Pre-Calc Homework Solutions 438

Pre-Calc Homework - 438 Chapter 10 Review/3 0/3 44 Area 0 1 sin2 3 d 2 1 1 2 2 1 sin(6 12 50 12 45 1.5 1.5 by 1 1 3 3 by 2 2 r 0 such as Using Area

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Unformatted text preview: 438 Chapter 10 Review /3 0 /3 44. Area 0 1 sin2 3 d 2 1 1 2 2 1 sin (6 ) 12 50. 12 45. [ 1.5, 1.5] by [ 1, 1] [ 3, 3] by [ 2, 2] r 0, such as . Using Area sin 2 and /2 dr d cos 2 sin 2 , where 0 sin 2 cos2 2 d sin 2 2 , so The curves cross where cos 2 the curves' symmetry, /4 2 0 2 /2 0 sin 2 cos cos /2 4 4 cos 2 )2 1] d /4 d 4 Length 4 0 1 [(1 2 /4 4 51. (a) v(t) sin 0 2 0 (cos 2 1 sin 4 8 1 2 2 2 cos 2 ) d sin 2 0 2 4 d [(4 cos t)i dt ( 2 sin t)j] ( 2 cos t)j ( 2 cos t)j] ( 2 2 a(t) ( 4 sin t)i d [( 4 sin t)i dt 46. ( 4 cos t)i (b) v [ 4.5, 4.5] by [ 2, 4] 2 sin t)j 2 4 4 sin 8 1 4 2 cos 4 3 Since the two curves are covered over different -intervals, find the two areas separately. Then 2 (c) At t r2 4 ,v 1 v a 2 va 2i j, a 2 2i j, and Area 0 1 [2(1 2 2 sin )]2 d 2 sin sin 1 2 2 cos cos 2 2 0 (1 )d 5 0 2 dx dt dy dt 5 0 2 cos 1 sin 2 4 1 (3)(3) 7 cos 1 38.94 . 9 1 8 47. t, 2, so 2 (2t) t 2 22 dt 5 0 52. (a) v(t) d [( dt 3 sec t)i ( 3 tan t)j] ( 3 sec2 t)j ( 3 sec2 t)j] (2 3 sec2 t tan t)j 0 3 3 Area ( a(t) 3 sec t tan t)i 3 sec t tan t)i 4 (t 2 3 4) 3/2 76 3 d [( dt 3(sec t tan2 t (b) v(0) 4 dt, (c) At t 0, v v a cos 1 va 2 sec3 t)i 48. dx dt 2t 1 1/ 1 dy , 2t 2 dt 4, so 2 Area 2 2 t 1 2t 2t 1 2 2t 2 3 sec2 0 tan2 0 3j, a 0 ( 3)( 0 3) 3 sec4 0 3i cos 1 which using NINT evaluates to dr 49. d sin 2 cos 2 /4 10.110. 0 90 , so cos 2 sin d /4 Area 0 0 2 /4 cos 2 sin2 2 d cos 2 53. v(t) dr dt (1 t i t 2)3/2 2 sin cos 0 v(t) 1 j (1 t 2)3/2 2 t (1 t 2)3/2 (1 2 1 t 2)3/2 1 1 t2 , 2 (2 2) 1.840 which is at a maximum of 1 when t 0. ...
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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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