As shown in the figure below, Mary is looking at a tree that is leaning at an angle of 84º with respect to the ground. The angle of elevation from where Mary is standing to the top of the tree is 49º. The length of the tree is 55 feet. Find the distance, x,
from Mary to the base of the tree. Round your answer to the nearest tenth of a foot.
55 ft
I feet
Х
?
84
49°
Х.

r his

Step-by-step explanation:rfrfrefeffrefeferfeferfe

you are saying it as if a fact, not a question, but yes, you would be correct? ; )

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