ISM_T11_C01_B

# ISM_T11_C01_B - 12 Chapter 1 Preliminaries 66 The points on...

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12 Chapter 1 Preliminaries 66. The points on or inside the circle centered at ( ) with radius 2 and on or inside the !ß! circle centered at ( 2 0) with radius 2. ±ß 67. x y 6y 0 x (y 3) 9. ## # # ²²³Ê ²² ³ The interior points of the circle centered at ( 3) with radius 3, but above the line !ß± y3 . œ± 68. x y 4x 2y 4 (x 2) (y 1) 9. # # ²±²´Ê ± ²² ´ The points exterior to the circle centered at (2 1) with radius 3 and to the right of the ß± line x 2. œ 69. (x 2) (y 1) 6 70. (x 4) (y 2) 16 ²² ±³ ±´ 71. x y 2, x 1 72. x y 4, (x 1) (y 3) 10 # # ²Ÿ   ²´ ± ²± ³ 73. x y 1 and y 2x 1 x 4x 5x # # # ²œ œ Êœ² œ x and y or x and y . Êœ œ œ ± œ ± Š‹ Š "" ÈÈ È È 55 5 5 22 Thus, A , B are the Š È È 5 5 ß ± points of intersection.

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Section 1.2 Lines, Circles, and Parabolas 13 74. x y 1 and (x 1) y 1 ±œ ² ± œ ## 1 ( y) y 2y Êœ²±œ # y and x or Êœ œ " ² Š‹ "" ÈÈ 22 y and x 1 . Thus, œ² œ ± A and B 1 Š ß ± ß² " " È È 2 2 are intersection points. 75. y x 1 and y x x x 1 ²œ œ Ê ²œ xx 1 0 x . Ê² ² œ Ê œ # # 15 È I f x, t h e n y x 1. œ œ±œ 35 ±± I f t h e n y x œ ²² Thus, A and B ßß are the intersection points. 76. y x and (x 1) (x 1) x Cœ² ² Ê ² œ x 3x 0 x . If ± " œ Ê œ # # È x , then y x . If œœ ² œ 5 3 x , then y x . ² œ ² Thus, A and B Š 35 5 3 35 35 ± ± # # È È ² are the intersection points. 77. y 2x 1 3x 1 œ ² Ê œ # x and y or x and y . Ê œ " " 33 Thus, A and B are the Š ² intersection points.
14 Chapter 1 Preliminaries 78. y (x 1) 0 2x 1 œœ± Êœ ±² x3 x 44 ## # 0 3x 8x 4 (3x 2)(x 2) Êœ ±²œ ± ± # x 2 and y 1, or x and Êœ œœ œ x2 43 # y . Thus, A(2 1) and B ß ß 49 3 9 # "" ˆ‰ are the intersection points. 79. x y 1 (x 1) y ²œœ± ² x (x 1) x 2x 1 ±œ ± ² # 0 2x 1 x . Hence ±²Êœ " # y x or y . Thus, # œ"± œ œ „ 3 4 3 È A and B are the Š‹ Š # # ßß ± ÈÈ 33 intersection points. 80. x y 1 x y y y # # ²œœ²Ê œ y(y 1) 0 y 0 or y 1. Ê± œ Ê œ œ If y 1, then x y 0 or x 0. " ± œ œ If y 0, then x 1 y 1 or x 1. ± œ œ Thus, A(0 1), B( 0), and C( 1 0) are the ß" ß ± ß intersection points. 81. (a) A (69° 0 in), B (68° .4 in) m 2.5°/in. ¸ß Ê œ ¸ ± 68° 69° .4 0 ± ± (b) A (68° .4 in), B (10° 4 in) m 16.1°/in. Ê œ ¸ ± 10° 68° 4 .4 ± ± (c) A (10° 4 in), B (5° 4.6 in) m 8.3°/in. ¸ ß Ê œ ¸ ± 10° 4.6 4 ± ± 82. The time rate of heat transfer across a material, , is directly proportional to the cross-sectional area, A, of the mate ? ? U > rial, to the temperature gradient across the material, (the slopes from the previous problem), and to a constant characteristic ?

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ISM_T11_C01_B - 12 Chapter 1 Preliminaries 66 The points on...

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