Question 1095296
{{{ s(t) = -16t^2 + 192t }}}
{{{ -16t^2 + 192t > 252 }}}
{{{ -4t^2 + 48t - 63 > 0 }}}
{{{ t = ( -b +- sqrt( b^2 - 4a*c )) / ( 2a ) }}}
{{{ a = -4 }}}
{{{ b = 48 }}}
{{{ c = -63 }}}
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{{{ t = ( -48 +- sqrt( 48^2 - 4*(-4)*(-63) )) / ( 2*(-4) ) }}}
{{{ t = ( -48 +- sqrt( 2304 - 1008 ) ) / ( -8 ) }}}
{{{ t = ( -48 +- sqrt( 1296 ) ) / (-8) }}}
{{{ t = ( -48 + 36 ) / (-8) }}}
{{{ t = 12/8 }}}
{{{ t = 3/2 }}}
and also:
{{{ t = ( -48 - 36 ) / (-8) }}}
{{{ t = 84/8 }}}
{{{ t = 10.5 }}}
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The interval of time for which {{{ s(t) > 252 }}} ft is
{{{ 1.5 < t < 10.5 }}} sec
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check:
here's the plot:
{{{ graph(  400, 400, -3, 15, -60, 600, -16x^2 + 192x ) }}}
Looks about right