The following equation is an example of a literal equation. 2(x+a)=4b a. solve the given equation for the variable a. in your final answer, include all of your work. b. in two or more complete sentences, explain the specific process that you followed in solving for a.

Find the exact value of each of the following. in each case, show your work and explain the steps you take to find the value. (a) sin 17π/6 (b) tan 13π/4 (c) sec 11π/3

Jose predicted that he would sell 48 umbrellas. he actually sold 72 umbrellas. what are the values of a and b in the table below? round to the nearest tenth if necessary

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) = .