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The length of a rectangle is increasing at a rate of $4$ inches per second while its width is decreasing at a rate of $3$ inches per second. At what rate, in square inches per second, is the area of the rectangle changing when its length is $23$ inches and its width is $18$ inches?

Aug 29, 2022

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At what rate, in square inches per second, is the area of the rectangle changing?

Hello Guest!

$$\Delta A/sec=\dfrac{(l+4in)(w-3in)-l\cdot w}{sec}\\ \Delta A/sec=\dfrac{(23in+4in)(18in-3in)-23in\cdot 18in}{sec}\\ \color{blue}\Delta A/sec=-\dfrac{9\ inch^2}{sec}$$

The area decreases at the rate of 9 square inches per second.

Aug 29, 2022