Question 993688
You need to find:
{{{ s > 1188 }}}
{{{ -12t^2 + 240t > 1188 }}}
{{{ -t^2 + 120t > 594 }}}
First find:
{{{ -t^2 + 120t = 594 }}}
Complete the square:
{{{ t^2 - 120t + ( -120/2 )^2 = -594 + ( -120/2 )^2 }}}
{{{ t^2 - 120t + 3600 = -594 + 3600 }}}
{{{ ( t - 60 )^2 = 3006 }}}
{{{ ( t - 60 )^2 = 54.827^2 }}}
{{{ t - 60 = 54.827 }}}
{{{ t = 114.827 }}}
and also:
{{{ t - 60 = -54.827 }}}
{{{ t = 5.173 }}}
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The values of {{{ t }}} for which {{{ -12t^2 + 240t > 1188 }}} are:
{{{ 5.173 < t < 114.827 }}}
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Check:
Let {{{ t = 5.1 }}}
{{{ -12t^2 + 240t > 1188 }}}
{{{ -12*5.1^2 + 240*5.1 > 1188 }}}
{{{ -12*26.01 + 1224 >1188 }}}
{{{ -312.12 + 1224 > 1188 }}}
{{{ 911.88 > 1188 }}}
This is not true, as it must be
Now check for:
{{{ t = 114.85 }}}, and the inequality
must also be NOT true