(a) Answer The maximum percentage of voter in republican and green is 44 % and 4 % and the minimum percentage of voters are 40 % and 0 % Explanation Given information: The indoor track is diagramed as: Calculation: Consider the right cervical part of the track as a semicircle. It is seen that there are two semi circle that make up to be a circle. Recall the circumference of a circle with radius r as. 2 π r Recall the circumference of the two part of the straight track as. 2 x Add the circumference and straight part of the track to find the perimeter of the track. P = 2 π r + 2 x = 2 ( π r + x ) Hence, the formula for the perimeter of the track is P = 2 ( π r + x ) (b) To determine The formula of x in terms of the perimeter of the track. Answer The required equations of the perimeter in terms of x is x = P − 2 π r 2 . Explanation Given information: The indoor track is diagramed as: Consider the formula for the perimeter of the track as P = 2 ( π r + x ) Solve the equation to find x . P = 2 ( π r + x ) P = 2 π r + 2 x 2 x = P − 2 π r x = P − 2 π r 2 Hence, the required equations of the perimeter in terms of x is x = P − 2 π r 2 . (c) To determine The value of x in terms of the perimeter of the track. Answer The required value of x is 173 ft . Explanation Given information: The perimeter of the track is given as 660 ft The radius of the semicircle is given as 50 ft Consider the formula for the perimeter of the track as x = P − 2 π r 2 Substitute 660 ft for P and 50 ft for r . x = 660 − 2 π × 50 2 = 172.92 = 173 ft Hence, the required value of x is 173 ft .

BIG IDEAS MATH Integrated Math 1: Student Edition 2016

16th Edition

ISBN: 9781680331127

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Houghton Mifflin Harcourt

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Question

Chapter 1.5, Problem 37E

(a)

To determine

The formula that can define the boundary of the given indoor track.

(a)

Expert Solution

Answer to Problem 37E

The maximum percentage of voter in republican and green is 44% and 4% and the minimum percentage of voters are 40% and 0%

Explanation of Solution

Given information:

The indoor track is diagramed as:

BIG IDEAS MATH Integrated Math 1: Student Edition 2016, Chapter 1.5, Problem 37E , additional homework tip 1

Calculation:

Consider the right cervical part of the track as a semicircle.

It is seen that there are two semi circle that make up to be a circle.

Recall the circumference of a circle with radius r as.

2πr

Recall the circumference of the two part of the straight track as.

Add the circumference and straight part of the track to find the perimeter of the track.

P=2πr+2x=2(πr+x)

Hence, the formula for the perimeter of the track is P=2(πr+x)

(b)

To determine

The formula of x in terms of the perimeter of the track.

(b)

Expert Solution

Answer to Problem 37E

The required equations of the perimeter in terms of x is x=P−2πr2 .

Explanation of Solution

Given information:

The indoor track is diagramed as:

BIG IDEAS MATH Integrated Math 1: Student Edition 2016, Chapter 1.5, Problem 37E , additional homework tip 2

Consider the formula for the perimeter of the track as

P=2(πr+x)

Solve the equation to find x .

P=2(πr+x)P=2πr+2x2x=P−2πrx=P−2πr2

Hence, the required equations of the perimeter in terms of x is x=P−2πr2 .

(c)

To determine

The value of x in terms of the perimeter of the track.

(c)

Expert Solution

Answer to Problem 37E

The required value of x is 173 ft .

Explanation of Solution

Given information:

The perimeter of the track is given as 660ft

The radius of the semicircle is given as 50ft

Consider the formula for the perimeter of the track as

x=P−2πr2

Substitute 660ft for P and 50ft for r .

x=660−2π×502=172.92=173 ft

Hence, the required value of x is 173 ft .

Chapter 1.5, Problem 36E

Chapter 1.5, Problem 38E

Chapter 1 Solutions

BIG IDEAS MATH Integrated Math 1: Student Edition 2016

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