Question 1062726
{{{ V(t) = 50000*sin( 15*( t-3 ) ) + 100000 }}}
{{{ V(0) = 50000*sin( 15*(-3) ) + 100000 }}}
{{{ V(0) = 50000*sin( -45 ) + 100000 }}}
( is the angle in degrees or radians? I'm guessing degrees )
{{{ V(0) = (-1/sqrt(2) )*50000 + 100000 }}}
{{{ V(0) = -35355.34 + 100000 }}}
{{{ V[0] = 64644.66 }}}
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(a)
The sine function varies from {{{ -1 }}} to {{{ 1 }}}
{{{ V[min] = 50000*(-1) + 100000 }}}
{{{ V[min] = 50000 }}}
and
{{{ V[max] = 50000*(1) + 100000 }}}
{{{ V[max]  = 150000 }}}
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(b) 
{{{ V[max] = 50000*(1) + 100000 }}}
{{{ sin( 15*( t-3 ) ) = 1 }}}
{{{ 15*( t - 3 ) = 90 }}}
{{{ t - 3 = 6 }}}
{{{ t = 9 }}}
The volume is maximum at 9 AM
and
{{{ V[min] = 50000*(-1) + 100000 }}}
{{{ sin( 15*( t-3 ) ) = -1 }}}
{{{ 15*( t-3 ) = 270 }}}
{{{ t - 3 = 18 }}}
{{{ t = 21 }}}
The volume is minimum at 9 PM 
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(c)
{{{ t = 10.5 }}}
{{{ 15*( t-3 ) = 15*( 10.5 - 3 ) }}}
{{{ 15*7.5 = 112.5 }}}
{{{ sin( 112.5 ) = .9239 }}}
{{{ V(10.5) = 50000*.9239 + 100000 }}}
{{{ V(10.5) = 46195 + 100000 }}}
{{{ V(10.5) = 146195 }}} kl
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(d)
{{{ V(t) = 130000 }}}
{{{ 130000 = 30000 + 100000 }}}
{{{ 50000*sin( 15*( t-3 ) ) = 30000 }}}
{{{ sin( 15*( t-3 ) ) = .6 }}}
{{{ 15*( t-3 ) = 36.8699 }}}
{{{ t - 3 = 2.458 }}}
{{{ t = 5.458 }}}
{{{ .458*60 = 27.48 }}}
{{{ .48*60 = 29 }}} 
and
{{{ 15*( t - 3 ) = 180 - 36.8699 }}}
{{{ 15*( t - 3 ) = 143.13 }}}
{{{ t - 3 = 9.542 }}}
{{{ t = 12.542 }}}
{{{ .542*60 = 32.52 }}}
{{{ .52*60 = 31.2 }}}
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The volume is greater than 130, 000 kl between
5:27:29 AM and 12:32:31 PM
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Lots of math! check it carefully