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Pre-Calc Homework Solutions 200

Pre-Calc Homework Solutions 200 - 200 Chapter 4 Review 56(a...

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56. (a) The distance between the particles is ) f ( t ) ) where f ( t ) 5 2 cos t 1 cos 1 t 1 } p 4 } 2 . Then f 9 ( t ) 5 2 sin t 1 sin 1 t 1 } p 4 } 2 Solving f 9 ( t ) 5 0 graphically, we obtain t < 1.178, t < 4.230, and so on. [0, 2 p ] by [ 2 2, 2] Alternatively, f 9 ( t ) 5 0 may be solved analytically as follows. f 9 ( t ) 5 sin 31 t 1 } p 8 } 2 2 } p 8 } 4 2 sin 31 t 1 } p 8 } 2 1 } p 8 } 4 5 3 sin 1 t 1 } p 8 } 2 cos } p 8 } 2 cos 1 t 1 } p 8 } 2 sin } p 8 } 4 2 3 sin 1 t 1 } p 8 } 2 cos } p 8 } 1 cos 1 t 1 } p 8 } 2 sin } p 8 } 4 5 2 2 sin } p 8 } cos 1 t 1 } p 8 } 2 , so the critical points occur when cos 1 t 1 } p 8 } 2 5 0, or t 5 } 3 8 p } 1 k p . At each of these values, f ( t ) 5 6 2 cos } 3 8 p } < 6 0.765 units, so the maximum distance between the particles is 0.765 units. (b) Solving cos t 5 cos 1 t 1 } p 4 } 2 graphically, we obtain t < 2.749, t < 5.890, and so on. [0, 2 p ] by [ 2 2, 2] Alternatively, this problem may be solved analytically as follows.
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