The arch of a bridge can be modeled by
d="TexFormula1" title="y=-\frac{1}{170}(x-225)(x+225)" alt="y=-\frac{1}{170}(x-225)(x+225)" align="absmiddle" class="latex-formula">, where 
and 
are measured in feet. The -axis represents the ground. Find the width of the arch of the bridge at ground level.
2 answers:
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For the largest area, half the fence is used parallel to the river, and the other half is used for the two ends of the rectangular space.
The dimensions are 475 m by 237.5 m.
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Let x represent the length along the river. Then the area (A) is found as
.. A = x*(950 -x)/2
This equation describes a parabola with its vertex (maximum) halfway between the zeros of x=0 and x=950. That is, the maximum area is achieved when half the fence is used parallel to the river.
The dimensions are 475 m by 237.5 m.
_____
Let x represent the length along the river. Then the area (A) is found as
.. A = x*(950 -x)/2
This equation describes a parabola with its vertex (maximum) halfway between the zeros of x=0 and x=950. That is, the maximum area is achieved when half the fence is used parallel to the river.