A classic physics problem states that if a projectile is shot vertically up into the air with an initial velocity of 177 feet per second from an initial height of 133 feet off the ground, then the height of the projectile, h, in feet, t seconds after it's shot is given by the equation:

h=−16t^2+177t+133

Find the two points in time when the object is 172 feet above the ground. Round your answers to the nearest hundredth of a second (two decimal places).

How many triangles can be drawn with side lengths 4 centimeters, 4.5 centimeters, and 9 centimeters? explain

Tell whether the two rates form a proportion

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.