Assuming that the rate of change of the price P of a certain commodity is proportional to the difference between demand D and supply S at any time t, the differential equations describing the price fluctuations with respect to time can be expressed as: dP/dt = k(D - s) where k is the proportionality constant whose value depends on the specific commodity. Solve the above differential equation by expressing supply and demand as simply linear functions of price in the form S = aP - b and D = e - fP

Find the area of the surface obtained by rotating the circle x² + y² = r² about the line y = r.

3) Recall that the power set of a set A is the set of all subsets of A: PA = {S: SC A}. Prove the following proposition. АСВ РАСРВ