Practice 1: Sahel starts the construction of an inscribed polygon in the circle
below. Sahel's brothers, Nil and Ravi, are trying to figure out what inscribed polygon
Sahel is constructing Nil claims it is an equilateral triangle. Ravi claims it is a
regular hexagon. Which brother is correct?

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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what are the three components of an essay prompt?

a.

position, counterargument, and question

c.

counterargument, question, directions

b.

quote, position, and question

d.

quote, question, directions

step-by-step explanation: