By Soo T. Tan
Market-leading utilized arithmetic FOR THE MANAGERIAL, existence, AND SOCIAL SCIENCES, fifth version, is a conventional textual content with a marginally sleek consider. This re-creation comprises expertise in this type of approach that either conventional and glossy practitioners locate the aid they should educate successfully. carrying on with its culture of mathematical accuracy, the hot 5th variation teaches through software and makes use of genuine and reasonable examples to encourage scholars. It combines strong thought with cutting edge studying instruments, incorporates a powerful complement package deal, and gives unequalled flexibility that makes the path effortless to coach. obtainable for majors and non-majors alike, the ebook makes use of an intuitive method that introduces summary ideas via examples drawn from universal, real-life stories to which scholars can relate. It additionally attracts functions from readers' fields of curiosity. furthermore, insightful Portfolios spotlight the careers of genuine humans and speak about how they include math into their specialist lives. various workouts be certain scholars have a high-quality knowing of textual content thoughts sooner than advancing to the following subject. Bringing robust assets to scholars' fingertips, the text's interesting array of supplements--including greater WebAssign, answer movies, and private Tutor--equips scholars with wide studying aid to aid them maximize their learn time.
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Extra info for Applied Mathematics: For the Managerial, Life, and Social Sciences, Fifth Edition
If ab ϭ 0, then a ϭ 0, b ϭ 0, or both. Property a c ϭ if ad ϭ bc b d ca a 2. ϭ cb b 1. 3. 4. 5. 6. 7. a Ϫa a ϭ ϭϪ Ϫb b b a # c ac ϭ b d bd ad a c a d Ϭ ϭ # ϭ b d b c bc a c ad ϩ bc ϩ ϭ b d bd a c ad Ϫ bc Ϫ ϭ b d bd Illustration (b, d 0) (b, c 0) (b 3 9 ϭ because 3 и 12 ϭ 9 и 4 4 12 4 # 3 3 ϭ # 4 8 8 0) (b, d 0) (b, c, d 0) (b, d 0) (b, d 0) 4 Ϫ4 4 ϭ ϭϪ Ϫ3 3 3 3 # 5 15 ϭ 4 2 8 3 5 3 2 3 Ϭ ϭ # ϭ 4 2 4 5 10 3 5 3 # 2ϩ4 # 5 13 ϩ ϭ ϭ 4 2 8 4 # # 5 3 2Ϫ4 5 7 3 Ϫ ϭ ϭϪ 4 2 8 4 In the rest of this book, we will assume that all variables are restricted so that division by zero is excluded.
15. Every natural number is an irrational number. 16. Every irrational number is a real number. 2 POLYNOMIALS In Exercises 17–36, state the real number property that justifies the statement. 21. u(2√ ϩ w) ϭ 2u√ ϩ uw 2x ϩ 1 2x Ϫ 1 33. a1a ϩ b2 aϪb aϩb Ϭ ϭ b ab aϪb 34. x ϩ 2y x ϩ 2y x Ϭ ϭ 3x ϩ y 6x ϩ 2y 3x ϩ y 35. c ab ϩ bc ϩ c a ϩ ϭ bϩc b b1b ϩ c2 36. y x2 Ϫ y xϩy Ϫ ϭ xϩ1 x x1x ϩ 12 19. u(3√ ϩ w) ϭ (3√ ϩ w)u 20. a2(b2c) ϭ (a2b2)c ϭ 12x Ϫ 12 1x ϩ 32 17. (2x ϩ y) ϩ z ϭ z ϩ (2x ϩ y) 18. 3x ϩ (2y ϩ z) ϭ (3x ϩ 2y) ϩ z 12x ϩ 12 1x ϩ 32 32.
2 can be found on page 14. 2 Concept Questions 1. Describe a polynomial of degree n in x. Give an example of a polynomial of degree 4 in x. 2. Without looking at the text, complete the following formulas: a. (1 ϩ b)2 ϭ ______ b. (a Ϫ b)2 ϭ ______ c. 2 Exercises 41. (2u Ϫ √)(2u ϩ √) In Exercises 1–12, evaluate the expression. 1. 34 2 3. a b 3 2. (Ϫ2)5 3 4. aϪ b 4 3 3 7. Ϫ2 a b 5 2 9. 23 и 25 11. (3y)2(3y)3 44. (3m ϩ 2)2 Ϫ 2m(1 Ϫ m) Ϫ 4 3 2 3 8. aϪ b aϪ b 3 4 3 2 46. (x Ϫ 2y)( y ϩ 3x) Ϫ 2xy ϩ 3(x ϩ y Ϫ 1) 3 10.