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{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 1 12 255 0 0 1 2 1 2 
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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 200 43 "Tangent Line to the Param
etric Curve Maplet" }}{PARA 0 "" 0 "" {TEXT 200 0 "" }}{PARA 0 "" 0 "
" {TEXT 200 12 "Chase Caruth" }}{PARA 0 "" 0 "" {TEXT 200 12 "MATH 151
-202" }}{PARA 0 "" 0 "" {TEXT 200 17 "November 22, 2005" }}{PARA 0 "" 
0 "" {TEXT 200 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "with(Maplets): with(Maplets[
Tools]): with(Maplets[Elements]): with(plots):\nStartEngine();" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "randomize():" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "lightorange:=\"#FFB300\":" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 530 "right:= [\"Bullseye!\", \"G
reat!\", \"That's absolutely right!\", \"You're unstoppable!\", \"Corr
ect!\", \"You nailed that one!\", \"YES!\", \"Way to go!\", \"I knew y
ou could do it!\", \"Perfecto!\", \"You're awesome!\", \"That's amazin
g!\", \"You're a math whiz!\", \"Whoop!\", \"Nice job!\", \"That's rig
ht!\", \"That's the way!\", \"I like the sound of that!\", \"Ding!  Th
at's correct!\", \"You're a genius!\", \"Right on the mark!\", \"Brick
...house!\", \"Oh yeah!\", \"Wonderful!\", \"Excellent!\", \"You got i
t!\", \"Can I get a what what!\", \"Holla!\", \"You're incredible!\"]:
 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 263 "wrong:=[\"Try again.
\", \"Nope.  I'm sorry.\", \"C'mon, you can do it.\", \"You can do bet
ter.\", \"You're close.\", \"Look closer.\", \"Put on your thinking ca
p.\", \"Better luck next time.\", \"Keep trying.\", \"Never give up.\"
, \"Try again.  I have faith in you.\", \"Try harder.\"]:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 309 "final:=[\"You know your parametric
 equations!  Move on to the next curve!\", \"You're doing so awesome! \+
 Keep on keepin' on!\", \"Wow!  That's awesome!  Don't stop now!\", \"
You got all of them right!  Way to go!  Go on to the next curve!\", \"
You're doing great!  Keep on truckin'!\", \"Oh yeah!  Try the next cur
ve!\"]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 191 "hint:=[\"Now tr
y it yourself.\", \"There it is.  Now figure it out.\", \"The hint is \+
great, but try it yourself.\", \"That was practice.  Try it again.\", \+
\"Don't settle for the hint.  Work it out.\"]:" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 2095 "ParamTanLine:=Maplet(onstartup = RunWindow(M
AIN),\nWindow[MAIN]('title'=\"Find the Tangent Line to the Parametric \+
Curve\",\n  [ halign=none,\n    [ Button(\"New Curve\", Evaluate('func
tion' = \"ask\")),\n      HorizontalGlue(),\n      Button(\"Quit\", Sh
utdown())\n    ],\n    [ \"The goal of this maplet is to find the vect
or equation for the line tangent to the curve\",\n      HorizontalGlue
()\n    ],\n    [ HorizontalGlue(),\n      \"r(t) =\",\n      MathMLVi
ewer['curve']('width'=250, 'height'=60),\n      \"at     t =\",\n     \+
 TextField['given_t'](\"a\", 'width'=10, 'editable'=false),\n      Hor
izontalGlue()\n    ],\n    [ Label[Lra](\"Find r(a):\"),\n      TextFi
eld['answer1']('width'=10, background=turquoise),\n      HorizontalGlu
e(),\n      Button(\"Submit\", Evaluate('function' = \"check1\")),\n  \+
    TextField['response1']('width'=25, 'editable'='false', background=
white),\n      Button(\"Show\", Evaluate('function' = \"show1\"))\n   \+
 ],\n    [ \"Find r'(t): \",\n      TextField['answer2']('width'=15, b
ackground=turquoise),\n      HorizontalGlue(),\n      Button(\"Submit
\", Evaluate('function' = \"check2\")),\n      TextField['response2'](
'width'=25, 'editable'='false', background=white),\n      Button(\"Sho
w\", Evaluate('function' = \"show2\"))\n    ],\n    [ Label[Lrpa](\"Fi
nd r'(a):\"),\n      TextField['answer3']('width'=10, background=turqu
oise),\n      HorizontalGlue(),\n      Button(\"Submit\", Evaluate('fu
nction' = \"check3\")),\n      TextField['response3']('width'=25, 'edi
table'='false', background=white),\n      Button(\"Show\", Evaluate('f
unction' = \"show3\"))\n    ],\n    [ \"Enter the vector equation of t
he tangent line:\",\n      HorizontalGlue()\n    ],\n    [ \"[x,y] =\"
,\n      TextField['answer4']('width'=20, background=turquoise),\n    \+
  HorizontalGlue(),\n      Button(\"Submit\", Evaluate('function' = \"
check4\")),\n      TextField['response4']('width'=25, 'editable'='fals
e', background=white),\n      Button(\"Show\", Evaluate('function' = \+
\"show4\"))\n    ],\n    [ TextField['reply']('width'=40, 'editable'='
false', background=white)\n    ],\n    [\"This Maplet was designed by \+
Chase Caruth, Class of 2009.    Copyright 2005\"\n    ]\n  ]\n)\n):" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 868 "ask:=proc()\nlocal gen1, \+
gen2, gen3, a, b, c, d, exponent_x, exponent_y, x, y;\nglobal eq, t0;
\ngen1:=rand(-5..5):\ngen2:=rand(1..3):\ngen3:=rand(-2..2):\na:=gen1()
;\nb:=gen1();\nc:=gen1();\nd:=gen1();\nexponent_x:=gen2();\nexponent_y
:=gen2();\nwhile(a=0 or c=0) do\n     a:=gen1();\n     c:=gen1();\nend
 do;\nx:=a*t^exponent_x + b*t^gen2();\ny:=c*t^exponent_y + d*t^gen2();
\neq:= [x, y];\nSet('curve'=MathML[Export](eq));\nt0:=gen3();\nSet('gi
ven_t'=t0);\nSet('Lra'(caption)=cat(\"Find r(\", t0 , \"):\"));\nSet('
Lrpa'(caption)=cat(\"Find r'(\", t0 , \"):\"));\nSet('answer1'=\"\"):
\nSet('response1'=\"\", 'response1'(background)=white);\nSet('answer2'
=\"\"):\nSet('response2'=\"\", 'response2'(background)=white);\nSet('a
nswer3'=\"\"):\nSet('response3'=\"\", 'response3'(background)=white);
\nSet('answer4'=\"\"):\nSet('response4'=\"\", 'response4'(background)=
white);\nSet('reply'=\"\", 'reply'(background)=white);\nend proc:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 491 "check1:=proc()\nlocal usera
nswer1, rightrand, wrongrand;\nglobal correctanswer1;\nrightrand := ra
nd(1..nops(right)):\nwrongrand := rand(1..nops(wrong)):\nuseranswer1:=
Get('answer1'::anything, corrections=true, update=true):\ncorrectanswe
r1:=subs(t=t0,eq);\nSet('reply'=\"\", 'reply'(background)=white);\nif \+
useranswer1=correctanswer1\n   then Set('response1'=right[rightrand()]
, 'response1'(background)=green);\n   else Set('response1'=wrong[wrong
rand()], 'response1'(background)=red);\nend if;\nend proc:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 273 "show1:=proc()\nlocal hintrand;\ngl
obal correctanswer1;\nhintrand := rand(1..nops(hint)):\ncorrectanswer1
:=subs(t=t0,eq);\nSet('answer1'=correctanswer1);\nSet('response1'=hint
[hintrand()], 'response1'(background)=lightorange);\nSet('reply'=\"\",
 'reply'(background)=white);\nend proc:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 481 "check2:=proc()\nlocal useranswer2, correctanswer2, r
ightrand, wrongrand;\nrightrand := rand(1..nops(right)):\nwrongrand :=
 rand(1..nops(wrong)):\nuseranswer2:=Get('answer2'::anything, correcti
ons=true, update=true):\ncorrectanswer2:=diff(eq,t);\nSet('reply'=\"\"
, 'reply'(background)=white);\nif useranswer2=correctanswer2\n   then \+
Set('response2'=right[rightrand()], 'response2'(background)=green);\n \+
  else Set('response2'=wrong[wrongrand()], 'response2'(background)=red
);\nend if;\nend proc:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 263 "
show2:=proc()\nlocal correctanswer2, hintrand;\ncorrectanswer2:=diff(e
q,t);\nhintrand := rand(1..nops(hint)):\nSet('answer2'=correctanswer2)
;\nSet('response2'=hint[hintrand()], 'response2'(background)=lightoran
ge);\nSet('reply'=\"\", 'reply'(background)=white);\nend proc:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 500 "check3:=proc()\nlocal usera
nswer3, rightrand, wrongrand;\nglobal correctanswer3;\nrightrand := ra
nd(1..nops(right)):\nwrongrand := rand(1..nops(wrong)):\nuseranswer3:=
Get('answer3'::anything, corrections=true, update=true):\ncorrectanswe
r3:=subs(t=t0, diff(eq,t));\nSet('reply'=\"\", 'reply'(background)=whi
te);\nif useranswer3=correctanswer3\n   then Set('response3'=right[rig
htrand()], 'response3'(background)=green);\n   else Set('response3'=wr
ong[wrongrand()], 'response3'(background)=red);\nend if;\nend proc:" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 282 "show3:=proc()\nlocal hint
rand;\nglobal correctanswer3;\nhintrand := rand(1..nops(hint)):\ncorre
ctanswer3:=subs(t=t0, diff(eq,t));\nSet('answer3'=correctanswer3);\nSe
t('response3'=hint[hintrand()], 'response3'(background)=lightorange);
\nSet('reply'=\"\", 'reply'(background)=white);\nend proc:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 678 "check4:=proc()\nlocal useranswer4,
 rightrand, wrongrand, finalrand;\nglobal correctanswer4;\nrightrand :
= rand(1..nops(right)):\nwrongrand := rand(1..nops(wrong)):\nfinalrand
 := rand(1..nops(final)):\nuseranswer4:=Get('answer4'::anything, corre
ctions=true, update=true):\ncorrectanswer4:=[correctanswer1[1]+correct
answer3[1]*t, correctanswer1[2]+correctanswer3[2]*t];\nif useranswer4=
correctanswer4\n   then Set('response4'=right[rightrand()], 'response4
'(background)=green);\n        Set('reply'=final[finalrand()], 'reply'
(background)=green);\n   else Set('response4'=wrong[wrongrand()], 'res
ponse4'(background)=red);\n        Set('reply'=\"\", 'reply'(backgroun
d)=white);\nend if;\nend proc:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 338 "show4:=proc()\nlocal hintrand;\nglobal correctanswer4;\nhintr
and := rand(1..nops(hint)):\ncorrectanswer4:=[correctanswer1[1]+correc
tanswer3[1]*t, correctanswer1[2]+correctanswer3[2]*t];\nSet('answer4'=
correctanswer4);\nSet('response4'=hint[hintrand()], 'response4'(backgr
ound)=lightorange);\nSet('reply'=\"\", 'reply'(background)=white);\nen
d proc:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "Display( ParamTa
nLine );" }}}{EXCHG }{EXCHG }{EXCHG }{EXCHG }{EXCHG }}{MARK "0 0 0" 0 
}{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }