By Soo T. Tan
Market-leading utilized arithmetic FOR THE MANAGERIAL, lifestyles, AND SOCIAL SCIENCES, fifth version, is a standard textual content with a touch sleek suppose. This new version contains know-how in this type of approach that either conventional and glossy practitioners locate the help they should educate successfully. carrying on with its culture of mathematical accuracy, the recent 5th version teaches via program and makes use of genuine and life like examples to inspire scholars. It combines sturdy concept with leading edge studying instruments, incorporates a powerful complement package deal, and gives unequalled flexibility that makes the path effortless to educate. obtainable for majors and non-majors alike, the e-book makes use of an intuitive strategy that introduces summary innovations via examples drawn from universal, real-life reviews to which scholars can relate. It additionally attracts functions from readers' fields of curiosity. additionally, insightful Portfolios spotlight the careers of genuine humans and speak about how they include math into their expert lives. quite a few workouts be certain scholars have a pretty good figuring out of textual content suggestions prior to advancing to the subsequent subject. Bringing strong assets to scholars' fingertips, the text's interesting array of supplements--including more desirable WebAssign, resolution video clips, and private Tutor--equips scholars with wide studying aid to aid them maximize their examine time.
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Additional info for Applied Mathematics: For the Managerial, Life, and Social Sciences, Fifth Edition
Example text
2. a. The associative law of addition states that a ϩ (b ϩ c) ϭ . b. The distributive law states that ab ϩ ac ϭ 3. What can you say about a and b if ab ϶ 0? How about a, b, and c if abc ϶ 0? 1 Exercises In Exercises 1–10, classify the number as to type. ) 1. Ϫ3 5. 211 ෆ2ෆ1ෆ 9. 4 2. Ϫ420 3 3. 8 4 4. Ϫ 125 6. Ϫ 25 p 7. 2 2 8. p 10. 71828. . In Exercises 11–16, indicate whether the statement is true or false. 11. Every integer is a whole number. 12. Every integer is a rational number. 13. Every natural number is an integer.
3)2 и (Ϫ3)3 12. (Ϫ2x)3(Ϫ2x)2 In Exercises 13–56, perform the indicated operations and simplify. 13. (2x ϩ 3) ϩ (4x Ϫ 6) 2 45. (2x ϩ 3y)2 Ϫ (2y ϩ 1)(3x Ϫ 2) ϩ 2(x Ϫ y) 4 6. Ϫ aϪ b 5 5. Ϫ43 42. (3r ϩ 4s)(3r Ϫ 4s) 43. (2x Ϫ 1) ϩ 3x Ϫ 2(x ϩ 1) ϩ 3 2 14. (Ϫ3x ϩ 2) Ϫ (4x Ϫ 3) 47. (t 2 Ϫ 2t ϩ 4)(2t 2 ϩ 1) 48. (3m 2 Ϫ 1)(2m 2 ϩ 3m Ϫ 4) 49. 2x Ϫ {3x Ϫ [x Ϫ (2x Ϫ 1)]} 50. 3m Ϫ 2{m Ϫ 3[2m Ϫ (m Ϫ 5)] ϩ 4} 51. x Ϫ {2x Ϫ [Ϫx Ϫ (1 Ϫ x)]} 52. 3x 2 Ϫ {x 2 ϩ 1 Ϫ x[x Ϫ (2x Ϫ 1)]} ϩ 2 53. (2x Ϫ 3)2 Ϫ 3(x ϩ 4)(x Ϫ 4) ϩ 2(x Ϫ 4) ϩ 1 54.
N ϭ a mϪn a 3. (am)n ϭ a mn m n Illustration x и x ϭ x2ϩ3 ϭ x 5 x7 ϭ x7Ϫ4 ϭ x 3 x4 (x 4)3 ϭ x 4и3 ϭ x12 mϩn 4. (ab)n ϭ an и bn a n an 5. a b ϭ n (b b b 2 0) 3 (2x)4 ϭ 24 и x 4 ϭ 16x 4 x 3 x3 x3 a b ϭ 3ϭ 2 8 2 It can be shown that these laws are valid for any real numbers a and b and any integers m and n. 28 1 FUNDAMENTALS OF ALGEBRA Simplifying Exponential Expressions The next two examples illustrate the use of the laws of exponents. EXAMPLE 4 Simplify the expression, writing your answer using positive exponents only.