SOLUTION: The radius of a circle as a function of time is defined by the equation, r(t)=4t^2+3t+1. Determine the rate of change in the area of the circle when dr/dt=11.
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Question 596252: The radius of a circle as a function of time is defined by the equation, r(t)=4t^2+3t+1. Determine the rate of change in the area of the circle when dr/dt=11.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
We have
so when dr/dt = 11, t = 1.
The area of the circle as a function of time is
)^2)
^2)
We differentiate both sides with respect to t:
(8t + 3))
Replace t = 1 to obtain
(11) = 176 \pi)
(units squared per unit of time)
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