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Pre-Calc Homework Solutions 321

# Pre-Calc Homework Solutions 321 - Chapter 7 Review 36 The...

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36. The radius of a horizontal cross section is ˇ 8 w 2 w 2 w y w 2 w , where y is distance below the rim. The area is p (64 2 y 2 ), the weight is 0.04 p (64 2 y 2 ) D y , and the work to lift it over the rim is 0.04 p (64 2 y 2 )( y ) D y . The total work is E 8 2 0.04 p y (64 2 y 2 ) dy 5 0.04 p E 8 2 (64 y 2 y 3 ) dy 5 0.04 p 3 32 y 2 2 } 1 4 } y 4 4 5 36 p < 113.097 in.-lb. 37. The width of a thin horizontal strip is 2(2 y ) 5 4 y , and the force against it is 80(2 2 y )4 y D y . The total force is E 2 0 320 y (2 2 y ) dy 5 320 E 2 0 ( 2 y 2 1 2 y ) dy 5 320 3 2 } 1 3 } y 3 1 y 2 4 5 } 12 3 80 } < 426.67 lb. 38. 5.75 in. 5 } 2 4 3 8 } ft, 3.5 in. 5 } 2 7 4 } ft, and 10 in. 5 } 5 6 } ft. For the base, Force 5 57 1 } 2 4 3 8 } 3 } 2 7 4 } 3 } 5 6 } 2 < 6.6385 lb. For the front and back, Force 5 E 5/6 0 57 1 } 2 7 4 } 2 y dy 5 } 3 2 9 4 9 } 3 } 1 2 } y 2 4 < 5.7726 lb. For the sides, Force 5 E 5/6 0 57 1 } 2 4 3 8 } 2 y dy 5 } 13 4 1 8 1 } 3 } 1 2 } y 2 4 < 9.4835 lb. 39. A square’s height is y 5 ( ˇ 6 w 2 ˇ x w ) 2 , and its area is y 2 5 ( ˇ 6 w 2 ˇ x w ) 4 . The volume is E 6 0 ( ˇ 6 w 2 ˇ x w ) 4 dx , which using NINT evaluates to exactly 14.4.
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