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\noindent {\bf Problem Statement}
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\vbox{\hsize=3.65in\noindent A piece of wire
$180$ inches long is bent into the shape of an isosceles trapezoid
whose base angles are $\pi/3$ radians.

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\noindent a) Suppose $x$ is the length of the longer base of the
trapezoid and $y$ is the length of one of the slanted sides. Label the
$\hphantom{\rm lengths}$}\vskip -\baselineskip \noindent lengths of
all sides in terms of $x$ and $y$ and deduce a relationship between
$x$ and $y$.

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\noindent b) Find a formula for the area $A$ of the trapezoid as a
function of the single variable $x$.  

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\noindent c) Use your calculator to graph the function $A=A(x)$. Are
there any upper or lower bounds between which the value of $x$ must
lie? If so, decide what happens to $A$ as $x$ approaches those bounds,
and explain by drawing pictures of the trapezoid in those cases.




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