You’ve arrived at your apartment, but before you can set up your furniture, you need to paint!. The dimensions of the living room are 20ft x 15ft x 8 ft. You need to paint all 4 walls and the ceiling. You will need to paint two coats and each gallon of paint covers 400 square feet. Calculate the total surface area that needs to be painted and how many cans of paint are needed.

Total surface area to be painted: _

Amount of paint cans needed: _

20ft(length) 15ft(width) 8ft(height) *dont paint the floor!

Determine how many paint cans will be needed by using the surface area
*1 gallon = 400 square feet

10

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

sweetheart, there isn't a cube below.