By Jean Michel Lemaire
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Extra resources for Aigebres Connexes et Homologie des Espaces de Lacets
71. To see how the distributive property is behind the mechanics of long multiplication, compute each of the following and compare: Long Multiplication 23 ϫ 12 65. The multiplicative inverse of any irrational number is an irrational number. 66. The multiplicative inverse of any nonzero rational number is a rational number. 67. If A ϭ 51, 2, 3, 46 and B ϭ 52, 4, 66, find: (A) 5x ƒ x ʦ A or x ʦ B6 (B) 5x ƒ x ʦ A and x ʦ B6 Use of the Distributive Property 23 ؒ 12 ϭ 23(2 ϩ 10) ϭ 23 ؒ 2 ϩ 23 ؒ 10 ϭ 72.
A. 0212v7ր3 Approximate the braking distance to the nearest foot for the car traveling on wet pavement at 70 miles per hour. 92. 5 ϫ 1021 grams and that it 100. BRAKING DISTANCE Approximately how many feet would it take the car in Problem 99 to stop on wet pavement if it were traveling at 50 miles per hour? ) bar67388_chR_014-035 11/15/06 14:48 Page 27 S E C T I O N R–3 R-3 27 Radicals Radicals Z From Rational Exponents to Radicals, and Vice Versa Z Properties of Radicals Z Simplifying Radicals Z Rationalizing Denominators What do the following algebraic expressions have in common?
477 ϫ 10Ϫ9 70. 892 ϫ 1016 5 5 71. 2 9ϩ 1 9 3 3 72. 2 2ϩ 1 2 3 8 7 For what real numbers are Problems 73–76 true? 73. 2x2 ϭ Ϫx 74. 2x2 ϭ x 3 3 75. 2 x ϭx 3 3 76. 2 x ϭ Ϫx In Problems 77 and 78, evaluate each expression on a calculator and determine which pairs have the same value. Verify these results algebraically. 77. (A) 13 ϩ 15 (C) 1 ϩ 13 (E) 28 ϩ 160 (B) 22 ϩ 13 ϩ 22 Ϫ 13 3 (D) 2 10 ϩ 6 13 (F) 16 3 78. (A) 2 2 2 ϩ 15 (C) 13 ϩ 17 (E) 210 ϩ 184 (B) 18 (D) 23 ϩ 18 ϩ 23 Ϫ 18 (F) 1 ϩ 15 In Problems 79–82, rationalize denominators.
Aigebres Connexes et Homologie des Espaces de Lacets by Jean Michel Lemaire