Introductory Technical Mathematics, 5th Edition

Front Cover......Page 1
Title Page......Page 4
Copyright......Page 5
Contents
......Page 6
Preface......Page 18
SECTION I: Fundamentals of General Mathematics......Page 24
1–1 Place Value......Page 25
1–2 Expanding Whole Numbers......Page 26
1–3 Estimating (Approximating)......Page 27
1–4 Addition of Whole Numbers......Page 28
1–5 Subtraction of Whole Numbers......Page 30
1–6 Problem Solving—Word Problem Practical Applications......Page 31
1–7 Adding and Subtracting Whole Numbers in Practical Applications......Page 32
1–8 Multiplication of Whole Numbers......Page 34
1–9 Division of Whole Numbers......Page 38
1–10 Multiplying and Dividing Whole Numbers in Practical Applications......Page 41
1–11 Combined Operations of Whole Numbers......Page 43
1–12 Combined Operations of Whole Numbers in Practical Applications......Page 45
UNIT EXERCISE AND PROBLEM REVIEW......Page 48
1–13 Computing with a Calculator: Whole Numbers......Page 52
2–1 Definitions......Page 56
2–2 Fractional Parts......Page 57
2–4 Equivalent Fractions......Page 58
2–6 Expressing Mixed Numbers as Improper Fractions......Page 59
2–7 Expressing Improper Fractions as Mixed Numbers......Page 60
2–9 Use of Common Fractions in Practical Applications......Page 61
2–10 Addition of Common Fractions......Page 63
2–11 Subtraction of Common Fractions......Page 68
2–12 Adding and Subtracting Common Fractions in Practical Applications......Page 71
2–13 Multiplication of Common Fractions......Page 75
2–14 Multiplying Common Fractions in Practical Applications......Page 79
2–15 Division of Common Fractions......Page 82
2–16 Dividing Common Fractions in Practical Applications......Page 85
2–17 Combined Operations with Common Fractions......Page 88
2–18 Combined Operations of Common Fractions in Practical Applications......Page 90
UNIT EXERCISE AND PROBLEM REVIEW......Page 92
2–19 Computing with a Calculator: Fractions and Mixed Numbers......Page 97
UNIT 3 Decimal Fractions......Page 104
3–2 Reading Decimal Fractions......Page 105
3–4 Writing Decimal Fractions......Page 106
3–6 Expressing Common Fractions as Decimal Fractions......Page 107
3–7 Expressing Decimal Fractions as Common Fractions......Page 108
3–8 Expressing Decimal Fractions in Practical Applications......Page 109
3–10 Subtracting Decimal Fractions......Page 111
3–11 Adding and Subtracting Decimal Fractions in Practical Applications......Page 112
3–12 Multiplying Decimal Fractions......Page 115
3–13 Multiplying Decimal Fractions in Practical Applications......Page 118
3–14 Dividing Decimal Fractions......Page 120
3–15 Dividing Decimal Fractions in Practical Applications......Page 123
3–16 Powers and Roots of Decimal Fractions......Page 126
3–17 Decimal Fraction Powers and Roots in Practical Applications......Page 129
3–18 Table of Decimal Equivalents......Page 132
3–19 Combined Operations of Decimal Fractions......Page 135
3–20 Combined Operations of Decimal Fractions in Practical Applications......Page 137
UNIT EXERCISE AND PROBLEM REVIEW......Page 141
3–21 Computing with a Calculator: Decimals......Page 148
4–1 Description of Ratios......Page 154
4–2 Order of Terms of Ratios......Page 155
4–3 Description of Proportions......Page 157
4–4 Direct Proportions......Page 160
4–5 Inverse Proportions......Page 162
UNIT EXERCISE AND PROBLEM REVIEW......Page 165
5–1 Definition of Percent......Page 169
5–3 Expressing Common Fractions and Mixed Numbers as Percents......Page 170
5–4 Expressing Percents as Decimal Fractions......Page 171
5–6 Types of Simple Percent Problems......Page 172
5–7 Finding Percentage in Practical Applications......Page 175
5–8 Finding Percent (Rate) in Practical Applications......Page 177
5–9 Finding the Base in Practical Applications......Page 179
5–10 More Complex Percentage Practical Applications......Page 180
UNIT EXERCISE AND PROBLEM REVIEW......Page 183
6–1 Meaning of Signed Numbers......Page 187
6–2 The Number Line......Page 189
6–4 Absolute Value......Page 190
6–5 Addition of Signed Numbers......Page 191
6–6 Subtraction of Signed Numbers......Page 194
6–7 Multiplication of Signed Numbers......Page 195
6–8 Division of Signed Numbers......Page 197
6–9 Powers of Signed Numbers......Page 198
6–10 Roots of Signed Numbers......Page 200
6–11 Combined Operations of Signed Numbers......Page 203
6–12 Scientific Notation......Page 205
6–13 Engineering Notation......Page 211
UNIT EXERCISE AND PROBLEM REVIEW......Page 214
SECTION II: Measurement......Page 220
7–1 Exact and Approximate (Measurement) Numbers......Page 221
7–3 Common Linear Measuring Instruments......Page 222
7–4 Degree of Precision of a Measurement Number......Page 223
7–5 Degrees of Precision in Adding and Subtracting Measurement Numbers......Page 224
7–6 Significant Digits......Page 225
7–7 Accuracy......Page 226
7–9 Absolute and Relative Error......Page 227
7–10 Tolerance (Linear)......Page 228
7–11 Unilateral and Bilateral Tolerance with Clearance and Interference Fits......Page 230
UNIT EXERCISE AND PROBLEM REVIEW......Page 232
8–1 Customary Linear Units......Page 237
8–2 Expressing Equivalent Units of Measure......Page 238
8–3 Arithmetic Operations with Compound Numbers......Page 241
8–4 Customary Linear Measure Practical Applications......Page 245
8–5 Customary Units of Surface Measure (Area)......Page 248
8–6 Customary Area Measure Practical Applications......Page 250
8–7 Customary Units of Volume (Cubic Measure)......Page 251
8–8 Customary Volume Practical Applications......Page 252
8–9 Customary Units of Capacity......Page 253
8–10 Customary Capacity Practical Applications......Page 254
8–11 Customary Units of Weight (Mass)......Page 255
8–13 Compound Units......Page 256
8–14 Compound Units Practical Applications......Page 258
UNIT EXERCISE AND PROBLEM REVIEW......Page 260
9–1 Metric Units of Linear Measure......Page 263
9–2 Expressing Equivalent Units within the Metric System......Page 265
9–4 Metric Linear Measure Practical Applications......Page 267
9–5 Metric Units of Surface Measure (Area)......Page 269
9–6 Arithmetic Operations with Metric Area Units......Page 270
9–8 Metric Units of Volume (Cubic Measure)......Page 271
9–10 Metric Volume Practical Applications......Page 273
9–11 Metric Units of Capacity......Page 274
9–12 Metric Capacity Practical Applications......Page 275
9–13 Metric Units of Weight (Mass)......Page 276
9–15 Compound Units......Page 277
9–16 Compound Units Practical Applications......Page 279
9–17 Metric Prefixes Applied to Very Large and Very Small Numbers......Page 280
9–18 Conversion Between Metric and Customary Systems......Page 284
UNIT EXERCISE AND PROBLEM REVIEW......Page 287
10–2 Reading Fractional Measurements......Page 291
10–3 Measurements that Do Not Fall on Rule Graduations......Page 293
10–4 Reading Decimal-Inch Measurements......Page 294
10–5 Reading Metric Measurements......Page 295
10–6 Vernier Calipers: Types and Description......Page 296
10–7 Reading Measurements on a Customary Vernier Caliper......Page 298
10–8 Reading Measurements on a Metric Vernier Caliper......Page 300
UNIT EXERCISE AND PROBLEM REVIEW......Page 302
11–1 Description of a Customary Outside Micrometer......Page 304
11–2 Reading a Customary Micrometer......Page 305
11–3 The Customary Vernier Micrometer......Page 306
11–4 Reading a Customary Vernier Micrometer......Page 307
11–6 Reading a Metric Micrometer......Page 309
11–7 The Metric Vernier Micrometer......Page 310
11–8 Reading a Metric Vernier Micrometer......Page 311
UNIT EXERCISE AND PROBLEM REVIEW......Page 313
SECTION III: Fundamentals of Algebra......Page 316
12–2 Algebraic Expressions......Page 317
12–3 Evaluation of Algebraic Expressions......Page 320
UNIT EXERCISE AND PROBLEM REVIEW......Page 325
13–1 Definitions......Page 328
13–2 Addition......Page 329
13–3 Subtraction......Page 331
13–4 Multiplication......Page 334
13–5 Division......Page 337
13–6 Powers......Page 341
13–7 Roots......Page 344
13–8 Removal of Parentheses......Page 347
13–9 Combined Operations......Page 348
13–10 Basic Structure of the Binary Numeration System......Page 349
UNIT EXERCISE AND PROBLEM REVIEW......Page 353
14–1 Expression of Equality......Page 359
14–2 Writing Equations from Word Statements......Page 360
14–3 Checking the Equation......Page 362
14–5 Solution of Equations by the Subtraction Principle of Equality......Page 364
14–6 Solution of Equations by the Addition Principle of Equality......Page 367
14–7 Solution of Equations by the Division Principle of Equality......Page 370
14–8 Solution of Equations by the Multiplication Principle of Equality......Page 372
14–9 Solution of Equations by the Root Principle of Equality......Page 375
14–10 Solution of Equations by the Power Principle of Equality......Page 377
UNIT EXERCISE AND PROBLEM REVIEW......Page 379
15–1 Equations Consisting of Combined Operations......Page 382
15–3 Substituting Values Directly in Given Formulas......Page 386
15–4 Rearranging Formulas......Page 389
UNIT EXERCISE AND PROBLEM REVIEW......Page 393
16–1 Description of the Cartesian (Rectangular) Coordinate System......Page 396
16–2 Graphing a Linear Equation......Page 397
16–3 Slope of a Linear Equation......Page 400
16–5 Point-Slope Equation of a Straight Line......Page 401
16–6 Determining an Equation, Given Two Points......Page 402
16–7 Describing a Straight Line......Page 403
UNIT EXERCISE AND PROBLEM REVIEW......Page 406
17–1 Graphical Method of Solving Systems of Equations......Page 408
17–2 Substitution Method of Solving Systems of Equations......Page 410
17–3 Addition or Subtraction Method of Solving Systems of Equations......Page 411
17–4 Types of Systems of Equations......Page 415
17–5 Determinants......Page 416
17–6 Cramer’s Rule......Page 417
17–7 Writing and Solving Systems of Equations from Word Statements, Number Problems, and Practical Applications......Page 418
UNIT EXERCISE AND PROBLEM REVIEW......Page 424
18–1 General or Standard Form of Quadratic Equations......Page 426
18–2 Incomplete Quadratic Equations ( ) ax2=c......Page 427
18–3 Complete Quadratic Equations......Page 431
18–4 Practical Applications of Complete Quadratic Equations. Equations Given......Page 434
18–5 Word Problems Involving Complete Quadratic Equations. Equations Not Given......Page 440
UNIT EXERCISE AND PROBLEM REVIEW......Page 444
SECTION IV: Fundamentals of Plane Geometry......Page 446
19–1 Plane Geometry......Page 447
19–2 Axioms and Postulates......Page 448
19–3 Points and Lines......Page 451
UNIT EXERCISE AND PROBLEM REVIEW......Page 452
20–1 Units of Angular Measure......Page 453
20–2 Units of Angular Measure in Degrees, Minutes, and Seconds......Page 454
20–4 Expressing Decimal Degrees as Degrees, Minutes, and Seconds......Page 455
20–5 Arithmetic Operations on Angular Measure in Degrees, Minutes, and Seconds......Page 458
20–6 Simple Semicircular Protractor......Page 464
UNIT EXERCISE AND PROBLEM REVIEW......Page 468
21–2 Types of Angles......Page 471
21–3 Angles Formed by a Transversal......Page 472
21–4 Theorems and Corollaries......Page 474
UNIT EXERCISE AND PROBLEM REVIEW......Page 481
UNIT 22 Triangles......Page 484
22–1 Types of Triangles......Page 485
22–2 Angles of a Triangle......Page 487
22–4 Isosceles Triangle Practical Applications......Page 491
22–5 Equilateral Triangle Practical Applications......Page 492
22–7 Pythagorean Theorem Practical Applications......Page 493
UNIT EXERCISE AND PROBLEM REVIEW......Page 496
23–1 Congruent Figures......Page 500
23–2 Similar Figures......Page 502
23–3 Practical Applications of Similar Triangles......Page 505
UNIT EXERCISE AND PROBLEM REVIEW......Page 511
24–1 Types of Polygons......Page 514
24–2 Types of Quadrilaterals......Page 516
24–4 Practical Applications of Polygon Interior and Exterior Angles......Page 518
24–5 Practical Applications of Trapezoid Median......Page 523
UNIT EXERCISE AND PROBLEM REVIEW......Page 525
25–1 Definitions......Page 528
25–2 Circumference Formula......Page 530
25–3 Arc Length Formula......Page 531
25–4 Radian Measure......Page 533
25–5 Circle Postulates......Page 535
25–6 Chords, Arcs, and Central Angles......Page 536
25–7 Practical Applications of Circle Chord Bisector......Page 538
25–9 Practical Applications of Circle Tangent......Page 541
25–10 Practical Applications of Tangents from a Common Point......Page 542
25–11 Angles Formed Inside and on a Circle......Page 545
25–12 Practical Applications of Inscribed Angles......Page 546
25–13 Practical Applications of Tangent and Chord......Page 547
25–14 Angles Outside a Circle......Page 549
25–15 Internally and Externally Tangent Circles......Page 551
25–16 Practical Applications of Internally Tangent Circles......Page 552
25–17 Practical Applications of Externally Tangent Circles......Page 553
UNIT EXERCISE AND PROBLEM REVIEW......Page 557
SECTION V: Geometric Figures: Areas and Volumes......Page 564
26–1 Areas of Rectangles......Page 565
26–2 Areas of Parallelograms......Page 569
26–3 Areas of Trapezoids......Page 573
26–4 Areas of Triangles Given the Base and Height......Page 576
26–5 Areas of Triangles Given Three Sides......Page 578
UNIT EXERCISE AND PROBLEM REVIEW......Page 582
27–1 Areas of Circles......Page 587
27–2 Ratio of Two Circles......Page 588
27–3 Areas of Sectors......Page 591
27–4 Areas of Segments......Page 593
27–5 Areas of Ellipses......Page 595
UNIT EXERCISE AND PROBLEM REVIEW......Page 597
28–2 Volumes of Prisms......Page 601
28–4 Volumes of Cylinders......Page 605
28–5 Computing Heights and Bases of Prisms and Cylinders......Page 607
28–6 Lateral Areas and Surface Areas of Right Prisms and Cylinders......Page 609
UNIT EXERCISE AND PROBLEM REVIEW......Page 612
29–1 Pyramids......Page 614
29–3 Volumes of Regular Pyramids and Right Circular Cones......Page 615
29–4 Computing Heights and Bases of Regular Pyramids and Right Circular Cones......Page 617
29–5 Lateral Areas and Surface Areas of Regular Pyramids and Right Circular Cones......Page 618
29–6 Frustums of Pyramids and Cones......Page 621
29–7 Volumes of Frustums of Regular Pyramids and Right Circular Cones......Page 622
29–8 Lateral Areas and Surface Areas of Frustums of Regular Pyramids and Right Circular Cones......Page 624
UNIT EXERCISE AND PROBLEM REVIEW......Page 628
30–1 Spheres......Page 630
30–3 Volume of a Sphere......Page 631
30–4 Volumes and Surface Areas of Composite Solid Figures......Page 633
UNIT EXERCISE AND PROBLEM REVIEW......Page 638
SECTION VI: Basic Statistics......Page 640
31–1 Types and Structure of Graphs......Page 641
31–2 Reading Bar Graphs......Page 642
31–3 Drawing Bar Graphs......Page 647
31–4 Drawing Bar Graphs with a Spreadsheet......Page 649
31–5 Circle Graphs......Page 654
31–6 Drawing Circle Graphs with a Spreadsheet......Page 658
31–7 Line Graphs......Page 660
31–8 Reading Line Graphs......Page 661
31–9 Reading Combined-Data Line Graphs......Page 663
31–11 Drawing Broken-Line Graphs......Page 667
31–12 Drawing Broken-Line Graphs with a Spreadsheet......Page 669
31–13 Drawing Straight-Line Graphs......Page 671
31–14 Drawing Curved-Line Graphs......Page 672
UNIT EXERCISE AND PROBLEM REVIEW......Page 676
32–1 Probability......Page 680
32–2 Independent Events......Page 682
32–3 Mean Measurement......Page 684
32–4 Other Average Measurements......Page 686
32–5 Quartiles and Percentiles......Page 687
32–6 Grouped Data......Page 690
32–7 Variance and Standard Deviation......Page 695
32–8 Statistical Process Control: X-Bar Charts......Page 700
32–9 Statistical Process Control: R-Charts......Page 704
UNIT EXERCISE AND PROBLEM REVIEW......Page 708
SECTION VII: Fundamentals of Trigonometry......Page 710
33–1 Ratio of Right Triangle Sides......Page 711
33–2 Identifying Right Triangle Sides by Name......Page 712
33–3 Trigonometric Functions: Ratio Method......Page 713
33–5 Determining Functions of Given Angles and Determining Angles of Given Functions......Page 715
UNIT EXERCISE AND PROBLEM REVIEW......Page 719
34–1 Variation of Functions......Page 722
34–2 Functions of Complementary Angles......Page 724
34–3 Determining an Unknown Angle When Two Sides of a Right Triangle Are Known......Page 726
34–4 Determining an Unknown Angle When an Acute Angle an One Side of a Right Triangle Are Known......Page 728
UNIT EXERCISE AND PROBLEM REVIEW......Page 732
35–1 Solving Problems Stated in Word Form......Page 734
35–2 Solving Problems Given in Picture Form that Require Auxiliary Lines......Page 739
35–3 Solving Complex Problems that Require Auxiliary Lines......Page 748
UNIT EXERCISE AND PROBLEM REVIEW......Page 757
36–1 Cartesian (Rectangular) Coordinate System......Page 762
36–2 Determining Functions of Angles in Any Quadrant......Page 763
36–3 Alternating Current Applications......Page 766
36–4 Determining Functions of Angles Greater Than 360°......Page 769
36–5 Instantaneous Voltage Related to Time Application......Page 770
36–7 Law of Sines......Page 771
36–8 Solving Problems Given Two Angles and a Side, Using the Law of Sines......Page 772
36–9 Solving Problems Given Two Sides and an Angle Opposite One of the Given Sides, Using the Law of Sines......Page 774
36–11 Solving Problems Given Two Sides and the Included Angle, Using the Law of Cosines......Page 778
36–12 Law of Cosines (Given Three Sides)......Page 781
36–13 Solving Problems Given Three Sides, Using the Law of Cosines......Page 782
36–14 Practical Applications of Oblique Triangles......Page 785
UNIT EXERCISE AND PROBLEM REVIEW......Page 792
37–2 Description and Naming Vectors......Page 797
37–3 Vector Ordered Pair Notation......Page 798
37–5 Adding Vectors......Page 799
37–6 Graphic Addition of Vectors......Page 801
37–7 Addition of Vectors Using Trigonometry......Page 805
37–8 General (Component Vector) Procedure for Vectors Using Trigonometry......Page 811
UNIT EXERCISE AND PROBLEM REVIEW......Page 816
APPENDIX A: United States Customary and Metric Units of Measure......Page 819
APPENDIX B: Formulas for Areas (A) of Plane Figures......Page 821
APPENDIX C: Formulas for Volumes and Areas of Solid Figures......Page 822
APPENDIX D: Answers to Odd-Numbered Exercises......Page 823
INDEX......Page 868