(a) If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt in terms of dr/dt.
(b) Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 1 m/s, how fast is the area of the spill increasing when the radius is 23 m?

a)

b) area of the spill increasing when the radius is 23 m

Step-by-step explanation:

Explanation:-

a)

Given  'A' is the area of a circle with radius 'r'

The area of the circle     ..(I)

Differentiating equation (I) with respective to 't'

b)

If the radius of the oil spill increases at a constant rate of 1 m/s

Given the radius r= 23m

Area of the spill increasing when the radius is 23 m

168

step-by-step explanation:

first off, we know that he drove 3.5 hours at a rate of 48 mph.

knowing that, we want to see how many miles he drove all-together.

in this case, we can just multiply 48 by 3.5.

48 * 3.5 = 168