:远离?telephone, telegraph trans-:跨、移?transmitter, transverse（横）, transform ultra-:外、极、超?ultrasonic（超声波）, ultraviolet ray(紫外线) un-:不?unable, unavoidable, unstable 1、派生法（Derivation） ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 1、派生法（Derivation） ? ? ? ? ? ? ? ? ? ? 1、派生法（Derivation） ? ? ? ? ? ? ? ? ? ? 1、派生法（Derivation） ? ? ? ? ? ? ? 1、派生法（Derivation） ? ? ? ? ? ? ? ? ? ? ? ? ? 2、复合法（composition） ? ? 直接结合：breakthrough, overestimate, bandwidth ? 连字符：general-purpose(多用途的)， stateof-the-art(达到最新技术发展水平的) 3、转化法（conversion） ? 4、拼缀法（blending） ? ? Transistor=transfer+resistor ? modem=modulator+demodulator 5、缩略法（shorting） ? (radio detection and ranging) 雷达 ? GPS (global positioning system) 全球定位系统 ? ? 主谓关系：被修饰的名词多数来自不及物动词和形容 ? 动宾关系：被修饰的名词必定来自于及物动词 ? The questions of convergence are not simple, and their study forms an important chapter in modern analysis. ? Many scientists have worked at the theory of magnetism since its discovery. ? ? ? ? ? ? 1. 2. 3. 4. ? 1. 2. A 随B 变化的曲线图 the graph (plot) of A as a function of B the graph (plot) of A versus (against) B the graph (plot) of the dependence of A on (upon) B the graph (plot) of the variation of A with B 这理论来源于 …… The theory comes (stems, emerges, originates) from …… The theory is obtained (provided, furnished) from …… ? 1. 2. ? 1. 2. 3. 4. ? ? ? ? A poster ? Poster of Crowd saliency (ECCV2014) ? Exercises 1. Choose the best answer for each of the following questions. (1) The theoretical foundation for the subject of statistics is contained in c . a. histogram b. the concept of probability c. the theory of probability d. decision-making and expert system Exercises (2) For engineering students it is most appropriate to keep the first interpretation – that of probability as an idealized proportion – in mind when studying the theory. What does “that” mean in the sentence? c . a. theory b. concept c. interpretation d. study Exercises (3) Find which is not an example of random variables b . a. the number of students attending class b. the number of bits used to denote ASCII codes c. the lifetime of a battery d. the waiting time at the crossroad Exercises (4) In general, the behavior of a continuous random variable is described by a d . a. distribution function b. probability function c. probability distribution d. probability density function Exercises (5) Random variables with different distributions can be generated c . a. by Monte Carlo numerical methods b. from an Gaussian distributed random sequence c. from uniformly distributed pseudorandom sequence d. based on the central limit theorem Exercises 2. Match the word pairs, one from Column A and one from Column B. Column A 1.random 2.expert 3.probability 4.densiy 5.computer 6.sample 7.statistical 8.impossible 9.standard 10.relative Column B a. space b. frequency c. simulation d. deviation e. function f. variable g. distribution h. event i. system j. inference Exercises 3. Translate the following sentences into Chinese. (1) A lot of information is required to specify the exact distribution of a random variable, and even more to specify the joint distribution of two or more variables. (2) The binomial and Poisson are discrete distributions, which have the widest applications among all discrete random variables. The probability distribution is especially useful to engineers because of its importance in statistical quality control. Exercises 3. Translate the following sentences into Chinese. (3) For any random variable the difference between the values of the distribution function at two pints is the probability that a value of the random variable will lie between those two points (or is equal to the upper one). (4) In general, the probability p of a random event can be interpreted as meaning that if the experiment is repeated a large number of times, the event would be observed about 100p percent of the time. Exercises 3. Translate the following sentences into Chinese. (5) In statistics it is customary to refer to any process of observation as an experiment. (6) If an event definitely cannot occur upon realization of the set of conditions it is called impossible. Exercises 4. Complete the sentences. You may have to change some words slightly. (1) Electronics _________ is the study and use of electrical devices that operate by controlling the flow of electron _______ or other ___________ electronically charged particle in devices such as vacuum tube and semiconductors. a. electron b. electronic c. electronics d. electronically Exercises (2) One of the best known computer ________ simulation which are very widely used in research, design and training is the flight simulator _______ upon which pilots receive much of their training. a. simulation b. simulator c. simulating d. simulate amplified (3) Signals are sent to amplifiers ________ to be __________. a. amplification b. amplifier c. amplifying d. amplify Exercises (4) (a) It follows that we can use the one table for the standard variates normal for all calculations involving normal _______. (b) However, a great many applications of probability theory concern quantitative variables _______ rather than qualitative events. (c) There are two approaches to measuring the _______ variation of random variables around their central values. The most variance a weighted important such measure is the _______, sum of sequential differences between the possible values and the mean. Exercises (d) Frequency response will be flat and bandwidth infinite because AC will be simply a rapidly ______ varying DC level to the ideal amplifier. a. various b. variable c. variate d. variance e. variation f. varying ? ? 1. 2. The central limit theorem Two parts: The normal distribution The central limit theorem New words ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Approximation 近似值 Arbitrary 任意的 Cumulative 累积的 Mean 均值 Parameter 参数 Population 总体 Robust 稳定的，(-ness，鲁棒性，稳定性) Symmetrical 对称的，均匀的(名词 symmetry) Tabulate 把…制成表格，列数 Variance 方差 Variate 变量 Independent identically distributed 独立同分布(abbr. i.i.d.) Standard deviation 标准偏差 Standard normal distribution 标准正态分布(均值为0，方差为1) Statistical inference 统计推理 Assignment Do exercises 1,2 ,3 and 4 in page 23; ? Read the reading material. ? Note: this passage is related with the probability theory which you will study. ? ? ? ? ? ? ? ? ? ? ? ? ? ? CPU: central processing unit ROM: read-only memory RAM: random access memory CDMA: Code Division Multiple Access GPS: Global Position System GPRS: General Packet Radio Service SNR: Signal Noise Ratio DSP: Digital Signal Processing DIP: Double In-line Package IC: Integrated Circuit PCB: Print Circuit Board GSM: Global System of Mobile Communications EDA: Electronic Design Automation

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# What Is 135% Of The Federal Poverty Level 2020? ## What is considered poverty level in 2020? 2020 POVERTY GUIDELINES FOR THE 48 CONTIGUOUS STATES AND THE DISTRICT OF COLUMBIAPersons in family/householdPoverty guideline1\$12,7602\$17,2403\$21,7204\$26,2005 more rows•Jan 21, 2020. ## How do you calculate federal poverty level? To calculate the percentage of poverty level, divide income by the poverty guideline and multiply by 100. ## Is federal poverty level based on gross income? The federal poverty guidelines, also known as the federal poverty level (FPL), are used to measure a household’s poverty status depending on your income. But not just the income you take home—your FPL is based on your modified adjusted gross income. ## What state is the poorest in the US? States, federal district, and territoriesRankStateSupplemental Poverty Measure (2017–2019 average) (Geographically Adjusted)-United States11.7%1New Hampshire8.3%2Utah8.0%3Maryland12.0%50 more rows ## What is the federal poverty level for one person? For families/households with more than 8 persons, add \$5,220 for each additional person….HHS Poverty Guidelines for 2021.2021 POVERTY GUIDELINES FOR THE 48 CONTIGUOUS STATES AND THE DISTRICT OF COLUMBIAPersons in family/householdPoverty guideline1\$12,8802\$17,4203\$21,9606 more rows•Jan 15, 2021 ## What is 150% of the federal poverty level for 2020? 48 Contiguous States and D.C.Persons in Household48 Contiguous States and D.C. Poverty Guidelines (Annual)100%150%1\$12,760\$19,1402\$17,240\$25,8603\$21,720\$32,5806 more rows•Aug 23, 2020 ## What is the poverty rate in the US 2020? 9.2 percentWe project that the poverty rate for 2020 will be 9.2 percent, with the rate for white, non-Hispanic people at 6.6 percent; the rate for Black, non-Hispanic people at 15.2 percent; and the rate for Hispanic people at 13.8 percent. ## What are the Obamacare income limits for 2020 for a family of 2? 48 Contiguous States and Washington DCNumber of persons in household2020 coverage2021 coverage1\$12,490\$12,7602\$16,910\$17,2403\$21,330\$21,7204\$25,750\$26,2001 more row•Jan 29, 2021 ## What percentage of Americans make over 100k? Percentage distribution of household income in the U.S. in 2019Annual household income in U.S. dollarsPercentage of U.S. households75,000 to 99,99912.3%100,000 to 149,99915.5%150,000 to 199,9998.3%200,000 and over10.3%5 more rows•Jan 20, 2021 ## What is 300% of the federal poverty level? Percentages Over 2021 Poverty GuidelinesFamily Size100%300%1\$12,880\$38,6402\$17,420\$52,2603\$21,960\$65,8804\$26,500\$79,50013 more rows ## What is 100 percent of the federal poverty level? 48 Contiguous States# of Persons in Household2021 Federal Poverty Level for the 48 Contiguous States (Annual Income)100%133%1\$12,880\$17,1302\$17,420\$23,1693\$21,960\$29,2076 more rows•Jan 26, 2021 ## What is 125% federal poverty level? Sponsor’s Household Size100% of HHS Poverty Guidelines*125% of HHS Poverty Guidelines*2\$17,420\$21,7753\$21,960\$27,4504\$26,500\$33,1255\$31,040\$38,8005 more rows•4 days ago ## What is considered a low income family? People earning more than 50% but less than 80% of the NSW or Sydney median income are described as earning a low income. ## What state has the highest poverty rate 2020? States With the Highest Poverty RatesMississippi.New Mexico.Louisiana.West Virginia.Arkansas.Kentucky.Alabama.Oklahoma.More items…•Sep 26, 2019

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# ULTIMATE SYMMETRY: Fractal Complex-Time and Quantum Gravity # IV.4.4 The Sexagesimal System Since the Sumerians divided the celestial orbs into twelve zodiac signs, they divided the orb into 360 degrees, so each zone spans 30 degrees from the celestial orb. If we consider a circle whose diameter equals one meter, the length of the thirty-degrees arc will be equal to one Cubit: . This calculation, however, is not accurate, because the Meter should be defined according to the Cubit and not the opposite, since the definition of the Meter suffered slight variations as we have seen in section I.2.2 above. The problem is that we don t have any precise value of the length of Cubit used in ancient systems, because various civilizations used slightly different cubits. The Egyptian Royal Cubit is the earliest attested standard measure, but the Cubit rods that have survived range from  to  meters. Nevertheless, even with the current conventional measurement units, when we make a pendulum with one meter length and we displace its mass with a small angle or distance, it will take almost exactly one second to return to its original equilibrium position, because: , where  is the gravitational acceleration due to gravity, as shown in Figure IV.11. Figure IV.11: The Cubit, the Meter and the Second are related through the motion of the Pendulum. A circle whose radius is one Meter, its circumference equals twelve Cubits, and when the length of a Pendulum is one Meter and the mass is displaced, it will take one Second to return to its equilibrium position. These definitions are NOT exact because these standard units have suffered various alterations throughout history, and it is not known exactly what is the ultimate reference. The Meter was originally defined in 1793 as one ten-millionth of the distance from the Equator to the North Pole. In 1799, it was redefined in terms of a prototype Meter bar, which was changed in 1889, and in 1960, it was redefined in terms of the wavelength of a certain emission line of krypton-86. Before that, in 1670-5, the Meter was suggested as the length of a pendulum with a one-second period, but the French Academy of Sciences selected the meridional definition over the pendular definition because the force of gravity varies slightly over the surface of the Earth, which affects the period of a pendulum. The current definition was adopted in 1983 as the length of the path traveled by light in a vacuum in  seconds. It may appear that the original 1670 definition of the meter, as the length of a pendulum with a one-second period, is purely conventional, and so it has been replaced in 1793 by the meridional definition, as one ten-millionth of the distance from the Equator to the North Pole, which also may appear to be purely conventional. However, whether the scientists who proposed these definitions knew it or not, this standard measurement system is fundamentally related to the ancient sexagesimal system and the physical properties of the Earth, through the pendulum parameters, as Figure IV.11. So clearly there is a very strong correlation between the sexagesimal system, which is still being used in measuring time, and the length of Meter and the gravity of the Earth. It is also evident that these and other fundamental numbers, such as  and , the golden ratio, have been clearly encoded in the dimensions and position of the Pyramids of Giza, such as the latitude of the Grand Gallery in the Great Pyramid of Giza () which coincides exactly with the value of the value of the speed of light in vacuum. The sexagesimal numeral system, with sixty as its base, was originated by the Sumerians, and continued to be used by the ancient Babylonians. In modern times, the decimal system is used for general computations, but the sexagesimal is still used in measuring angles, geographic coordinates, and time. The number 60, is a superior highly composite number. It has twelve numbers distinctive factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60, which means that many fractions involving sexagesimal numbers can be simplified when expressed in the sexagesimal system. That is why it is still quite convenient in expressing time, because one hour can be divided evenly into durations of 30, 20, 15, 12, 10, 6, 5, 4, 3, 2, and 1 minutes. In many ancient texts, the sexagesimal is used most uniformly and consistently in mathematical tables of data, because of its mathematical advantages for writing and calculating fractions. Ptolemy used the base 60 to express the fractional parts of numbers in his Almagest. In particular, his table of chords, which was essentially the only extensive trigonometric table for more than a millennium, has fractional parts in base 60. Infinity can be described as a recursive loop, that recurs indefinitely, such as the squaring or integrating curves. This concept is like confining an unlimited spirit into a body. Contemporary computer science uses this kind of recursion to model the fractal structures in nature, such as Koch Snowflake fractal in Figure I.2. Figure IV.12: The Babylonian sexagesimal system is based on dividing the circle into 360 degrees, and each degree into 60 seconds. The circle is also divided into 12 zones, each of 30 degrees span. # Other Pages Related to Search Keywords: • ... Space Transcendence Read this short concise exploration of the Duality of Time Postulate: DoT: The Duality of Time Postulate and Its Consequences on General Relativity and Quantum Mechanics ... • ## ... Ancient Babylonia =>: • ... exactly with the value of the value of the speed of light in vacuum. The sexagesimal numeral system, with sixty as its base, was originated by the Sumerians, and continued to be used by the ancient Babylonians. In modern times, the decimal system is used for general computations, but the s ... • ## ... Physical Properties =>: • ... ventional. However, whether the scientists who proposed these definitions knew it or not, this standard measurement system is fundamentally related to the ancient sexagesimal system and the PHYSICAL PROPERTIES of the Earth, through the pendulum parameters, as Figure IV.11. So clearly there ... • ## ... Fractal Structure =>: • ... efinitely, such as the squaring or integrating curves. This concept is like confining an unlimited spirit into a body. Contemporary computer science uses this kind of recursion to model the FRACTAL STRUCTURE s in nature, such as Koch Snowflake fractal in Figure I.2. Figure IV.12: The Babylo ... • ## ... Celestial Orbs =>: • ... and Quantum Mechanics ... • ## ... Koch Snowflake =>: • ... egrating curves. This concept is like confining an unlimited spirit into a body. Contemporary computer science uses this kind of recursion to model the fractal structures in nature, such as Koch Snowflake fractal in Figure I.2. Figure IV.12: The Babylonian sexagesimal system is based on di ... • ## ... Fractal Structures =>: • ... efinitely, such as the squaring or integrating curves. This concept is like confining an unlimited spirit into a body. Contemporary computer science uses this kind of recursion to model the FRACTAL STRUCTURES in nature, such as Koch Snowflake fractal in Figure I.2. Figure IV.12: The Babylo ... • ## ... Zodiac Signs =>: • ... ATE SYMMETRY: Fractal Complex-Time and Quantum Gravity by Mohamed Haj Yousef Search Inside this Book IV.4.4 The Sexagesimal System Since the Sumerians divided the celestial orbs into twelve ZODIAC SIGNS , they divided the orb into 360 degrees, so each zone spans 30 degrees from the celestia ... • ## ... Decimal System =>: • ... speed of light in vacuum. The sexagesimal numeral system, with sixty as its base, was originated by the Sumerians, and continued to be used by the ancient Babylonians. In modern times, the DECIMAL SYSTEM is used for general computations, but the sexagesimal is still used in measuring angl ... • ## ... Meter Length =>: • ... tandard measure, but the Cubit rods that have survived range from  to  meters. Nevertheless, even with the current conventional measurement units, when we make a pendulum with one METER LENGTH and we displace its mass with a small angle or distance, it will take almost exactly on ... • ## ... Ancient System =>: • ... site, since the definition of the Meter suffered slight variations as we have seen in section I.2.2 above. The problem is that we don t have any precise value of the length of Cubit used in ANCIENT SYSTEM s, because various civilizations used slightly different cubits. The Egyptian Royal Cu ... • ## ... Twelve Zodiac =>: • ... cs ... The science of Time is a noble science, that reveals the secret of Eternity. Only the Elites of Sages may ever come to know this secret. It is called the First Age, or the Age of ages, from which time is emerging. Ibn al-Arabi [The Meccan Revelations: Volume I, page 156. - Trns. Mohamed Haj Yousef] ### The Sun from the West: Welcome to the Single Monad Model of the Cosmos and Duality of Time Theory ### Message from the Author: I have no doubt that this is the most significant discovery in the history of mathematics, physics and philosophy, ever! By revealing the mystery of the connection between discreteness and contintuity, this novel understanding of the complex (time-time) geometry, will cause a paradigm shift in our knowledge of the fundamental nature of the cosmos and its corporeal and incorporeal structures.

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# Return the scalar dtype or NumPy equivalent of Python type of an object To return the scalar dtype or NumPy equivalent of Python type of an object, use the numpy.obj2sctype() method. The 1st parameter is the object of which the type is returned The default parameter, if given, is returned for objects whose types cannot be determined. If not given, None is returned for those objects. ## Steps At first, import the required library − import numpy as np To return the scalar dtype or NumPy equivalent of Python type of an object, use the numpy.obj2sctype() method − print("Using the obj2sctype() method in Numpy") Checking for int − print("Result...",np.obj2sctype(np.array([45, 89]))) print("Result...",np.obj2sctype(np.array([389, 7985]))) Checking for float − print("Result...",np.obj2sctype(np.float32)) print("Result...",np.obj2sctype(np.float64)) print("Result...",np.obj2sctype(np.array([5., 25., 40.]))) Checking for complex − print("Result...",np.obj2sctype(np.array([5.6j])) ## Example import numpy as np # To return the scalar dtype or NumPy equivalent of Python type of an object, use the numpy.obj2sctype() method. # The 1st parameter is the object of which the type is returned # The default parameter, if given, is returned for objects whose types cannot be determined. # If not given, None is returned for those objects. print("Using the obj2sctype() method in Numpy") # checking for int print("Result...",np.obj2sctype(np.array([45, 89]))) print("Result...",np.obj2sctype(np.array([389, 7985]))) # checking for float print("Result...",np.obj2sctype(np.float32)) print("Result...",np.obj2sctype(np.float64)) print("Result...",np.obj2sctype(np.array([5., 25., 40.]))) # checking for complex print("Result...",np.obj2sctype(np.array([5.6j]))) ## Output Using the obj2sctype() method in Numpy Result... <class 'numpy.int64'> Result... <class 'numpy.int64'> Result... <class 'numpy.float32'> Result... <class 'numpy.float64'> Result... <class 'numpy.float64'> Result... <class 'numpy.complex128'> Updated on: 24-Feb-2022 127 Views

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NTNUJAVA Virtual Physics LaboratoryEnjoy the fun of physics with simulations! Backup site http://enjoy.phy.ntnu.edu.tw/ntnujava/ August 16, 2020, 12:16:27 am "Wisdom is the harmony, healthy and happiness in life." ...Wisdom Pages: [1]   Go Down Author Topic: Similarity between RLC circuit and spring with damping  (Read 22816 times) 0 Members and 1 Guest are viewing this topic. Click to toggle author information(expand message area). Fu-Kwun Hwang Hero Member Offline Posts: 3085 « Embed this message on: October 11, 2009, 05:20:56 pm » posted from:Taipei,T\'ai-pei,Taiwan A mass m attached to a vertical spring (spring constant k) in gravity field: The above system can be described with $F=m a_y= mg -ky -b v_y$ or $m\frac{d^2y}{dt^2}+b\frac{dy}{dt}+ky=mg$ For a RLC circuit with DC source Vc: The above system can be described with $Vc=V_L+V_R+V_C$ or $L \frac{d^2Q}{dt^2}+I\frac{dQ}{dt}+\frac{Q}{C}=Vc$, where $I=\frac{dQ}{dt}, V_R=I R, V_C=Q/C , V_L=L\frac{dI}{dt}$ The differential equation are the same for the above two systems. So a damped spring system can be simulated with RLC circuit (or RLC circuit can be simulated with damped spring system,too!). Embed a running copy of this simulation Embed a running copy link(show simulation in a popuped window) Full screen applet or Problem viewing java?Add http://www.phy.ntnu.edu.tw/ to exception site list • Please feel free to post your ideas about how to use the simulation for better teaching and learning. • Post questions to be asked to help students to think, to explore. • Upload worksheets as attached files to share with more users. Let's work together. We can help more users understand physics conceptually and enjoy the fun of learning physics! springRLC.gif (19.7 KB, 819x524 - viewed 1532 times.) Logged mahi01 Newbie Offline Posts: -5 « Embed this message Reply #1 on: July 30, 2020, 10:05:31 pm » posted from:Delhi,Delhi,India mcafee antivirus is a commonly used antivirus that detects and kills PC infections, enables mail worms, Trojan programs, and so on, making your mcafee.com/activate  infrastructure free of infections and other malware day-to-day challenges. makes. For more accurate travel download www.mcafee.com/activate Mcafee Antivirus to protect your PC or PC from infection and ensure data. mcafee activation can be easily processed using the activation code from the mcafee retail card and using it online on the Mcafee website page. Click our mcafee.com/activate link for more information. Logged mahi01 Newbie Offline Posts: -5 « Embed this message Reply #2 on: July 30, 2020, 10:06:51 pm » posted from:Delhi,Delhi,India Mcafee activation can be easily processed using activation code from mcafee retail card and using it online on Mcafee Website page. you canmcafee activate enter code  download and activate security of your device online.mcafee antivirus is widely used a antivirus helps to detect and neutralize download mcafee with activation code computer virus, the mail worms,the trojan programs,and also helps  your system free of virus and This is very beneficial for you For more mcafee installation with product key  information by visiting our website Logged Pages: [1]   Go Up "Wisdom is the harmony, healthy and happiness in life." ...Wisdom

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# Sets of real Numbers ```Sets of real Numbers Warm Up Write all names that apply to each number. 1. 7 8 5. 0 2. 36 6. − 100 3. 24 7. 5. 45 4. 0.75 8. 18 − 6 • Clarify understanding of the real number system. • Characterize sets and subsets of the real numbers. • Identify sets for real-world situations. • Identify all of the possible subsets of the real numbers for a given number. • Decide whether a statement about a subset of the real numbers is true or false. • Identify the set of numbers that best describes a real world situation. Write all names that apply to each number. -10 12 3 • Real numbers are composed of rational and irrational numbers. • Whole numbers are rational numbers. Identify the set of numbers that best describe the situation. Explain your choice. • The amount of time that has passed since midnight. • The number of tickets sold to a basketball game. Knowing the types of numbers to expect in different situations can alert you to incorrect math as well as to impossible situations. For basketball is not possible, but an average number of shots can equal 13.5. 1 11 Ronald states that the number is not rational because when converted into a decimal, it does not terminate. Nathaniel says it is rational because it is a fraction. Which boy is correct? Explain. Irrational numbers can never be precisely represented in decimal form. Why is this? Exit Ticket 1. Write all the names that apply to −1. 5. 2. Tell whether the given statement is true or false. Explain your choice. All numbers between 1 and 2 are rational numbers. 3. Identify the set of numbers that best describes the situation. Explain your choice. The choices on a survey question change the total points for the survey by -2, -1, 0, 1, or 2 points. ```

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# Periodicity Edited by Jamie (ScienceAid Editor), Taylor (ScienceAid Editor) Periodicity has to do with the patterns of behaviour and properties that are seen in the periodic table. ### The Blocks The periodic table can be divided into various blocks based on the more advanced electron|configuration introduced at this level. There are the s, p and d blocks. An element is in the s-block, for example, if its outermost electron is in the s sub energy level. Elements in the same block have similar properties. For example, the transition metals are all in d-block. Under this heading, we will look at the properties of the elements in period 3 (Na, Mg, Al, Si, P, S, Cl, Ar) in atomic radius. The atomic radius of an atom is defined as half the distance between the nuclei of two covalently bonded atoms, (called the covalent radius) as shown in the diagram below. However, it is not possible to get this measurement for noble gases since they do not bond. So instead we use the Van der Waals radius. As you go along a period, the atomic radius decreases. This is because the increasing number of protons exerts more pull on the electrons and so moves them closer to the nucleus. Hence they take up less volume. ### Period 3: Electronegativity Electronegativity is the ability of an atom or molecule to attract electrons. Click here to see how this affects bonding. It is measured using the Pauling scale where fluorine is given a value of 4 (the highest) and Francium 0.7 the lowest. As you move along the period, the electronegativity increases as you can see in the below diagram. This trend is because as more protons are added and the nucleus' charge becomes higher, and the atom has more attractive power. Noble gases do not have electronegativity. ### Period 3: Conductivity Across period 3, conductivity of both electricity and heat is a story of two halves... Na, Mg, and Al all form metallic structures where the delocalized electrons can move freely and carry electronic charge or heat energy. Si, O, S, Cl and Ar however are insulators, this is because they bond covalently where the electrons are in a fixed position so cannot transfer electric charge or heat. APA (American Psychological Association) Periodicity. (2017). In ScienceAid. Retrieved Jan 24, 2018, from https://scienceaid.net/chemistry/fundamental/periodicity.html MLA (Modern Language Association) "Periodicity." ScienceAid, scienceaid.net/chemistry/fundamental/periodicity.html Accessed 24 Jan 2018. Chicago / Turabian ScienceAid.net. "Periodicity." Accessed Jan 24, 2018. https://scienceaid.net/chemistry/fundamental/periodicity.html. ScienceAid welcomes all comments. If you do not want to be anonymous, register or log in. It is free. ## Article Info Categories : Fundamental Recent edits by: Jamie (ScienceAid Editor)

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# What is the equation for wave pace? ## What is the equation for wave pace? So in a time of 1 interval, the wave has moved a distance of 1 wavelength. Combining this data with the equation for pace (pace = distance/time), it may be mentioned that the pace of a wave can be the wavelength/interval. ## How do you calculate wave pace and interval? Formulas and equations for frequency and wavelength The system for frequency is: f (frequency) = 1 / T (interval). f = c / λ = wave pace c (m/s) / wavelength λ (m). The system for time is: T (interval) = 1 / f (frequency). λ = c / f = wave pace c (m/s) / frequency f (Hz). ## How do you calculate the wavelength of a wave? How to calculate wavelength 1. Determine the frequency of the wave. For instance, f = 10 MHz . 2. Choose the speed of the wave. 3. Substitute these values into the wavelength equation λ = v/f . 4. Calculate the consequence. 5. You can even use this instrument as a frequency calculator. ## What is the system for wavelength and frequency? The frequency, f, is 1/T, so the equation relating wave pace, frequency, and wavelength is v = f λ . ## What is wavelength equal to? Wavelength is normally denoted by the Greek letter lambda (λ); it is the same as the pace (v) of a wave practice in a medium divided by its frequency (f): λ = v/f. ## What is wave frequency? Frequency, in physics, the variety of waves that cross a hard and fast level in unit time; additionally, the variety of cycles or vibrations undergone throughout one unit of time by a physique in periodic movement. ## Why is frequency V? It is NOT the letter v, it’s the Greek letter nu. It stands for the frequency of the sunshine wave. Frequency is outlined because the variety of wave cycles passing a hard and fast reference level in a single second. This is one cycle of the wave and if all that passed off in a single second, then the frequencey of the wave is 1 Hz. Gamma rays ## What is the frequency of a wave with a interval of 0.2 seconds? So, the frequency of the wave is 5 Hz. ## What is the frequency of a wave whose time interval is 0.05 seconds? Answer. The wave frequency is 20 Hz. ## How do you calculate the variety of waves? Frequency divided by the pace of sunshine is ν/c, which from the above equation is 1/λ. When wavelength is measured in metres, 1/λ represents the variety of waves of the wave practice to be present in a size of 1 metre or, if measured in centimetres, the quantity in a single centimetre. ## What is the frequency of this wave 1234? Since a longitudinal wave consists of 1 compression and 1 rarefaction due to this fact the frequency of the given wave is 2 Hz. ## What is the interval of a water wave with a frequency of 0.5 Hz? Answer: Frequency refers back to the variety of occurrences of a periodic occasion per time and is measured in cycles/second. In this case, there may be 1 cycle per 2 seconds. So the frequency is 1 cycles/2 s = 0.5 Hz. ## What type of frequency do radio waves have? Radio waves are a sort of electromagnetic (EM) radiation with wavelengths within the electromagnetic spectrum longer than infrared gentle. They have have frequencies from 300 GHz to as little as 3 okHz, and corresponding wavelengths from 1 millimeter to 100 kilometers. ## What is the speed of a wave that has a frequency of 400 Hz and a wavelength of 0.5 meters? • Therefore, the speed of the wave is 200 m/s. ## What is the interval of a wave whose frequency is 256 cycles per second? Frequency = 256 Hz. (a) Period = 1/frequency = 1/256 = 0.0039s. (b) Speed = 340m/s. Wavelength = pace/frequency = 340/256 = 1.33m. 4 Hz ## Which waves could be polarized? Only transverse waves could be polarized however longitudinal waves can’t be polarized. ## What is the pace of those waves? If the crest of an ocean wave strikes a distance of 20 meters in 10 seconds, then the pace of the ocean wave is 2.0 m/s. On the opposite hand, if the crest of an ocean wave strikes a distance of 25 meters in 10 seconds (the identical period of time), then the pace of this ocean wave is 2.5 m/s. ## What impacts wave pace? Waves and Energy: The pace of a wave is dependant on 4 elements: wavelength, frequency, medium, and temperature. Wave pace is calculated by multiplying the wavelength occasions the frequency (pace = l * f). Certain situations make the next calculations straightforward. pace is fixed in a given medium. ## What do you name the peak of a wave? wave is a known as the crest, and the low level known as the trough. The distance between successive crests or troughs known as the wavelength. The top of a wave is the amplitude.… ## What are 4 elements of a wave? Wave Crest: The highest a part of a wave. Wave Trough: The lowest a part of a wave. Wave Height: The vertical distance between the wave trough and the wave crest. Wave Length: The distance between two consecutive wave crests or between two consecutive wave troughs. ## What are the 8 elements of a wave? The fundamental properties (elements) of a wave embody: frequency, amplitude, wavelength and pace. Frequency is a measure of what number of waves cross some extent in a sure period of time. The larger the frequency, the nearer the waves are collectively and the better the power carried by the waves will probably be. ## What are the 2 kinds of waves? Waves are available two varieties, longitudinal and transverse. Transverse waves are like these on water, with the floor going up and down, and longitudinal waves are like of these of sound, consisting of alternating compressions and rarefactions in a medium. ## What are the most important kinds of waves? There are two fundamental kinds of wave movement for mechanical waves: longitudinal waves and transverse waves. The animations beneath display each kinds of wave and illustrate the distinction between the movement of the wave and the movement of the particles within the medium by means of which the wave is travelling. ## What are the 5 wave behaviors? All waves behave in sure attribute methods. They can endure refraction, reflection, interference and diffraction. These fundamental properties outline the behaviour of a wave – something that displays, refracts, diffracts and interferes is labelled a wave.

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# In hydrogen – like atom (z = 11), nth line of Lyman series has wavelength λ. The de- Broglie’s wavelength of electron in the level from which it originated is also λ. Find the value of n? Navjyot Kalra 9 years ago Hello Student, Note : nth line of Lyman series means electron jumping from (n + 1 )th orbit to 1st orbit. For an electron to revolve in (n + 1)th orbit. 2πr = (n + 1 )λ ⇒ λ = 2π / (n + 1) x r = 2π / (n + 1) [ 0.529 x 10-10] (n + 1)2 / Z ⇒ 1 / λ = Z / 2π [0.529 x 10-10] (n + 1) …(i) Also we know that when electron jumps from (n + 1)th orbit to 1st orbit 1/ λ = RZ2 [ 1 / 12 – 1 / (n + 1)2 = 1.09 x 107 Z2 [ 1 – 1 / (n + 1)2] From (i) and (ii) Z / 2π (0.529 x 10-10) (n + 1) = 1. 09 x 107 Z2 [1 – 1 / (n + 1)2] On solving, we get n = 24 Thanks Navjot Kalra

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# bit array ## [C++] An Interesting Bit Array Example Here is an interesting bit array task and its solution in C++ that I thought it’s worth to share with you. You are given four integers values: N, A, B, and C. You need to use them in order to create the sequence called bitArray with the following pseudo-code: Task: calculate the number of distinct integer in the bitArray sequence. Solution Input: four space separated integers on a single line, N, A, B, and C  respectively. Where N = 32, A = 16, B = 16, C = 16. Output: one integer that denotes the number of distinct integer in the bitArray sequence equals 7 as we set N, A, B, C values. If you’d like to read the input from the console simply comment out line 57 and 62 and toggle comment selection on line 58, 59, 60 and 61.

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# How to calculate surface roughness in disparity map? Hello! I am developing small project connected with security. I created simple face detection/recognition and stereo matching. So i have disparity map of the face region. The first disparity map belongs to real face, the second is photo of the face showed from the phone. I want to determine where is real and where not. i think that for this propose can be used something like "surface roughness", but i cant figure out how to calculate it. Please tell me the method can be used for calculate "surface roughness", or better way to do the same. Thanks! edit retag close merge delete If you are using a stereo camera (I suppose so), you need to let the cameras be really close one to each other to see such differences. Try with a printed photo to compare against it first of all, to see if you can cheat the system. I think that the first result that you can see is that using real face you get different results: The nose is darker, the eyes are blacked. But Stereo matching even if can be used for that, is not intended for that kind of use. In fact, if you use a human puppy and if you exploit only the depth you can probably have the same result. So... is the focus of your project recognize faces only using disparity map? ( 2019-08-06 10:26:08 -0500 )edit @HYPEREGO. thank you for quick reply. I have implemented stereo vision using two cameras and SGBM. I am also implemented face detection and recognition using DNNs. Now, i want to add some extra feature. As i can see, the disparity map of real face is more rough than fake, and i want to try implement some protection using this. But i do not know siautable algoritm for this task. Maybe i misstake and this method cannot give enogh accuracy, but i am experementing. ( 2019-08-06 11:04:54 -0500 )edit 2 You could try making a normalized histogram of depths over the whole image, or if you can somehow identify a face region or subface region (concentric circle regions?), histograms over those areas, normalize them, and look for some sort of interesting shape or metrics about the histogram curves. I'd think that the depths of a flat image of a face will have flat (linear) characteristics due to the correlations on a flat image, but the actual face will have bumps, You could also try using the depth maps to create contours based on lines across the image (slices down or across) and see how close (in a fuzzy logic way), they come to meeting the slice profiles of real faces. Beware glasses, beards, printed face masks, mannikins, pets, etc. ( 2019-08-06 20:46:00 -0500 )edit 1 @opalmirror, thank you for useful tip! i could calculate the histograms and histogram of real and fake faces. And they are differ considerably. Histogram of real face as you said had bumps, and fake had nearly one high line. You can see the histograms here real and fake. But now i do not know the algorithm for estimate this difference programmatically. Can you show me any suitable method, or where i can find information about it, please. ( 2019-08-07 03:28:55 -0500 )edit 1 Prostoi, I am sorry, this is an application area (not an opencv operational question). It's also not an area where I have not researched or have experience. I am unable to provide any detailed additional guidance. If it were me, I might try next: normalization of the global depth bias, face skew (face pitch, yaw. roll), scale (to standard size), maybe median filter, then comparison of depth data against known good and bad reference faces. Since you're more interested in classifying (is it a face? true/false) rather than grading (probability it might be a face or segmentation within the face area), this naturally leads to a Support-vector machine or CNN. Best of luck! ( 2019-08-07 13:31:56 -0500 )edit 1 @opalmirror, thank you! I tried to find any opencvs or mathematical algorithm, but totally forget about SVM. I already have experience with it - i used SVMs for face recognition and i think that i easily can implement fake-detector using SVM. I will post answer with my result. ( 2019-08-08 01:46:06 -0500 )edit Sort by ยป oldest newest most voted So. i solved my problem. Firstly i calculated histogram of face disparity map. Then i collected a small dataset with real and fake face histograms. After that i created SVM and trained it with dataset. And it works perfectly! But my first attempt was to use OpenCVs implementation of SVM and it works poor. So i used dlibs SVM and it works good with same parameters and dataset. All the code for it is in my github repository. And this is opencv version that not works, maybe you can tell me why. Thank you all for your help! more Thanks for posting your answer. So, the SVM decides "this histogram looks like the histogram from other faces, and not like the histogram from other non-faces". That's pretty cool. Glad I was able to help. If you like, you could open a new question comparing the working (dlib) and non-working (opencv) SVM code, with input and output data showing the problem. I know of SVMs but have never implemented one, so maybe that could interest other answers for you. ( 2019-08-09 14:47:04 -0500 )edit Oh, if you are satisfied with your own answer, you can mark it correct too, more karma points. :) ( 2019-08-09 15:00:09 -0500 )edit 1 @opalmirror, thank you for supporting and feedback! I solved my problem with SVM when i maked sample code for question and this sample code works cool! That maybe means problem in me, not in OpenCV. But maybe not. So, if you want to view the code - here is that sample and here is not working code. And i cannot mark my answer correct because it require 20 reputation but i do not have enough. Thanks to all for supporting! ( 2019-08-10 07:23:13 -0500 )edit 1 I will go ahead and mark it correct for you then. Thanks for contributing a good question, discussion, and answering it on the forum. :) ( 2019-08-12 13:21:56 -0500 )edit Official site GitHub Wiki Documentation

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Browse Plans New Plans # Decimal To Fraction Worksheet Pdf Peating Convert Changing By Cameron Dyett at April 15 2019 08:58:27 What are the Features of a Worksheet? _ Worksheets provide Excel users with many features. The primary feature provided by worksheets is the ability to store edit and manipulate data in one central location. However, with the creation of worksheets users can now calculate many simple and complex math and financial problems as well as display their stored data with many unique custom charts and graphs. If the materials do not specifically indicate "brain_based," determine if they are at least "brain_friendly." This would mean that you are looking for lots of color, material interesting to the child, many varied activities_especially involving movement, and using several of the senses. I saw one company whose worksheets included the instruction to "say the number out loud as you..." This is very good! Speaking out loud is very important for learning to occur. Ideally, all worksheets should include this instruction. If you can't find any that do, then you need to add that instruction yourself. NEVER use "skill and drill" worksheets. These are the worksheets just made up of columns of problems. There are better materials out there, so don't resort to skill and drill. The very worst problem of skill and drill worksheets is the greatly increased chance of a practiced mistake. The same problem will likely appear several times on the same sheet. A wrong answer once means a wrong answer several times; and a practiced mistake takes hundreds of correct repetitions to fix. This danger alone is important enough to never use any worksheet. I am quite serious about how difficult it is to repair a practiced mistake. Learning is hard enough. Re_learning is much more difficult. ## Decimal To Fraction Worksheet Pdf Convert Im ### Worksheet Decimal To Fraction Pdf Recurring #### Decimal To Fraction Worksheet Pdf Peating Co ##### Decimal To Fraction Worksheet Pdf Ideas Of O ###### Worksheet E Decimal To Fraction Pdf Grade Re One of the features of Excel that is often overlooked is working with grouped worksheets. When you group the worksheets within a workbook, you can perform operations to several worksheets at one time. This eliminates the necessity of doing the same operation over and over to different worksheets. To group worksheets which are next to each other in the workbook: Click on the sheet tab for the first worksheet. Hold the Shift Key. Click on the last sheet tab to be included in the group. To group worksheets which are not right next to each other: Click on the sheet tab for the first worksheet. Hold the Control Key. Click on each sheet tab to be included in the group

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# How To Show Percentage Increase In Excel Percent Increase In Excel Percent Change Excel Formula Excel Formula For Percentage Increase Between Two Numbers How To Show Percentage Increase In Excel Graph how to show percentage increase in excel percent increase in excel percent change excel formula excel formula for percentage increase between two numbers how to show percentage increase in excel graph. show percentage difference excel how to increase in graph formula percent decrease calculate percentages tech advisor,how do you show percentage increase in excel i change to,show percentage change excel formula percent between two numbers find in how to increase decrease,how to show percentage increase in excel graph by calculate percent formula decrease difference between 2 numbers,formula to show percent increase decrease excel percentage difference between two numbers,show percent increase decrease excel change percentage how do i in to graph,excel formula to show percentage difference between two numbers calculate change percent increase 2,show percentage increase excel formula percent how function to decrease difference,how do i show percentage increase in excel formula to between two numbers line graph difference,show percentage difference in excel chart of change decrease formula to how do i increase.

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Computing Future Values The Future Values Class COSC 1336 Lab 3: Computing Future Values The FutureValues Class Objectives Call methods with parameters and return values.Use the Math class.Use Scanner to input values. Hand-in Requirements All projects and laboratories will be submitted electronically through Canvas. Zip up your entire lab directory to submit as the source. (Right click on the lab folder and followSend To > Compressed (zipped) Folder or 7-Zip > Add to “lab3.zip”.) The lab folder should include the following: FutureValues.javaFutureValuesOutput.txt Tasks Write a program that printsLab 3 written by YOURNAME and calls two methods. 1.Compute and return the future value of an account based on the present value of the account, the interest rate, and the number of years.2.Compute and return the future value of an annuity based on the payment per year, the interest rate, and the number of years. For each method, the main method needs to obtain input from the user, call the method with the input values, save the result of the method in a local variable, and print the inputs and the result. DetailsFuture Value Using Compound Interest If thepresent valueof an account is \$1000 and the interest rate is 5%, then after one year, the account will increase by \$50 (5% of \$1000). In the second year, the interest applies to all \$1050, so the account will increase by \$52.50 (5% of \$1050). Getting future interest on past interest is calledcompound interest. A general formula for future value assumingpis the present value,ris the interest rate, andyis the number of years is: future value =p* (1 r/100)yYour method should have the following characteristics: It should have three double parameters:present value interest rate number of yearsIt should return a double, the future value.It should use Math.pow in the calculation.It shouldnothave any print statements. The main method should do all the printing. For examples with similar characteristics, see the hypotenuse method in the book and the max3 method in the lecture notes. Future Value of an Annuity For a typical annuity, you pay a certain amount every year (or some other period of time) for so many years, and an interest rate is applied to your payments. It’s like a bank account where you deposit money regularly and wait several years to withdraw anything. In return, you are guaranteed a certain interest rate. For example, suppose the payment is \$100 by the end of each year and the interest rate is 5%. In the first year, your annuity will be worth \$100. In the second year, you get \$5 interest (5% of \$100), and you make a payment of \$100, so the annuity will be worth \$205 after two years. In the third year, you get \$10.25 interest (5% of \$205), and you make another payment of \$100, so the annuity will be worth \$315.25 after three years. A general formula for the future value of an annuity assumingpis the yearly payment,ris the interest rate, andyis the number of years is: future value =p* (1 r/100)y 1 r/100Your method should have the following characteristics: It should have three double parameters:yearly payment interest rate number of yearsIt should return a double, the future value.It should use Math.pow in the calculation.It shouldnothave any print statements. The main method should do all the printing. For examples with similar characteristics, see the hypotenuse method in the book and the max3 method in the lecture notes. Printing Money When you are printing doubles, you will find out that Java often prints a lot of decimal places. To print out your monetary amounts as reasonable looking Strings, try the following method in your lab. // Returns a String \$dollars.cents rounded to the nearest cent. // For example, moneyString(12.3456) returns “\$12.35”. public static String moneyString(double amount) { DecimalFormat dollarsAndCents = new DecimalFormat(“\$ Calculate the price of your order 550 words We'll send you the first draft for approval by September 11, 2018 at 10:52 AM Total price: \$26 The price is based on these factors: Academic level Number of pages Urgency Basic features • Free title page and bibliography • Unlimited revisions • Plagiarism-free guarantee • Money-back guarantee • 24/7 support On-demand options • Writer’s samples • Part-by-part delivery • Overnight delivery • Copies of used sources • Expert Proofreading Paper format • 275 words per page • 12 pt Arial/Times New Roman • Double line spacing • Any citation style (APA, MLA, Chicago/Turabian, Harvard) Our guarantees Delivering a high-quality product at a reasonable price is not enough anymore. 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# Distance between Seattle, WA (BFI) and Cordova, AK (CDV) Flight distance from Seattle to Cordova (Seattle Boeing Field – Merle K. (Mudhole) Smith Airport) is 1289 miles / 2074 kilometers / 1120 nautical miles. Estimated flight time is 2 hours 56 minutes. Driving distance from Seattle (BFI) to Cordova (CDV) is 2395 miles / 3854 kilometers and travel time by car is about 51 hours 59 minutes. 1289 Miles 2074 Kilometers 1120 Nautical miles 2 h 56 min 166 kg ## How far is Cordova from Seattle? There are several ways to calculate distances between Los Angeles and Chicago. Here are two common methods: Vincenty's formula (applied above) • 1289.011 miles • 2074.462 kilometers • 1120.120 nautical miles Vincenty's formula calculates the distance between latitude/longitude points on the earth’s surface, using an ellipsoidal model of the earth. Haversine formula • 1286.216 miles • 2069.964 kilometers • 1117.691 nautical miles The haversine formula calculates the distance between latitude/longitude points assuming a spherical earth (great-circle distance – the shortest distance between two points). ## How long does it take to fly from Seattle to Cordova? Estimated flight time from Seattle Boeing Field to Merle K. (Mudhole) Smith Airport is 2 hours 56 minutes. ## What is the time difference between Seattle and Cordova? The time difference between Seattle and Cordova is 1 hour. Cordova is 1 hour behind Seattle. Seattle time to Cordova time converter ## Flight carbon footprint between Seattle Boeing Field (BFI) and Merle K. (Mudhole) Smith Airport (CDV) On average flying from Seattle to Cordova generates about 166 kg of CO2 per passenger, 166 kilograms is equal to 366 pounds (lbs). The figures are estimates and include only the CO2 generated by burning jet fuel. ## Map of flight path and driving directions from Seattle to Cordova Shortest flight path between Seattle Boeing Field (BFI) and Merle K. (Mudhole) Smith Airport (CDV). ## Airport information Origin Seattle Boeing Field City: Seattle, WA Country: United States IATA Code: BFI ICAO Code: KBFI Coordinates: 47°31′47″N, 122°18′7″W Destination Merle K. (Mudhole) Smith Airport City: Cordova, AK Country: United States IATA Code: CDV ICAO Code: PACV Coordinates: 60°29′30″N, 145°28′40″W

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## Calculus 8th Edition a) A differentialable function $z=f(x,y)$ is defined as the linear approximation and continuous on $(a,b)$ when it is near to $(x,y)$. This can be described as: $\triangle z=f_x(a,b)\triangle x+f_x(a,b) \triangle y+\epsilon_1 \delta x+\epsilon_2 \triangle y$ Here $\epsilon_1,\epsilon_2$ approaches to $0$ when $(\triangle x,\triangle y)$ approaches to $0$. b) This means that the first partial derivatives of the function $f(x,y)$ , that is, $f_z, f_y$ should be continuous and exist near the point $(a,b)$

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• ### Pure silicon mystery Physics Forums · I noticed that the temperature coefficient of resistivity of pure silicon is a rather high negative number so just out of curiosity I wanted to see at what temp the resistivity would drop to zero. The formula is ρ-ρ0 = ρ0α(T-T0) where ρ is the final resistivity ρ0 is the reference Get Price • ### Table of Electrical Resistivity and Conductivity · Electrical resistivity represented by the Greek letter ρ (rho) is a measure of how strongly a material opposes the flow of electric current. The lower the resistivity the more readily the material permits the flow of electric charge. Electrical conductivity is the reciprocal quantity of resistivity. Conductivity is a measure of how well a Get Price • ### Electrical properties of Silicon (Si) · Electron mobility versus temperature for different doping levels. 1.High purity Si (N d < 10-12 cm-3) time-of-flight technique (Canali et al. 1973 ) 2.High purity Si (N d < 4·10-13 cm-3) photo-Hall effect (Norton et al. 1973 ) 3.N d = 1.75·10 16 cm-3 N a = 1.48·10 15 cm-3 Hall effect (Morin and Maita 1954 ). 4.N d = 1.3·10 17 cm-3 N a = 2.2·10 15 cm-3 Hall effect (Morin and Maita Get Price • ### Intrinsic Silicon Properties · • resistivity ρ= 1/σ • resistance of an n or p region –R = ρl A = wt • drift current (flow of charge carriers in presence of an electric field E x)n/p drift current density Jxn = σ n E x = qμ nn nE x Jxp = σ p E x = qμ pp pE xtotal drift current density in x direction Jx = q(μ nn μ pp) E x = σE x mobility = average velocity per Get Price • ### Question The resistivity of a pure silicon is about MCQs The resistivity of a pure silicon is about (A) 100 O cm(B) 6000 O cm Get Price • ### Resistivity CalculatorSIEGERT WAFER · Resistivity Calculator (for Silicon) Inputs. Dopant. Doping Concentration cm-3 Resistivity Ω x cm Accuracy. Decimal places The calculation is triggered automatically when you change values in the fields. Results. Mobilität cm 2 /Vs P Concentration cm-3 N Concentration cm Get Price • ### Properties of siliconScienceDirect · Silicon is a group IV element in the periodic table and is a semiconductor with a bandgap of 1.12 eV which means that pure silicon at room temperature is almost an insulator. By doping with group III or group V elements the resistivity of silicon can be varied over a wide range. 1.1.4.1. Introduction—dopants and impurities in silicon Get Price • ### Silicon Basics --General Overview.Columbia University · File ee4494 silicon basics.ppt revised 09/11/2001 copyright james t yardley 2001 Page 29 Density of states in conduction band N C (cm-3)€ 3.22E 19 Density of states in valence band N V (cm-3)€ 1.83E19€ Note at equilibrium n = p ≡ n i where n i is the intrinsic carrier concentration. For pure silicon then n2 NN exp(E /kT) i = c V Get Price • ### SOLVED CALC A rod of pure silicon (resistivity r CALC A rod of pure silicon (resistivity ρ = 2300 Ω ⋅ m) is carrying a current. The electric field varies sinusoidally with time according to E = E 0 sin ω t where E 0 = 0.450 V / m ω = 2 π f and the frequency f = 120 H z (a) Find the magnitude of the maximum conduction current density in the wire. (b) Assuming E = E 0 find the maximum Get Price • ### Electrical Properties of Pure Silicon and Silicon Alloys Electrical resistivity and Hall measurements have been made over the temperature range from 87° to 900°K on pure silicon and on silicon alloys containing from 0.0005 to 1.0 percent boron (p-type impurity) or phosphorus (n-type impurity). X-ray measurements indicate that both elements replace silicon in the lattice. It is shown that each added boron atom contributes one acceptor level and it Get Price • ### Table of ResistivityHyperPhysics Concepts 19 rows ·  · Resistivity ρ (ohm m) Temperature coefficient α per degree C Conductivity σ x Get Price • ### Electrical Properties of Heavily Doped Silicon Journal of · Measurements have been made of the temperature dependences of the electrical resistivity and Hall coefficient in samples of n‐ and p‐type silicon having impurity concentrations in the 10 18 to 10 20 cm −3 range. The resistivity data extend from 4° to 900°K and the Hall data from 4° to 300°K. The results exhibit two noteworthy features viz. (1) a hump or maximum in the resistivity Get Price • ### Resistance and Resistivity · Physics · Silicon (pure) − 70 10 − 3 size 12 Change its resistivity length and area to see how they affect the wire s resistance. The sizes of the symbols in the equation change along with the diagram of a wire. Section Summary. The resistance R size 12 R of a cylinder of length. Get Price • ### 4.4 Electrical conductivity of minerals and rocks · For example pure pyrite FeS 2 has a resistivity of about 3x10-5 Ohm-m but with minor amounts of copper mixed in this can increase to 10 Ohm-m. 3 The range of resistivity for some typical ore minerals is as follows Minerals Resistivity Ohm-m Chalcopyrite CuFeS 2 1.2 x 10-50.3 Pyrite FeS Get Price • ### SOLVED If resistivity of pure silicon is 3000Ωm and the If resistivity of pure silicon is 3000 Ω m and the electron and hole mobilities are 0.12 m 2 V − 1 s − 1 and 0.045 m 2 V − 1 s − 1 respectively. The resistivity of a specimen of the material when 10 19 atoms of Phosphorous are added per m 3 is Get Price • ### Pure silicon mystery Physics Forums · I noticed that the temperature coefficient of resistivity of pure silicon is a rather high negative number so just out of curiosity I wanted to see at what temp the resistivity would drop to zero. The formula is ρ-ρ0 = ρ0α(T-T0) where ρ is the final resistivity ρ0 is the reference Get Price • ### Semiconductor Materials Junctions and Devices · Pure silicon has a considerably higher resistivity in the order of 60 000 obm-centimeters. As used in semiconductor devices however these materials contain carefully controlled amounts of certain impurities which reduce their resistivity to about 2 ohm–centimeters at room temperature ( this resistivity decreases rapidly as the temperature Get Price • ### Resistivity and Conductivity Monitoring in Ultra Pure Water · Ultra Pure Water (UPW) Facts • Ultra Pure Water (UPW) production contains three stages Pre-treatment • Resistivity and conductivity measurements are commonly made to detect ionic contamination. Ultra Pure Water quality is critical in power generation as well as the semiconductor and pharmaceutical industries. Get Price • ### Solecon LaboratoriesResistivity and Concentration · To calculate silicon carrier concentration values we use carrier mobility values derived from Thurber Mattis Liu and Filliben National Bureau of Standards Special Publication 400-64 The Relationship Between Resistivity and Dopant Density for Phosphorus-and Boron-Doped Silicon (May 1981) Table 10 Page 34 and Table 14 Page 40. Get Price • ### 4.4 Electrical conductivity of minerals and rocks · For example pure pyrite FeS 2 has a resistivity of about 3x10-5 Ohm-m but with minor amounts of copper mixed in this can increase to 10 Ohm-m. 3 The range of resistivity for some typical ore minerals is as follows Minerals Resistivity Ohm-m Chalcopyrite CuFeS 2 1.2 x 10-50.3 Pyrite FeS Get Price • ### Pure silicon mystery Physics Forums · I noticed that the temperature coefficient of resistivity of pure silicon is a rather high negative number so just out of curiosity I wanted to see at what temp the resistivity would drop to zero. The formula is ρ-ρ0 = ρ0α(T-T0) where ρ is the final resistivity ρ0 is the reference Get Price • ### Question The resistivity of a pure silicon is about MCQs The resistivity of a pure silicon is about (A) 100 O cm(B) 6000 O cm Get Price • ### Table of Electrical Resistivity and Conductivity · Electrical resistivity represented by the Greek letter ρ (rho) is a measure of how strongly a material opposes the flow of electric current. The lower the resistivity the more readily the material permits the flow of electric charge. Electrical conductivity is the reciprocal quantity of resistivity. Conductivity is a measure of how well a Get Price • ### Electrical Properties of Pure Silicon and Silicon Alloys · Electrical resistivity and Hall measurements have been made over the temperature range from 87° to 900°K on pure silicon and on silicon alloys containing from 0.0005 to 1.0 percent boron (p -type impurity) or phosphorus (n -type impurity). X-ray measurements indicate that both elements replace silicon in the lattice. Get Price • ### SiliconElectrical Resistivity and Electrical Conductivity · Electrical resistivity of Silicon is 2.3E12 nΩ·m. ConductorsSemiconductorsResistors Substances in which electricity can flow are called conductors . Get Price • ### Electrical Properties of Pure Silicon and Silicon Alloys Electrical resistivity and Hall measurements have been made over the temperature range from 87° to 900°K on pure silicon and on silicon alloys containing from 0.0005 to 1.0 percent boron (p-type impurity) or phosphorus (n-type impurity). X-ray measurements indicate that both elements replace silicon in the lattice. It is shown that each added boron atom contributes one acceptor level and it Get Price • ### Resistance and Resistivity · Physics · Silicon (pure) − 70 10 − 3 size 12 Change its resistivity length and area to see how they affect the wire s resistance. The sizes of the symbols in the equation change along with the diagram of a wire. Section Summary. The resistance R size 12 R of a cylinder of length. Get Price • ### (HiResTM ) SILICON FOR GHz THz TECHNOLOGY · High resistivity silicon is defined as monocrystalline silicon having a bulk resistivity larger than 1 kΩcm. Although Czochralski grown monocrystalline silicon is often specified up to 1.5 kΩcm Float Zone grown monocrystalline silicon is the only growth technology that is able to have bulk resistivitites Get Price • ### Semiconductor Materials Junctions and Devices · Pure silicon has a considerably higher resistivity in the order of 60 000 obm-centimeters. As used in semiconductor devices however these materials contain carefully controlled amounts of certain impurities which reduce their resistivity to about 2 ohm–centimeters at room temperature ( this resistivity decreases rapidly as the temperature Get Price

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# Yellow Skies Stinkapoor Nsforsinkiesjobsforfts.com Top Questions 29 votes 11 votes 10 votes ## Prove that the derivative of an even differentiable function is odd, and the derivative of an odd is even. asked Sep 28 '12 at 12:22 9 votes 9 votes ## Is this proof correct for : Does $F(A)\cap F(B)\subseteq F(A\cap B)$ for all functions $F$? asked Oct 30 '12 at 16:53 8 votes 5 votes ## Deal 4 cards from a deck. What is the probability that we get one card from each suit? asked Oct 12 '12 at 13:34 Top Answers No answers with score of 5 or more

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0748. Shortest Completing Word # 748. Shortest Completing Word# ## 题目 # Find the minimum length word from a given dictionary `words`, which has all the letters from the string `licensePlate`. Such a word is said to complete the given string `licensePlate` Here, for letters we ignore case. For example, `"P"` on the `licensePlate` still matches `"p"` on the word. It is guaranteed an answer exists. If there are multiple answers, return the one that occurs first in the array. The license plate might have the same letter occurring multiple times. For example, given a `licensePlate` of `"PP"`, the word `"pair"` does not complete the `licensePlate`, but the word `"supper"` does. Example 1: ``````Input: licensePlate = "1s3 PSt", words = ["step", "steps", "stripe", "stepple"] Output: "steps" Explanation: The smallest length word that contains the letters "S", "P", "S", and "T". Note that the answer is not "step", because the letter "s" must occur in the word twice. Also note that we ignored case for the purposes of comparing whether a letter exists in the word. `````` Example 2: ``````Input: licensePlate = "1s3 456", words = ["looks", "pest", "stew", "show"] Output: "pest" Explanation: There are 3 smallest length words that contains the letters "s". We return the one that occurred first. `````` Note: 1. `licensePlate` will be a string with length in range `[1, 7]`. 2. `licensePlate` will contain digits, spaces, or letters (uppercase or lowercase). 3. `words` will have a length in the range `[10, 1000]`. 4. Every `words[i]` will consist of lowercase letters, and have length in range `[1, 15]`. ## 题目大意 # • 单词列表（words）长度在区间 [10, 1000] 中。 • 每一个单词 words[i] 都是小写，并且长度在区间 [1, 15] 中。 ## 解题思路 # • 给出一个数组，要求找出能包含 `licensePlate` 字符串中所有字符的最短长度的字符串。如果最短长度的字符串有多个，输出 word 下标小的那个。这一题也是简单题，不过有 2 个需要注意的点，第一点，`licensePlate` 中可能包含 `Unicode` 任意的字符，所以要先把字母的字符筛选出来，第二点是题目中保证了一定存在一个最短的单词能满足题意，并且忽略大小写。具体做法按照题意模拟即可。 ## 代码 # `````` package leetcode import "unicode" func shortestCompletingWord(licensePlate string, words []string) string { var ret string for _, w := range words { if match(lp, w) { if len(w) < len(ret) || ret == "" { ret = w } } } return ret } func genCnter(lp string) [26]int { cnter := [26]int{} for _, ch := range lp { if unicode.IsLetter(ch) { cnter[unicode.ToLower(ch)-'a']++ } } return cnter } func match(lp [26]int, w string) bool { m := [26]int{} for _, ch := range w { m[ch-'a']++ } for k, v := range lp { if m[k] < v { return false } } return true } `````` Apr 8, 2023

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# Civil Engineering Objective Questions { Surveying } 260. The distance between the point of intersection of an up grade + gi% and downgrade g2% and the highest point of the vertical curve of length L, is 261. A level when set up 25 m from peg A and 50 m from peg B reads 2.847 on a staff held on A and 3.462 on a staff held on B, keeping bubble at its centre while reading. If the reduced levels of A and B are 283.665 m and 284.295 m respectively, the collimation error per 100 m is 262. In a telescope the object glass of focal length 14 cm, is located at 20 cm from the diaphragm. The focussing lens is midway between them when a staff 16.50 m away is focussed. The focal length of the focussing lens, is 263. The bearing of C from A is N 300 E and from B, 50 metres east of A, is N 60? W. The departure of C from A is 264. The latitude of point C as stated in Q. No. 3.285, is 265. If the long chord and tangent length of a circular curve of radius R are equal the angle of deflection, is 266.  Pick up the correct statement from the following : Page 38 of 60

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English ## Calculation assistance 88 FxTrader_ 2015.10.04 14:48   Hi all,In the below code I'm try to ( subtract A Value From High in the 0 bar ) , can any help please.``` //----    double MAv = iMA( NULL, 0, 13, 0, 0, 0, 0);    double spread = MarketInfo (Symbol(), MODE_SPREAD);    double minlot = MarketInfo (Symbol(), MODE_MINLOT);    double maxlot = MarketInfo (Symbol(), MODE_MAXLOT);    double step = MarketInfo (Symbol(), MODE_LOTSTEP);    double margin = MarketInfo (Symbol(), MODE_MARGINREQUIRED);    double leverage = NormalizeDouble ((Bid/(margin/100))*1000,0);      string SPREAD="",PIPS="",HILO="", MAVV="";            double OPEN = iOpen(NULL,0,0);       double CLOSE = iClose(NULL,0,0);       double SPRD = (Ask - Bid)/Point;       double High_Today = iHigh(NULL,0,0);       double Low_Today = iLow(NULL,0,0);                 PIPS =  DoubleToStr((CLOSE-OPEN)/Point,0);          SPREAD = (DoubleToStr(SPRD,Digits-4));          HILO = DoubleToStr((High_Today-Low_Today)/Point,0);          MAVV = (DoubleToStr(MAv,Digits));                                  Comment( "SPREAD "+DoubleToStr(SPRD/10,1),""          "\n", "PIPS TO OPEN "+PIPS,""          "\n", "Hi TO Low "+HILO,""          "\n", "MIN LOT "+minlot,""          "\n", "MAX LOT "+maxlot,""          "\n", "STEP "+step,""          "\n", "MA 13  "+MAVV,""          "\n", "CLOSE "+CLOSE,""          "\n",                                   // here i need the subtracted results  ( MAVV - High_Today)                                                  // if price ballow MA or Low_Today if price above MA )                   "\n", "MARGIN "+DoubleToStr(margin/100,2));          //--- ``` Moderator3517 GumRai 2015.10.04 15:00 #   `      double High_Today = iHigh(NULL,0,0);`will only get today's high if it is attached to the D1 chart. Otherwise it will get the high of the current chart time-frame.

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## Stochastic Processes Assignment Help | Homework Help Looking for Stochastic Processes Assignment Help? Then, you have come to the right place. We are offering superior quality academic writing help to students across the globe on the stochastic processes. You can seek the help of our Stochastic Processes Assignment Help professionals who hold ample experience and knowledge in writing the assignments flawlessly and at a fair price. The assignments crafted by our experts will help you score excellent grades in the exams. The assignments will be composed based on the specifications given by your professors and by adhering to university standards. The experts are well-versed with the terminologies and concepts related to stochastic processes so that they can deliver quality assignments and help students achieve better grades. Needless to say, the assignments can be used as study material by students. 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A group of random variables is indexed to a different set and have properties of each finite subset of the index set. These random variables are indexed together to form a joint probability distribution. This is the most interesting yet challenging subject for students in their statistics. It is important for them to practice to gain in-depth knowledge of it. Moreover, the brightest students also face difficulty in writing this assignment without experts’ assistance. This mathematical stochastic process is a kind of mathematical structure that is developed from the concept of a physical stochastic process. This is applied inside and outside the field of probability. This represents the numerical values of a system that would change over time randomly like growing the population of bacteria, fluctuation of current, or movement of gas molecules. This is popularly used in mathematical models that would vary in a random way. This is applied in different areas like physics, neuroscience, chemistry, ecology, biology; signal processing, cryptography, telecommunications, and computer science. ## Popular Stochastic Processes Coursework Help Topics Following are the topics on which our experts are offering their guidance and assistance to students across the globe to secure good grades include: • Markov Processes: This is a random process where the future would be dependent on the past or the present. This process would turn out to be a critical class in the random processes. This process is a natural stochastic analog of the deterministic processes that are derived using differential and difference equations. If you are asked to solve processes related to Markov processes, you can seek the help of our adept Stochastic Processes project Help statisticians who are available for you round the clock. They will help you in solving simple to complicated statistical problems in no time. • Markov time: This is also called stopping time which is a particular type of random time. There is a random variable whose value is understood at a point of time at which a stochastic process would showcase its behavior. This stopping time is a mechanism that would decide whether or not to continue the process based on past and present events. There is a finite point of time at which the process has to stop. If you are facing a challenge in writing the assignment on this topic, without hesitating, you can approach our experts. They will help you in completing the assignment flawlessly. The assignments composed by our Stochastic Processes homework Help experts will be to the point and address all the requirements that are given by your professor. • Dynkin’s Formula: This is a theorem that would give the right value of smooth statistics of a particular Ito diffusion at a point the event stops. 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Many Proofs of Pythagorean Theorem ### Many Proofs of Pythagorean Theorem List of animations posted on this page.(Click the text to watch animation.) See Euclid's classical solution in animation See Rectangle variation by Lecchio (1753) in animation See Yanney's proof (1903) in animation See Generalization to parallelogram by Pappus of Alexandria in animation See Graphical proof by Pythagoras in animation Go to Proof by Pythagoras See Perigal's dissection (1873) in animation See variation of Perigals' dissection proof in animation See Dudeney's construction of 1917 in animation See Hisashi Abe's origami solution-1 in animation See Hisashi Abe's origami solution-2 in animation See Mario Pacek's dynamic solution in animation See Leonardo Da Vinci's proof in animation See Thâbit ibn Quarra's proof in animation See Liu Hui's dissection in animation See J.E.Böttcher's proof in animation See Generalization to parallelogram in animation Probably the most famous theorem of all Geometry studies is the "Pythagorean Theorem". The name came from the famous Greek mathematician Pythagoras of Samos(circa 569-475 BC) who was a spiritual leader of the group studying mathematics. In Book I of Euclid's Element, this theorem is stated as Proposition 47. "In right angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle." ***************************** Euclid_prop_47.dwg ***************************** ```There are far more proofs offered of Pythagoras' theorem than of any other proposition in mathematics. "The Pythagorean Proposition" published by Elisha Scott Loomis in 1940 contains 367 proofs !. ``` #### Proof by Euclid in "Element" ***************************** Pythagorean_theorem_01.dwg ***************************** You can see the process in animation. ```This is one of the most elegant of many proofs. The center of the argumnet is that the areas of triangles ACK, BCK , ACE and MCE are exactly the same. Therefore the areas of ACKH and MCEL ,which are twice that of triangle ACK & MCE respectively, are the same. Similar argument is true for yellow colored parts, i.e.,ABFG & BMLD. ``` To create this drawing and animation: Then from command line, type Euclid_47_1 ```Following two proofs use rectangle and square instead of triangle. ``` #### Variation of Euclid's Proof #1 Ref. 1 (Elisha Scott Loomis) lists this proof as Geometric Proof #42, published by Lecchio in 1753. ***************************** Pythagorean_theorem_05.dwg ***************************** You can see the process in animation. To create this drawing and animation: Then from command line, type Euclid_47_3 #### Variation of Euclid's Proof #2 B.F.Yanney published this proof in 1903 (Ref. 6) (p.283). This is very similar to #8 . ***************************** Pythagorean_theorem_11.dwg ***************************** ```Areas of LMOA = LKCA = ACED and similarly, areas of HBOM = HBCK = HFDK Hence ABHL = LMOA + HBOM = ACDE + HFDK ``` You can see the process in animation. To create this drawing and animation: Then from command line, type Euclid_47_9 #### Generalization by Pappus of Alexandria (Ref. 3) In the figure NA = LM ***************************** Pythagorean_theorem_06.dwg ***************************** You can see the process in animation. To create this drawing and animation: Then from command line, type Euclid_47_4 ```Pythagoras also offered a very simple proof. ``` #### Proof by Pythagoras ***************************** Pythagorean_theorem_09.dwg ***************************** You can see the process in animation. To create this drawing and animation: Then from command line, type Euclid_47_7 #### General Concept of Dissection There are many clever proofs using dissections. The general concept for using dissection can be explained as follows: ****** tesselation_1.dwg ****** ****** tesselation_2.dwg ****** ****** tesselation_3.dwg ****** (1)In this example, the size of three squares a,b & c are given.(tesselation_1.dwg) (2)Create a gapless pattern made up of two squares (a & b).(tesselation_2.dwg) (3)Create a mesh like pattern using "c" on some transparent paper.(tesselation_3.dwg) Then move the "mesh-C" over the pattern a-b so that the corner of mesh-C matches some characteristic points like center or edge of squares. example follows: ***************************** Pythagorean_theorem_12.dwg ***************************** To create this drawing : Then from command line, type dissection ```Any combination of triangles and quadrilaterals cut out by the yellow square will make up two small squares. So this method will create infinite number of dissection. There are two interesting cases,i.e. center of squares and edge of squares. ``` #### Corner of smaller square-b is chosen To create this drawing : Then from command line, type dissection Then match the corner point to the corner of smaller square. This is Perigal's dissection of 1873. *********** dissection_case_2.dwg *********** #### Perigal's dissection of 1873 ***************************** Pythagorean_theorem_02.dwg ***************************** You can see the process in animation. To create this drawing and animation: Then from command line, type Euclid_47_2b ```The cross-hatched area in Perigal's dissection can be further divided into one square and 2 triangles. This leads us to the next variation. ``` #### Variation of Perigal's dissection ***************************** Pythagorean_theorem_03.dwg ***************************** You can see the process in animation. To create this drawing and animation: Then from command line, type Euclid_47_2c #### Center of larger square-a is chosen To create this drawing : Then from command line, type dissection Then select the center of the larger square(b x b). This is Henry Dudeney's construction of 1917. ************ dissection_case_3.dwg ************ #### Henry Dudeney's construction of 1917 ***************************** Pythagorean_theorem_04.dwg ***************************** You can see the process in animation. To create this drawing and animation: Then from command line, type Euclid_47_2d #### Corner of smaller square-b is chosen-2 When #5-a case is turned upside down, and move the yellow frame to a different corner point of smaller square, then another interesting dissection is found. #### Origami solution by Hisashi Abe Origami process:Prepare a square piece of paper. ```1. fold along line BE. 2. fold line CF by locating point E on line BE. This makes CF perpendicular to BE. 3. fold line GD by locating F on line CF. GD is now perpendicular to CF. Note here that BCH and CDG are identical, and GD = CH. ``` Here, this process is done by computer. To create this drawing : Then from command line, type Abe_origami ************* Abe_origami_0.dwg ************* ```Cut out two trianlges BCH and DGC. Move BCH upward so that line BC matches line AD. Move DGC left so that line DC matches line AB. ``` ***************************** Abe_origami_a.dwg ***************************** You can see the process in animation. To create this drawing and animation: Then from command line, type Abe_origami_a ```Since BCH = CDG, essentially the same result can be achieved by rotating these trianlges. i.e. rotating BCH around point B, and CDG around point D. ``` ***************************** Abe_origami_b.dwg ***************************** You can see the process in animation. To create this drawing and animation: Then from command line, type Abe_origami_b ```But this picture does not look neat. The reason is the gap between two small triangles,green and cyan. The picture would look nice and clean if cyan colored triangle and green colored triangle meet at point F. The following solution by Mario Pacek does just that. ``` #### Dynamic proof by Mario Pacek I found this interesting proof in Pythagorean Theorem by Alexander Bogomolny. Dr.Bogomolny says that this proof was done by Mario Pacek (aka Pakoslaw Gwizdalski). ***************************** Pythagorean_theorem_10.dwg ***************************** You can see the process in animation. To create this drawing and animation: Then from command line, type Euclid_47_8 ### More of innovative proofs #### Proof by Leonardo Da Vinci This is a very famous proof by Leonardo Da Vinci(1452-1519).(Ref.3)(p. 31) ***************************** Pythagorean_theorem_07.dwg ***************************** You can see the process in animation. To create this drawing and animation: Then from command line, type Euclid_47_5 #### Proof by Thâbit ibn Quarra(828-901) This proof is by Thâbit ibn Qurra(828-901)(Ref.6)(p 282-283). Ref.6 gives a detailed discussion of his works. ***************************** Pythagorean_theorem_08.dwg ***************************** You can see the process in animation. To create this drawing and animation: Then from command line, type Euclid_47_6 #### Proof by Liu Hui(3rd century AD) using Dissection His proof was only in description ,so researchers tried to reconstruct his idea. The following is one of them. ***************************** Pythagorean_theorem_13.dwg ***************************** You can see the process in animation. To create this drawing and animation: Then from command line, type dissect_1 #### Proof by J.E.Böttcher using Dissection Ref.1 lists the following dissection proof as Geometric Proofs #19 (p. 112) and gives credit to Johannes Eduard Böttcher (1847 - 1919). ***************************** Pythagorean_theorem_14.dwg ***************************** You can see the process in animation. To create this drawing and animation: Then from command line, type dissect_2 #### Generalized Pythagorean Theorem for a Parallelogram This proof is published by David S. Wise (Ref. 9), and it was reprinted in Ref. 5 (p.9). On Sept 14, 2011, the author ,David S. Wise, kindly notified me by e-mail as follows: "I later found out that it was already known as Apollonius's parallelogram theorem." When the parallelogram is a rectangle, this is Pythagorean theorem. ***************************** Pythagorean_theorem_15.dwg ***************************** You can see the process in animation. To create this drawing and animation: Then from command line, type gen_Pythagoras #### De Gua's Theorem: Generalization of the Pythagorean theorem to three dimensions De Gua's theorem is a generalization of the Pythagorean theorem to three dimensions and named for Jean Paul de Gua de Malves.(1712-1785) This theorem was presented to the Paris Academy of Sciences in 1783. If a tetrahedron has a right angle corner (a corner like a cube), then the square of the area of the face opposite the right angle corner is the sum of the squares of the areas of the other three faces. ``` Then De Gua's theorem states (Area of ABC)2= (area of OAB)2 + (area of OBC)2 + (area of OCA)2 Let OA = a, OB = b and OC = c. Then this theorem can be written as follows: (Area of ABC)2= (1/4){(ab)2 + (bc)2 + (ca)2} One easy way to prove this is the use of Heron's formula for the area of a triangle. ``` *********************************** DeGua_model.dwg *********************************** To create this drawing : Then from command line, type DeGua #### Spherical Pythagorean Theorem For a right triangle ABC on a sphere of radius R with a right angle at vertex C and sides of length a,b,and c, then ``` cos(c/R) = cos(a/R) * cos(b/R) . ``` ******************************* spherical_Pythagorean.dwg ******************************** red great circle represents equator, yellow one represents longitude line of zero and 180, and green color represents longitude=90 degrees line. Point A : 100 deg East and on the equator Point B : 180 deg East and 30 deg North Point C : 180 deg East and on the equator Radius of the Earth is chosen to be 6373 km(=3956 mile). To create this drawing : Then from command line, type sphere_pythagorean ```Spherical Pythagoreantheorem states: cos(c/R) = cos(a/R) * cos(b/R) (1) Maclaurin series for cos(x) is : cos(x) = 1 - x2/2! + x4/4! - x6/6! + ... Using this formula in (1) gives us: 1 - (c/R)2/2 + (c/R)4/24 -...= {1 - (a/R)2/2 + (a/R)4/24 -...}{1 - (b/R)2/2 + (b/R)4/24 -...} =1 - (a/R)2/2 - (b/R)2/2 + (ab)2/(4 R4) +... Or c2 + (terms of higher powers of c)/R2 = a2 + b2 + (terms of higher powers of a & b)/R2 When R is large relative to a,b and c, then terms divided by R2 becomes negligibly small, and we have a classical Pythagorean theorem ,i.e. c2 = a2 + b2 ``` ##### Number check on this model From the drawing shown above , it is possible to obtain arc length a,b and c. Keep exploding the 3D objects until it is not possible to explode anymore. Then use LIST command to get arc length. This is the result. ``` a = 3333.7534 b = 7778.7579 c = 8086.6416 and R = 6367 Use these values to compute cos(a/R),etc. Just run the command check_theorem, and the results are cos(a/R) = 0.866025 cos(b/R) = 0.34202 So cos(a/R)*cos(b/R) = 0.296198 This is very, very close the value of cos(c/R) cos(c/R) = 0.296198 Finally* cos(c/R)/{cos(a/R)*cos(b/R)} = 0.99999996 And for reference, c2/{a2 + b2} = 0.91302773 *Note:This results are based on the number extracted from the graphical objects. If all the length of a,b and c are computed using the trigonometry, numerical precision is much higher (up to at least 12-th decimal place). ``` #### On Internet 1. Pythagoras' Theorem, by Bill Casselman, The University of British Columbia. 2. Many more interesting proofs by Alexander Bogomolny 3. A proof of the Pythagorean Theorem by Liu Hui (third century AD) reference for dissection Proof #9 Go to   Fun_Math Content Table All questions/complaints/suggestions should be sent to takaya.iwamoto@comcast.net Last Updated July 9-th, 2006

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# Sergei Yakovenko's blog: on Math and Teaching ## Real numbers as solutions to infinite systems of equalities In the past we already extended our number system by adding “missing” elements which are assumed to satisfy certain equations, based only on knowing what these equations are. It turns out that we may extend the set of rational numbers $\mathbb Q$ to a much larger set of real numbers $\mathbb R$ by adding solutions to (infinite numbers) of inequalities. As before, the properties of these new numbers could be derived only from the properties of inequalities between the rational numbers. On one leg, the idea can be explained as follows. Since for any two rational numbers $r,s\in\mathbb Q$ one and only one relation out of three is possible, $r$ < $s$, $r=s$ or $r$ > $s$, we can uniquely define any, say, positive rational unknown number $x$ by looking at the two sets, $L=\{l\in\mathbb Q: 0\le l\le x\}$ and $R=\{r\in\mathbb Q: x\le r\}$. (You don’t have to be too smart at this moment: $x$ is the only element in the intersection $L\cap R$ 馃槈 However, sometimes the analogous construction leads to problems. For instance, if $L=\{l\in\mathbb Q: l\ge 0, l^2\le 2\}$ and $R=\{r\in\mathbb Q: r^2\ge 2\}$, then $L\cap R=\varnothing$, since the square root of two is not a rational number, but $L\cup R=\mathbb Q_+$, i.e., for any positive rational number we can say whether is smaller or larger the missing number $\sqrt 2$. This allows to derive all properties of $\sqrt 2$, including its approximation with any number of digits. Proceeding this way, we introduce (positive) real numbers by indication, what is their relative position to all rational numbers. This allows to describe the real numbers completely. The details can be found here. ## A didactic digression Some of you complained about insufficient number of problems that are discussed during the tutorials. Everybody knows that problems and questions for self-control are the most important elements of study mathematics, especially in comparison with other disciplines. The rationale behind is the assumption that a student who understands the subject, should be able to answer these questions immediately or after some reflection. Composing such problems is an easy thing: you any mathematical argument you can stop for a second and ask yourself: “why I can do as explained?” or “under what conditions are my actions justified?”. In the lecture notes (see the link above) tens of such problems are explicitly formulated. Similar problems will await you on the exam. However, remember one simple thing. If you already know how to solve a problem, this is not a problem but rather a job. Unless you solve these problems yourselves, there is no sense in memorizing their solutions: knowing solution of one such problem won’t help you with solving another problem unless you really understand what’s going on. There are no “typical problems”: each one of them is of its own sort, though, of course, some problems can be solved by similar methods. A practical advice: you should not expect that all problems that appear on the exam will be discussed at length at the tutorials. There are no ready recipes to memorize. Only to understand honestly. Believe me, this is easier than memorize by heart endless formulas and algorithms. # Real numbers There are certain situations when the rational numbers are apparently not sufficient: for instance, the function $f(x)=x^2-2$ is negative at $x=0$, positive at $x=2$ but does not take the intermediate value zero: $\forall x\in\mathbb Q\ f(x)\ne 0$. Another situation concerns the possibility to define the notions of supremum and infimum for infinite sets: the set $A=\{x\in\mathbb Q: x^2<2\}$ is bounded from two sides, but among its upper bounds $B=\{b\in\mathbb Q:\ \forall a\in A\ a\leqslant b\}$ there is no minimal one. The idea is to adjoin to $\mathbb Q$ solutions of infinitely many inequalities. For any rational number $a\in\mathbb Q$ one can associate two subsets $L,R\subset\mathbb Q$ as follows: $L=\{l\in \mathbb Q: l\le a\}$ and $R=\{r\in\mathbb Q: a\le r\}$. Then the number $a$ is the unique solution to the infinite system of inequalities of the form $l\le x\le r$ for different choices of $l\in L,\ r\in R$. This system has the following two features: 1. it is self-consistent (non-contradictory): any lower bound $l$ is no greater than any upper bound $r$, i.e., $L\le R$, and 2. it is maximal: together the two sets give $\mathbb Q=L\cup R$, and none of the sets can be enlarged without violating the first condition. Definition. A (Dedekind) cut is any pair of subsets $L,R\subseteq\mathbb Q$ satisfying the two conditions above. If a rational number $a\in\mathbb Q$ satisfies all the inqualities $l\le a,\ a\le r$ for all $l\in L,\ r\in R$, then we call it a root (or a solution) of the cut. Every rational number is the solution to some cut $\alpha=(L,R)$ as above, and this happens if and only if $L\cap R=\{a\}$. Yet not all cuts have rational solutions (give an example!). We can associate cuts without rational solutions with “missing” numbers which we want to adjoin to $\mathbb Q$. For this purpose we have to show how cuts can be ordered (in a way compatible with the order on $\mathbb Q$) and how arithmetic operations can be performed on cuts. ## Order on cuts Let $\alpha=(L,R),\ \beta=(L',R')$ be two different cuts. We declare that $\alpha\triangleleft\beta$, if $L\cap R'\ne\varnothing$, i.e., if there is a rational number $a\in\mathbb Q$ that is at the same time an upper bound for the cut $\alpha$ and a lower bound for the cut $\beta$. If both cuts have rational solutions, this number would be squeezed between these solutions. In the similar way we define the opposite order $\alpha\triangleright\beta$ if and only if $L'\cap R\ne\varnothing$. To see that this definition is indeed a complete order, we need to check that for any two cuts $\alpha,\beta$ one and only one of the three possibilities holds: $\alpha\triangleleft\beta,\ \alpha\triangleright\beta$ or $\alpha=\beta$ (meaning that $L=L',R=R'$). This is a routine check: if the first two possibilities are excluded, then $L\cap R'=L'\cap R=\varnothing$, and therefore $(L\cup L', R\cup R')$ is a self-consistent cut. But because of the maximality condition, this means that $L\cup L'=L=L'$ and $R\cup R'=R=R'$, that is, $\alpha=\beta$. ## Arithmetic operations on cuts If $\alpha=(L,R),\ \beta=(L',R')$ are two cuts which have rational solutions $a,b$, then these solutions satisfy inequalities $L\le a\le R,\ L'\le b\le R'$ (check that you understand the meaning of this inequality between sets and numbers ;-)!) Adding these inequalities together means that $c=a+b$ satisfies the infinite system of inequalities $L+L'\le c\le R+R'$, where $L+L'$ stands for the so called Minkowski sum $L+L'=\{l+l':\ l\in L,\ l'\in L'\}$ (the same for $R+R'$). This allows to define the summation on cuts. Definition. The sum of two cuts $\alpha=(L,R),\beta=(L',R')$ is the cut $\gamma=(L+L',R+R')$ with the Minkowski sum in the right hand side. To define the difference, we first define the cut $-\alpha$ as follows, $-\alpha=(-R,-L)$, where (of course!) $-L=\{-l: l\in L\},\ -R=\{-r: r\in R\}$. Note that the upper and lower bounds exchanged their roles, since multiplication by $-1$ changes the direction (sense) of the inequalities. Then we can safely define $\alpha-\beta$ as $\alpha + (-\beta)$. Again, one has to check that this definition is well-behaving and all arithmetic properties are preserved. To define multiplication, one has to exercise additional care and start with multiplication between positive cuts $\alpha,\beta\triangleright 0$ (do it yourselves!) and then extend it for negative cuts and the zero cut. After introducing this definition, one has to make a lot of trivial checks: 1. that for cuts having rational solutions, we get precisely what we expected, that is, the new operation agrees with the old one on the rational numbers, 2. that they have the same algebraic properties (associativity, distributivity, commutativity etc) as we had for the rational numbers, 3. that they agree with the order that we introduced earlier exactly as this was the case with the rational numbers, 4. … … …. …. … Of course, nobody ever wrote the formal proofs of these endless properties! (Life is short and one should not waste it for nothing). Yet every mathematician can certainly provide a formal proof for any of them, and nobody of countless students who passed through this ordeal ever voiced any concern about validity of these endless nanotheorems. So wouldn’t we. ## Achievement of the stated goals Once we constructed the extension of the rational numbers by all cuts and denote the result $\mathbb R$ and call it the set of real numbers, one has to verify that all the problems we started with, were actually resolved. There is a number of theorems about the real numbers that look dull and self-evident unless we know that a heavy price had to be paid for that. Namely, we can guarantee that: 1. Any subset $A\subset\mathbb R$ which admits at least one upper bound, admits the minimal upper bound called $\sup A=\sup_{a\in A}a$ (and, of course, the analogous statement holds for $\inf A$). 2. If $\varnothing\ne I_k=[a_k,b_k]\subseteq\mathbb R$ is a family of nested nonempty closed intervals, $I_1\supseteq I_2\supseteq I_3\supseteq\cdots$, then the intersection $I_\infty=\bigcap_{k=1}^\infty I_k$ is also nonempty. 3. Any function $f:[a,b]\to\mathbb R$ continuous on the closed segment $[a,b]$, takes any intermediate value between $f(a)$ and $f(b)$. For more detailed exposition, read the lecture notes here. ## Construction of real numbers The idea of extending the number system from the set of rational numbers $\mathbb Q$ by adjoining roots of polynomial equations is very interesting, but faces obvious difficulties: we need to treat all possible polynomial equations, and this still give us no guarantees whatsoever that transcendental equations (trigonometric, exponential etc). will be solvable when we expect them to be. The alternative is to extend the set of rationals by adding “solutions to systems of inequalities”. In order for such a system to represent a unique “new” number, the equations need to be consistent (compatible between themselves) and possess some uniqueness property. These two requirements can be implemented by consideration of the so called Dedekind cuts, which can be informally considered as sets of rational “approximations” (lower and upper) for the missing number. In the lectures we pursue this strategy and explain how the cuts can be compared, how arithmetic operations on the cuts can be defined and why the addition of all possible cuts results in a “complete” number system. The detailed exposition, as before, is downloadable as a pdf file. Please take a time to signal (in the comments to this post or by any other way) about all errors, inevitable in the first draft. Blog at WordPress.com.

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https://www.indiabix.com/logical-reasoning/statement-and-assumption/discussion-861

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# Logical Reasoning - Statement and Assumption - Discussion ### Discussion :: Statement and Assumption - Section 3 (Q.No.3) In each question below is given a statement followed by two assumptions numbered I and II. You have to consider the statement and the following assumptions and decide which of the assumptions is implicit in the statement. • (A) If only assumption I is implicit • (B) If only assumption II is implicit • (C) If either I or II is implicit • (D) If neither I nor II is implicit • (E) If both I and II are implicit. 3. Statement: Believe me, I have read it in newspaper X. Assumptions: 1. Newspaper X gives reliable information/news. 2. I am reporting exactly as it is given in newspaper X. [A]. Only assumption I is implicit [B]. Only assumption II is implicit [C]. Either I or II is implicit [D]. Neither I nor II is implicit [E]. Both I and II are implicit Explanation: The narrator in the statement clearly insists on the reliability of the fact that what he said, he had read it in newspaper X, and not on the truth of what he said. So, only II is implicit Aabhas said: (Apr 3, 2011) If Newspaper X does not give reliable information... why would he say " Believe me " ? Anup said: (Jun 6, 2012) I think here narrator only communicates what he read in newspaper X to someone else and he expects him/her to believe him as newsaper X being an evidence. He doesn't mean to justify what is written in newspaper X.Newspaper X may have some unrealiable content also. Vik said: (Nov 2, 2013) Well. It seems that a narrator consider some event/situation as true. It may be the only story in this paper considered by him as truthful (so 1st is not implicit). However, how can we sure that he understood the given information correctly and/or that he retold it right (that is "report[ed] exactly as it is given in newspaper") ? so 2nd does not seem implicit to me. Chait said: (Mar 13, 2015) A: India's GDP forecast for 2015-16 is 7%. B: How can you say that? A: Believe me, I read it in Economic Times. It should be implicit that what A is reporting what A read. It has nothing to do with the reliability of the newspaper. Because A is asking B to believe him. If the reliability of the newspaper had to be implicit, A could have stated, "This is what ET says, if you don't believe me". Therefore, ET must be reliable.

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https://community.fabric.microsoft.com/t5/Power-Query/Create-new-column-based-on-3-other-columns/m-p/2161380

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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. Helper I ## Create new column based on 3 other columns Hi everyone, First of all, sorry for my poor english 😅 I'm new to Power Query and I'm a bit stuck trying to create the following rule. I have the following table, with the first 4 columns and I need to create column number 5 (named "NEED THIS") Row ID Time Task NEED THIS 1 AAA 27-10-2021 13:02:55 1 1 2 AAA 27-10-2021 13:02:57 1 3 AAA 27-10-2021 13:03:07 1 4 AAA 27-10-2021 13:03:58 2 2 5 AAA 27-10-2021 13:04:05 2 6 AAA 27-10-2021 13:04:38 3 3 7 AAA 27-10-2021 13:05:22 4 4 8 AAA 27-10-2021 13:05:31 4 9 AAA 27-10-2021 13:06:11 2 2b 10 AAA 27-10-2021 13:06:24 2 11 AAA 27-10-2021 13:07:47 3 3b 12 AAA 27-10-2021 13:08:37 4 4b 13 AAA 27-10-2021 13:08:43 4 14 AAA 27-10-2021 13:09:57 3 3c 15 AAA 27-10-2021 13:10:44 3 16 AAA 27-10-2021 13:12:20 4 4c 17 AAA 27-10-2021 13:13:49 5 5 18 AAA 27-10-2021 13:13:59 5 19 AAA 27-10-2021 13:15:02 6 6 20 BBB 29-10-2021 15:22:18 1 1 21 BBB 29-10-2021 15:22:52 1 22 BBB 29-10-2021 17:02:11 2 2 23 BBB 29-10-2021 17:05:29 3 3 24 BBB 29-10-2021 17:05:35 3 25 BBB 29-10-2021 17:44:03 2 2b 26 BBB 29-10-2021 18:01:11 3 3b 27 BBB 30-10-2021 10:28:12 4 4 28 BBB 30-10-2021 10:28:51 4 29 BBB 30-10-2021 10:40:48 5 5 30 BBB 30-10-2021 11:01:09 6 6 31 BBB 30-10-2021 11:02:50 6 The column I need is for the purpose of identifying the first time a task occurs for the same ID. For some reason, sometimes it appears that the same task occurs more than once in a row, for those cases, I am only interested in identifying the first time it occurs. for example, in row 7 and 8 the same task (4) occurs more than once in a row,  in cases like this I am only interested in identifying the first time it occurs (row 7). But I am also interested in being able to identify when a task is repeated, but not in a row. For example, in row 12 and 13, task 4 occurs again for the same ID (AAA), but this set of tasks does not occur immediately after or before tasks 4 that are in row 7 and 8, in this case I I would like to be able to identify the first time this task is repeated (row 12), but adding a letter to it, since it is the second time it happens for the same ID (if it is the second time it happens, I would like to add a letter "b", if it is the third time it happens, I would like to add a letter "c" ...and so on). If someone can help me or guide me, I will be deeply grateful Thanks !! 1 ACCEPTED SOLUTION Super User Here you go @rodfernandez ``````let Source = Table.FromRows(Json.Document(Binary.Decompress(Binary.FromText("fZNNbsQwCIWvMsp6RuLHxA675BrRbNr736FAnGashkqQBfqEIe+x7xNOz2ldV/tSfSG8CAgfyAqkIlbFyPdzn+gfsnbyESRnpMVIlpyU5tVIJyUji4J08ug55yR7T450smakKHm/Eulky0nGTh6vLxk5K+K50VegCDlLZdgJU5mqlnou1dumQjXleq7V2VSqpoWHxTDVajn0jxG+DzZTC0FL6Wxvm8mFpATntL1tJphF8R8vkYFmilnIifYJMslQzNtWnSPjBHygbdscXS7U7aLx4se1YI4KDUcQXvuLVr+syzMHyhlqjZfB3OGgBGUZNCBJ0GLHxaNpab5lmwIew344keovy3CxoNQUxwOjlqMyXljseYcWiza4gOEWRR8WlkFaxgw1vaCjNsD7Bw==", BinaryEncoding.Base64), Compression.Deflate)), let _t = ((type nullable text) meta [Serialized.Text = true]) in type table [Row = _t, ID = _t, Time = _t, Task = _t, #"NEED THIS" = _t]), #"Changed Type with Locale" = Table.TransformColumnTypes(Source, {{"Time", type datetime}}, "en-BM"), #"Grouped Rows" = Table.Group( #"Changed Type with Locale", { {"First Group Index", each Table.AddIndexColumn(_, "First Index", 1, 1, Int64.Type )}, {"All Rows", each _, type table [Row=nullable text, ID=nullable text, Time=nullable datetime, Task=nullable text, NEED THIS=nullable text]}}, GroupKind.Local), #"Grouped Rows1" = Table.Group( #"Grouped Rows", { {"Second Group Index", each Table.AddIndexColumn(_, "Second Index", 1, 1, Int64.Type)} } ), #"Expanded Second Group Index" = Table.ExpandTableColumn(#"Grouped Rows1", "Second Group Index", {"First Group Index", "All Rows", "Second Index"}, {"First Group Index", "All Rows", "Second Index"}), #"Expanded First Group Index" = Table.ExpandTableColumn(#"Expanded Second Group Index", "First Group Index", {"Time", "NEED THIS", "First Index"}, {"Time", "NEED THIS", "First Index"}), #"Expanded First Group Index", "Letter", each if [First Index] = 1 and [Second Index] = 1 then [Task] else if [First Index] = 1 then [Task] & Character.FromNumber(96+[Second Index]) else null, type text ), #"Removed Other Columns" = Table.SelectColumns(#"Added Letter",{"ID", "Task", "Time", "NEED THIS", "Letter"}) in #"Removed Other Columns"`````` It returns this. I used null. You could replace that with "" if you want, which is empty. What I did was: 1. Grouped by task and *D, but used GroupKind.Local so it would break the groups by the repeating tasks. So not all 2s were grouped together. Only Groups of 2s were. 2. Then I grouped the entire thing again by the ID and task. 3. Each grouping added an index, and preserved all rows. 4. Then I expanded carefully the indexes and all rows. 5. Then used a formula to find where the groups were 1 for first index and something for the second. If the first, just returned the task. For the 2nd and following, added b, c, d, etc. How to use M code provided in a blank query: 1) In Power Query, select New Source, then Blank Query 2) On the Home ribbon, select "Advanced Editor" button 3) Remove everything you see, then paste the M code I've given you in that box. 4) Press Done 5) See this article if you need help using this M code in your model. Did I answer your question? Mark my post as a solution! Did my answers help arrive at a solution? Give it a kudos by clicking the Thumbs Up! DAX is for Analysis. Power Query is for Data Modeling Proud to be a Super User! MCSA: BI Reporting 3 REPLIES 3 Super User Here you go @rodfernandez ``````let Source = Table.FromRows(Json.Document(Binary.Decompress(Binary.FromText("fZNNbsQwCIWvMsp6RuLHxA675BrRbNr736FAnGashkqQBfqEIe+x7xNOz2ldV/tSfSG8CAgfyAqkIlbFyPdzn+gfsnbyESRnpMVIlpyU5tVIJyUji4J08ug55yR7T450smakKHm/Eulky0nGTh6vLxk5K+K50VegCDlLZdgJU5mqlnou1dumQjXleq7V2VSqpoWHxTDVajn0jxG+DzZTC0FL6Wxvm8mFpATntL1tJphF8R8vkYFmilnIifYJMslQzNtWnSPjBHygbdscXS7U7aLx4se1YI4KDUcQXvuLVr+syzMHyhlqjZfB3OGgBGUZNCBJ0GLHxaNpab5lmwIew344keovy3CxoNQUxwOjlqMyXljseYcWiza4gOEWRR8WlkFaxgw1vaCjNsD7Bw==", BinaryEncoding.Base64), Compression.Deflate)), let _t = ((type nullable text) meta [Serialized.Text = true]) in type table [Row = _t, ID = _t, Time = _t, Task = _t, #"NEED THIS" = _t]), #"Changed Type with Locale" = Table.TransformColumnTypes(Source, {{"Time", type datetime}}, "en-BM"), #"Grouped Rows" = Table.Group( #"Changed Type with Locale", { {"First Group Index", each Table.AddIndexColumn(_, "First Index", 1, 1, Int64.Type )}, {"All Rows", each _, type table [Row=nullable text, ID=nullable text, Time=nullable datetime, Task=nullable text, NEED THIS=nullable text]}}, GroupKind.Local), #"Grouped Rows1" = Table.Group( #"Grouped Rows", { {"Second Group Index", each Table.AddIndexColumn(_, "Second Index", 1, 1, Int64.Type)} } ), #"Expanded Second Group Index" = Table.ExpandTableColumn(#"Grouped Rows1", "Second Group Index", {"First Group Index", "All Rows", "Second Index"}, {"First Group Index", "All Rows", "Second Index"}), #"Expanded First Group Index" = Table.ExpandTableColumn(#"Expanded Second Group Index", "First Group Index", {"Time", "NEED THIS", "First Index"}, {"Time", "NEED THIS", "First Index"}), #"Expanded First Group Index", "Letter", each if [First Index] = 1 and [Second Index] = 1 then [Task] else if [First Index] = 1 then [Task] & Character.FromNumber(96+[Second Index]) else null, type text ), #"Removed Other Columns" = Table.SelectColumns(#"Added Letter",{"ID", "Task", "Time", "NEED THIS", "Letter"}) in #"Removed Other Columns"`````` It returns this. I used null. You could replace that with "" if you want, which is empty. What I did was: 1. Grouped by task and *D, but used GroupKind.Local so it would break the groups by the repeating tasks. So not all 2s were grouped together. Only Groups of 2s were. 2. Then I grouped the entire thing again by the ID and task. 3. Each grouping added an index, and preserved all rows. 4. Then I expanded carefully the indexes and all rows. 5. Then used a formula to find where the groups were 1 for first index and something for the second. If the first, just returned the task. For the 2nd and following, added b, c, d, etc. How to use M code provided in a blank query: 1) In Power Query, select New Source, then Blank Query 2) On the Home ribbon, select "Advanced Editor" button 3) Remove everything you see, then paste the M code I've given you in that box. 4) Press Done 5) See this article if you need help using this M code in your model. Did I answer your question? Mark my post as a solution! Did my answers help arrive at a solution? Give it a kudos by clicking the Thumbs Up! DAX is for Analysis. Power Query is for Data Modeling Proud to be a Super User! MCSA: BI Reporting Helper I Amazing thanks! Super User Glad I was able to help out @rodfernandez Did I answer your question? Mark my post as a solution! Did my answers help arrive at a solution? Give it a kudos by clicking the Thumbs Up! DAX is for Analysis. Power Query is for Data Modeling Proud to be a Super User! MCSA: BI Reporting Announcements #### New forum boards available in Real-Time Intelligence. Ask questions in Eventhouse and KQL, Eventstream, and Reflex. #### Fabric Monthly Update - May 2024 Check out the May 2024 Fabric 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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https://www.vedantu.com/question-answer/find-the-distance-between-2-3-and-4-5-a-2sqrt-2-class-11-maths-cbse-5f5f905a9427543f91cfe3c1

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Courses Courses for Kids Free study material Offline Centres More Store # Find the distance between (2, 3) and (-4, 5).A. $2\sqrt 2$B. $2\sqrt {10}$C. $2\sqrt {17}$D. $\sqrt {10}$ Last updated date: 18th Jun 2024 Total views: 413.1k Views today: 5.13k Verified 413.1k+ views Hint: We will use the distance formula $d = \sqrt {{{({x_2} - {x_1})}^2} + {{({y_2} - {y_1})}^2}}$ where the two points are $({x_1},{y_1})$ and $({x_2},{y_2})$ and thus equated with the given four options and thus, we will get our answer. Let us first discuss the distance formula:- Let the two points be $({x_1},{y_1})$ and $({x_2},{y_2})$. So, the distance d between between the given two points are given by: $d = \sqrt {{{({x_2} - {x_1})}^2} + {{({y_2} - {y_1})}^2}}$. This distance is known as Euclidean distance. This is an application of Pythagorean Theorem. The Pythagorean Theorem consists of a formula ${a^2} + {b^2} = {c^2}$ which is used to figure out the value of (mostly) the hypotenuse in a right triangle. The a and b are the two "non-hypotenuse" sides of the triangle (Opposite and Adjacent). So, if we compare the two given points (2, 3) and (-4, 5) with $({x_1},{y_1})$ and $({x_2},{y_2})$, we will have:- ${x_1} = 2$, ${y_1} = 3$, ${x_2} = - 4$ and ${y_2} = 5$. Putting all these values in the mentioned distance formula that is $d = \sqrt {{{({x_2} - {x_1})}^2} + {{({y_2} - {y_1})}^2}}$. So, we will get the following expression: $d = \sqrt {{{( - 4 - 2)}^2} + {{(5 - 3)}^2}}$ $\therefore d = \sqrt {{{( - 6)}^2} + {{(2)}^2}}$ $\therefore d = \sqrt {36 + 4}$ $\therefore d = \sqrt {40}$ There is no such option. So, we will simplify the number inside the root more to get the desired value. $40 = 2 \times 2 \times 2 \times 5$ Therefore, $\sqrt {40} = \sqrt {2 \times 2 \times 2 \times 5} = 2 \times \sqrt {2 \times 5}$. Hence, $d = 2\sqrt {10}$. So, the correct answer is “Option B”. Note: Students must note that even if you interchange the points in the distance formula, it would not affect the result which says that if two points are A and B, then AB = BA. This is happening because we are eventually squaring the difference of terms which will neglect – sign. Sometimes, it is also possible that you may have the option of without simplified value inside the root and after simplifying, we would not be able to match it to any option. So, always remember to check the earlier result before you simplify. Fun Fact:- There are a lot of types of differences in real numbers only. There is even one which is known as Taxi-Cab distance.

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http://uk.ask.com/question/weights-of-plywood-sheets

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# Weights of Plywood Sheets? The weight of plywood sheets can vary depending on the size of the plywood and the exact type of wood it is made of. In general, plywood weighs about three pounds per inch of thickness. Plywood is a flexible manufactured wood that can be used to build various things around a home, including railings and decks. Plywood can also be made to create picnic tables, swing sets, and treehouses. Plywood is a quality wood for such projects because it does not shrink or crack like natural wood can. Reference: Q&A Related to "Weights of Plywood Sheets?" Plywood usually comes in sheets that are four foot by eight foot. Plywood is made by compressing many layers of wood to create the thickness desired. http://answers.ask.com/Business/Constructions_and_... A full 4'x8' sheet or 3/4" plywood weighs 68.16 lbs. http://wiki.answers.com/Q/What_is_the_Weight_of_.7... thickness and type of wood are varibles oak and maple are heaver than pine 3/4 is heaver than 1/4 and 1/2 http://wiki.answers.com/Q/How_much_does_a_sheet_of... when asking this question you first need to take into account that plywood comes in different thicknesses therefore weight per particualr thickness of sheet plywood will vary-- in http://wiki.answers.com/Q/What_is_the_weight_of_4x... Top Related Searches Explore this Topic The weight of treated plywood sheets can be roughly twenty three pounds. This weight is approximate because the weight of the treated plywood sheets can vary ... A sheet of plywood will vary widely in weight, based on the type, manufacturer, origin, and batch. Softwood panel dimensions is usually 1.2525 m x 2.4 m or slightly ... To be able to calculate the weight of plywood, you need to know what it is composed of. Hardwood plywood weighs more per sheet than plywood made from pine. Most ...

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https://warreninstitute.org/the-diagram-shows-the-mechanism-of-a-general-enzyme-catalyzed-reaction/

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# Enzyme reaction mechanism depicted in diagram. Sure! Here's a 90-word introduction for your blog post: Welcome to Warren Institute, where we delve into the fascinating world of Mathematics education. In this article, we'll explore the intricate mechanism of a general enzyme-catalyzed reaction, depicted in a detailed diagram. Understanding the process of enzyme-catalyzed reactions is crucial in grasping the fundamentals of biochemistry and biology. We'll dissect each step, highlighting the key components and their roles in this essential biochemical pathway. Join us as we unravel the mysteries behind this fundamental process in the world of science. ## The Role of Enzymes in Mathematics Education Enzymes play a crucial role in Mathematics education, as they provide a tangible example of how reaction mechanisms can be understood and modeled mathematically. By studying the mechanism of a general enzyme-catalyzed reaction, students can gain insights into concepts such as kinetics, rate laws, and equilibrium, which are fundamental to mathematical modeling in chemistry and biochemistry. Understanding the intricacies of enzyme-catalyzed reactions can enhance students' ability to interpret and solve mathematical problems related to chemical kinetics. ## Mathematical Representation of Enzyme-Catalyzed Reactions In Mathematics education, the diagram showing the mechanism of a general enzyme-catalyzed reaction serves as a visual representation that can be translated into mathematical equations. The diagram allows students to identify the reactants, intermediates, and products involved in the reaction, which can then be expressed using mathematical symbols and equations. This helps students develop their skills in translating real-world processes into mathematical models, fostering a deeper understanding of how mathematics can be applied to describe biochemical phenomena. ## Connecting Enzyme Kinetics with Mathematical Concepts By delving into the mechanism of enzyme-catalyzed reactions, students can connect the principles of enzyme kinetics with mathematical concepts such as differential equations, rate constants, and reaction order. Understanding how enzymes facilitate reactions through specific mechanisms provides a context for applying mathematical tools to analyze and predict the behavior of biochemical systems. This integration of mathematics and biochemistry enhances students' ability to tackle complex problem-solving tasks involving enzyme kinetics and related mathematical concepts. ## Implications for Cross-Disciplinary Learning Studying the mechanism of enzyme-catalyzed reactions in the context of Mathematics education offers opportunities for cross-disciplinary learning. Students can explore how mathematical principles are utilized to describe and analyze biological processes, fostering a holistic understanding of the interconnectedness between mathematics and the natural sciences. This approach encourages students to appreciate the relevance of mathematics in diverse fields, preparing them to apply mathematical reasoning and modeling techniques to a wide range of scientific phenomena. ### How can the diagram of an enzyme-catalyzed reaction be used to illustrate mathematical concepts such as rates of reaction and kinetics in a classroom setting? The diagram of an enzyme-catalyzed reaction can be used to illustrate rates of reaction and kinetics in a classroom setting by applying mathematical concepts such as rate equations and graphical analysis to interpret the reaction's speed and progression over time. ### What are some effective teaching strategies for using the diagram of an enzyme-catalyzed reaction to engage students in mathematical problem-solving related to chemical reactions? One effective teaching strategy is to incorporate the enzyme-catalyzed reaction diagram into mathematical problem-solving by using it as a visual aid to help students understand and analyze the mathematical aspects of chemical reactions. This can be done by guiding students to interpret the diagram's components, such as substrate concentration and reaction rate, and then applying mathematical concepts, such as rate equations and kinetic modeling, to solve problems related to the reaction. ### How can the diagram of an enzyme-catalyzed reaction be integrated into mathematics education to demonstrate principles of calculus, such as rate of change and integration, in the context of chemical kinetics? The diagram of an enzyme-catalyzed reaction can be integrated into mathematics education to demonstrate principles of calculus, such as rate of change and integration in the context of chemical kinetics by using the reaction rate equation and concentration-time graphs to illustrate how calculus concepts can be applied to model and analyze the kinetics of the reaction. ### What are some potential misconceptions or challenges that students may encounter when interpreting the diagram of an enzyme-catalyzed reaction from a mathematical perspective, and how can educators address these effectively? Some potential misconceptions or challenges that students may encounter when interpreting the diagram of an enzyme-catalyzed reaction from a mathematical perspective include understanding the role of variables, rate equations, and the concept of equilibrium. Educators can address these effectively by emphasizing the importance of units and dimensions, providing real-life examples, and using visual aids to illustrate the mathematical concepts involved. ### In what ways can the diagram of an enzyme-catalyzed reaction be utilized to promote interdisciplinary learning between mathematics and biology in the context of STEM education? The diagram of an enzyme-catalyzed reaction can be utilized to promote interdisciplinary learning between mathematics and biology in the context of STEM education by integrating mathematical modeling and analysis of reaction kinetics and statistical data analysis with biological concepts, fostering a deeper understanding of both fields. In conclusion, understanding the mechanism of an enzyme-catalyzed reaction is crucial for grasping the intricate world of biochemistry. The diagram serves as a visual aid to comprehend the process and its variables, making it an invaluable resource for educators and students in the field of mathematics education.

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https://rd.springer.com/chapter/10.1007/978-3-319-65919-0_13?error=cookies_not_supported&code=0d35ae10-8d25-4f3f-8afb-02ac693b3cf1

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Correction to: Linear Programming Using MATLAB® Correction Part of the Springer Optimization and Its Applications book series (SOIA, volume 127) The original version of the book was inadvertently published without updating the following corrections: Preface: On page ix, the last line reads: April 2017 November 2017 Chapter 1: On page 5, 10th line from top reads: A more efficient approach is the Primal-Dual Exterior Point Simplex Algorithm (PDEPSA) proposed by Samaras [23] and Paparrizos [22]. A more efficient approach is the Primal-Dual Exterior Point Simplex Algorithm (PDEPSA) proposed by Samaras [23] and Paparrizos et al. [22]. Chapter 2: On page 68, alignment of the following equations in Table 2.8 were as follows: s0 = jPλjsj and the direction dB = −jPλjhj, where hj = AB−1A. j. It should be as follows: s0 = jPλjsj and the direction dB = −jPλjhj, where hj = AB−1A. j. And if dB ≥ 0 then if s0 = 0 then STOP. The LP problem is optimal. else choose the leaving variable xB[r] = xk using the following relation: $$a = \frac{x_{B[r]}} {-d_{B[r]}} =\min \left \{ \frac{x_{B[i]}} {-d_{B[i]}}: d_{B[i]} < 0\right \},i = 1,2,\cdots \,,m$$ if a = , the LP problem is unbounded. It should be as follows: if dB ≥ 0 then if s0 = 0 then STOP. The LP problem is optimal. else choose the leaving variable xB[r] = xk using the following relation: $$a = \frac{x_{B[r]}} {-d_{B[r]}} =\min \left \{ \frac{x_{B[i]}} {-d_{B[i]}}: d_{B[i]} < 0\right \},i = 1,2,\cdots \,,m$$ if a = , the LP problem is unbounded. Chapter 4: On page 211, 15th line from top, the sentence reads: The column “Total size reduction” in Table 4.2 is calculated as follows: − (mnew + nnewmn)∕((m + n). The column “Total size reduction” in Table 4.2 is calculated as follows: − (mnew + nnewmn)∕(m + n). Chapter 8: On page 345, 7th line from bottom, the sentence reads: There are elements in vector h1 that are greater than 0, so we perform the minimum ratio test (where the letter x is used below to represent that hil ≤ 0, therefore $$\frac{x_{B[i]}} {h_{il}}$$ is not defined): There are elements in vector h1 that are greater than 0, so we perform the minimum ratio test (where the letter x is used below to represent that hil ≤ 0, therefore $$\frac{x_{B[i]}} {h_{il}}$$ is not defined): Chapter 10: On page 439, alignment of the following equation in Table 10.1 was as follows: s0 = jPλjsj and the direction $$d_{B} = -\sum _{j\in P}\lambda _{j}h_{j}$$, where $$h_{j} = A_{B}^{-1}A_{.j}$$. Step 2.1. (Test of Optimality). if P = ∅ then STOP. (LP.1) is optimal. else if dB ≥ 0 then if s0 = 0 then STOP. (LP.1) is optimal. It should be as follows: s0 = jPλjsj and the direction dB = −jPλjhj, where hj = AB−1A. j. Step 2.1. (Test of Optimality). if P = ∅ then STOP. (LP.1) is optimal. else if dB ≥ 0 then if s0 = 0 then STOP. (LP.1) is optimal.

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https://curriculum.roundrockisd.org/fourth-grade/math-deepening-fraction-number-sense-and-connecting-whole-number-addition-and-subtraction-concepts-to-fractions/

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• Home • / • / • Math: Deepening Fraction Number Sense and Connecting Whole Number Addition and Subtraction Concepts to Fractions # Math: Deepening Fraction Number Sense and Connecting Whole Number Addition and Subtraction Concepts to Fractions ### Suggested Time Frame: 25 Instructional Days ##### Focus TEKS Represent Fractions (including Improper Fractions and Mixed Numbers) • 4.3A represent a fraction a/b as a sum of fractions 1/b, where a and b are whole numbers and b > 0, including when a > b; – S RC1 • 4.3B decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations; – S RC1 • 4.3G represent fractions and decimals to the tenths or hundredths as distances from zero on a number line. – S RC1 [include measuring lengths to the nearest half, fourth, eighth, and tenth of a unit, as appropriate] • 4.9A represent data on a frequency table, dot plot, or stem-and-leaf plot marked with whole numbers and fractions; – R RC4 Equivalent Fractions • 4.3C determine if two given fractions are equivalent using a variety of methods; – S RC1 Compare Fractions with Like and Unlike Denominators • 4.3D compare two fractions with different numerators and different denominators and represent the comparison using the symbols >, =, or <; – R RC1 Add and Subtract Fractions with Like Denominators • 4.3E represent and solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line and properties of operations; – R RC2 • 4.3F evaluate the reasonableness of sums and differences of fractions using benchmark fractions 0, 1/4, 1/2, 3/4, and 1, referring to the same whole; and – S RC2 Problem Solving (Some of the types of problems students should be solving during this unit) • 4.8C solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate. – R RC3 [word problems using measurement contexts, focus on fractions in this unit, addition and subtraction only in this unit] • 4.9B solve one- and two-step [addition and subtraction] problems using data in whole number, decimal, and fraction form in a frequency table, dot plot, or stem-and-leaf plot. – S RC4 ##### Computational Fluency TEKS Estimation (Use to verify reasonableness of products and quotients) • 4.4G round to the nearest 10, 100, or 1,000 or use compatible numbers to estimate solutions involving whole numbers; – S RC2 Multiply Whole Numbers • 4.4B determine products of a number and 10 or 100 using properties of operations and place value understandings; – S RC2 • 4.4D use strategies and algorithms, including the standard algorithm, to multiply up to a four-digit number by a one-digit number and to multiply a two-digit number by a two-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties; – S RC2 Divide Whole Numbers • 4.4F use strategies and algorithms, including the standard algorithm, to divide up to a four-digit dividend by a one-digit divisor; – S RC2 ##### Spiral Review TEKS Operations & Algebraic Reasoning • Computation (The types of computation students should be doing when solving word problems during spiral review.) • 4.4A add and subtract whole numbers and decimals to the hundredths place using the standard algorithm; – R RC2 • 4.4B determine products of a number and 10 or 100 using properties of operations and place value understandings; – S RC2 • 4.4D use strategies and algorithms, including the standard algorithm, to multiply up to a four-digit number by a one-digit number and to multiply a two-digit number by a two-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties; – S RC2 • 4.4F use strategies and algorithms, including the standard algorithm, to divide up to a four-digit dividend by a one-digit divisor; – S RC2 • 4.4G round to the nearest 10, 100, or 1,000 or use compatible numbers to estimate solutions involving whole numbers; and – S RC2 • Problem Solving (Some of the types of problems students should be solving during spiral review.) • 4.4H solve with fluency one- and two-step problems involving multiplication and division, including interpreting remainders. – R RC2 • 4.8C solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate. – R RC3 [word problems using measurement contexts, whole numbers, all four operations] • 4.9B solve one- and two-step problems using data in whole number, decimal, and fraction form in a frequency table, dot plot, or stem-and-leaf plot. – S RC4 • Representations (Pictorial and Symbolic) • 4.5A represent multi-step problems involving the four operations with whole numbers using strip diagrams and equations with a letter standing for the unknown quantity; – R RC2

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# zsm: Zero sum multinomial distribution as derived by McKane In untb: Ecological Drift under the UNTB ## Description The Zero sum multinomial distribution of species abundances as derived by McKane 2004. ## Usage `1` ```zsm(J, P, m) ``` ## Arguments `J` Size of local community `P` Abundance in metacommunity `m` Probability of immigration ## Value Returns a vector of size `J` showing the probability of the stationary abundance being 0,1,2,...,J. ## Note The function uses `lgamma()` to avoid numerical overflow ## Author(s) Robin K. S. Hankin ## References A. J. McKane and others 2004. “Analytic solution of Hubbell's model of local community dynamics”. Theoretical Population Biology 65:67-73 ## Examples ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72``` ``` sum(zsm(164,0.1,0.5)) # should be 1 # McKane et al 2004: figure 1. layout(matrix(1:4,2,2)) par(mai=0.2+rep(0,4)) plot(1,type="n",log="y",ylim=c(1e-9,1),xlim=c(0,64),xlab="",ylab="Ps(N)", axes=FALSE,main=expression(J==64)) axis(1,pos=1e-9) axis(2,pos=0,at=10^(-(0:9))) segments(64,1e-9,64,1) segments(60,1e-9,64,1e-9) f <- function(P){points(0:64,zsm(64,P=P,m=0.05),type="l")} for(i in 1:9){f(i/10)} f(0.99) f(0.999) f(0.01) f(0.001) text(07,3.2e-7,adj=0,expression(P==0.999)) text(49,3.2e-7,adj=0,expression(P==0.001)) text(45,0.1,expression(m==0.05)) plot(1,type="n",log="y",ylim=c(1e-5,1),xlim=c(0,64),xlab="",ylab="Ps(N)", axes=FALSE,main="") axis(1,pos=1e-5) axis(2,pos=0,at=10^-(0:5)) segments(60,1e-5,64,1e-5) segments(64,1e-5,64,1) par(xpd=FALSE) g <- function(m){points(0:64,pmax(zsm(64,P=0.1,m=m),1e-5),type="l")} g(0.0001) g(0.0005) g(0.002) g(0.01) g(0.02) g(0.05) g(0.5) g(0.999) text(50,0.4,expression(P==0.1)) plot(1,type="n",log="y",ylim=c(1e-9,1),xlim=c(0,1e5),xlab="",ylab="Ps(N)", axes=FALSE,main=expression(J==10000)) axis(1,pos=1e-9) axis(2,pos=0) segments(1e5,1e-9,1e5,0.1) h <- function(P){points(0:1e5,pmax(zsm(1e5,P=P,m=0.05),1e-9),type="l")} for(i in 1:9){h(i/10)} h(0.01) h(0.99) text(75000,0.1,expression(m==0.5)) plot(1,type="n",log="y",ylim=c(1e-40,1),xlim=c(0,1e5),xlab="",ylab="Ps(N)", axes=FALSE,main="") axis(1,pos=1e-40) axis(2,pos=0,at=1/10^c(40,32,24,16,8,0)) segments(1e5,1e-40,1e5,1) i <- function(m){points(0:1e5,pmax(zsm(1e5,P=0.1,m=m),1e-40),type="l")} i(0.0001) i(0.0002) i(0.0005) i(0.001) i(0.002) i(0.005) i(0.01) i(0.02) i(0.5) text(60000,1e-4,expression(P==0.1)) ``` untb documentation built on March 19, 2018, 9:03 a.m.

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Question 79 # The Poisson ratios of soil sample 1 & 2 are $$\mu_{1}$$ and $$\mu_{2}$$ respectively and the coefficient of earth pressure at rest for soil sample 1 and 2 are $$K_{1} and K_{2}$$ respectively.If $$\frac{\mu_{1}}{\mu_{2}}$$= 1.5 and $$\frac{1-\mu_{1}}{1-\mu_{2}}$$=0.875 then $$\frac{k_{1}}{k_{2}}$$ will be • Get 300+ previous papers with solutions PDF ##### Akashdeep Singh 2 years, 6 months ago 3 years ago

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Warning: Undefined array key "numbers__url_substractions" in /home/clients/df8caba959271e8e753c9e287ae1296d/websites/crazy-numbers.com/includes/fcts.php on line 156 Number 15565: mathematical and symbolic properties | Crazy Numbers Discover a lot of information on the number 15565: properties, mathematical operations, how to write it, symbolism, numerology, representations and many other interesting things! ## Mathematical properties of 15565 Is 15565 a prime number? No Is 15565 a perfect number? No Number of divisors 8 List of dividers Warning: Undefined variable \$comma in /home/clients/df8caba959271e8e753c9e287ae1296d/websites/crazy-numbers.com/includes/fcts.php on line 59 1, 5, 11, 55, 283, 1415, 3113, 15565 Sum of divisors 20448 Prime factorization 5 x 11 x 283 Prime factors Warning: Undefined variable \$comma in /home/clients/df8caba959271e8e753c9e287ae1296d/websites/crazy-numbers.com/includes/fcts.php on line 59 5, 11, 283 ## How to write / spell 15565 in letters? In letters, the number 15565 is written as: Fifteen thousand five hundred and sixty-five. And in other languages? how does it spell? 15565 in other languages Write 15565 in english Fifteen thousand five hundred and sixty-five Write 15565 in french Quinze mille cinq cent soixante-cinq Write 15565 in spanish Quince mil quinientos sesenta y cinco Write 15565 in portuguese Quinze mil quinhentos sessenta e cinco ## Decomposition of the number 15565 The number 15565 is composed of: 1 iteration of the number 1 : The number 1 (one) represents the uniqueness, the unique, a starting point, a beginning.... Find out more about the number 1 3 iterations of the number 5 : The number 5 (five) is the symbol of freedom. It represents change, evolution, mobility.... Find out more about the number 5 1 iteration of the number 6 : The number 6 (six) is the symbol of harmony. It represents balance, understanding, happiness.... Find out more about the number 6

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### Home > CAAC > Chapter 6 > Lesson 6.2.3 > Problem6-66 6-66. Use generic rectangles to multiply each of the following expressions. 1.  $( x + 2 ) ( x - 5 )$ • Draw a generic rectangle. A generic rectangle where the outside upper left edge is x and the lower left edge is + 2. The bottom left edge is x and the bottom right edge is negative 5. • Multiply the value of the column and the value of the row to find the value of each box in the rectangle. A generic rectangle where the outside upper left edge is x and the lower left edge is + 2. The bottom left edge is x and the bottom right edge is negative 5. The interior is labeled as follows: Upper left box is x squared. Upper right box is negative 5 x. Lower left box is 2 x. Lower right box is negative 10. • $(x+2)(x−5)=x^2−3x−10$ 1.  $( y + 2 x ) ( y + 3 x )$ • See the hints in part (a). A generic rectangle where the outside upper left edge is y and the lower left edge is + 2 x. The bottom left edge is y and the bottom right edge is positive 3 x. • $(y+2x)(y+3x)=y^2+5xy+6x^2$  A generic rectangle where the outside upper left edge is y and the lower left edge is + 2 x. The bottom left edge is y and the bottom right edge is positive 3 x. The interior is labeled as follows: Upper left box is y squared. Upper right box is 3 x y. Lower left box is 2 x y. Lower right box is 6 x squared. 1.  $( 3 y - 8 ) ( - x + y )$ • See the hints in parts (a) and (b). Generic rectangle left edge top$3y\$ interior top left blank interior top right blank left edge bottom$-8\$ interior bottom left blank interior bottom right blank left edge bottom$-x$ right edge bottom$+y$ 1.  $(x-3y)(x+3y)$ • See the hints in part (a). Generic rectangle interior top left blank interior top right blank interior bottom left blank interior bottom right blank

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Cody # Problem 2082. Vector parallel to plane? Solution 2006090 Submitted on 6 Nov 2019 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 a = 1; b= 1; c=1; d=1969; vec=[1 1 1]; y_correct = false; assert(isequal(parallel2plane(a,b,c,d,vec),y_correct)) 2   Fail a = 1; b= 1; c=1; d=1969; vec=[0 -1492 1492]; y_correct = true; assert(isequal(parallel2plane(a,b,c,d,vec),y_correct)) Assertion failed. 3   Pass a = 1; b= 2; c=3; d=1969; vec=[0 -1492 1492]; y_correct = false; assert(isequal(parallel2plane(a,b,c,d,vec),y_correct)) 4   Fail a = 1; b= 2; c=3; d=1969; vec=[1 0 -1/3]; y_correct = true; assert(isequal(parallel2plane(a,b,c,d,vec),y_correct)) Assertion failed. 5   Fail a = 0; b= 5; c=7; d=1969; vec=[0 49 -35]; y_correct = true; assert(isequal(parallel2plane(a,b,c,d,vec),y_correct)) Assertion failed. ### Community Treasure Hunt Find the treasures in MATLAB Central and discover how the community can help you! Start Hunting!

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Question The circle shown has a radius of 4 cm. What is the area of the circle to 1 decimal place? Answers 1. thanhcong Answer: A = 50.2 cm^2 Step-by-step explanation: The area of a circle is given by A = pi r^2  where r is the radius A = (3.14) * 4^2 A =50.24 To 1 decimal place A = 50.2 cm^2 2. Ladonna Answer: 50.3 cm^2 to 1 dec. place. Step-by-step explanation: Area = pi r^2 = pi * 4^2 = 16 * pi = 50.265

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All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars perplexus dot info How long did I walk from the Airport ? (Posted on 2002-07-02) I was going to take a trip to my friend's house in San Jose by airplane. If my airplane had arrived on time as scheduled, my friend would drive out to pick me up from San Jose's airport. She would get to the ariport just as I would be leaving it, and drive me to her house. This way, I would come to her house at 12:00. But as it happened, my airplane arrived at the airport 1 hour earlier. So I walked from the airport directly to my friend's house. On the way to her house, I met her driving to pick me up. I got into the car, and we drove me to the house. This way, I arrived at the house at 11:40. How long did I spend walking? (The only thing known about my walking speed and my friend's driving speed is that they are different and they are constant.) See The Solution Submitted by vohonam Rating: 3.8333 (6 votes) Comments: ( Back to comment list | You must be logged in to post comments.) Puzzle Solution Comment 9 of 9 | Let the time taken by the friend to drive to the airport be t hours. Since, her driving speed is a constant, it must take her precisely the same time (t hours) to drive back to her house. Thus, the total time taken by the friend to drive to the airport and back is 2t hours. Now, we know that it took the friend 12:00 - 11:40 = 20 minutes or one-third hour less to pick up the individual and drive back to her house, so that the total time taken for the onward truncated journey is (2t - 1/3)/2 = (t - 1/6) hours. Thus, the friend's onward journey by car to the airport was shorter by one-sixth hour. Therefore, if the individual had arrived at the airport precisely m hours before the designated time, then it follows that he would have to walk for (m - 1/6) hours, whenever m >= 1/6 By the problem, it is known that m=1, and consequently, the individual walked for (1 - 1/6) = 5/6 hours, or 50 minutes. Edited on May 17, 2008, 7:48 am Posted by K Sengupta on 2008-05-09 15:49:19 Search: Search body: Forums (0)

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Find answers, ask questions, and connect with our community around the world. Activity Discussion Math Arithemetic sequence question • # Arithemetic sequence question Posted by on June 3, 2023 at 11:00 pm Find the next three terms in the arithmetic sequence: 3, 7, 11, 15, … 2 Members · 1 Reply • 1 Reply • ### Deivakani Dk Member June 4, 2023 at 12:29 pm Helpful 2 Not Helpful Arithmetic sequence follows the order a,a+d,a+2d,a+3d…. First term is a , a= 3 Second term a+d= 7 . substitute a here to find d 3+d=7, d=4 Third term a+2d=11 Fourth term a+3d=15 We need to fifth,sixth and seventh term Fifth term a+4d= 3+4*4 = 19 Sixth term a+5d = 3+5*4= 23 Seventh term a+6d=3+6*4= 27 The next three terms are 19,23,27 Log in to reply. Start of Discussion 0 of 0 replies June 2018 Now +

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# Atmospheric Dispersion Calculator ## Air Pollution Control Stacks Equation Formulas ### Solving for plume rise for neutral stability conditions. #### Inputs: stack gas exit speed (Vs) meter/secondcentimeter/hourcentimeter/secondfoot/dayfoot/hourfoot/minutefoot/secondinch/dayinch/hourinch/minuteinch/secondkilometer/daykilometer/hourkilometer/minutekilometer/secondknotmach sea level 15 Cmeter/daymeter/hourmeter/minutemile/daymile/hourmile/minutemile/secondmillimeter/secondspeed of light in vacuumyard/second average wind speed (u) meter/secondcentimeter/hourcentimeter/secondfoot/dayfoot/hourfoot/minutefoot/secondinch/dayinch/hourinch/minuteinch/secondkilometer/daykilometer/hourkilometer/minutekilometer/secondknotmach sea level 15 Cmeter/daymeter/hourmeter/minutemile/daymile/hourmile/minutemile/secondmillimeter/secondspeed of light in vacuumyard/second stack heat emission rate (Qh) wattfoot-pound/secondhorsepowerjoule/secondkilojoule/secondkilowattnewton-meter/second #### Conversions: stack gas exit speed (Vs)= 0 = 0meter/second stack diameter (d)= 0 = 0meter average wind speed (u)= 0 = 0meter/second stack heat emission rate (Qh)= 0 = 0kilojoule/second #### Solution: plume rise (Δh)= NOT CALCULATED #### Other Units: Change Equation Select to solve for a different unknown Gaussian plume dispersion model developed by Pasquill plume contaminant concentration at a point in space plume contaminant concentration at ground level contaminant concentration at ground level alongthe plume centerline contaminant concentration at ground level alongthe plume centerline when the emission source isat ground level wind speed at elevation from known wind speed and elevation wind speed at elevation weather station wind speed elevation weather station elevation stability parameter effective stack height effective stack height physical stack height plume rise plume rise stack gas exit speed stack diameter average wind speed stack heat emission rate plume rise for neutral stability conditions plume rise stack gas exit speed stack diameter average wind speed stack heat emission rate plume rise stack gas exit speed stack diameter average wind speed stack heat emission rate Where C = downwind concentration Q = pollution source emission rate u = average wind speed σy = y direction plume standard deviation σz = z direction plume standard deviation x = position in the x direction or downwind direction y = position in the y direction z = position in the z direction H = effective stack height References - Books: 1) P. Aarne Vesilind, J. Jeffrey Peirce and Ruth F. Weiner. 1994. Environmental Engineering. Butterworth Heinemann. 3rd ed. Online Web Apps, Rich Internet Application, Technical Tools, Specifications, How to Guides, Training, Applications, Examples, Tutorials, Reviews, Answers, Test Review Resources, Analysis, Homework Solutions, Worksheets, Help, Data and Information for Engineers, Technicians, Teachers, Tutors, Researchers, K-12 Education, College and High School Students, Science Fair Projects and Scientists By Jimmy Raymond Contact: aj@ajdesigner.com

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If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. ## AP®︎/College Chemistry ### Unit 7: Lesson 6 Using the reaction quotient # Worked example: Using the reaction quotient to find equilibrium partial pressures AP.Chem: TRA‑8 (EU) , TRA‑8.B (LO) In some equilibrium problems, we first need to use the reaction quotient to predict the direction a reaction will proceed to reach equilibrium. Once we know this, we can build an ICE table, which we can then use to calculate the concentrations or partial pressures of the reaction species at equilibrium. Created by Jay. ## Want to join the conversation? • I dont see the point of comparing the reaction quotient with the equilibrium pressure, cant you just use an ICE table assuming +x on reactant side and -x on product side, and when you solve for x the signs will balance out to get the equilibrium partial pressures? (1 vote) • We need to know the reaction quotient because we need to know whether the production of reactants or products is favored. Essentially we need to know if the reactants/products are increasing or decreasing. Knowing the reaction quotient allows us to know reactant concentrations will increase as opposed to them decreasing. This ultimately gives us the correct information for the ICE table. Hope that helps. (1 vote) • Sorry to ask something completely unrelated to chemistry, but at shouldn't it be -0.192? Because 0.40 - 0.208 = -0.192.

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# Virtual Solar System (formula for gravity in 3d) Tags: 1. Feb 22, 2015 ### Mipada I've made a virtual solar system in Java3d. I'm trying to implement the orbiting of planets and ships. I get the basic formula Code (Text): F = G((m1*m2)/r^2))[\code] and saw a discussion here about the formula in 3d but, I don't know how to read a letter with an arrow over it, lol.  Can someone help me with the details? Note:doubles can't seem to hold the big distances and the minute force of gravity at those distances.  I've ended up creating a BigVector3d class.  It holds BigDecimal numbers and allows me to use vectors (at least to hold 3d numbers in one object).  I'll post that for someone else to use. Fundamentally I'm doing this. (Sorry, I can't find the usual code formatting commands I've seen before.  And, I don't know if this is in the right forum.) [code] vv = vv + av;//velocity vector = velocity vector + acceleration vector lv = lv + vv;//location vector = location vector + velocity vector (for x, y, z) [\code] My main loop calls acceleration(Mass3d m2) [code] for (int j = 0;j < mass.size();j++){ for (int i = j;i < mass.size();i++)//skip previously done masses { mass.get(j).acceleration(mass.get(i));//for each other mass } } [\code] Then i try using this formula. [code] acceleration(Mass3D m2){ //F = -((G*m1*m2 * r.x)/r3) * r3 //split force between two masses.  I don't think this part works at all. m1.location.add(F/2); m2.location.sub(F/2); } [\code] How can i get the gravitational force for the x, y, z components? Last edited: Feb 22, 2015 2. Feb 23, 2015 ### Mipada I found this formula. and tried to implement it as: //FX if (BD.get(X).doubleValue() > 0.000000009){//avoid div by 0 error FX = FX.add(BG);//big gravity FX = FX.multiply(BM);//big mass FX = FX.divide(BD.get(X).pow(2), mc);//big distance (x dist^2) FX = FX.multiply(BD.get(X));//big distance FX = FX.multiply(NEG1);//make negative } else{//distance is 0, no force applied FX = new BigDecimal("0"); } Giving me the Earth pulling on a small ship in orbit, a value of FX5=-9960977999999.9991344000 in meters per second. I'll check the numbers and get back to you. Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

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# Calculate the lag distance (a part of safe stopping sight distance) for a design speed of 70 km/h for two-way traffic on a single lane road. Take reaction time of the driver as 2.5 seconds and coefficient of friction as 0.35 This question was previously asked in JSSC JE Civil Re-Exam 31 Oct 2022 Official Paper-II View all JSSC JE Papers > 1. 58.92 m 2. 48.61 m 3. 97.22 m 4. 117.84 m Option 3 : 97.22 m Free JSSC JE Full Test 1 (Paper 1) 5.4 K Users 120 Questions 360 Marks 120 Mins ## Detailed Solution Concept: Stopping Side Distance: Stopping sight distance (SSD) is the minimum sight distance available on a highway at any spot having sufficient length to enable the driver to stop a vehicle traveling at design safely without collision with any other obstruction. SSD = Lag distance + Braking distance $$% MathType!MTEF!2!1!+- % feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uaiaado % facaWGebGaeyypa0JaamODaiaadshacqGHRaWkdaWcaaqaaiaadAha % daahaaWcbeqaaiaaikdaaaaakeaacaaIYaGaam4zaiaadAgaaaaaaa!40DC! SSD = vt + \frac{{{v^2}}}{{2gf}}$$$$SSD = vt + \frac{{{v^2}}}{{2gf}}$$ Where, v = Design speed (m/sec) f = Coefficient of longitudinal friction t = reaction time g = Acceleration due to gravity Note: (i) For two-lane two-way traffic, SSD = SSD (ii) For single-lane two-way traffic, SSD = 2 × SSD Calculation: Given, v = 70 km/hr = 70 × 0.278 = 19.46 m/sec f = 0.35, t = 2.5 seconds Lag distance = v × t Lag distance = 19.46 × 2.5 = 48.65 m ∵ For two-lane two-way traffic, Lag distance = 2 × lag distance for single lane lag distance = 2 × 48.65 = 97.3 m So, Lag distance = 97.3 m

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