You and your friend would like to build a tent that is 6 feet wide by 4 feet tall by 8 feet long. You bought a piece of canvas that is 14 feet by 10 feet to be able to make the tent. Remember you will need to put canvas on the floor of your tent. Will you have enough canvas to build the tent?

Yes, with 12 feet leftover.

Step-by-step explanation:

For this problem, you will need to find the area of the floor and the area of both sides of the tent. To find the area of the floor, you will simply need to do 6(8) = 48. To find the area of the sides, you will need to use the Pythagorean theorem to find the height of the sides. Simply divide 6 by 2 to find b². So, the formula will be 3²+4² = c². Solve to get c = 5. Now, find the area of the rectangle by using the formula for area. 8(5) = 40. Multiply 40 by 2 because there are two sides. Now add the total area of both sides and the floor to get a total of 128. Now to see if the canvas can cover the area of the tent, do 140 - 128 to get 12. So the answer is yes, with 12 feet leftover.

Work:

Area of the floor:

6(8) = 48

Area of the sides:

A = 8(h)(2)

A = 16(h)

h² = 3² + 4²

h² = 9 + 16

=

h = 5

A = 8(5)(2)

A = 80

Total area of the tent:

80 + 48 = 128

Total area of the canvas:

14(10) = 140

Answer to the question:

140 - 128 = 12

By the way, sorry for the late answer. I bet this was on a test, right?

answer: 230 miles ( vote ! )

step-by-step explanation:

180.39 minus 17.99 equals 162.4

then divide 162.4 by .80 to get 230

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