Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

1st Edition

ISBN: 9780078682278

Author: McGraw-Hill, Berchie Holliday

Publisher: Glencoe/McGraw-Hill

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Question

Chapter 1.8, Problem 27E

To determine

To find: a compound inequality representing a and r.

Expert Solution

Answer to Problem 27E

0.60(200−a)≤r≤0.90(200−a)

Explanation of Solution

Given information:

The variable a and r represents the age and targeted heart rate respectively.

Maximum heart rate =220−a

The percentage range of r is 60% to 90%

Calculation:

The inequality for minimum targeted heart rate can be represented as follows:

r≥60%(200−a)r≥60100(200−a)r≥0.60(200−a)

The inequality for maximum targeted heart rate can be represented as follows:

r≤90%(200−a)r≤90100(200−a)r≤0.90(200−a)

Therefore, the compound inequality is 0.60(200−a)≤r≤0.90(200−a)

To determine

To graph: the inequality.

Expert Solution

Answer to Problem 27E

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 1.8, Problem 27E , additional homework tip 1

Explanation of Solution

Given information:

The variable a and r represents the age and targeted heart rate respectively.

Maximum heart rate =220−a

The percentage range of r is 60% to 90%

The inequality evaluated is as follows:

0.60(200−a)≤r≤0.90(200−a)

Calculation:

Since the inequality has the sign (≤ or ≥) , so a solid line will be used to graph a line r=0.90(200−a) and r=0.60(200−a) .

The table values for r=0.90(200−a) is as follows:

a	−100	−50	0	200	300	450
r	270	225	180	0	−90	−225

The table values for r=0.60(200−a) is as follows:

a	−100	−50	0	200	300	450
r	180	150	120	0	−60	−150

Put the test points in the inequality and check the true test point as follows:

Test point (a,r)	Inequality, 0.60(200−a)≤r≤0.90(200−a)	True/False test point
(0,0)	0.60(200−0)≤0≤0.90(200−0)0.60(200)≤0≤0.90(200)120≤0≤180	False
(300,0)	0.60(200−300)≤0≤0.90(200−300)0.60(−100)≤0≤0.90(−100)−60≤0≤−90	False
(−100,200)	0.60(200−(−100))≤200≤0.90(200−(−100))0.60(200+100)≤200≤0.90(200+100)0.60(300)≤200≤0.90(300)180≤200≤270	True
(100,80)	0.60(200−100)≤80≤0.90(200−100)0.60(100)≤80≤0.90(100)60≤80≤90	True
(450,−200)	0.60(200−450)≤−200≤0.90(200−450)0.60(−250)≤−200≤0.90(−250)−150≤−200≤−225	False
(−50,50)	0.60(200−(−50))≤50≤0.90(200−(−50))0.60(200+50)≤50≤0.90(200+50)0.60(250)≤50≤0.90(250)150≤50≤225	False

Plot the graph for inequality and shade the true point region as follows:

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 1.8, Problem 27E , additional homework tip 2

Here, red line represents r=0.90(200−a) and blue line represents r=0.60(200−a) .

Chapter 1.8, Problem 26E

Chapter 1.8, Problem 28E

Chapter 1 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

Ch. 1.1 - Prob. 1CFU Ch. 1.1 - Prob. 2CFU Ch. 1.1 - Prob. 3CFU Ch. 1.1 - Prob. 4CFU Ch. 1.1 - Prob. 5CFU Ch. 1.1 - Prob. 6CFU Ch. 1.1 - Prob. 7CFU Ch. 1.1 - Prob. 8CFU Ch. 1.1 - Prob. 9CFU Ch. 1.1 - Prob. 10CFU

Ch. 1.1 - Prob. 11CFU Ch. 1.1 - Prob. 12CFU Ch. 1.1 - Prob. 13CFU Ch. 1.1 - Prob. 14CFU Ch. 1.1 - Prob. 15CFU Ch. 1.1 - Prob. 16CFU Ch. 1.1 - Prob. 17E Ch. 1.1 - Prob. 18E Ch. 1.1 - Prob. 19E Ch. 1.1 - Prob. 20E Ch. 1.1 - Prob. 21E Ch. 1.1 - Prob. 22E Ch. 1.1 - Prob. 23E Ch. 1.1 - Prob. 24E Ch. 1.1 - Prob. 25E Ch. 1.1 - Prob. 26E Ch. 1.1 - Prob. 27E Ch. 1.1 - Prob. 28E Ch. 1.1 - Prob. 29E Ch. 1.1 - Prob. 30E Ch. 1.1 - Prob. 31E Ch. 1.1 - Prob. 32E Ch. 1.1 - Prob. 33E Ch. 1.1 - Prob. 34E Ch. 1.1 - Prob. 35E Ch. 1.1 - Prob. 36E Ch. 1.1 - Prob. 37E Ch. 1.1 - Prob. 38E Ch. 1.1 - Prob. 39E Ch. 1.1 - Prob. 40E Ch. 1.1 - Prob. 41E Ch. 1.1 - Prob. 42E Ch. 1.1 - Prob. 43E Ch. 1.1 - Prob. 44E Ch. 1.1 - Prob. 45E Ch. 1.1 - Prob. 46E Ch. 1.1 - Prob. 47E Ch. 1.1 - Prob. 48E Ch. 1.1 - Prob. 49E Ch. 1.1 - Prob. 50E Ch. 1.1 - Prob. 51E Ch. 1.1 - Prob. 52E Ch. 1.1 - Prob. 53E Ch. 1.1 - Prob. 54E Ch. 1.1 - Prob. 55E Ch. 1.1 - Prob. 56E Ch. 1.1 - Prob. 57E Ch. 1.2 - Prob. 1GCE Ch. 1.2 - Prob. 2GCE Ch. 1.2 - Prob. 3GCE Ch. 1.2 - Prob. 4GCE Ch. 1.2 - Prob. 5GCE Ch. 1.2 - Prob. 1CFU Ch. 1.2 - Prob. 2CFU Ch. 1.2 - Prob. 3CFU Ch. 1.2 - Prob. 4CFU Ch. 1.2 - Prob. 5CFU Ch. 1.2 - Prob. 6CFU Ch. 1.2 - Prob. 7CFU Ch. 1.2 - Prob. 8CFU Ch. 1.2 - Prob. 9CFU Ch. 1.2 - Prob. 10CFU Ch. 1.2 - Prob. 11E Ch. 1.2 - Prob. 12E Ch. 1.2 - Prob. 13E Ch. 1.2 - Prob. 14E Ch. 1.2 - Prob. 15E Ch. 1.2 - Prob. 16E Ch. 1.2 - Prob. 17E Ch. 1.2 - Prob. 18E Ch. 1.2 - Prob. 19E Ch. 1.2 - Prob. 20E Ch. 1.2 - Prob. 21E Ch. 1.2 - Prob. 22E Ch. 1.2 - Prob. 23E Ch. 1.2 - Prob. 24E Ch. 1.2 - Prob. 25E Ch. 1.2 - Prob. 26E Ch. 1.2 - Prob. 27E Ch. 1.2 - Prob. 28E Ch. 1.2 - Prob. 29E Ch. 1.2 - Prob. 30E Ch. 1.2 - Prob. 31E Ch. 1.2 - Prob. 32E Ch. 1.2 - Prob. 33E Ch. 1.2 - Prob. 34E Ch. 1.2 - Prob. 35E Ch. 1.2 - Prob. 36E Ch. 1.2 - Prob. 37E Ch. 1.2 - Prob. 38E Ch. 1.2 - Prob. 39E Ch. 1.3 - Prob. 1CFU Ch. 1.3 - Prob. 2CFU Ch. 1.3 - Prob. 3CFU Ch. 1.3 - Prob. 4CFU Ch. 1.3 - Prob. 5CFU Ch. 1.3 - Prob. 6CFU Ch. 1.3 - Prob. 7CFU Ch. 1.3 - 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Prob. 9CFU Ch. 1.4 - Prob. 10CFU Ch. 1.4 - Prob. 11E Ch. 1.4 - Prob. 12E Ch. 1.4 - Prob. 13E Ch. 1.4 - Prob. 14E Ch. 1.4 - Prob. 15E Ch. 1.4 - Prob. 16E Ch. 1.4 - Prob. 17E Ch. 1.4 - Prob. 18E Ch. 1.4 - Prob. 19E Ch. 1.4 - Prob. 20E Ch. 1.4 - Prob. 21E Ch. 1.4 - Prob. 22E Ch. 1.4 - Prob. 23E Ch. 1.4 - Prob. 24E Ch. 1.4 - Prob. 25E Ch. 1.4 - Prob. 26E Ch. 1.4 - Prob. 27E Ch. 1.4 - Prob. 28E Ch. 1.4 - Prob. 29E Ch. 1.4 - Prob. 30E Ch. 1.4 - Prob. 31E Ch. 1.4 - Prob. 32E Ch. 1.4 - Prob. 33E Ch. 1.4 - Prob. 34E Ch. 1.4 - Prob. 35E Ch. 1.4 - Prob. 1MCQ Ch. 1.4 - Prob. 2MCQ Ch. 1.4 - Prob. 3MCQ Ch. 1.4 - Prob. 4MCQ Ch. 1.4 - Prob. 5MCQ Ch. 1.4 - Prob. 6MCQ Ch. 1.4 - Prob. 7MCQ Ch. 1.4 - Prob. 8MCQ Ch. 1.4 - Prob. 9MCQ Ch. 1.4 - Prob. 10MCQ Ch. 1.5 - Prob. 1CFU Ch. 1.5 - Prob. 2CFU Ch. 1.5 - Prob. 3CFU Ch. 1.5 - Prob. 4CFU Ch. 1.5 - Prob. 5CFU Ch. 1.5 - Prob. 6CFU Ch. 1.5 - Prob. 7CFU Ch. 1.5 - Prob. 8CFU Ch. 1.5 - Prob. 9CFU Ch. 1.5 - Prob. 10CFU Ch. 1.5 - Prob. 11CFU Ch. 1.5 - Prob. 12E Ch. 1.5 - 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