{VERSION 2 3 "SGI IRIS UNIX" "2.3" } {USTYLETAB {CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 256 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "courier" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "courie r" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 4 4 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 19 "MAT331 - Exercise 4" }} {PARA 257 "" 0 "" {TEXT 256 10 "More Maple" }}}{SECT 0 {PARA 3 "" 0 " " {TEXT -1 8 "1. Roses" }}{PARA 0 "" 0 "" {TEXT -1 29 "Make several pi ctures of the " }{XPPEDIT 18 0 "n" "I\"nG6\"" }{TEXT -1 41 "-leaved ro se given by the polar equation " }{XPPEDIT 18 0 "r(theta)=sin(n*theta) " "/-%\"rG6#%&thetaG-%$sinG6#*&%\"nG\"\"\"F&F," }{TEXT -1 31 " for var ious integer values of " }{XPPEDIT 18 0 "n" "I\"nG6\"" }{TEXT -1 46 ". How\nis the number of ``petals'' related to " }{XPPEDIT 18 0 "n" "I \"nG6\"" }{TEXT -1 1 "?" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 21 "2. Th e dog on a leash" }}{PARA 0 "" 0 "" {TEXT -1 77 "This problem is relat ed to the ``dog on a leash'' example discussed in class." }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 2 "a." }}{PARA 0 "" 0 "" {TEXT -1 27 "Conside r the set of points " }{XPPEDIT 18 0 "p" "I\"pG6\"" }{TEXT -1 67 " in \+ the plane for which \ndist(p,y-axis) + dist(p,(1,0)) = c\nwhere " } {XPPEDIT 18 0 "c" "I\"cG6\"" }{TEXT -1 86 " is a constant greater than 1. Make a good picture of this set for various values of " } {XPPEDIT 18 0 "c" "I\"cG6\"" }{TEXT -1 21 ", in particular, for " } {XPPEDIT 18 0 "c" "I\"cG6\"" }{TEXT -1 12 " in the set " }{XPPEDIT 18 0 "\{1.01,1.1,1.5,2,3,10\}" "<($\"$,\"!\"#$\"#6!\"\"$\"#:!\"\"\"\"#\" \"$\"#5" }{TEXT -1 95 ". If you like, you may put all the graphs on o ne set of axes. You should probably use either " }{TEXT 257 12 "impli citplot" }{TEXT -1 4 " or " }{TEXT 258 13 " contourplot." }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 2 "b." }}{PARA 0 "" 0 "" {TEXT -1 107 "Show t hat the equation for the set of points in the plane which satisfy\n \011dist(p,y-axis) - dist(p,(1,0)) = c" }}{PARA 0 "" 0 "" {TEXT -1 26 "is a parabola of the form " }{XPPEDIT 18 0 "x=a*y^2+b" "/%\"xG,&*&%\" aG\"\"\"*$%\"yG\"\"#F'F'%\"bGF'" }{TEXT -1 31 ", for an appropriate ch oice of " }{XPPEDIT 18 0 "a" "I\"aG6\"" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "b" "I\"bG6\"" }{TEXT -1 1 "." }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 2 "c." }}{PARA 0 "" 0 "" {TEXT -1 77 "What do you get if you replac e the y-axis with an arbitrary line of the form " }{XPPEDIT 18 0 "y=m* x+b" "/%\"yG,&*&%\"mG\"\"\"%\"xGF'F'%\"bGF'" }{TEXT -1 88 "? Can you \+ get a nice form (that is, without square roots) for the relationship b etween " }{XPPEDIT 18 0 "x" "I\"xG6\"" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "y" "I\"yG6\"" }{TEXT -1 1 "?" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 14 "3. Casey Jones" }}{PARA 0 "" 0 "" {TEXT -1 315 "Consider a trai n moving at a speed of 60 mph directly north. The center of each whee ls of the train is always 1 foot above the track, and extend 1.2\" bel ow the track. The engine is red, and it is a Tuesday. At exactly 4 pm , there is a point on the train moving due south. Where is it, and wh at is its velocity? " }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 6 "Hints." } }{PARA 0 "" 0 "" {TEXT -1 25 "One mile is 5,280 feet. " }}{PARA 0 "" 0 "" {TEXT -1 49 "Cycloids and Trochoids are interesting objects. " } }{PARA 0 "" 0 "" {TEXT -1 91 "Ben Franklin wanted a turkey for the nat ional bird, because he thought eagles were nasty. " }}{PARA 0 "" 0 " " {TEXT -1 42 "Maple is better at arithmetic than I am. " }}{PARA 0 " " 0 "" {TEXT -1 22 "One foot equals 12\". " }}{PARA 0 "" 0 "" {TEXT -1 47 "Most of the words in this problem are irrelvant" }}}}}{MARK "1 \+ 1 8" 1 }{VIEWOPTS 1 1 0 1 1 1803 }