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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 417 "## PROBLEM 5\n## Th
is problem can be solved by looking at the curved edge\n## of the trai
n track as a section of a circle.  Converting\n## miles to feet, we en
d up with the following two\n## equations with two unknowns:\n##     2
*theta*radius=5281  ->  theta=5281/(2*radius) \n##   radius*sin(theta)
=5280/2 ->\n##                radius*sin(5281/(2*radius))=2640\n## So \+
we'll solve the above equation for the radius first.    " }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "fsolve(r*sin(5281/(2*r))=2640);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#$!+]!3N$y!\"&" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 83 "## Since root is negative, check to see if the p
ositive root\n## is also a solution:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 26 "(0-%)*sin(5281/(2*(0-%)));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"++++SE!\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 44 "## So radius=78335.08050 feet\n## Now find h:" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 12 "78335.08050;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"+]!3N$y!\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 30 "h:=(%)-((%)^2-(2640^2))^(1/2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#>%\"hG$\"(X)\\W!\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }
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