T2- TEST2 -12A 9-2-2023

A 5 ft ladder is leaning against a wall and sliding towards the floor. The top of the ladder is sliding down the wall at a rate of 2 ft/sec. How fast is the base of the ladder sliding away from the wall when the base of the ladder is 3 ft from the wall?

We need to enclose a field with a fence. We have 500 feet of fencing material and a building is on one side of the field so we won't need any fencing on that side. Determine the dimensions of the field that will enclose the largest area.

BONUS**********************

Oil spills out of a tanker at the rate of 14 feet cube per minute. The oil spreads in a circle with a thickness of 0.3 ft. Determine the rate at which the radius of the spill is increasing when the radius reaches 100 feet.

A box with no top is to be built by taking a 20 in-by-16 in sheet of cardboard, cutting x-in. squares out of each corner and folding up the sides. Find the value of x that maximizes the volume of the box.

f the cost of manufacturing x items is C(x) = x 4 + 12x 2 + 60x + 25, find the marginal cost function and compare the marginal cost at x = 60 with the actual cost of manufacturing the 60th item.

find (a) the elasticity of demand and (b) the range of prices for which the demand is elastic (E < −1). f (p) = 200(40 − p)