2x+11) D. (x +4)2x141 A.100
B. 110
C. 120
D.130
c
(2-32-40
46. The distance of 36 km on the ground is represented by a line of 1.8 cm on a map.
What is the scale of the map?
A. 1:20
B. 1: 200 C. 1: 2000 D. 1:20 000
47. A piece of wood is to be cut into three pieces in the ratio 5: 4:3. If the length of the
shortest piece is 2cm, how long was the piece of wood?
A. 12 cm B. 8 cm C.9 cm D. 10 cm
-3
3
147​

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

b

step-by-step explanation: