Question

A hypothetical square shrinks at a rate of 49 squared meters per minute. At what rate are the sides of the square changing when the sides are 13m each?

Answer 1

-3.769 m/min

Step-by-step explanation:

`(dA)/(dt)` = Rate of change of area = -49 m²/min (negative due to shrinking)

s = Side length = 13 m

`(ds)/(dt)` = Rate of change of side

Area of a square is given by

`A=s^2`

Differentiating with respect to time

`(dA)/(dt)=(ds^2)/(dt)\\\Rightarrow (dA)/(dt)=2s(ds)/(dt)\\\Rightarrow (ds)/(dt)=(dA)/(dt)* (1)/(2s)\\\Rightarrow (ds)/(dt)=-49* (1)/(13)\\\Rightarrow (ds)/(dt)=-3.769\ m/min`

The rate of change of the sides of the square is -3.769 m/min