1. A restaurant supplier services the restaurants in a circular area in such way that the radius r is increasing at the rate of 2 miles per year at the moment when r = 5 miles. How fast is the area increasing?

Using implicit differentiation, it is found that the area is increasing at a rate of 62.8 miles squared per year.

The area of a circle of radius r is given by:

Applying implicit differentiation, the rate of change is given by:

In this problem:

Then:

The area is increasing at a rate of 62.8 miles squared per year.

A similar problem is given at link

A= π*r²

dA/dt= π*r*dr/dt

dA/dt= π*5*2= 10π km/yr

351°f

step-by-step explanation: