A hot air balloon is anchored to the ground by a 152-foot long rope. The balloon hovers 132 feet above the ground.

what statement is true?

a) the angle the rope makes with the ground is about 30 degrees

b) The angle the rope makes with the ground is about 87 degrees

c) the horizontal distance between the anchor and balloon is about 201 feet

d) the horizontal distance between the anchor and the balloon is about 75feet

y > 1/3x

y < = -x + 4

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step-by-step explanation:

bob the banana

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

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step-by-step explanation: