John has a bow that it shaped like a half-sphere. The bow has a volume of 1 in Soup is the bow and John has two sindrical cups to scoop the soup out of the bow.
to one cup has a diameter of 2 inches and a begint of 6 indres. How many cups of soup san Sohn sesuo
out of the bow to empty it? Round the number of scoops to the nearest whole number
one cup has a diameter of 4 inches and a hegt of 3 inches Hou sienny cups of soup can John
out of the bou to empty it? Round the number of scoops to the nearest whole number
b.

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step-by-step explanation:

what’s the question?

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