Solutions Manual for Basic Technical Mathematics with Calculus, 12th Edition by Allyn J. Washington

Instructor's Solutions Manual for
Basic Technical Mathematics and
Basic Technical Mathematics with Calculus, 12th Edition
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Chapter 1 Basic Algebraic Operations .....................................................................................1
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Chapter 2 Geometry..............................................................................................................104
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Chapter 3 Functions and Graphs ..........................................................................................171

Chapter 4 The Trigonometric Functions ..............................................................................259
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Chapter 5 Systems of Linear Equations; Determinants ........................................................346

Chapter 6 Factoring and Fractions........................................................................................490

Chapter 7 Quadratic Equations .............................................................................................581
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Chapter 8 Trigonometric Functions of Any Angle ...............................................................666

Chapter 9 Vectors and Oblique Triangles ............................................................................723
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Chapter 10 Graphs of the Trigonometric Functions ...............................................................828

Chapter 11 Exponents and Radicals .......................................................................................919
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Chapter 12 Complex Numbers .............................................................................................1001

Chapter 13 Exponential and Logarithmic Functions ............................................................1090
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Chapter 14 Additional Types of Equations and Systems of Equations ................................1183

Chapter 15 Equations of Higher Degree...............................................................................1290
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Chapter 16 Matrices; Systems of Linear Equations .............................................................1356

Chapter 17 Inequalities .........................................................................................................1477
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Chapter 18 Variation ............................................................................................................1598

Chapter 19 Sequences and the Binomial Theorem ...............................................................1634

Chapter 20 Additional Topics in Trigonometry ...................................................................1696
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, Chapter 21 Plane Analytic Geometry ...................................................................................1812

Chapter 22 Introduction to Statistics ....................................................................................2052
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Chapter 23 The Derivative ...................................................................................................2126

Chapter 24 Applications of the Derivative ...........................................................................2310
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Chapter 25 Integration ..........................................................................................................2487
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Chapter 26 Applications of Integration ................................................................................2572

Chapter 27 Differentiation of Transcendental Functions .....................................................2701

Chapter 28 Methods of Integration .......................................................................................2839
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Chapter 29 Partial Derivatives and Double Integrals ...........................................................2991

Chapter 30 Expansion of Functions in Series .......................................................................3058
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Chapter 31 Differential Equations ........................................................................................3181
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, Chapter 1
Basic Algebraic Operations
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1.1 Numbers
7 12
1. The numbers –7 and 12 are integers. They are also rational numbers since they can be written as and .
1 1
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2. The absolute value of –6 is 6, and the absolute value of –7 is 7. We write these as 6  6 and 7  7 .

3. 6  4 ; –6 is to the left of –4.
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–7 –6 –5 –4 –3 –2 –1 0 1
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3 1 2 2
4. The reciprocal of is  1  .
2 3/ 2 3 3

3
5. 3 is an integer, rational   , and real.
1
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4 is imaginary.

7
6. is irrational (because 7 is an irrational number) and real.
3
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 6 
6 is an integer, rational   , and real.
 1 


7.  is irrational (because  is an irrational number) and real.
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6
1
is rational and real.
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8.  6 is imaginary.
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233
2.33  is rational and real.
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9. 3 3
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3  3
 
 
2 2

10. 0.857  0.857
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2  2
19 19
 
4 4
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, 2 Chapter 1 Basic Algebraic Operations


11. 6  8 ; 6 is to the left of 8.
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3 4 5 6 7 8 9 10 11

12. 7  5 ; 7 is to the right of 5.
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3 4 5 6 7 8 9 10 11
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13.   3.1416;  (3.1415926 ) is to the left of 3.1416.

( ) (3.1416)
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3.141592 3.1416

14. 4  0 ; –4 is to the left of 0.
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–6 –5 –4 –3 –2 –1 0 1 2

15. 4   3 ; –4 is to the left of  3 ,   3    3  3 .
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–6 –5 –4 –3 –2 –1 0 1 2
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16.  2  1.42; (  2   1.414.  1.414 ),  2 is to the right of –1.42.



–1.44 –1.43 –1.42 –1.41 –1.40
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2 3 2 3
17.    ;   0.666 is to the right of   0.75 .
3 4 3 4
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–0.8 –0.7 –0.6 –0.5 –0.4

18. 0.6  0.2 ; –0.6 is to the left of 0.2.
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–0.6 –0.5 –0.4 –0.3 –0.2 –0.1 0 0.1 0.2
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Copyright © 2023 Pearson Education, Inc.