Aditya's boat has come untied and drifted away from the dock. It is now lodged against several rocks. Aditya is standing, perpendicular to the ground, on top of a cliff that is 35 feet above the
water in the lake. If she stands 10 feet from the edge of the cliff, she can visually align the top of
the cliff with the water at the back of her boat. Her eye level is 5.5 feet above the round. Her
line of site forms a 29° angle with the ground on the cliff, as well as with the water at the base of
the boat.

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

8(1/6)

step-by-step explain:

49/6= 48

8 (1/6)