Solve for x in the triangle. Round your answer to the nearest tenth.

x = 6.9

Step-by-step explanation:

We're going to use SOH CAH TOA.

If we look at the angle (58°), and see what the relevant sides of the triangle are, we can see that the hypotenuse (our known side) is the H (hypotenuse), and the side labelled 'x' (our unknown side) is the A (adjacent).

According to SOH CAH TOA, we'll use cos (C), since we're working with the adjacent and the hypotenuse.

The equation for CAH is cos (Ф°) = A/H

In this case, Ф = 58°, A = x, and H = 13

So cos (58°) = x/13

Solve for x by multiplying both sides by 13 and using your calculator to evaluate.

13 cos (58°) = x

x = 6.88895

To the nearest tenth, x = 6.9

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

the answer is 8.64

step-by-step explanation: