Question

question: a rectangle has an area that is decreasing at a rate of 541 square inches per hour with the width being held constant. determine the rate of change of the length if the width is 3 inches. (enter the answer as an exact value. do not include the units in your answer.) provide your answer below:

Explanation:

Step1: Recall area formula

$A = lw$, since $w$ is constant, $\frac{dA}{dt}=w\frac{dl}{dt}$

Step2: Solve for $\frac{dl}{dt}$

Given $\frac{dA}{dt}=- 541$, $w = 3$, then $\frac{dl}{dt}=\frac{\frac{dA}{dt}}{w}=\frac{-541}{3}$

Answer:

$-\frac{541}{3}$