Which equation has a constant of proportionality equal to 111? Choose 1 Choose 1 (Choice A) A y=\dfrac{10}{11}xy= 11 10 xy, equals, start fraction, 10, divided by, 11, end fraction, x (Choice B) B y=\dfrac{7}{8}xy= 8 7 xy, equals, start fraction, 7, divided by, 8, end fraction, x (Choice C) C y=\dfrac{3}{15}xy= 15 3 xy, equals, start fraction, 3, divided by, 15, end fraction, x (Choice D) D y=xy=x

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