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The radius of circular plate changes at the rate 2 cm/s. at what rate does the area changes when the radius of plate is 1/π cm?

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Final answer:

The rate at which the area changes when the radius of the plate is 1/π cm is 4 cm^2/s.

Step-by-step explanation:

To find the rate at which the area changes, we can use the derivative of the area formula.

The area of a circle is given by A = πr^2, where r is the radius.

We are given that the radius is changing at a rate of 2 cm/s, so we can substitute this value into the derivative.

dA/dt = 2πr(dr/dt)

Plugging in r = 1/π cm and dr/dt = 2 cm/s, we can calculate the rate at which the area changes.

dA/dt = 2π(1/π)(2) = 4 cm^2/s

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