{VERSION 6 0 "IBM INTEL NT" "6.0" } {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 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 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 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 "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 Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 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 2 1 2 2 2 2 1 1 1 1 } 1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 257 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {PARA 0 "" 0 "" {TEXT -1 97 "Name ________________ Precal culus Exploration 4 Quiz Date ____________ " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 68 "Note tha t you must show all work on each problem to get full credit." }}{PARA 0 "" 0 "" {TEXT 258 2 "1." }{TEXT -1 91 " Write an equation of the cir cle that is tangent to the y-axis and whose center is (2, 3). " }} {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 259 2 "2." }{TEXT -1 126 " Rewrite the equation of the circ le below in standard form and find its center and radius. Also, accura tely sketch the circle." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#/,**&\"\"#\"\"\")%\"xGF&F'F'*&\"\"%F'F)F'!\"\"*& F&F')%\"yGF&F'F'F/F,#F,\"\")" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 260 2 "3." }{TEXT -1 105 " Find any points of intersection \+ of the following line and circle, and accurately sketch the two figure s." }}{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 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 10 "Problem 1." }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 262 10 "Problem 1." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 1254 "restart:\nn:=1:\na:=1:\nb:=0:\nc:=4:\nh:=2:\nk:=3:\nr:=2:\nx left:=-2:\nxright:=6:\nybot:=-2:\nytop:=6:\n#f:=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:\n#y1:=f(x1):\n#y2:=f(x2):\n#`Exercise `||n||`.`;\n(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);\n#p[0]:=plot(f(x),x=xl eft..xright,y=ybot..ytop,color=blue):\np[1]:=plot(g1(x),x=xleft..xrigh t,y=ybot..ytop,color=navy):\np[2]:=plot(g2(x),x=xleft..xright,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):\np[5]:=plot([[ 0,k],[h,k]],linestyle=2,color=red):\n#p[6]:=plot([[x2,y2]],style=point ,symbol=circle,color=red):\np[6]:=plot([[4,-8],[4,8]],linestyle=1,colo r=blue):\n#p[8]:=plot([[x2,y2],[x2,0]],linestyle=2,color=red):\nCombin edPlot:=plots[display](\n [seq(p[i],i=1..5)],\n \+ scaling=constrained,\n labels=[``,``],\n \+ #tickmarks=[5,9],\n #view=[x_left..x_right,y_ve rtex-20..y_vertex+20],\n titlefont=[HELVETICA,DEFAULT,1 4],\n 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#-F$6%7$Fe[n7$Ff[nF_[lFj[nFh\\n-F$6&7#7$F+F_[lFj[nF\\\\nF`\\n-F$6%7$7$ F_[lF_[lFc]nFj[nFh\\n-F$6%7$Fc]nFc]nFj[nFh\\n-%&TITLEG6$%9Chapter~6.2, ~Exercise~19G-%%FONTG6%%*HELVETICAG%(DEFAULTG\"#9-%+AXESLABELSG6%%!GFh ^n-F`^n6#Fc^n-%(SCALINGG6#%,CONSTRAINEDG-%%VIEWG6$;F(Fgz;F($\"#5F*" 1 2 0 1 10 0 2 9 1 4 1 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 10 "Problem 2." }}{EXCHG {PARA 256 "" 0 "" {TEXT -1 10 "Problem 2." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 183 "2*x^2-4*x+2*y ^2-y=-1/8;\neq1:=student[completesquare](2*x^2-4*x);\neq2:=student[com pletesquare](2*y^2-y);\neq1+eq2=-1/8;\neq1+eq2+17/8=17/8-1/8;\n(1/2)*( eq1+eq2+17/8)=(1/2)*(17/8-1/8);``;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#/,**&\"\"#\"\"\")%\"xGF&F'F'*&\"\"%F'F)F'!\"\"*&F&F')%\"yGF&F'F'F/F, #F,\"\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq1G,&*&\"\"#\"\"\"),&% 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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);\n#p[0]:=plot(f(x),x=xl eft..xright,y=ybot..ytop,color=blue):\np[1]:=plot(g1(x),x=xleft..xrigh t,y=ybot..ytop,color=navy):\np[2]:=plot(g2(x),x=xleft..xright,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):\np[5]:=plot([[ 0,k],[h,k]],linestyle=2,color=red):\n#p[6]:=plot([[x2,y2]],style=point ,symbol=circle,color=red):\np[6]:=plot([[4,-8],[4,8]],linestyle=1,colo r=blue):\n#p[8]:=plot([[x2,y2],[x2,0]],linestyle=2,color=red):\nCombin edPlot:=plots[display](\n [seq(p[i],i=1..5)],\n \+ scaling=constrained,\n labels=[``,``],\n \+ #tickmarks=[5,9],\n #view=[x_left..x_right,y_ve rtex-20..y_vertex+20],\n titlefont=[HELVETICA,DEFAULT,1 4],\n title=``):\nCombinedPlot;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&*$),&%\"xG\"\"\"F)!\"\"\"\"#F)F)*$),&%\"yGF)#F)\"\"% F*F+F)F)F)" }}{PARA 13 "" 1 "" {GLPLOT2D 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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 Points: `*[x1,y1]=evalf([x1,y1],3),[x2 ,y2]=evalf([x2,y2],3);\np[0]:=plot(f(x),x=xleft..xright,y=ytop..ybot,c olor=blue):\np[1]:=plot(g1(x),x=xleft..xright,y=ytop..ybot,color=navy) :\np[2]:=plot(g2(x),x=xleft..xright,y=ytop..ybot,color=navy):\np[3]:=p lot([[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]],linest yle=2,color=red):\np[6]:=plot([[x2,y2]],style=point,symbol=circle,colo r=red):\np[7]:=plot([[0,y2],[x2,y2]],linestyle=2,color=red):\np[8]:=pl ot([[x2,y2],[x2,0]],linestyle=2,color=red):\nCombinedPlot:=plots[displ ay](\n [seq(p[i],i=0..8)],\n scaling=cons trained,\n labels=[``,``],\n #tickmarks= [5,9],\n #view=[x_left..x_right,y_vertex-20..y_vertex+2 0],\n titlefont=[HELVETICA,DEFAULT,14],\n \+ title=` `):\nCombinedPlot;\n`Substitute: `*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;\n sort(4*(expand(F(x,f(x)))-r^2))=0;\nx=x1,x2,` `*y=y1,y2;\n`Intersectio n 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\"p0k&*F-$\"3YLLLe%G?G%F-7$$!3uKL$3f_KF-7$$!3k++]P8#\\4(F-$\"3K++vo1YZIF-7$$!3Kmm;/siqmF-$\"3;LL3-OJ NGF-7$$!3Q****\\(y$pZiF-$\"3p***\\P*o%Qi#F-7$$!3jKLL$yaE\"eF-$\"3Kmmm \"RFjS#F-7$$!3s%HaF-$\"33LL$e4OZ@#F-7$$!3]******\\$*4)*\\F-$\"3 u*****\\n\\!**>F-7$$!3o******\\_&\\c%F-$\"3%)*****\\ixCy\"F-7$$!3%)*** ***\\1aZTF-$\"3#******\\KqPd\"F-7$$!3Imm;/#)[oPF-$\"39LL3-TC%Q\"F-7$$! 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