Let a(t)a(t) be the area of a circle with radius r(t)r(t), at time tt in min. suppose the radius is changing at the rate of drdt=5drdt=5 ft/min. find the rate of change of the area at the moment in time when r=6r=6 ft

The relationship between the rates of change can be found by taking the derivative of area with respect to time.

... a(t) = π·r(t)²

... a'(t) = 2π·r(t)·r'(t)

At the time of interest, we have

... a'(t) = 2π·(6 ft)·(5 ft/min) = 60π ft²/min

The rate of change of area at that time is 60π ≈ 188.5 ft²/min.

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step-by-step explanation:

step-by-step explanation:

to find if any function is an inverse of the other, put the first equation in as x in the next one. then simplify and solve. if at the end you get the statement y = x, then it is an inverse. if you get anything else, it is not.