Two-thirds of a number is more than five less than the number. write as an equation.

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) = .

Afamily has five members. a mom, a dad, two sisters, & a brother. the family lines up single file. what is the probabillity that the mom is at the front of the line

Ametal rod is 2/5 meters long. it will be cut into pieces that are each 1/30 meters long. how many pieces will be made from the rod?