Pre-Calc Homework Solutions 159

Pre-Calc Homework Solutions 159 - Section 4.4 21. If the...

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21. If the upper right vertex of the rectangle is located at ( x , 4 cos 0.5 x ) for 0 , x , p , then the rectangle has width 2 x and height 4 cos 0.5 x , so the area is A ( x ) 5 8 x cos 0.5 x . Then A 9 ( x ) 5 8 x ( 2 0.5 sin 0.5 x ) 1 8(cos 0.5 x )(1) 52 4 x sin 0.5 x 1 8 cos 0.5 x . Solving A 9 ( x ) graphically for 0 , x , p , we find that x < 1.72. Evaluating 2 x and 4 cos 0.5 x for x < 1.72, the dimensions of the rectangle are approximately 3.44 (width) by 2.61 (height), and the maximum area is approximately 8.98. 22. Let the radius of the cylinder be r cm, 0 , r , 10. Then the height is 2 ˇ 1 w 0 w 0 w 2 w r w 2 w and the volume is V ( r ) 5 2 p r 2 ˇ 1 w 0 w 0 w 2 w r w 2 w cm 3 . Then V 9 ( r ) 5 2 p r 2 1 } 2 ˇ 1 w 0 w 1 0 w 2 w r w 2 w } 2 ( 2 2 r ) 1 (2 p ˇ 1 w 0 w 0 w 2 w r w 2 w )(2 r ) 5 5 The critical point for 0 , r , 10 occurs at r 5 ! } 2 § 0 3 § 0 } § 5 10 ! } 2 3 } § . Since V 9 ( r ) . 0 for 0 , r , 10 ! }
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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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