BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1.6, Problem 88E
To determine

To find: The length of two pieces of wire in inches to nearest tenth.

Expert Solution

Answer to Problem 88E

The length of two pieces of wire is 169.1 inches and 190.9 inches.

Explanation of Solution

Given:

A wire of length 360 inches is cut into two pieces. A square is formed from one piece and a circle is formed from other piece.

Calculation:

Let the side of square be x and radius of circle be r.

Tabulate the given information into the language of algebra.

In words In algebra
Radius of circle r
Area of circle πr2
Length of side of square x
Area of square x2

Model the equation for the above information.

Areaofcircle=Areaofsquareπr2=x2x=πr

The length of wire is equal to sum of perimeter of circle and perimeter of square.

Perimeterofsqaure+Perimeterofsquare=3604x+2πr=360 (1)

Substitute πr for x in above equation.

4(πr)+2πr=3604×1.77×r+2×3.14×r=3607.08r+6.28r=36013.36r=360

Solve above equation for r.

r=36013.36r=26.95

Substitute 26.95 for r and 3.14 for π into equation (1).

4x+2(3.14)(26.95)=3604x+169.246=3604x=190.8

The length of one wire is 190.8 inches.

The length of other wire is,

length=360190.8=169.2

The length of other wire is 169.2 inches.

Thus, the length of two pieces of wire is 169.1 inches and 190.9 inches.

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