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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 258 10 "MATH-1850 " }{TEXT -1 3 "
   " }{TEXT 259 18 "COMPUTER PROBLEM 9" }{TEXT -1 56 "     DUE:  Tuesd
ay, November 14, 2000, in your lab class" }}{PARA 0 "" 0 "" {TEXT -1 
17 "\nTeam members:   " }{TEXT 266 54 "(All lines for answers below wi
ll extend as you type.)" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 16 "          (1)   " }{TEXT 260 0 "" }
{TEXT -1 0 "" }{TEXT 263 17 "     SOLUTION    " }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 16 "          (2)   " }{TEXT 
261 0 "" }{TEXT -1 0 "" }{TEXT 264 9 "         " }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 16 "          (3)   " }{TEXT 
262 0 "" }{TEXT -1 0 "" }{TEXT 265 9 "         " }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 25 "Score:               / 6
\n" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 257 33 "INSTRUCTIONS (Click box i
n front)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 1192 "It is strongly suggested that this project be worked in
 teams (of up to 3  persons). Approaches may be discussed among differ
ent teams, but each team must write their OWN report.\nREQUIREMENTS OF
 REPORT:\n- Mathematical contents (correctness and completeness) count
s most. Solve the problems and show all essential calculations (comman
ds and output) and plots. Please do not submit work that is not essent
ial (e.g. checking out how the function fplot in Problem 1 works - thi
s may be essential to your understanding, but it s not essential for t
he reader).\n- Explain the steps you carry out. Explain the approaches
/techniques that you use.\n- Add explanations and answer questions whe
re asked to do so. By all means, include additional explanations/obser
vations/conclusions that come to your mind! (This could translate to e
xtra credit.)\nHOW TO SUBMIT THE REPORT\nEach team submits ONE printed
 copy (stapled) by the due date. (Please save the electronic version, \+
as you will be asked to submit that, too, at a future time.)\nYou can \+
print from inside your Maple worksheet (choose File/Print or click on \+
the printer button). Set the ZOOM FACTOR to 100% (smallest magnifying \+
glass) before printing.\n" }{TEXT 256 62 "Please remove these instruct
ions before submitting the report." }}}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 267 9 "PROBL
EM A" }{TEXT -1 80 "   Find the equation of the tangent line to the gr
aph of the implicit function  " }{XPPEDIT 18 0 "x^2+2*y = x*y^3+154;" 
"6#/,&*$%\"xG\"\"#\"\"\"*&\"\"#F(%\"yGF(F(,&*&F&F(*$F+\"\"$F(F(\"$a\"F
(" }{TEXT -1 24 "  at the point (5, - 3)." }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 50 "(a)  Find the derivative \+
of the implicit function:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
100 "(dy)/(dx) = implicitdiff(x^2+2*y = x*y^3+154, y, x); der := impli
citdiff(x^2+2*y = x*y^3+154, y, x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 14 "(b)  Find the " }{TEXT 268 5 "e
xact" }{TEXT -1 110 " value of the slope of the tangent line to the gr
aph of the implicit function at the point (5, - 3) using the " }{TEXT 
269 4 "subs" }{TEXT -1 9 " command:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 29 "mtan := subs(x=5, y=-3, der);" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 103 "(c)  Find the equat
ion of the tangent line to the graph of the implicit function at the p
oint (5, - 3):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "y + 3 = m
tan*(x-5); y = solve(%, y);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 270 9 "
PROBLEM B" }{TEXT -1 6 "  If  " }{TEXT 271 1 "s" }{TEXT -1 1 "(" }
{TEXT 272 1 "t" }{TEXT -1 4 ") = " }{XPPEDIT 18 0 "2*t^3-7*t^2+4*t+1;
" "6#,**&\"\"#\"\"\"*$%\"tG\"\"$F&F&*&\"\"(F&*$F(\"\"#F&!\"\"*&\"\"%F&
F(F&F&\"\"\"F&" }{TEXT -1 86 "  is the position function which gives t
he position (in meters) of a particle at time " }{TEXT 256 1 "t" }
{TEXT -1 102 " (in seconds), then find the acceleration of the particl
e at the time(s) when the particle is stopped." }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 34 "(a)  Define the posi
tion function " }{TEXT 273 1 "s" }{TEXT -1 20 " using Maple syntax:" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "s := t -> 2*t^3 - 7*t^2 + \+
4*t + 1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "s(t);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 48 "(b
)  Define the instantaneous velocity function " }{TEXT 274 1 "v" }
{TEXT -1 21 " using Maple syntax: " }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "v:=D(s);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "
v(t);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 52 "(c)  Define the instantaneous acceleration function " }
{TEXT 275 1 "a" }{TEXT -1 46 " using Maple syntax and the position fun
ction " }{TEXT 280 1 "s" }{TEXT -1 1 ":" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "a := (D@@2)(s);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 5 "a(t);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 97 "(d)  Find the time(s) when the particle i
s stopped.  Don't forget to put units on your answer(s)." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "solve(v(t) = 0);" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT 276 19 "Answer to Part (d) " }{TEXT 277 3 "   " }{XPPEDIT 18 0 "
1/3;" "6#*&\"\"\"\"\"\"\"\"$!\"\"" }{TEXT 281 17 " sec, 2 sec      " }
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 187 
"(e)  Find the acceleration of the particle when it is stopped.  Don't
 forget to put units on your answer(s).  Also, explain the information
 that the answer(s) give you about the particle." }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 13 "a(1/3); a(2);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 278 
19 "Answer to Part (e) " }{TEXT 279 8 "   -10  " }{XPPEDIT 18 0 "m/(se
c^2);" "6#*&%\"mG\"\"\"*$%$secG\"\"#!\"\"" }{TEXT 282 8 " ,  10  " }
{XPPEDIT 18 0 "m/(sec^2);" "6#*&%\"mG\"\"\"*$%$secG\"\"#!\"\"" }{TEXT 
283 19 "   At the time of  " }{XPPEDIT 18 0 "1/3" "6#*&\"\"\"\"\"\"\"
\"$!\"\"" }{TEXT 284 78 "  sec when the particle was stopped, the part
icle decelerated at a rate of 10 " }{XPPEDIT 18 0 "m/(sec^2);" "6#*&%
\"mG\"\"\"*$%$secG\"\"#!\"\"" }{TEXT 285 99 "  and at the time of 2 se
c when the particle was stopped, the particle accelerated at a rate of
 10 " }{XPPEDIT 18 0 "m/(sec^2);" "6#*&%\"mG\"\"\"*$%$secG\"\"#!\"\"" 
}{TEXT 286 7 " .     " }}}}{MARK "2 0 0" 8 }{VIEWOPTS 1 1 0 1 1 1803 }