Verify the parallelogram law for vectors u and v in r^n: ||u + v||^2 + ||u - v||^2 = 2||u||^2 + 2||v||^2

At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 16 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 the pile is 12 feet high? (hint: the formula for the volume of a cone is v = 1 3 πr2h.)

Why did the ice arena get so hot after the big game (this is math related google it to find the paper

If the ratio of sum of the first m and n terms of an ap is m2 : n2 , show that the ratio of its mth and nth terms is (2m − 1) : (2n − 1).