please show all work thanks 4 cost l Consider the curve give

please show all work! thanks!

4 cost l. Consider the curve given the parametric equations y() 2 sint a) What is the integral that will give the area enclosed? (Write y in terms of x) b) Look only at the top half ofthe curve. What is the volume integral of the ellipsoid generated by rotating about the x-axis? c) What is the circumference of the cll (Length of Curve use symmetry. Answer must be a number.) d What is the surface area integral for the ellipsoid? When a person weighing 250 pounds stands on a weighing machine, the in spring gets compressed termal by 0.2 inches. What is the compression length if a person weigh 150 pounds stands on the same machine? A force of IN will stretch a rubber band 5 cm. How much work is done on the rubber band by a 3N force? (Hint: First figure out how much the rubber bad is stretched by the 3N force. Be very careful with your units.) A construction crane lifts a bucket that is filled with 150 lb sand at a constant rate. Sand is lost at the

Solution

2.

Using the equation:

F = kx

k = F/x

k = 250/0.2 = 1250 pounds/in

Now when F1 = 150 pounds

x = F1/k

x = 150/1250 = 0.12 inch

3.

F = kx

k = F/x

k = 1/0.05 = 20 N/m

Now when F = 3 N

x = F/k = 3/20 = 0.15 m

Workdone is given by:

W = F*x

W = 3*0.15 = 0.45 N-m