Question 1092840
{{{ 2400/60 = 40 }}} yd of fence
{{{ x }}} = width
{{{ 40 - 2x }}}  = length
Let {{{ A }}} = area
{{{ A = x*( 40 - 2x ) }}}
{{{ A = -2x^2 + 40x }}}
The x-value for the maximum area is
given by the formula:
{{{ x[max] = -b/(2a) }}}
{{{ a = -2 }}}
{{{ b = 40 }}}
{{{ x[max] = -40/(2*(-2)) }}}
{{{ x[max] = 10 }}} yds
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Plug this result back into equation to get {{{ A[max] }}}
{{{ A[max] = -2*10^2 + 40*10 }}}
{{{ A[max] = -200 + 400 }}}
{{{ A[max] = 200 }}} yd2
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Here's the plot of the Area function:
{{{ graph( 400, 400, -2, 25, -20, 250, -2x^2 + 40x ) }}}