The hypotenuse of the right triangle is 5y inches long. The lengths of the legs are x + 8 and x + 3 inches. If the perimeter of the triangle is 55 inches and the length of the hypotenuse minus the length of the shorter leg is 5 inches, how many inches long is the hypotenuse?

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .

Which is the correct first step in finding the area of the base of a cylinder with a volume of 26x cubic meters and a height of 6.5 meters? v=bh 6.5=b(26x) v=bh v=26pi+(6.5) v=bh v=26pi(6.5) v=bh 26pi=b(6.5)

Atravel agent is booking a trip to england, scotland, ireland, and france for a group of senior citizens. the agent sent surveys to the group, asking which countries they would like to visit, in order, and created the shown preference schedule (e = england, i = ireland, s = scotland, f = france). which country is the condorcet winner? number of votes 15 12 16 19 1st f e e i 2nd e s i s 3rd s i s e 4th i f f f 1. scotland 2. england 3. france 4.ireland