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Lera25 [3.4K]
3 years ago
6

the circular ripple caused by dropping a stone in a pond is increasing in area at a constant rate of 20 square meters per second

. Determine how fast the radius of this circular ripple is increasing when the area of the circular region is 25 pi
Mathematics
1 answer:
mojhsa [17]3 years ago
4 0

Answer:

  2/π ≈ 0.637 m/s

Step-by-step explanation:

The rate of change of area with respect to time is ...

  A = πr²

  dA/dt = 2πr·dr/dt

Filling in given values in the above equations, we can find r and dr/dt.

  25π = πr²   ⇒   r = 5

  20 = 2π·5·dr/dt

  dr/dt = 20/(10π) = 2/π . . . . meters per second

The radius is increasing at the rate of 2/π ≈ 0.637 meters per second.

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