## Each side of a square is increasing at a rate of 4 cm/s. At what rate (in cm2/s) is the area of the square increasing when the area of the s

Question

Each side of a square is increasing at a rate of 4 cm/s. At what rate (in cm2/s) is the area of the square increasing when the area of the square is 25 cm2

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6 months 2021-07-28T14:36:20+00:00 1 Answers 3 views 0

The area of the square is increasing at a rate of 40 square centimeters per second.

Step-by-step explanation:

The area of the square (), in square centimeters, is represented by the following function:

(1)

Where is the side length, in centimeters.

Then, we derive (1) in time to calculate the rate of change of the area of the square (), in square centimeters per second:

(2)

Where is the rate of change of the side length, in centimeters per second.

If we know that and , then the rate of change of the area of the square is:

The area of the square is increasing at a rate of 40 square centimeters per second.