I have two questions, but not a lot of points, so here we go: 1. The length of one leg of a right triangle is 2 cm less than three times the other leg. The area of the triangle is 48 cm^2. Find the length of each leg.
2. In between periods at a hockey game, the marketing department uses a slingshot to launch t-shirts into the crowd. The release point is 5 ft above the surface of the ice, and the shirts are shot with an initial velocity of 52 ft/s. Suppose a shirt is caught 17 ft above the ice on its way down by a fan in the stands. How long is the ball in the air? ie; How many seconds after launching is the t-shirt at 17 feet?
Formula: h=-16t^2+vt+c
h=height in feet, t=time in motion in seconds, v=initial upward velocity, c=initial height in feet

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.