Pre-Calculus Homework Solutions 197

Pre-Calculus Homework Solutions 197 - 57. 47. C; x2 x2 36...

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Unformatted text preview: 57. 47. C; x2 x2 36 ¬(9 x)2 36 ¬81 18x x2 36 ¬81 18x 45 ¬ 18x 2.5 ¬x 48. 3-4-5, 6-8-10, 12-16-20, 24-32-40, 27-36-45 49. 3 4 5 60 6 8 10 480 8 60 12 16 20 3840 64 60 24 32 40 30,720 512 60 27 36 45 43,740 729 60 Yes, the conjecture holds true. x 1 3 3x 3 27 27 7.6 1012 The sequence of numbers approaches positive infinity. 58. x 4 2 1.41... 1.18... 1.09... 1.04... 1 2 1.41... 1.18... 1.09... 1.04... 1.02... x2 The sequence of numbers converges to 1. 59. x 4 0.25 4 0.25 1 x 0.25 4 0.25 4 Page 356 Maintain Your Skills The sequence of numbers alternates between 0.25 and 4. 60. No; 12 13 25, so the sides do not satisfy the Triangle Inequality. 50. Let x represent the geometric mean. 61. 7 3 x 3 62. 18 2 14 63. 2 x ¬ 12 x2 ¬36 x ¬ 36 or 6 51. Let x represent 9 x x ¬ 12 2 x ¬108 x ¬ 108 or 6 x ¬10.4 52. Let x represent 11 x ¬7 x x2 ¬77 x ¬ 77 x ¬8.8 53. Let x represent 6 x x ¬9 x2 ¬54 x ¬ 54 or 3 x ¬7.3 54. Let x represent 2 x x ¬7 x2 ¬14 x ¬ 14 x ¬3.7 55. Let x represent 2 x x ¬5 x2 ¬10 x ¬ 10 x ¬3.2 56. x 5 2x 10 the geometric mean. 73 3 3 3 2 2 2 2 18 2 2 92 28 2 27 2 64. 3 11 3 3 3 3 65. 24 the geometric mean. 2 12 66. 3 26 67. 3 2 2 3 3 3 3 the geometric mean. 68. 15 3 69. 2 6 8 3 3 8 8 7 3 33 3 33 24 2 2 12 2 12 3 3 43 2 18 3 62 3 22 15 3 3 28 8 42 8 the geometric mean. 70. 25 10 the geometric mean. 7-3 10 10 53 25 10 10 2 2 5 10 2 Special Right Triangles Page 360 Check for Understanding 10 2.51... 2.51... 2.24... 2.11... 2.24... 2.11... 1. Sample answer: Construct two perpendicular lines. Use a ruler to measure 3 cm from the point of intersection on one ray. Use the compass to copy the 3 cm segment. Connect the two endpoints to form a 45°-45°-90° triangle with sides of 3 cm and a hypotenuse of 3 2 cm. 2.05... The sequence of numbers converges to 2. 199 Chapter 7 ...
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