Question 1061238
{{{ h = -16t^2 + 128t }}}
{{{ 152 = -16t^2 + 128t }}}
Divide both sides by {{{ 8 }}}
{{{ 19 = -2t^2 + 16t }}}
{{{ -2t^2 + 16t - 19 = 0 }}}
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{{{ t = ( -b +- sqrt( b^2 - 4*a*c ))/(2*a) }}}
{{{ a = -2 }}}
{{{ b = 16 }}}
{{{ c = -19 }}}
{{{ t = ( -16 +- sqrt( 16^2 - 4*(-2)*(-19) ))/(2*(-2)) }}}
{{{ t = ( -16 +- sqrt( 256 - 152 ))/(-4)) }}}
{{{ t = ( -16 + sqrt( 104 ) ) / (-4) }}}
{{{ t = ( -16 + 10.2 ) / (-4) }}}
{{{ t = 5.8/4 }}}
{{{ t = 1.45 }}} sec
and, also
{{{ t = ( -16 - sqrt( 104 ) ) / (-4) }}}
{{{ t = ( -16 - 10.2 ) / (-4) }}}
{{{ t = 26.2/4 }}}
{{{ t = 6.55 }}} sec
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check answer:
Here's the plot:
{{{ graph( 500, 500, -2, 10, -30, 300, -16x^2 + 128x ) }}}
It's hard to see, but I think
my answers are close