question the side lengths of a square increase at a rate of 4 cm/s. find the rate at which the area of the…

question the side lengths of a square increase at a rate of 4 cm/s. find the rate at which the area of the square is increasing when the side length is 11 cm. provide your answer below: the area of the square is increasing at a rate of cm²/s.

question the side lengths of a square increase at a rate of 4 cm/s. find the rate at which the area of the square is increasing when the side length is 11 cm. provide your answer below: the area of the square is increasing at a rate of cm²/s.

Answer

Explanation:

Step1: Define variables

Let the side - length of the square be $s$ and the area be $A$. Then $A = s^{2}$.

Step2: Differentiate with respect to time $t$

Using the chain - rule, $\frac{dA}{dt}=2s\frac{ds}{dt}$.

Step3: Substitute given values

We know that $\frac{ds}{dt}=4$ cm/s and $s = 11$ cm. Substitute these values into the equation: $\frac{dA}{dt}=2\times11\times4$.

Step4: Calculate the result

$\frac{dA}{dt}=88$ cm²/s.

Answer:

88