* CALCULATOR POLICY:*

- The following calculators are allowed to be used on this examination: TI-81, 82, 83, 85, 86; Sharp EL-8200, EL-8200C. Any other calculator is subject to confiscation, and its user may be accused of cheating.
- ONLY programs distributed in connection with MAT 131 and 132 may be stored in the calculators. Any other use of calculator memory to store information relevant to this examination will be considered cheating.

- (30 points) Solve the following initial value problems, where
*y*is an unknown function of*x*. Show all your work.- (a)
- (b)

- (a)

The tank is in the shape of a cone.

A tank is in the form of a right circular cone with the point down.
The base of the cone is d = 6m in diameter, and the height of
the cone is h = 3m. The tank is filled with water (density 1000kg/m^{3}).
Calculate the work it takes to empty this tank by pumping the water
out over the top. A kilogram
at the surface of the Earth weighs 9.81 newtons .

- (a) In the diagram below sketch in the slopefield
*at the 9 gridpoints shown*, for the differential equation .

Draw appropriate slopes at the 9 gridpoints shown. - (b) Use these slopes to sketch an approximate solution to the initial value problem