Water flows from an inverted conical tank with circular orifice at the rate dx *= -0.6zr*/29 where r is the radius of the orifice, x is the height of the liquid level from the vertex of the cone, and A(x) is the arez of the cross section of the tank x units above the orifice. Supposer = 0.1 ft, g = 32.1 ft/s, and the tank has an initial water level of 8 ft and the initial volume of 512 (7/3) ft. Use the Runge-Kutta method of order four to find the following a. The water level after 10 min with h = 20 s b. The time: when the tank will be empty.

Create a bucket by rotating around the y axis the curve y = 5 ln(x-3) from y = 0 to y = 9. If this bucket contains a liquid with density 740 kg/m³ filled to a height of 7 meters, find the work required to pump the liquid out of this bucket (over the top edge). Use 9.8 m/s2 for gravity. Work = Joules

The outside diameter of a basketball is 9 inches. Use a differential to calculate the volume of material used to make the ball if the thickness is 5/8 inch. (Hint: The volume of a sphere is V = (4/3)(pi)(r^3))

Water is leaking out of an inverted conical tank at a rate of 11500.000 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 9.000 meters and the diameter at the top is 4.500 meters. If the water level is rising at a rate of 21.000 centimeters per minute when the height of the water is 2.000 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute.