If the area of a square is increased by 69%, then the side of the square is increased by what percent?

Percent Increase in measure of the side of a square = 30%

Step-by-step explanation:

Let the measure of the side of a square = s

Area of the square = (Side)²

                                = s²

If the area of the square is increased by 69%

Area of the new square = s² + 69% of s²

                                        = s² + 0.69s²

                                        = 1.69s²

Therefore, measure of the side of the new square = √(Area of the square)

                                                                                    = √(1.69s²)

                                                                                    = 1.3s

Measure of side of the old square = s

Therefore, increase in measure of the square = 1.3s - s

                                                                            = 0.3s

Percent increase in the measure of the side of the square

=

=

= 30%

final total: 63

step-by-step explanation:

60 times sales tax

60 times 0.05

3

60 + 3

63

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