Pre-Calc Homework Solutions 316

Pre-Calc Homework Solutions 316 - 316 Section 7.5(d 0 if we...

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23. The work to raise a thin disk is p r 2 (56) h 5 p ( ˇ 1 w 0 w 2 w 2 w y w 2 w ) 2 (56)(10 1 2 2 y ) D y 5 56 p (12 2 y )(100 2 y 2 ) D y . The total work is E 10 0 56 p (12 2 y )(100 2 y 2 ) dy , which evaluates using NINT to < 967,611 ft-lb. This will come to (967,611)($0.005) < $4838, so yes, there’s enough money to hire the firm. 24. Pipe radius 5 } 1 6 } ft; Work to fill pipe 5 E 360 0 p 1 } 1 6 } 2 2 (62.4) y dy 5 112,320 p ft-lb. Work to fill tank 5 E 385 360 p (10) 2 (62.4) y dy 5 58,110,000 p ft-lb. Total work 5 58,222,320 p ft-lb, which will take 58,222,320 p 4 1650 < 110,855 sec < 31 hr. 25. (a) The pressure at depth y is 62.4 y , and the area of a thin horizontal strip is 2 D y . The depth of water is } 1 6 1 } ft, so the total force on an end is E 11/6 0 (62.4 y )(2 dy ) < 209.73 lb. (b) On the sides, which are twice as long as the ends, the initial total force is doubled to < 419.47 lb. When the tank is upended, the depth is doubled to } 1 3 1 } ft, and the force on a side becomes E 11/3 0 (62.4 y )(2 dy ) < 838.93 lb, which means that the fluid force doubles. 26. 3.75 in. 5 } 1 5 6 } ft, and 7.75 in. 5 } 3 4 1 8 } ft.
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