Use the result in Exercise to prove each of the following inequalities. Assume that p, q,...

Use the result in Exercise to prove each of the following inequalities. Assume that p, q, r, and s all are nonnegative.

(a)

(b)

Exercise

Given two positive numbers a and b, we define the geometric mean (G.M.) and the arithmetic mean (A.M.) as follows:

Prove that for all nonnegative numbers a and b we have

Exercise concern the environmental problem known as acid rain. The principal source contributing to acid rain is sulfur dioxide, emitted into the atmosphere through the burning of fossil fuels. Once in the clouds, the sulfur dioxide combines with water vapor to form one of the nasty ingredients of acid rain—sulfuric acid.