A heavy rope, 40 ft long, weighs 0.3 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.)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.

The base x of the right triangle in the figure increases at a rate of 7 cm/s, while the height remains constant at h = 21 cm. 4 How fast is the angle 0 changing when x = 35? (Use symbolic notation and fractions where needed.) de dt x=35 = rad/s

Sketch the situation if necessary and use related rates to solve for the quantity. A 6 -ft-tall person walks away from a 10 -ft lamppost at a constant rate of 3 ft/sec. What is the rate that the tip of the shadow moves away from the top of the pole when the person is 10 ft away from the pole? 10 10 6 X + Click here to create a new row The rate that the tip of the shadow moves away from the pole is + ft/sec. © Rice University 201

Anika and Barry drive go karts, east and south, respectively. Starting from the same place at the same time & and each at 18ft/s. How fast is the distance between them growing when they're 40 feet from the starting point ?