The sum of two numbers is 80 if four times the smaller number is subtracted from the larger number, the result is 10. find the two numbers. the larger number is? the smaller number is?

What is the slope simplify your answer and write it as a proper fraction, improper fraction, or integer

What is the correlation coefficient between the variables? round to three decimal places. enter your answer in the box

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) = .