Melanie simplified the expression StartStartFraction StartFraction (cotangent (x)) Over (1 Over secant (x)) EndFraction EndEndFractionas shown below. Step 1: StartStartFraction StartFraction (cosine (x) Over sine (x)) EndFraction OverOver (cosine (x)) EndFraction EndEndFraction Step 2: StartFraction cosine (x) Over sine (x) EndFraction times StartFraction 1 Over cosine (x) EndFraction Step 3: StartFraction 1 Over sine (x) EndFraction Step 4: tangent (x) In which step did Melanie make the first error, and which expression should she have written in that step?

answer: 180

step-by-step explanation:

12-2=10

20-2=18

18x10=180

1

step-by-step explanation:

it's the only multiple of both and the least

1e+27

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