The radius, r, of a sphere is increasing at 0.03 meters per second. the rate of increase is constant.

a. what is the rate of increase in its volume when the radius of the sphere is 18 meters?

b. what is the rate of increase in the sphere’s surface area when the volume is 288 cubic meters?

c. express the rate at which the volume of the sphere changes with respect to the surface area of the sphere (as a function of r).

, i don't get any of this. an explanation would be great, !

so what is the problem what are they asking you to solve

step-by-step explanation:

so what is the problem what are they asking you to solve

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt