1) a) A 13 foot ladder leans against a vertical wall. If the lower end of the ladder is pulled

away at the rate of 2 feet per second, how fast is the top of the ladder coming down

the wall at

i. the instant the top is 12 feet above the ground

ii. 5 feet above the ground?

b) Two cars are riding on roads that meet at a 60" angle. Car A is 3 miles from the

intersection traveling at 40 mph and car B is 2 miles away from the intersection

traveling at 50 mph. How fast are the two cars separating if

i. they are both traveling away from the intersection and

ii. car A is traveling away from the intersection and car B is traveling towards it?

2) a) A farmer has 2,000 feet of fencing to enclose a pasture area. The field will be in

the shape of a rectangle and will be placed against a river where there is no

fencing needed.

i. What is the largest area field that can be created

ii. What are its dimensions?

b) An open box is to be made from a piece of metal 16 by 30 inches by cutting

out squares of equal size from the corners and bending up the sides.

i. What size square should be cut out to create a box with greatest

volume.

ii. What is the maximum volume as well?