Calculus

The area of a circle is changing at a rate of 2 in.^(2)/sec. At what rate is its radius changing when the radius is 9 in.?

a. (9/2)in./sec.

b. (2/9)in./sec.

c. (2/9pie)in./sec.

d. (1/9pie)in./sec.

e. (1/9)in./sec.

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  1. A = πr^2
    d(A)/dt = 2πr dr/dt

    given: dA/dt = 2
    find : dr/dt when r = 9

    2 = 2π(9) dr/dt
    dr/dt = 1/(9π) inches/sec

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