. You've been asked to design a heat (internal combustion) engine with an efficiency of at least 30% on a hot day, when the coolant temperature (TL) is 47°C. Assuming your engine achieves 50% of the ideal Carnot efficiency, what is the minimum temperature TH of the "hot reservoir" (combustion temperature) needed to achieve the desired actual efficiency of 30% or greater?

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) = .

Ascientist has discovered an organism that produces five offspring exactly one hour after its own birth, and then goes on to live for one week without producing any additional offspring. each replicated organism also replicates at the same rate. at hour one, there is one organism. at hour two, there are five more organisms. how many total organisms are there at hour seven? 2,801 19,531 19,607 97.655