A street light is 21 feet high and casts a 40-foot shadow. At the same time, a cell-phone tower next to the street light casts a 57-foot shadow. Which proportion can be used to find
the height, H, of the cell-phone tower?

Determine the volume of a cylinder bucket if the diameter is 8.5 in. and the height is 11.5 in.

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) = .

Two florida panthers were weighed. one weighs 6x+21 pounds and the two together weigh 14x+11 pounds how much does he other panther weigh alone