There is a pie eating contest with 14 participants. there are 29 pies that are all eaten. which of the following best describes how many pies each person ate if they are very evenly matched?

Ernest is purchasing a $175,000 home with a 30-year mortgage. he will make a $15,000 down payment. use the table below to find his monthly pmi payment.

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) = .

If you have 12 feet of string and you cut it into equal length of 5 inches each how much string will be left