The work of a student to find the dimensions of a rectangle of area 8 + 16x and width 4 is shown below:

step 1: 8 + 16x
step 2: 4(4) + 4(12x)
step 3: 4(4 + 12x)
step 4: dimensions of the rectangle are 4 and 4 + 12x

in which step did the student first make an error and what is the correct step?

step 3; 4 + (4 + 12x)
step 3; 4 + (4 ⋅ 12x)
step 2; 4(2) + 4(4x)
step 2; 4(2) + 4x(2)

best answer gets !

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

answer is  

a.

p = 78

step-by-step explanation: