Mathematics, 24.03.2020 21:14 tylerkitchen44
A heavy rope, 60 ft long, weighs 0.3 lb/ft and hangs over the edge of a building 130 ft high. (Let x be the distance in feet below the top of the building. Enter xi* as xi.) (a) How much work W is done in pulling the rope to the top of the building? Show how to approximate the required work by a Riemann sum. lim n→[infinity] n Δx i = 1 Express the work as an integral. 0 dx Evaluate the integral. ft-lb (b) How much work W is done in pulling half the rope to the top of the building? Show how to approximate the required work by a Riemann sum. lim n→[infinity] n Δx i = 1 Express the work as an integral. 0 dx Evaluate the integral. ft-lb
Answers: 3
![W=\int\limits^{60}_0 {0.3x} \, dx \\\\=0.3[\frac{x^2}{2}]\imits^{60}_0\\\\=0.15(60)^2\\=(0.15)(3600)\\\\W=540ft-lb](/tpl/images/0561/4693/7cfcb.png)
![W=\int\limits^{30}_0 {0.3x} \, dx +\int\limits^{60}_{30} {(0.3)(60-x)} \, dx\\\\=[0.15x^2]^{30}_0-0.15[60-x^2]^{60}_{30}\\\\=(0.15)(30)^2-(0.15)(60-(60))^2+(0.15)(60-(30))^2 \\\\=135-0+135\\\\W=270ft-lb](/tpl/images/0561/4693/73842.png)
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A heavy rope, 60 ft long, weighs 0.3 lb/ft and hangs over the edge of a building 130 ft high. (Let x...
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