The denominator of a fraction is four more than three times the numerator. If both numerator and denominator are decreased by three, the simplified result is 417. Find the original fraction

Rob spent 25%, percent more time on his research project than he had planned. he spent an extra h hours on the project. which of the following expressions could represent the number of hours rob actually spent on the project? two answers

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 a flying disk is 139 meters in the air and travels at an average of 13 m/s how long is it in the air