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Unformatted text preview: HW 7 Solutions Math 1920 March 10, 2009 Problem 10.5.30 Substitute x = r cos( ) and y = r sin( ) to get y = x . Line with slope m = 1 and intercept b = 0. Problem 10.5.36 We have r = 4tan( ) sec ( ) = 4( sin( ) cos 2 ( ) ) and therefore r cos 2 ( ) = 4sin( ) and r 2 cos 2 ( ) = 4 r sin( ). Now substitute x = r cos( ) and y = r sin( ) and get y = 4 x 2 , a parabola with vertex (0 , 0) which opens upward. Problem 10.5.41 Substitute x = r cos( ) and x 2 + y 2 = r 2 into r 2 = 4 r cos( ). That gives x 2 + y 2 = 4 x x 2 +4 x + y 2 = 0 ( x +2) 2 4+ y 2 = 0 ( x +2) 2 + y 2 = 2 2 . A circle with center C( 2 , 0) and radius 2. Problem 10.5.53 Substitute r 2 = x 2 + y 2 and get r 2 = 4 which gives r = 2 or r = 2. The two equations produce the same graph. Problem 10.5.54 Substitute r cos( ) = x and r sin( ) = y into x 2 y 2 = 1 and get r 2 cos 2 ( ) r 2 sin 2 ( ) = 1 r 2 ( cos 2 ( ) sin 2 ( )) = 1 r 2 cos (2 ) = 1. Problem 10.6.33 We have r = 2sin( ) and r = 2sin(2 ) sin ( ) = sin (2 ) = 2 sin ( ) cos ( ) sin ( ) 2 sin...
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 Spring '06
 PANTANO
 Multivariable Calculus, Slope

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