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McGraw Hill Glencoe Algebra 1, 2012 View details

7. Mixed Expressions and Complex Fractions

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Exercise 34 Page 724

a We are given that the speed

v

of an object spinning in a circle equals the circumference of the circle divided by the time

T

it takes the object to complete one revolution. Let's write the defined speed of a spinning object.

Speed = \frac{Circumference}{Time}

We want to write above formula using the variables

v,

T,

and

r

(the radius of the circle). To do so, let's first remember the formula for the circumference of the circle.

Circumference = 2 π r

Now we can substitute

Speed = v,

Circumference = 2 π r,

and

Time = T

into the speed formula.

v = \frac{2 π r}{T}

b We are given that a scooter has tires with a radius of

3 \frac{1}{2}

inches and the tires make one revolution every

\frac{1}{1 0}

seconds. To find the scooter's speed, we will substitute

r = 3 \frac{1}{2}

and

T = \frac{1}{1 0}

into the formula that we found in Part A.

v = \frac{2 π r}{T}

SubstituteII

$r = 3 \frac{1}{2}$ , $T = \frac{1}{1 0}$

v = \frac{2 \cdot π \cdot 3 \frac{1}{2}}{\frac{1}{1 0}}

▼

Solve for

v

MixedToFrac

$a \frac{b}{c} = \frac{a \cdot c + b}{c}$

v = \frac{2 \cdot π \cdot \frac{7}{2}}{\frac{1}{1 0}}

MoveLeftFacToNum

$a \cdot \frac{b}{c} = \frac{a \cdot b}{c}$

v = \frac{\frac{1 4 π}{2}}{\frac{1}{1 0}}

FracToDiv

$\frac{a}{b} = a \div b$

v = \frac{1 4 π}{2} \div \frac{1}{1 0}

DivFracByFracDiv

$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \cdot \frac{d}{c}$

v = \frac{1 4 π}{2} \cdot \frac{1 0}{1}

MultFrac

Multiply fractions

v = \frac{1 4 0 π}{2}

UseCalc

Use a calculator

v = 219.911485 \dots

RoundDec

Round to $1$ decimal place(s)

v \approx 219.9

We found that the speed of the scooter is about

219.9

inches per second. However, we are asked to find the speed in miles per hour. To do so we will first convert our speed in inches to miles using a conversion factor.