Sam built a fence that was 54 \text { feet}54 feet54, start text, space, f, e, e, t, end text long. She built the same length of fence each day for 666 days. How many inches of fence did Sam build each day?

Step-by-step explanation:

Given:

Sam:

Length of fence built, l = 54 ft

Rate, r = 54 ft in 6 days

Therefore, in 1 day, 54/6 ft was built

= 9 ft of fence

Converting ft to in,

1 ft = 12 in

9 ft = 12 × 9

= 108 in of fence.

what "following statement"?

step-by-step explanation:

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