Solutions Manual – Precalculus: A Right Triangle Approach, 5th Edition by J. S. Ratti

SOLUTIONS MANUAL




** All Chapters included
** Problems & Exercises

,Table of Contents are given below


Chapter P Basic Concepts of Algebra

Chapter 1 Equations and Inequalities

Chapter 2 Graphs and Functions

Chapter 3 Polynomial and Rational Functions

Chapter 4 Exponential and Logarithmic Functions

Chapter 5 Trigonometric Functions

Chapter 6 Trigonometric Identities and Equations

Chapter 7 Applications of Trigonometric Functions

Chapter 8 Systems of Equations and Inequalities

Chapter 9 Matrices and Determinants

Chapter 10 The Conic Sections

Chapter 11 Further Topics in Algebra

, Chapter P Basic Concepts of Algebra
P.1 The Real Numbers and Their b. 3  4  1  1
Properties
c. 2  3  7  6  7  1  1
Practice Problems
8.
1. Let x = 2.132132132….
Then, 1000x = 2132.132132…
1000 x  2132.132132  d  7, 2  7  2  9  9
x 2.132132 
999 x  2130 9. a. 3  5  20  15  20  5
2130 710
x  b. 5  12  6  2  5  2  2  5  4  1
999 333
2. a. Natural numbers: 2, 7 9 1 8
c.  5  7   5  7  2  35  33
4 4
b. Whole numbers: 0, 2, 7
3   x  4 for x = 6
2
21 d.
c. Integers: 6,   3, 0, 2, 7
7 3  6  4  3  2 2  3  4  1
2

d. Rational numbers:
21 1 4 7 3 7  2 3 7  2  3 17
6,    3 ,  , 0, , 2, 7 10. a.     
7 2 3 4 8 42 8 8 8
8 2 8  5 2  3 8  5  2  3 34
e. Irrational numbers: 3, 17 b.     
3 5 35 53 35 15
f. Real numbers: the set B
9 7 9 7 3 3  7 3
c.    
3. a. 23  2  2  2  8 14 3 14  3 2  7  3 2

b. 3a  2  3a 3a   9a 2 5
d. 8  5  16  5  16  5  2  8  2
4 15 8 15 8  15 8  3  5 3
1 1 1 1 1 1
c.        16
2 2 2 2 2 16
4. a. 2  0 true because 2 is to the left of 0 11. a.  x  2   3  x  3  2   3  3
on the number line. 1 10
 1 3  3  3
3 3
b. 5  7 true because 5 is to the left of 7 on
the number line. x 1 1 22
b. 7  7 7 
c. 4  1 false because 4 is to the left of y 3 3 3
1 on the number line.
39
5. A  3,  1, 0, 1, 3 , B  4,  2, 0, 2, 4 12. C   4  13  4  17C
3
A  B  0
Concepts and Vocabulary
A  B  4,  3,  2,  1, 0, 1, 2, 3, 4
1. Whole numbers are formed by adding the
6. a. I1  I 2   ,   number zero to the set of natural numbers.
b. I1  I 2   2, 5 2. The number −3 is an integer, but it is also a
rational number and a real number.
7. a. 10  10 3. If a < b, then a is to the left of b on the
number line.


1

, 2 Chapter P Basic Concepts of Algebra


4. If a real number is not a rational number, it is 24. 100 x  142.3535
an irrational number.
x  1.4235
5. True 99 x  140.93
140.93 14, 093
5 1 x 
6. False.  2 99 9900
2 2
25. Rational 26. Rational
7. True
27. Rational 28. Rational
  
8. False. An example is 2  2  2  2  4,  29. Rational 30. Rational
which is rational.
31. Irrational 32. Irrational
Building Skills
Exercises 33-38 refer to the set
 12 17 
9. 0.3 , repeating A  19,  ,  3, 0, 2, 10, , 11
 3 4 
10. 0.6 , repeating
33. Natural numbers: 2, 11
11. 0.8 , terminating
34. Whole numbers: 0, 2, 11
12. 0.25 , terminating
12
35. Integers: 19,   4, 0, 2, 11
13. 0.27 , repeating 3

14. 0.3 , repeating 12 17
36. Rational numbers: 19,  , 0, 2, , 11
3 4
15. 3.16 , repeating
37. Irrational numbers: 3, 10
16. 2.73 , repeating
38. Real numbers: All numbers in set A are real
375 15 numbers.
17. 3.75  
100 4
39. 10 3
235 47 base: 10; exponent: 3
18. 2.35   
100 20 10 3  10  10  10  1000
19. 10 x  53.3 20. 10 x  96.6
40. 5 4
x  5.3 x  9.6 base: 5; exponent: 4
9 x  48 9 x  87
5 4  5  5  5  5  625
48 16 87 29
x  x  3
9 3 9 3 2
16 41.  
5.3   3
3
2
base: ; exponent: 3
21. 100 x  213.13 22. 100 x  323.23 3
x  2.13 x  3.23 2
3
2 2 2 8
99 x  211 99 x  320      
3 3 3 3 27
211 320
x x 4
99 99 5
42.  
2
23. 100 x  452.323
x  4.523 5
base: ; exponent: 4
99 x  447.8 2
4
447.8 4478 2239 5 5 5 5 5 625
x         
99 990 495 2 2 2 2 2 16