Algebra and Trigonometry With Modeling and Visualization 6th Edition - Solutions Manual by Gary K. Rockswold

INSTRUCTOR’S SOLUTIONS
MANUAL
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MATH MADE VISIBLE
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A LGEBRA AND T RIGONOMETRY
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WITH M ODELING AND
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V ISUALIZATION
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P RECALCULUS WITH M ODELING
AND V ISUALIZATION
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S IXTH E DITION
Gary Rockswold
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Minnesota State University, Mankato

with


Terry Krieger
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Rochester Community and Technical College

and
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Jessica Rockswold
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, Table of Contents
Chapter 1 Introduction to Functions and Graphs 1
Chapter 2 Linear Functions and Equations 52
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Chapter 3 Quadratic Functions and Equations 134
Chapter 4 More Nonlinear Functions and Equations 217
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Chapter 5 Exponential and Logarithmic Functions 368
Chapter 6 Trigonometric Functions 453
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Chapter 7 Trigonometric Identities and Equations 558
Chapter 8 Further Topics in Trigonometry 657
Chapter 9 Systems of Equations and Inequalities 758
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Chapter 10 Conic Sections 863
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Chapter 11 Further Topics in Algebra 910
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
Appendix E Rotation of Axes 1023
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, Chapter 1: Introduction to Functions and Graphs
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1.1: Numbers, Data, and Problem Solving

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1. is a real and rational number.
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24
2. 100,000 is a real number, rational number, integer, and natural number.
3. 7.5 is a real and rational number.
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4. 12.3 is a real and rational number.
5. 90 2 is a real number.
6. 71 is an integer, real number, and rational number.
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7. Natural number: 9  3 ; whole number: 9 ; integers: 3 , 9 ; rational numbers: 3 , , 9 , 1.3 ;
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irrational numbers:  ,  2
3 3 3
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8. Natural numbers:  3 , 5.6  103  5600 ; whole numbers: , 0 , 5.6  103 ; integers: , 0 , 5.6  103 ;
1 1 1
3 5 3
rational numbers: ,  , 0.45 , 0 , 5.6  10 ; irrational number: 7
1 8
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9. Natural number: None; whole number:0; integer: 0,  4  2 ; rational numbers: 0, , 5.1 106 , 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
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10 9
11. Shoe sizes are normally measured to within half sizes. Rational numbers are most appropriate.
12. Population is measured using natural numbers.
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
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negative numbers, the integers would be most appropriate.
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
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20. (4  5) 2  32  3 9  (  1)2  9  3(3)  1  9  9  17
84 4
21. 95   4   22  0
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42 2
6  42  23 6  16  8 6  2
22.    4
3 4 1 1



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, 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
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25.     8
23 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
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28. 5  (4)3  43  5  (64)  64  5  64  64  5
29. 8.2  101
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30. 1.45  107
31. 3.65  103
32. 0.62  6.2  101
33. 2450  2.45  103
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34. 105.6  1.056  102
35. 0.56  5.6  101
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36. 0.00456  4.56  103
37. 0.0087  8.7  103
38. 1, 250, 000  1.25 106
39. 206.8  2.068  102
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40. 0.00007  7  105
41. 106  0.000001
42. 9.11 1031  0.000000000000000000000000000000911
There are 30 zeros between the decimal point and the digits 911.
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43. 2  108  200, 000, 000
44. 8, 000, 000, 000
45. 1.567  102  156.7
46. 5.68  101  0.568
47. 5  105  500, 000
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48. 3.5  103  3500
49. 0.045  105  4500
50. 5.4 105  0.000054
51. 67  103  67, 000
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52. 0.0032  101  0.00032
53. (4  103 )(2  105 )  4  2  1035  8  108 ; 800, 000, 000
(3  101 )(3  104 )  3  3  1014  9  105 ; 900, 000
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54.
55. (5  102 )(7  104 )  5  7  102 4  35  102  3.5  101 ; 0.35




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