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Business Calc Homework w answers_Part_65

Business Calc Homework w answers_Part_65 - Chapter 7 Review...

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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. 40. Choose 50 cm as a conveniently large upper limit. E 50 20 } 3.4 ˇ 1 2 w p w } e 2 ( x 2 17.2) 2 /(2 ? 3.4 2 ) dx , evaluates, using NINT to < 0.2051 (20.5%). 41. Answers will vary. Find m , then use the fact that 68% of the class is within s of m to find s , and then choose a conveniently large number b and calculate E b 10 } s ˇ 1 2 w p w } e 2 ( x 2 m ) 2 /(2 s 2 ) dx . 42. Use f ( x ) 5 } ˇ 1 2 w p w } e 2 x 2 /2 . (a) E 1 2 1 f ( x ) dx evaluates, using NINT, to < 0.6827 (68.27%). (b) E 2 2 2 f ( x ) dx < 0.9545 (95.45%) (c) E 3 2 3 f ( x ) dx < 0.9973 (99.73%) 43. Because f ( x ) $ 0 and E 2‘ f ( x ) dx 5 1 44. [ 2 1, 3] by [ 2 1, 3] A shell has radius x and height 2 x 2 } 2 x } 5 } 3 2 } x . The total volume is E 1 0 2 p ( x ) 1 } 3 2 } x 2 dx 5 p 3 x 3 4 5 p . 45. [ 2 3, 3] by [ 2 3, 3] A shell has radius x and height } 1 x } . The total volume is E 2 1/2 2 p ( x ) 1 } 1 x } 2 dx 5 E 2 1/2 2 p dx 5 3 2 p x 4 5 3 p . 46. 3 2 } p 2 } , } 3 2 p } 4 by [ 2 2, 2] A shell has radius x and height sin x . The total volume is E p 0 2 p ( x )(sin x ) dx 5 2 p 3 sin x 2 x cos x 4 5 2 p 2 . 47. [ 2 1, 4] by [ 2 4, 1] The curves intersect at x 5 1 and x 5 3. A shell has radius x and height x 2 3 2 ( x 2 2 3 x ) 5 2 x 2 1 4 x 2 3. The total volume is E 3 1 2 p ( x )( 2 x 2 1 4 x 2 3) dx 5 2 p E 3 1 ( 2 x 3 1 4 x 2 2 3 x ) dx 5 2 p 3 2 } 1 4 } x 4 1 } 4 3 } x 3 2 } 3 2 } x 2 4 5 } 16 3 p } .
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