EMERGENCY! PLEASE HELP! Write the ratio using ":".

*If the scale factor is a:b, then the ratio of areas is a^2:b^2, and the ratio of volumes is a^3:b^3.

Prism C : Prism D
scale factor:
ratio of areas: 16:49
ratio of volumes:

Cylinder X : Cylinder Y
scale factor: 3:5
ratio of areas:
ratio of volumes:

Cone M : Cone N. scale factor:
ratio of areas:
ratio of volumes: 1:8

1.3 million hoops i believe

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

is there more to this question?