Identify the values of the variables. give your answers in simplest radical form.

2 sqrt(3) = n

k = 4 sqrt(3)

Step-by-step explanation:

We know that cos 30 = adjacent/ hypotenuse

cos 30 = 6 /k

Multiply each side by k

k cos 30 = 6k * k

k cos 30 = 6

Divide each side by cos 30

k cos 30/ cos 30 = 6/ cos 30

k = 6 / cos 30

k = 6/ (sqrt(3)/2)

k =12 / sqrt(3)

We cannot leave the sqrt in the denominator

k = 12 / sqrt(3) * sqrt(3)/sqrt(3)

k = 12 sqrt(3)/3

k = 4 sqrt(3)

We know tan 30 = opposite/adjacent

                tan 30 = n/6

Multiply each side by 6

                  6 tan 30 = n

                  6 * (sqrt(3)/3) = n

                   6/3 * sqrt(3) = n

                    2 sqrt(3) = n

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is

cost of 2 dresses if one cost at $27.50 is  

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is   $25.5+$55+$17.50=$98

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