Exercise 32 Page 30

We want to find the radius of the first Ferris wheel if the circumference of the Navy Pier Wheel is 56 percent of the circumference of the first Ferris wheel. To do so, consider that the new circumference is equal to the product of 0.56 multiplied by the old circumference. 439.6 = 0.56 C Now, we will use inverse operations to isolate C on one side of the equation.

439.6 = 0.56 C

▼

Solve for C

DivEqn

.LHS /0.56.=.RHS /0.56.

439.6/0.56 = 0.56 C/0.56

CrossCommonFac

Cross out common factors

439.6/0.56 = 0.56 C/0.56

SimpQuot

Simplify quotient

439.6/0.56 = C

UseCalc

Use a calculator

785 = C

RearrangeEqn

Rearrange equation

C = 785

Recall the formula for the radius found in Part A. r = C/2π Let's substitute C= 785 into the above formula and calculate the radius of the first wheel.

r = C/2π

Substitute

C= 785

r = 785/2π

UseCalc

Use a calculator

124.936630 ... = r

RoundInt

Round to nearest integer

125 ≈ r

RearrangeEqn

Rearrange equation

r ≈ 125

The radius of the first Ferris wheel was about 125 feet.

We want to find the speed of the first Ferris wheel if it took 9 minutes to make a complete revolution. To do so, consider that the distance can be written as a product of the speed and time. Then, the distance will be equal to the product of the speed multiplied by 9. Also, it will be equal to the circumference of the wheel. C=9x Here, x represents the speed of the first Ferris wheel. Now, we will substitute C= 785 into the above equation and solve it for x.

C=9x

▼

Solve for x

Substitute

C= 785

785=9x

DivEqn

.LHS /9.=.RHS /9.

785/9=9x/9

CrossCommonFac

Cross out common factors

785/9=9x/9

SimpQuot

Simplify quotient

785/9=x

UseCalc

Use a calculator

87.222222 ... = x

RoundDec

Round to 1 decimal place(s)

87.2 ≈ x

RearrangeEqn

Rearrange equation

x ≈ 87.2

The speed of the first Ferris wheel was about 87.2 feet per minute.