{VERSION 4 0 "IBM INTEL NT" "4.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Input" 2 19 "" 0 1 255 0 0 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{PSTYLE "Normal " -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 3" -1 5 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 1 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal " -1 256 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 1 1 1 1 } 1 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 18 "M odule 1 : Algebra" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 3 "" 0 "" {TEXT -1 25 "101 Numbers - Big & Small" }}{PARA 4 "" 0 "" {TEXT -1 70 "_____________________________________________________________________ _" }}{PARA 4 "" 0 "" {TEXT -1 24 "A. Arithmetic Operations" }}{PARA 0 "" 0 "" {TEXT -1 82 "_________________________________________________ _________________________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 294 "In Maple, you can perform all of the usu al mathematical operations - however with far more accuracy and contro l. The basic format of a Maple command is a mathematical statement ter minated with a semicolon.The > symbol is Maple's prompt for a new stat ement. That's where you type your statement." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 92 " The star key \"*\" is used for multiplication The slash \"/\" key is used for division" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "1234 - 56789; 1234 * 5678; 123456 / 2572;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!&bb&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"(_m+(" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"#[" }}}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 58 " Don't use commas when typing l arge numbers in Maple" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 47 "A1. Compute the product 123,456,789*987,654,321" }}{PARA 0 "" 0 "" {TEXT -1 33 " A. on a handheld calculator" }}{PARA 0 " " 0 "" {TEXT -1 20 " B. using Maple" }}{PARA 0 "" 0 "" {TEXT -1 6 " " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "123456789*98765 4321;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"3p_j76jK>7" }}}{PARA 0 "" 0 "" {TEXT -1 34 " C. are the answers the same?" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 69 "Maple also allows you to compute exponents using the ^ key (shi ft 6)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "3^4;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#\")" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "3^40;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"5,)Gp0famd@\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "3^400;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#\"jv,!)3MLGVC>8.wB`Gg z-d_`aW3XTpmX#=2$zHp'=\"fND[L_\\:eT8Z%H&)Hzl:MHe^b3i#4KArGw:ty7'\\z];i zMfdrUY7dK`l3\"z]0(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "3^400 0;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#\"`br,+)3#=5bt+_!o#>R'G?-MeHzBbJ7\"4[dO)opo%e#)y4;\"Gg)*p\\sci5MI==Mb\\/?_iQ _$=$)4J0F!)f)3fnx%f>mg]Q?;$Q-j^ejz-=Fq_5q'G5n4vsU9uWT_un:j#fxi*GPI>@!G %ou+)fbiY7jpg$yZ:oC$)H`8oy\"HCAGt&GuI+.IKO(=w?h7P3MwE.V1Gk*)yt)[-iE^%= l,tKkCB$*)4%yX:TSatuE![0_k4*y?(eSW,xXR$o$oKm=hfAosKsFbo&z%[8gF0#zBZ=*o z'f*3WHtaw)Rn'4W_,yzag%>I[?_27F2M)H/O4(***)fwGwm5aEl:u7/8!G7Cdd@')Gm-m GuZA`rqpM6^9[(*3SH8&)Q%Q;tClM*zj:w\">nO9L!\\6-+%oomaLkclJ#*)zm(\\$fGE? %R&p*3D'4@[zG1DAc0)e*41A5`_Gu!pU>(Rug_'G[l\"fzxuWdbs5qi(*Hok))p/!y@[Gt /_JZp(eE$ofS!48:#=vCm[AEn7Ba]A)46!)zJsEsrD]%oPI#yY. 9a?r=6H9K+4_%)H![@\"zBrHDhB/;B.%Gu`r&)*zJRZ*=*p@m[piwJ$Q^'GF0b[%yk%**p yqD_*)4S%3>h/qWr(eFZ'fIQsL\"[Xo[\"[7\"fHlH!QRir\"*pt>>^!3Ov# [nKwKT94b&=]o:.3*))z7y`]p*\\T(RG$GD3*zO#**Hbo%fIXvgVm_qP8>/$yRXZ<(*oZw j$>jihOH'H)))yt]IA%4a82v8rc.t-4Y.1WLe7FyE\"3WZoIK[vsy'Q,7D&4'f$)GV U!RfZrh%)))p5V45/%[7c)y:OL?Qf%fD(e9^,?$*R$R7$\\v%*3&)f7R 0bI" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "2^(-9);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6##\"\"\"\"$7&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "6^(-14);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"\"\", '4kTOy" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 126 "You are not limited to find integer powers of whole numbers. You \+ can also use real numbers for both the base and the exponent." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "3.417 ^ 5.338;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+!pAm0(!\"(" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 14 "A2. Compute " }{XPPEDIT 19 1 "5^100;" "6#*$\" \"&\"$+\"" }}{PARA 0 "" 0 "" {TEXT -1 27 "A. on a handheld calculator " }}{PARA 0 "" 0 "" {TEXT -1 14 "B. using Maple" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "5^100;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"aoD1k1$*y-x/I-4^V1KnHiy#Gl&G " 0 "" {MPLTEXT 1 0 8 "123^456;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#\"dfnhlcN2;?DWjmQ->C.c99;gO/R(=K-,'ph;VI#z&)3&z-woeF@I* f6)QLHrZ%[^g&H$*H0ZbLGGcX$G%y!H-Iy8p'Rl$yH/5fCIVY,gqml[$)z`&Qp8+`rBbZ8 qbBh:h!eW)Q4qxf l4OYg#pb4\\@uBJo::FJ[[NSdFsQ\"y\"o*\\C1)oDE!>NgO74#3-G+.x[yO?\"3%y=b1$ o^1j99:NB9'48dDL.])>r7m9/9)3KJ&fks;5nNw7h9x4h'[#4([F***QY^[ uU\\8ULlE,\"z;npYTjoG#\\w]y%*Rw4t6d;')zNkM1Rp(fk<'yy[&oS#=*H(oW\"fh<9E 5.0GI'p,o*yZgWK:2%)>+0!*4i')4;uDc*eWlkj<&fn\\!z?,5)**p:gs'>Q9=@!*\\;u_ .!G\\s=FOpBCa0QY9E9mG6#z2*R\\Z5nGQ\")))H;)>0!p))>3%fHPEjpu0i9$3qc))4s( o+D**" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 151 "Even with a calculator or computer, it c an be somewhat laborious to completely factor an integer into primes. \+ However, Maple can do that automatically." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "ifactor( 48 );" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#*&)-%!G6#\"\"#\"\"%\"\"\"-F&6#\"\"$F* " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "ifactor( 2^10 - 1);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#*(-%!G6#\"\"$\"\"\"-F%6#\"#6F(-F%6#\"# JF(" }}}{PARA 5 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 49 "A4. Find the prime factorizations for e ach number" }}{PARA 0 "" 0 "" {TEXT -1 7 "A.4.800" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "ifactor( 480 0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*()-%!G6#\"\"#\"\"'\"\"\"-F&6# \"\"$F*)-F&6#\"\"&F(F*" }}}{PARA 0 "" 0 "" {TEXT -1 9 "B. 16,371" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "ifactor(16371);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*()-%!G6#\"\"$ \"\"#\"\"\"-F&6#\"# " 0 "" {MPLTEXT 1 0 18 "ifactor(98800271);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&-%!G6#\"%45\"\"\"-F%6#\"&>z*F(" }}}{PARA 0 "" 0 "" {TEXT -1 3 "D. " }{XPPEDIT 19 1 "2^64-1;" "6#,&*$\"\"#\"#k\"\"\"F'!\"\"" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "if actor(2^64-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*0-%!G6#\"\"$\"\"\"- F%6#\"\"&F(-F%6#\"# " 0 "" {MPLTEXT 1 0 17 "ifactor(10^64-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*B)-%!G6#\"\"$\"\"#\"\"\"-F&6#\"#6F*-F&6#\"#w*F*-F&6#\"(`B)eF*-F&6#\"&d)pF *-F&6#\"(du='F*-F&6#\"&T)>F*" }}}{PARA 0 "" 0 "" {TEXT -1 144 "(Note : Part C os this problem would be rather difficult to do by hand since \+ the smnallest prime that divides this number is greater than 1,000)" } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 70 "_________ _____________________________________________________________" }} {PARA 4 "" 0 "" {TEXT -1 22 "B. Order Of Operations" }}{PARA 0 "" 0 " " {TEXT -1 82 "_______________________________________________________ ___________________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 75 "Maple adheres to the same order of operations that we use in mathematics. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 18 "2 + 3 * 4 - 5 * 6;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!#;" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 125 "By inserting parentheses, we force the operations with in them to take place sooner, thus rendering different overall results ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "2+ ( 3* 4 - 5) * 6;" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#\"#W" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 125 "You can enter various complicated expression by using parentheses carefully. Here is how to enter some rational expressions." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "29 /(100 - 11*3^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#H" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "(3^4 - 2^6) / ( 3^2 - 2^3);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"#<" }}}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 4 "" 0 "" {TEXT -1 119 "B1. Compute \011\n A. 1234567 2 \320 12345662\011\011 B. 5566 \320 6655\011 C. " }{XPPEDIT 19 1 "(5^100-1)/(5^25-1); " "6#*&,&*$\"\"&\"$+\"\"\"\"F(!\"\"F(,&*$F&\"#DF(F(F)F)" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 1 " " }}{PARA 4 "" 0 "" {TEXT -1 70 "_________________________________________________________ _____________" }}{PARA 4 "" 0 "" {TEXT -1 23 "C. Shortcut To Retyping " }}{PARA 0 "" 0 "" {TEXT -1 82 "_____________________________________ _____________________________________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 99 "One shortcut that we use often in Maple is the % key. This refe rs to most recently executed result." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "13*23 + 1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$+$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "%/5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#g" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "%/5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#7" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "29^2; 4727 - 29*137;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"$T)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$a(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "(% + %%) / 29; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#b" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 18 "LENGTH OF A NUMBER" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 87 "Recall when comput ed 3^400 earlier, we got quite a large number. But exactly how large? " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "3^400;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#\"jv,!)3MLGVC>8.wB`Gg z-d_`aW3XTpmX#=2$zHp'=\"fND[L_\\:eT8Z%H&)Hzl:MHe^b3i#4KArGw:ty7'\\z];i zMfdrUY7dK`l3\"z]0(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "leng th(3^400);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$\">" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "3^4000; length(%);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#\"`br,+)3#=5bt+_!o#>R'G?-MeHzB bJ7\"4[dO)opo%e#)y4;\"Gg)*p\\sci5MI==Mb\\/?_iQ_$=$)4J0F!)f)3fnx%f>mg]Q ?;$Q-j^ejz-=Fq_5q'G5n4vsU9uWT_un:j#fxi*GPI>@!G%ou+)fbiY7jpg$yZ:oC$)H`8 oy\"HCAGt&GuI+.IKO(=w?h7P3MwE.V1Gk*)yt)[-iE^%=l,tKkCB$*)4%yX:TSatuE![0 _k4*y?(eSW,xXR$o$oKm=hfAosKsFbo&z%[8gF0#zBZ=*oz'f*3WHtaw)Rn'4W_,yzag%> I[?_27F2M)H/O4(***)fwGwm5aEl:u7/8!G7Cdd@')Gm-mGuZA`rqpM6^9[(*3SH8&)Q%Q ;tClM*zj:w\">nO9L!\\6-+%oomaLkclJ#*)zm(\\$fGE?%R&p*3D'4@[zG1DAc0)e*41A 5`_Gu!pU>(Rug_'G[l\"fzxuWdbs5qi(*Hok))p/!y@[Gt/_JZp(eE$ofS!48:#=vCm[AEn7Ba]A)46!)zJsEsrD]%oPI#yY.9a?r=6H9K+4_%)H![@\"zBrH DhB/;B.%Gu`r&)*zJRZ*=*p@m[piwJ$Q^'GF0b[%yk%**pyqD_*)4S%3>h/qWr(eFZ'fI< m%G?2OS:>QsL\"[Xo[\"[7\"fHlH!QRir\"*pt>>^!3Ov#[nKwKT94b&=]o:.3*))z7y`] p*\\T(RG$GD3*zO#**Hbo%fIXvgVm_qP8>/$yRXZ<(*oZwj$>jihOH'H)))yt]IA%4 a82v8rc.t-4Y.1WLe7FyE\"3WZoIK[vsy'Q,7D&4'f$)GVU!RfZrh%)) )p5V45/%[7c)y:OL?Qf%fD(e9^,?$*R$R7$\\v%*3&)f7R0bI" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"%4>" }}}{PARA 5 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 133 "C1. How many digits are in the following numbers?\n \+ A. 1234567\011\011 B. 55566\011 \+ C. 2(36)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 2 "\011\011" }}{PARA 4 "" 0 "" {TEXT -1 70 "_________________ _____________________________________________________" }}{PARA 4 "" 0 "" {TEXT -1 12 "D. Fractions" }}{PARA 0 "" 0 "" {TEXT -1 82 "_________ ______________________________________________________________________ ___" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT -1 62 "By simply entering a fraction, Maple aut omatically reduces it." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "56628377 / 63290539;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6##\"#<\"#>" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 85 "Maple is also able to compute problems wi th fractions without converting to decimals." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "5/12 + 7/24;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6##\"#<\"#C" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 54 "You can also subtract, multiply , and divide fractions." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "1/72 + 1/48 - 1/18 + 1/27;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"(\"$K%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "517/689 * 583/611;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"$@\"\"$p\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 157 "When dividing fractions, its important to be a little \+ careful. Are the following two double decker fractions equivalent? exe cute the statements and find out!" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "517/689 / 583/611;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"\"\"'@ZZ" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "(517/689) / (583/611);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"%4A\"%4G" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 127 "Using parentheses judiciously, we can perform more compl ex problems. For example, the expression would be entered in this way \+ :" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "1/ ( 3/4 - 2/3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# \"#7" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 11 "D1. Compute" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 " " }{XPPEDIT 19 1 "16579076 5/52746197-80143857/25510582;" "6#,&*&\"*l2zl\"\"\"\"\")(>YF&!\"\"F&*& \")dQ9!)F&\")#e5b#F(F(" }{TEXT -1 90 "\n \011\n A. on a hand-held calculator, and B. using Maple C. Are the answers the same?\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6##\"+2q" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 82 "_______________________________________________________ ___________________________" }}{PARA 4 "" 0 "" {TEXT -1 11 "E. Decimal s" }}{PARA 0 "" 0 "" {TEXT -1 82 "____________________________________ ______________________________________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 323 "Maple is also capable of working with decimal numbers. However , unlike a hand-held calculator which has a limited number of decimal \+ places, Maple can do more precise computations with a virtually unlimi ted number of places. Maples\325 super-calculator features are useful \+ for working with both rational and irrational numbers." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "1.37^42 .19;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+&\\JY'e!\"%" }}}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 11 "THE NUMBER " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 209 "The numb er is a constant in mathematics and is recognized by Maple and typed \+ as Pi (note the capitalization of P but not i). Normally displayed as a symbol. To view in a decimal form, use the evalf command." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "Pi;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#PiG" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 10 "evalf(Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# $\"+aEfTJ!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "evalf( Pi, 1000);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#$\"cin*>?k@4f>6m(y#>+8m!oAr @`!yd=yd>v$f(y`B)Q'Gcf6toavG/\\`#)f.t9pw<<1U\"Q3K`(e')GvQy8.+,r\")=J>E N]oWLD3B_UEI3pMb%fW-&f=j4;GtJ(f5&*\\!yHP)*****\\8@2(=0'*48xu(HO\")f\"= W.k3'>-H@6c*>?aB*e#*ozAz]5P&e\\l9IM&\\A,4Wo9syrjt\"4'*ydFMrdyF3cj_9F\" o0+K^SpwY=[n%Q_n<$Hwr@R0x-P%4')z@q!>PZA&RY\\R@g3VmlSCOtO$)H\"\\>,$=QzA \"*[s_d)=Nn&\\F'*zBYu![&=^5$z6E$>QffdOqs0L%4;^T>&p9%Q@lY?)[0`I8 ,g.f#*yOk`r\"4a#HG'4#4_\")[<)e:jg1qeCPFT\"\\-E2OR8#[mKa/h[.YBpc[c94>?r _;$y'yL#[cZGhWLfmv4\")GW'>QI\\&*[HiW'fb5@&Q>q-TG]u6\"[G\"3%f`sJAe]&4Y% Q4ZmI#G8l3[@)z1<@MD[.G')**3iG1k\"yI#fW\\(4#e5v$*Rpr>%)G]zKQVEYQKz*e`Ef TJ!$***" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "Pi * 173.28^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%#PiG$\"*%ef-I!\"%" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 39 "E1. Compute /2 to 2,000 decimal places." }{TEXT 256 1 "\n" } {TEXT -1 274 "E2. Compute the area and circumference of a circle with \+ radius 3,429.2 meters.\nE3. Compute the area of an annulus (ring shape d figure) of inner radius 395 and thickness 4.5 \011\n (Hint compute \+ the area of the outer circle, then subtract the area of the smaller ci rcle inside)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 5 "ROOTS" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 195 "To compute square roots, you can use the sqrt command. Notice that Maple is smart enough to si mplify square roots as much as possible without converting to decimals , just as you would do by hand." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "sqrt(30); sqrt(441); sqr t(24);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$-%%sqrtG6#\"#I\"\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"#@" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#,$*$-%%sqrtG6#\"\"'\"\"\"\"\"#" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 86 "Of course, we can use the evalf command t o express these numbers in decimal form also." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "evalf( sqrt( 2) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+iN@99!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "11 + sqrt(31); evalf(%);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,&\"#6\"\"\"*$-%%sqrtG6#\"#JF%F%" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+Okxc;!\")" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 213 "You can compute other ro ots using fractional exponents. For example, finding the cube root of \+ a number is the same as raising the number to the 1/3 power. You can a lso compute other rational and irrational powers!" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "64^(1/3);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#*$)\"#k#\"\"\"\"\"$F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "10^(1/4); evalf(%);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#*$)\"#5#\"\"\"\"\"%F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+5%z#y " 0 "" {MPLTEXT 1 0 21 "7^ (3/5); evalf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$)\"\" (#\"\"$\"\"&\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+]e49K!\"*" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "sqrt(2)^sqrt(3); evalf(% );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#)*$-%%sqrtG6#\"\"#\"\"\"*$-F&6# \"\"$F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+aYjA=!\"*" }}}{PARA 256 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 98 "E2. Compute in exact (non-decimal form) and decimal for m with 100 decimal place accuracy\n \n A. " }{XPPEDIT 19 1 "sqrt(80 0);" "6#-%%sqrtG6#\"$+)" }{TEXT -1 60 " \+ B. " }{XPPEDIT 19 1 "sqrt(3^12);" "6#-%%sqrt G6#*$\"\"$\"#7" }{TEXT -1 55 " \+ C. " }{XPPEDIT 19 1 "10*sqrt(7);" "6#*&\"#5\"\"\"-%%sqrtG6 #\"\"(F%" }{TEXT -1 9 "\n D. " }{XPPEDIT 19 1 "8^(10/3)+81^(7/4); " "6#,&)\"\")*&\"#5\"\"\"\"\"$!\"\"F()\"#\")*&\"\"(F(\"\"%F*F(" } {TEXT -1 40 " E. " }{XPPEDIT 19 1 "sqrt(345^2+59512^2);" "6#-%%sqrtG6#,&*$\"$X$\"\"#\"\"\"*$\"&7&fF)F*" }{TEXT -1 31 " F." }{XPPEDIT 19 1 "(1-sqrt (3))^(1-sqrt(3));" "6#),&\"\"\"F%-%%sqrtG6#\"\"$!\"\",&F%F%-F'6#F)F*" }{TEXT -1 1 "\n" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 19 "E3. Compute \011" } {XPPEDIT 19 1 "sqrt(2)-54608393/38613956;" "6#,&-%%sqrtG6#\"\"#\"\"\"* &\")$R3Y&F(\")cRhQ!\"\"F," }{TEXT -1 93 "\011\011\011\011\n\011\n \+ A. using a hand-held calculator, B. using Maple C. are the answers \+ the same?. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 16 "RAT IONAL NUMBERS" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 146 "Maple usually leaves fractions in fraction form. However , we can force it to express fractions in decimal form using the evalf command once again." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "1/7;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6## \"\"\"\"\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+H9dG9!#5" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 216 "Maple displays 10 decima l places or so as a default. If this is not enough accuracy and you wo uld like greater precision, you can specify the exact number of decima l places as a second parameter to the evalf command." }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "evalf( 1/7 , 200);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#$\"cw9dG9dG9dG9dG9dG9dG9dG9 dG9dG9dG9dG9dG9dG9dG9dG9dG9dG9dG9dG9dG9dG9dG9dG9dG9dG9dG9dG9dG9dG9dG9d G9dG9dG9!$+#" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 426 "Fractions are also called rational numbers because their decimal expansions always have repeating blocks of digits. By looking at the decimal representation of a rational number you can see the re peating cycle of digits. For example, you might notice the repeating p attern of 6 digits in the decimal expansion of 1/7 above. Some numbers have greater periods which can only be seen when greater numbers of d igits are displayed." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "12/31 ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 ##\"#7\"#J" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "evalf( % );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+Ux'4(Q!#5" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 16 "evalf( %, 100 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+Ux'4(Q!#5" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 81 "E1. How many digits repeat in each of these rational numb ers?\011\n \n A. " }{XPPEDIT 19 1 "345/111;" "6#*&\"$X$\" \"\"\"$6\"!\"\"" }{TEXT -1 52 "\011 \+ B. " }{XPPEDIT 19 1 "1/17;" "6#*&\"\"\"F$\"# " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "3 0" 1 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }