Which expression is equivalent to (4 + 6i)2?
–20 + 48i
8 + 12i 1
6 – 36i
20 + 48i

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

we need to see the graph to know but

strong positive is if it is going up from left to right in a straight diagonal line (like this /)

strong negative is the same but from right to left (like this \)

weak negative is the same as strong negative but its more straight line still right to left

and weak positive is the same as strong positive but more a straight line still left to right though.