Question

the length of a rectangle increases at a rate of 0.5 cm/sec and the width decreases at a rate of 0.5 cm/sec at the time when the length is 10cm and the width is 7 cm what is the rate of change in the area of the rectangle?

Answer 1

Explanation:

let length=x

width=y

area A=xy

`(dA)/(dt)=x(dy)/(dt)+y(dx)/(dt)\\ (dx)/(dt)=0.5 ~cm/sec\\(dy)/(dt)=-0.5~cm/sec\\(dA)/(dt)=10*(-0.5)+7(0.5)=-5+3.5=-1.5`

area is decreasing at the rate of 1.5 cm^2/sec