Taylor is building doghouse to sell. each doghouse requires 3 full sheet of plywood which taylor cut into new shapes the plywood is shipped in bundles of 13 full sheet how manydoghouse can taylor make 12 bundles of plwood

The table shows a pattern of exponents. what is the pattern as the exponents decrease?

Find the pattern and use it to list the nth term in the sequence. 6, 12, 20, 30, 42, 56, the nth term of the sequence is

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) = .