(b) Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate

Question

(b) Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 1 m/s, how fast is the area of the spill increasing when the radius is 33 m?

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Eden 2 weeks 2021-09-13T05:08:23+00:00 1 Answer 0

Answers ( )

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    2021-09-13T05:09:28+00:00

    Answer:

      66π m²/s ≈ 207.3 m²/s

    Step-by-step explanation:

    The area is given by …

      A = πr²

    and its rate of change is given by …

      A’ = 2πr·r’

    Filling in the given values, we have …

      A’ = 2π(33 m)(1 m/2) = 66π m²/s ≈ 207.3 m²/s

    The area of the spill is increasing at the rate of 66π m²/s ≈ 207.3 m²/s.

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