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A heavy rope, 40 ft long, weighs 0.5 lb/ft and hangs over the edge of a building 90 ft high. (Let x be the distance in feet below the top of the building. Enter $x_i^*$ as $x_i$.) (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. $$ lim_{n o infty} sum_{i=1}^n left( frac{5}{10} x_i ight) Delta x $$ Express the work as an integral. $$ int_0^{40} left( frac{5}{10} x ight) dx $$ Evaluate the integral. 400 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. $$ lim_{n o infty} sum_{i=1}^n left( 0.5(x_i + 20) ight) Delta x $$ Express the work as an integral. $$ int_0^{20} left( ight) dx $$ Evaluate the integral. ft-lb Need Help? Read It Watch It

          A heavy rope, 40 ft long, weighs 0.5 lb/ft and hangs over the edge of a building 90 ft high. (Let x be the distance in feet below the top of the building. Enter $x_i^*$ as $x_i$.)
(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.
$$ lim_{n 	o infty} sum_{i=1}^n left( frac{5}{10} x_i 
ight) Delta x $$
Express the work as an integral.
$$ int_0^{40} left( frac{5}{10} x 
ight) dx $$
Evaluate the integral.
400 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.
$$ lim_{n 	o infty} sum_{i=1}^n left( 0.5(x_i + 20) 
ight) Delta x $$
Express the work as an integral.
$$ int_0^{20} left( 
ight) dx $$
Evaluate the integral.
ft-lb
Need Help? Read It Watch It

$A heavy rope, 40 ft long, weighs 0.5 lb/ft and hangs over the edge of a building 90 ft high. (Let x be the distance in feet below the top of the building. Enter xi^* as xi.) (a) How much work W is done in pulling the rope to the top of the building? Show how to approximate the required work by a Riemann sum. limn o infty sumi=1^n left( frac510 xi ight) Delta x Express the work as an integral. int0^40 left( frac510 x ight) dx Evaluate the integral. 400 ft-lb (b) How much work W is done in pulling half the rope to the top of the building? Show how to approximate the required work by a Riemann sum. limn o infty sumi=1^n left( 0.5(xi + 20) ight) Delta x Express the work as an integral. int0^20 left( ight) dx Evaluate the integral. ft-lb Need Help? Read It Watch It$

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