Question 1083859
The general formula for a cosine function is:
{{{ h(t) = A*cos( B*t + C ) + D }}}
{{{ abs(A) }}} is the amplitude 
{{{ C/B }}} is the phase shift
{{{ ( 2*pi )/abs( B ) }}} = period
{{{ abs( D ) }}} is the vertical shift
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(A)
The plot of a point that is a minimum at {{{ t=0 }}}
and then goes to a maximum and back to a
minimum would be a negative cosine function:
{{{ h(t) = -A*cos( B*t + C ) + D }}}
{{{ h(t) = -80*cos( B*t + C ) + 85 }}}
Two turns in 6 minutes is {{{ ( 4*pi )/6 = ( 2*pi )/3 }}}
{{{ B = ( 2*pi )/3 }}}
{{{ C = 0 }}} since there will be no phase shift
So now I have:
{{{ h(t) = -80*cos( ( ( 2*pi )/3)*t ) + 85 }}}
( checking this, when {{{ t = 6 }}}, {{{ B*t = 4*pi }}}
which is 2 turns )
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(B)
{{{ h(t) = -80*cos( ( ( 2*pi )/3)*t ) + 85 }}}
{{{ t = 1 }}}
{{{ h(1) = -80*cos( ( ( 2*pi )/3) ) + 85 }}}
{{{ h(1) = -80*cos( .667*pi ) + 85 }}}
{{{ h(1) = -80*(-.5 ) + 85 }}}
{{{ h(1) = 40 + 85 = 125 }}}
At 1 min, her height is 125 ft
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This kind of makes sense, because at {{{ t = 1.5 }}},
The ferris wheel is at maximum height:
{{{ h(t) = -80*cos( ( ( 2*pi )/3)*t ) + 85 }}}
{{{ h(1.5) = -80*cos( ( ( 2*pi )/3)*(3/2) ) + 85 }}}
{{{ h(1.5) = -80*cos( pi ) + 85 }}}
{{{ h(1.5) = -80*(-1) + 85 }}}
{{{ h(1.5) = 165 }}} ft
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Hope this helps -get other opinions if needed