Math Is Fun Forum

Can someone help me with these two problems?

I'm having trouble with this two numbers, help is greatly appreciated.

Im having a hard time solving this 2 numbers, I already solved 3 of them but this two are hard for me.

My teacher gave us an assignment he never discussed with my class, please help me with this Differential Calculus problem.

1.) The product of two positive numbers is 100, If the sum of their cubes is a minimum, find the numbers.

2.) A poster is to have an area of 120 square inches with one inch margins at the bottom and sides and  2 inch margin at the top. What dimensions will give the largest printed area?

3.)An open box with a square base is to contain 100 cm^3. Find it's dimensions for a minimum amount of material in making the box.

4.) A ladder 13 feet long rests againts a vertical wall. If the bottom of the ladder slides away from the wall at the rate of 0.5 ft/sec, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 5 feet from the wall?

5.) At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at the rate of 20 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude. At what rate is the height of the pile changing when it is 10 feet high?

6.) The radius of a spherical ballon is increasing at a rate of 5 inches per minute. Find the rate of change of the volume when
r = 3 inches.

7.) Two cars start moving from the same point. One travels south at 40 m/hr and the other travels at 30 m/hr. At what rate is the distance between the cars increasing two hours later?

Help is greatly appreciated.