Math 29 Landers Unit 1: Introduction to course concepts 3. Joe is paving a small rectangular space just outside his back door with concrete pavers that are
1-ft by 1-ft and cost $1.45 each. He measured the area and it is 36-in by 65-in. He has done
the following calculation and feels that something must be wrong because he can't believe this
project would cost $282.75. Find Joe's mistake and explain it to him.
Hint: Draw a picture of a paver that will help Joe understand his error.
Joe's reasoning:
"The patio is a rectangle, so its area is 36-inches x 65-inches = 2340 square inches.
The pavers are measured in feet. Since there are 12 inches in a foot, converting the area to
feet I get 2340+ 12 = 195 feet. Since the pavers are 1-foot by 1-foot, I need 195 pavers,
which will cost me 195x$1.45=$282.75!"

c

step-by-step explanation:

c

step-by-step explanation:

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

cross multiplying, we get :

⇒ (3) × (5) = (9) × (x)

⇒ 15 = 9x