If the radius of the circle above is 12 in, what is the area of the circle? A. 576 sq in B. 144 sq in C. 12 sq in D. 24 sq in

Step-by-step explanation:

Formula for the area of a circle of radius r is A = πr², where r is the radius.

Here, A = π(12 in)²  = 144π in², or approximately  452.89 in².

Double check to ensure that you have copied down the possible answers correctly.  Answer B would be correct if you were to insert π.  (See above.)

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

a

step-by-step explanation: