Algebra and Trigonometry (3rd Edition) (Beecher/Penna/Bittinger Series)
Judith A. Beecher, Judith A. Penna, Marvin L. Bittinger
Language: English
Pages: 1063
ISBN: B00XIHIGXA
Format: PDF / Kindle (mobi) / ePub
These authors have created a book to really help students visualize mathematics for better comprehension. By creating algebraic visual side-by-sides to solve various problems in the examples, the authors show students the relationship of the algebraic solution with the visual, often graphical, solution. In addition, the authors have added a variety of new tools to help students better use the book for maximum effectiveness to not only pass the course, but truly understand the material.
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Addison-Wesley BBEPMC08_0321279115.QXP 1/7/05 3:25 PM Page 712 712 Chapter 8 • Systems of Equations and Matrices Products of Matrices Matrix multiplication is defined in such a way that it can be used in solving systems of equations and in many applications. Matrix Multiplication For an m ϫ n matrix A ͓ aij͔ and an n ϫ p matrix B ͓ bij͔, the product AB ͓ cij͔ is an m ϫ p matrix, where cij ai 1 и b 1 j ϩ ai 2 и b 2 j ϩ ai 3 и b 3 j ϩ и и и ϩ ain и bnj. In other words, the
4560 Maximum (0, 0) (60, 0) x ͑0, 60͒ P 40 и 0 ϩ 75 и 60 4500 The carpentry shop will make a maximum profit of $4560 when 24 bookcases and 48 desks are produced. Copyright © 2006 Pearson Education, Inc., publishing as Pearson Addison-Wesley BBEPMC08_0321279115.QXP 1/7/05 3:26 PM Page 744 744 Chapter 8 • Systems of Equations and Matrices 8.7 Exercise Set In Exercises 1– 8, match the inequality with one of the Graph. graphs (a) – (h), which follow. 9. y Ͼ 2 x Ճ 10. 2 y
the following form: 7 x 2 Ϫ 29 x ϩ 24 A ϩ B ϩ C . ͑2 x Ϫ 1͒ ͑ x Ϫ 2͒2 2 x Ϫ 1 x Ϫ 2 ͑ x Ϫ 2͒2 As in Example 1, we add the expressions on the right: 7 x 2 Ϫ 29 x ϩ 24 A͑ x Ϫ 2͒2 ϩ B͑2 x Ϫ 1͒͑ x Ϫ 2͒ ϩ C͑2 x Ϫ 1͒. ͑2 x Ϫ 1͒ ͑ x Ϫ 2͒2 ͑2 x Ϫ 1͒ ͑ x Ϫ 2͒2 Copyright © 2006 Pearson Education, Inc., publishing as Pearson Addison-Wesley BBEPMC08_0321279115.QXP 1/7/05 3:26 PM Page 751 Section 8.8 • Partial Fractions 751 Then we equate the numerators. This gives us 7 x 2 Ϫ 29 x ϩ
;͒ B: ͑5, 300Њ ,͒ ͑5, Ϫ60Њ ,͒ 79. (d) 81. (g) 83. ( j) 85. (b) 87. (e) 89. (k) ͑Ϫ5, 120Њ ;͒ C: ͑2, 150Њ ,͒ ͑2, 510Њ ,͒ ͑Ϫ2, 330Њ ;͒ D: ͑3, 225Њ ,͒ 91. 93. ͑3, Ϫ135Њ ,͒ ͑Ϫ3, 45Њ ;͒ answers may vary r ϭ sin u tan u r ϭ eu/10 2 DOT 4 3 5 15. ͑3, 270Њ , ͒ 17. ͑6, 300Њ , ͒ ͩ3, ͪ2 ͩ6, ͪ3 11 5 Ϫ3 3 Ϫ6 6 19. ͑8, 330Њ , ͒ 21. ͑2, 225Њ , ͒ ͩ8, ͪ6 ͩ2, ͪ4 7 Ϫ2 Ϫ4 23. ͑2, 60Њ , ͒ 25. ͑5, 315Њ , ͒ ͩ2, ͪ3 ͩ5, ͪ4 95. 97. 27. ͑7.616, 66.8Њ , ͒ ͑7.616, 1.166͒
we Origin see symmetry with respect to both axes We replace x with Ϫ x and y with Ϫ y: and with respect to the origin. x 2 ϩ y 4 5 ͑Ϫ x͒2 ϩ ͑Ϫ y͒4 5 x 2 ϩ y 4 . 5 The resulting equation is equivalent to the original equation, so the graph is symmetric with respect to the origin. Copyright © 2006 Pearson Education, Inc., publishing as Pearson Addison-Wesley BBEPMC01_0312279093.QXP 12/2/04 2:19 PM Page 152 152 Chapter 1 • Graphs, Functions, and Models Even and Odd
