Pre-Calc Homework Solutions 460

Pre-Calc Homework Solutions 460 - 460 Appendix A5.2 p, and...

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Unformatted text preview: 460 Appendix A5.2 p, and let P(x, y) be a 4px. Now (b) Around the y-axis: 9x 2 x V 2 3 39. Let P1( p, y1) be any point on x point where a tangent intersects y 2 y2 4px 2y dy dx 4y 2 36 x 2 4 4 2 y 9 4 2 4y 0 4p y x dy dx y1 ( p) 2p ; then the slope of a y dy dx 2p y tangent line from P1 is y2 y2 1 2 4 2 y and we use the positive root 9 3 4 2 2 4 2 4 y dy 2 4 y dy 0 9 9 4 3 3 y 16 27 0 9x 2 4 4 2 yy1 yy1 2p yy1 2y1 2px y2 4p 2p 2. Since x 2p 2 y 2 0 16p 2 y2 , we have 4p 42. 9x 2 4y 2 36 y 2 x 4) dx 16 24) 1x 24 8 3 36 y 3 2 4 2 3 2 x2 2 4 on yy1 1 2 y 2 2p 2 the interval 2 9 4 4 2 4V 9 x3 4 3 x2 4 dx y2 y 2p 2 4y12 2 (x 2 4x y1 y12 4p 2. Therefore 9 4 64 3 8 9 56 4 3 8 the slopes of the two tangents from P1 are m1 2p y1 y12 y1 2 4p 2 4p (y12 2 3 (56 4 4p 2 and m2 4p 2) 2p y1 y12 43. x 2 V y2 3 1 y 2)2 dy 2 C y y 2 on the interval 3 3 y 3 m1m2 1 the lines are 3 3 ( 1 y 2) dy w x2 H 2 w(0)2 2H 2 perpendicular. 40. Let y 1 x2 on the interval 0 4 2 44. y x 0 (1 y 3 3 0 wx 2 2H 0 3 ( 1 24 y 2)2 dy x 2. The area of w x dx H C; y 0 when wx 2 is the 2H the inscribed rectangle is given by A(x) 2x 2 1 x2 4 00 CC 0; therefore y 4x 1 and the height is 2y) A (x) x2 (since the length is 2x 4 x2 x2 4 1 x2 . 4 1 4 equation of the cable's curve. 45. drA dt drB dt d (r dt A rB) 0 rA rB a constant Thus A (x) 4 1 x 4 2 04 1 x2 x2 4 x 1 2 x2 4 0 2 (only the 46. PF will always equal PB because the string has constant length AB FP PA AP PB. 0 x2 2x s Appendix A5.2 (pp. 606611) 1. 16x 2 25y 2 a2 c a positive square root lies in the interval). Since A(0) A(2) 0 we have that A( 2) 4 is the maximum 2. x 41. (a) Around the x-axis: 9x 2 y V 2 2 400 b2 x2 25 y2 16 1 3 c e 25 16 area, when the length is 2 2 and the height is 4y 2 36 y 2 0 y2 3 ; F( 3, 0); directrices are 5 5 a 25 3 = e 3 5 9 9 2 x 4 2. 2x 2 c e 2 x2 a2 b2 1 2 a e 2 1 2 9 2 9x 0 9 2 x and we use the positive root 4 2 9 2 2 9 2 9 x dx 2 9 x dx 0 4 4 y2 2 1 1 1 2 c a ; F(0, 1); directrices are 3 3 2 x 4 0 24 y 0 2 ...
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.

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