SOLUTIONS MANUAL
MATH MADE VISIBLE
ALGEBRA AND
TRIGONOMETRY WITH
MODELING AND
R
U
VISUALIZATION
SE
IS
PRECALCULUS WITH MODELING
AND VISUALIZATION
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6TH EDITION
N
N
O
Gary Rockswold
C
Terry Krieger
ED
Jessica Rockswold
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❖ ALL CHAPTERS
❖ PDF DOWNLOAD
, Table of Contents
Chapter 1 Introduction to Functions and Graphs 1
Chapter 2 Linear Functions and Equations 52
Chapter 3 Quadratic Functions and Equations 134
Chapter 4 More Nonlinear Functions and Equations 217
Chapter 5 Exponential and Logarithmic Functions 368
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Chapter 6 Trigonometric Functions 453
Chapter 7 Trigonometric Identities and Equations 558
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Chapter 8 Further Topics in Trigonometry 657
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Chapter 9 Systems of Equations and Inequalities 758
Chapter 10 Conic Sections 863
Chapter 11 Further Topics in Algebra
IS 910
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Chapter R Reference: Basic Concepts from Algebra and Geometry 978
Appendix C Partial Fractions 1011
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Appendix D Percent Change and Exponential Functions 1018
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Appendix E Rotation of Axes 1023
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,Chapter 1: Introduction to Functions and Graphs
1.1: Numbers, Data, and Problem Solving
21
1. is a real and rational number.
24
2. 100,000 is a real number, rational number, integer, and natural number.
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3. 7.5 is a real and rational number.
4. 12.3 is a real and rational number.
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5. 90 2 is a real number.
6. 71 is an integer, real number, and rational number.
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2
7. Natural number: 9 3 ; whole number: 9 ; integers: 3 , 9 ; rational numbers: 3 , , 9 , 1.3 ;
9
irrational numbers: , 2
8. Natural numbers:
3
1
3 5 3
3
1
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rational numbers: , , 0.45 , 0 , 5.6 10 ; irrational number: 7
3
3 , 5.6 103 5600 ; whole numbers: , 0 , 5.6 103 ; integers: , 0 , 5.6 103 ;
1
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1 8
1
9. Natural number: None; whole number:0; integer: 0, 4 2 ; rational numbers: 0, , 5.1 106 , 2.33 ,
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3
0.7 , 4 ; irrational number: 13
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10. Natural numbers: 100 10 ; whole number: 100 ; integers: 103 , 100 ; rational numbers: 103 , ,
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5.7 2
100 , , , 1.457 ; irrational number: 3
10 9
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11. Shoe sizes are normally measured to within half sizes. Rational numbers are most appropriate.
12. Population is measured using natural numbers.
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13. Speed limit is measured using natural numbers.
14. Gasoline is usually measured to a fraction of a gallon using rational numbers.
15. Temperature is typically measured to the nearest degree in a weather forecast. Since temperature can include
negative numbers, the integers would be most appropriate.
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16. Compact disc sales could be measured in natural numbers, since fractions of a disc are not allowed.
17. | 5 8 7 | | 5 56 | | 51| 51
18. 2(16 3 5) 2 2(16 15) 2 2(1) 2 2 2 1
19. 62 3(2 4) 4 62 3( 2) 4 36 3(16) 36 48 84
20. (4 5) 2 32 3 9 ( 1)2 9 3(3) 1 9 9 17
84 4
21. 95 4 22 0
42 2
6 42 23 6 16 8 6 2
22. 4
3 4 1 1
Copyright ©2018 Pearson Education, Inc.
, 2 Chapter 1 Introduction to Functions and Graphs
23. 132 122 169 144 25 5
13 9 16 13 25 13 5 8
24. 2
| 5 7 |2 | 2 |2 4 4
4 9 32 3 13 27 40
25. 8
23 5 5 5 5
5 10 15 5
26. 10 2 10 2 10 2 3 5 3
5 5 3
27. 52 20 4 2 25 5 2 32
28. 5 (4)3 43 5 (64) 64 5 64 64 5
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29. 8.2 101
30. 1.45 107
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31. 3.65 103
32. 0.62 6.2 101
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33. 2450 2.45 103
34. 105.6 1.056 102
35. 0.56 5.6 101
36.
37.
0.00456 4.56 103
0.0087 8.7 103
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38. 1, 250, 000 1.25 106
206.8 2.068 102
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39.
40. 0.00007 7 105
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41. 106 0.000001
42. 9.11 1031 0.000000000000000000000000000000911
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There are 30 zeros between the decimal point and the digits 911.
43. 2 108 200, 000, 000
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44. 8, 000, 000, 000
1.567 102 156.7
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45.
46. 5.68 101 0.568
47. 5 105 500, 000
48. 3.5 103 3500
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49. 0.045 105 4500
50. 5.4 105 0.000054
51. 67 103 67, 000
52. 0.0032 101 0.00032
53. (4 103 )(2 105 ) 4 2 1035 8 108 ; 800, 000, 000
54. (3 101 )(3 104 ) 3 3 1014 9 105 ; 900, 000
55. (5 102 )(7 104 ) 5 7 102 4 35 102 3.5 101 ; 0.35
Copyright ©2018 Pearson Education, Inc.
