Use f(x) = 1/2x and f -1(x) = 2x to solve the problems.

f(2) =

f−1(1) =

f−1(f(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.)

Adrawer contains 12 identical white socks, 18 identical black socks and 14 identical brown socks. what is the least number of socks you must choose, without looking, to be certain that you have chosen two socks of the same colour?

Maria found the least common multiple of 6 and 15. her work is shown below. multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, . . multiples of 15: 15, 30, 45, 60, . . the least common multiple is 60. what is maria's error?