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"Curve 5" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 263 10 "Problem 2." }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 1595 "restart:\neq1:=student[completesquare](2*x^2 -5*x);\neq2:=student[completesquare](2*y^2+y);``;\n2*x^2+2*y^2-5*x+y=0 ;\nsort(eq1+eq2)=0;\neq1+eq2+13/4=13/4;\n(1/2)*(eq1+eq2+13/4)=(1/2)*(1 3/4);\n(1/2)*(eq1+eq2+13/4)=(sqrt((1/2)*(13/4)))^`2`;\n`Center: `*[5/4 ,-1/4],` Radius `=sqrt((1/2)*(13/4)),evalf(sqrt((1/2)*(13/4)));\nn:=2 :\na:=-2:\nb:=1:\nc:=8:\nh:=5/4:\nk:=-1/4:\nr:=sqrt((1/2)*(13/4)):\nxl eft:=-1:\nxright:=3:\nybot:=-2:\nytop:=2:\nf:=x->solve(a*x+b*y=c,y):\n g:=x->solve((x-h)^2+(y-k)^2=r^2,y):\ng1:=x->op(1,[g(x)]):\ng2:=x->op(2 ,[g(x)]):\nx1:=solve(f(x)=g1(x),x):\nx2:=solve(f(x)=g2(x),x):\n#x2:=x1 :\n#y1:=f(x1):\n#y2:=f(x2):\n#`Exercise `||n||`.`;\n#a*x+b*y=c,` `*(x -h)^2+(y-k)^2=r^2;\n#y=f(x),` `*y=g1(x),` `*y=g2(x);\n#`Intersection Points: `*[x1,y1]=evalf([x1,y1],3),[x2,y2]=evalf([x2,y2],3);\np[0]:=p lot(f(x),x=xleft..xright,y=ybot..ytop,color=blue):\np[1]:=plot(g1(x),x =xleft..xright,y=ybot..ytop,color=navy):\np[2]:=plot(g2(x),x=xleft..xr ight,y=ybot..ytop,color=navy):\np[3]:=plot([[h,k]],style=point,symbol= circle,color=red):\np[4]:=plot([[h,0],[h,k]],linestyle=2,color=red):\n p[5]:=plot([[0,k],[h,k]],linestyle=2,color=red):\n#p[6]:=plot([[x2,y2] ],style=point,symbol=circle,color=red):\n#p[7]:=plot([[0,y2],[x2,y2]], linestyle=2,color=red):\n#p[8]:=plot([[x2,y2],[x2,0]],linestyle=2,colo r=red):\nCombinedPlot:=plots[display](\n [seq(p[i],i=1.. 5)],\n scaling=constrained,\n labels=[`` ,``],\n #tickmarks=[5,9],\n #view=[x_lef t..x_right,y_vertex-20..y_vertex+20],\n titlefont=[HELV ETICA,DEFAULT,14],\n title=``):\nCombinedPlot;" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%$eq1G,&*&\"\"#\"\"\"),&%\"xGF(#\"\"&\"\"%!\"\"F'F(F(#\"#D\"\")F/" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq2G,&*&\"\"#\"\"\"),&%\"yGF(#F(\" \"%F(F'F(F(#F(\"\")!\"\"" }}{PARA 11 "" 1 "" 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"" {XPPMATH 20 "6$/,&%\"x G\"\"\"%\"yG!\"\"\"\"$/,**&%#~~GF&)F%\"\"#F&F&*$)F'F/F&F&*&\"#5F&F%F&F (*&\"\"%F&F'F&F&!#8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 106 "eq1:=student[completesquare ](x^2+6*x);\neq2:=student[completesquare](y^2-4*y);\neq1+eq2=-8;\neq1+ eq2+13=13-8;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq1G,&*$),&%\"xG\" \"\"\"\"$F*\"\"#F*F*\"\"*!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$e q2G,&*$),&%\"yG\"\"\"\"\"#!\"\"F+F*F*\"\"%F," }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,(*$),&%\"xG\"\"\"\"\"$F)\"\"#F)F)\"#8!\"\"*$),&%\"yGF )F+F-F+F)F)!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&*$),&%\"xG\"\"\" \"\"$F)\"\"#F)F)*$),&%\"yGF)F+!\"\"F+F)F)\"\"&" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" } {TEXT 261 20 "Exercise 19, p. 223." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 1311 "restart:\nn:=33:\nn:=19:\na:=-2:\nb:=1:\nc:=8:\nh:=-3:\nk:=2:\nr :=sqrt(5):\nxleft:=-6:\nxright:=6:\nybot:=-6:\nytop:=10:\nf:=x->solve( a*x+b*y=c,y):\ng:=x->solve((x-h)^2+(y-k)^2=r^2,y):\ng1:=x->op(1,[g(x)] ):\ng2:=x->op(2,[g(x)]):\nx1:=solve(f(x)=g1(x),x):\nx2:=solve(f(x)=g2( x),x):\n#x2:=x1:\ny1:=f(x1):\ny2:=f(x2):\n`Exercise `||n||`.`;\na*x+b* y=c,` `*(x-h)^2+(y-k)^2=r^2;\ny=f(x),` `*y=g1(x),` `*y=g2(x);\n`Int ersection Points: `*[x1,y1]=evalf([x1,y1],3),[x2,y2]=evalf([x2,y2],3); \np[0]:=plot(f(x),x=xleft..xright,y=ybot..ytop,color=blue):\np[1]:=plo t(g1(x),x=xleft..xright,y=ybot..ytop,color=navy):\np[2]:=plot(g2(x),x= xleft..xright,y=ybot..ytop,color=navy):\np[3]:=plot([[x1,y1]],style=po int,symbol=circle,color=red):\np[4]:=plot([[0,y1],[x1,y1]],linestyle=2 ,color=red):\np[5]:=plot([[x1,y1],[x1,0]],linestyle=2,color=red):\np[6 ]:=plot([[x2,y2]],style=point,symbol=circle,color=red):\np[7]:=plot([[ 0,y2],[x2,y2]],linestyle=2,color=red):\np[8]:=plot([[x2,y2],[x2,0]],li nestyle=2,color=red):\nCombinedPlot:=plots[display](\n [ seq(p[i],i=0..8)],\n scaling=constrained,\n \+ labels=[``,``],\n #tickmarks=[5,9],\n \+ #view=[x_left..x_right,y_vertex-20..y_vertex+20],\n t itlefont=[HELVETICA,DEFAULT,14],\n title=`Chapter 6.2, \+ Exercise `||n):\nCombinedPlot;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%-Ex ercise~19.G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/,&*&\"\"#\"\"\"%\"xGF' !\"\"%\"yGF'\"\")/,&*&%#~~GF'),&F(F'\"\"$F'F&F'F'*$),&F*F'F&F)F&F'F'\" \"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%/%\"yG,&*&\"\"#\"\"\"%\"xGF(F( \"\")F(/*&%#~~GF(F$F(,&F'F(*$,(\"\"%!\"\"*$)F)F'F(F2*&\"\"'F(F)F(F2#F( F'F(/F,,&F'F(F/F2" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/*&%6Intersection ~Points:~G\"\"\"7$!\"#\"\"%F&7$$F(\"\"!$F)F,/7$!\"%F,7$$F0F,$F,F," }} {PARA 13 "" 1 "" {GLPLOT2D 486 486 486 {PLOTDATA 2 "6/-%'CURVESG6$7S7$ $!\"'\"\"!$!\"%F*7$$!3z******\\TVQd!#<$!3e*******HooZ$F07$$!3l****\\-r %3^&F0$!3I*****\\?%p@IF07$$!3A+++l;!\\D&F0$!3W+++IL!)4DF07$$!3o*****\\ lfs*\\F0$!3Q******4$>X*>F07$$!3%)****\\s@%3u%F0$!3o*****\\M%o\"[\"F07$ 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ot:=10:\nf:=x->solve(a*x+b*y=c,y):\ng:=x->solve((x-h)^2+(y-k)^2=r^2,y) :\ng1:=x->op(1,[g(x)]):\ng2:=x->op(2,[g(x)]):\nx1:=solve(f(x)=g1(x),x) :\nx2:=solve(f(x)=g2(x),x):\n#x2:=x1:\ny1:=f(x1):\ny2:=f(x2):\nF:=(x,y )->(x-h)^2+(y-k)^2:\n#`Exercise `||n||`. Graph the following line and \+ circle, and then find any points of #intersection.`;\ny=f(x),` `*(x-h )^2+(y-k)^2=r^2;\n#y=f(x),` `*y=g1(x),` `*y=g2(x);\n#`Intersection P oints: `*[x1,y1]=evalf([x1,y1],3),[x2,y2]=evalf([x2,y2],3);\np[0]:=plo t(f(x),x=xleft..xright,y=ytop..ybot,color=blue):\np[1]:=plot(g1(x),x=x left..xright,y=ytop..ybot,color=navy):\np[2]:=plot(g2(x),x=xleft..xrig ht,y=ytop..ybot,color=navy):\np[3]:=plot([[x1,y1]],style=point,symbol= circle,color=red):\np[4]:=plot([[0,y1],[x1,y1]],linestyle=2,color=red) :\np[5]:=plot([[x1,y1],[x1,0]],linestyle=2,color=red):\np[6]:=plot([[x 2,y2]],style=point,symbol=circle,color=red):\np[7]:=plot([[0,y2],[x2,y 2]],linestyle=2,color=red):\np[8]:=plot([[x2,y2],[x2,0]],linestyle=2,c olor=red):\nCombinedPlot:=plots[display](\n [seq(p[i],i= 0..8)],\n scaling=constrained,\n labels= [``,``],\n #tickmarks=[5,9],\n #view=[x_ left..x_right,y_vertex-20..y_vertex+20],\n titlefont=[H ELVETICA,DEFAULT,14],\n title=` `):\nCombinedPlot;\n`Su bstitute: `*y=f(x),` into `*F(x,y)=r^2;\nF(x,f(x))=r^2;\nexpand(F(x,f( x)))=r^2;\nexpand(F(x,f(x)))-r^2=0;\nsort(4*(expand(F(x,f(x)))-r^2))=0 ;\nx=x1,x2,` `*y=y1,y2;\n`Intersection Points: `*[x[1],y[1]]=evalf([x1 ,y1],3),[x[2],y[2]]=evalf([x2,y2],3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/%\"yG,&*&\"\"#!\"\"%\"xG\"\"\"F(#F*F'F(/,&*&%#~~GF*),&F)F*F*F*F'F* F**$),&F$F*F'F*F'F*F*\"#D" }}{PARA 13 "" 1 "" {GLPLOT2D 486 486 486 {PLOTDATA 2 "6/-%'CURVESG6$7S7$$!#5\"\"!$\"3++++++++X!#<7$$!3!pmmm\"p0 k&*F-$\"3YLLLe%G?G%F-7$$!3uKL$3f_KF-7$$!3k++]P8#\\4(F-$\"3K ++vo1YZIF-7$$!3Kmm;/siqmF-$\"3;LL3-OJNGF-7$$!3Q****\\(y$pZiF-$\"3p*** \\P*o%Qi#F-7$$!3jKLL$yaE\"eF-$\"3Kmmm\"RFjS#F-7$$!3s%HaF-$\"33L L$e4OZ@#F-7$$!3]******\\$*4)*\\F-$\"3u*****\\n\\!**>F-7$$!3o******\\_& \\c%F-$\"3%)*****\\ixCy\"F-7$$!3%)******\\1aZTF-$\"3#******\\KqPd\"F-7 $$!3Imm;/#)[oPF-$\"39LL3-TC%Q\"F-7$$!3%HLLL=exJ$F-$\"3[mmm\"4z)e6F-7$$ !3lKLLL2$f$HF-$\"3GjmmmOlz'*!#=7$$!3%)****\\PYx\"\\#F-$\"3=****\\(=t)e uF]q7$$!3gLLLL7i)4#F-$\"31ommmh5$\\&F]q7$$!3o)***\\P'psm\"F-$\"3S$*** \\(=[jL$F]q7$$!3?****\\74_c7F-$\"3)f***\\iXg#G\"F]q7$$!3M:LL$3x%z#)F]q $!3LBML$e9Eg)!#>7$$!3()HLL3s$QM%F]q$!31NL$eR\"3GGF]q7$$!3]^omm;zr)*!#? $!3ulmmT5k]\\F]q7$$\"3fVLLezw5VF]q$!3!=nm\"zRQbrF]q7$$\"3-.++v$Q#\\\") F]q$!3_,+](=>Y2*F]q7$$\"3%\\LL$e\"*[H7F-$!3Znm;zXu96F-7$$\"3=++++dxd;F -$!34+++]y))G8F-7$$\"3e+++D0xw?F-$!3H++]i_QQ:F-7$$\"35,+]i&p@[#F-$!3b+ +D\"y%3TF-7$$\"3ElmmmZvOLF-$!3iKLL$Qx $o@F-7$$\"3%4+++v+'oPF-$!3Y+++v.I%Q#F-7$$\"3UKL$eR<*fTF-$!3?mm\"zpe*zD F-7$$\"3K-++])Hxe%F-$!3;,++D\\'Qz#F-7$$\"3!fmm\"H!o-*\\F-$!3%HL$e9S8&* HF-7$$\"3X,+]7k.6aF-$!3s++D1#=b?$F-7$$\"3#emmmT9C#eF-$!3\"HLL$3s?6MF-7 $$\"33****\\i!*3`iF-$!3a***\\7`Wli$F-7$$\"3;NLLL*zym'F-$!3enmmm*RR$QF- 7$$\"3'eLL$3N1#4(F-$!3%zmmTvJg/%F-7$$\"3,pm;HYt7vF-$!3]MLe9tOcUF-7$$\" 37-+++xG**yF-$!31,++]Qk\\WF-7$$\"3gpmmT6KU$)F-$!3![LL3dg6n%F-7$$\"3qNL LLbdQ()F-$!3%ymmmw(Gp[F-7$$\"3[++]i`1h\"*F-$!3C++D\"oK03&F-7$$\"3A-+]P ?Wl&*F-$!35,+v=5s#G&F-7$$\"#5F*$!3++++++++bF--%'COLOURG6&%$RGBG$F*F*F_ [l$\"*++++\"!\")-F$6$7V7$$!3W+++!Q*Q*)fF-$!3!=&eI%RLWn\"F-7$$!3y****** 4WzvfF-$!3ttJ4SSg3:F-7$$!3E+++qWg[fF-$!3%4oY^!z$\\G\"F-7$$!3D+++NXT@fF -$!3Z8Q'on0q6\"F-7$$!3%)******fY.neF-$!3g%[<3Jeea)F]q7$$!3;+++$yaE\"eF -$!3jviA])39W'F]q7$$!3)******\\8for&F-$!31StkG!QJT$F]q7$$!3`+++&[j5i&F -$!3yU5ZE^%41*Fgr7$$!3r******RyEDbF-$\"3'poo1Wz[E\"F]q7$$!3M+++\">s%Ha F-$\"3uKR[tVM%>$F]q7$$!3%)******z*G;K&F-$\"3QovX$*fhY^F]q7$$!3K+++qdy8 _F-$\"3!z]*))Gwp9pF]q7$$!3\"*******fD%f5&F-$\"3bX`x02&G`)F]q7$$!3Q+++] $*4)*\\F-$\"3d(4r*GD`-5F-7$$!3g*******HF:y%F-$\"3?9z-&G$4r7F-7$Feo$\"3 1Cxjlc'e]\"F-7$$!3?+++]zCcVF-$\"3lL'z&)*p:1PQM%F]q$\"3CpBF7[!z'HF- 7$$!3c********4zr)*F`s$\"3R*[6,?%)4!HF-7$$\"3#)********zw5VF]q$\"3?\\; 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John Pais" }}{PARA 0 "" 0 "" {TEXT -1 28 "Mathematics Department-MIC DS" }}{PARA 0 "" 0 "" {TEXT -1 45 "E-mail: pais@micds.org or pais@kine tigram.com" }}{PARA 0 "" 0 "" {TEXT -1 33 "URL: http://kinetigram.com /micds" }}{PARA 0 "" 0 "" {TEXT -1 37 "_______________________________ ______" }}}{MARK "32 0" 33 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }