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bezimeni [28]
3 years ago
5

Let A(t) be the area of a circle with radius r(t), at time t in min. Suppose the radius is changing at the rate of drdt=6 ft/min

. Find the rate of change of the area at the moment in time when r=9 ft
Mathematics
1 answer:
mylen [45]3 years ago
5 0

Answer:

The rate of change is 108\pi ft^(2)/min

Step-by-step explanation:

The area of a circle is given by the following equation:

A(t) = \pi r^{2}

To solve this question, we have to realize the implicit differentiation in function of t. We have two variables, A and r. So

\frac{dA(t)}{dt} = 2\pi r \frac{dr}{dt}

We have that:

\frac{dr}{dt} = 6, r = 9.

We want to find \frac{dA}{dt}

So

\frac{dA(t)}{dt} = 2\pi*9*6

\frac{dA}{dt} = 108\pi

Since the area is in square feet, the rate of change is in ft^(2)/min.

So the rate of change is 108\pi ft^(2)/min

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