"The volume of this rectangular prism is 144 cubic inches. I know this because 8×9×2=144. So, this shape can be filled with 288 1 inch cubes. Part A: What is the student's mistake? Explain your answer.

If an x intercept only touches the x axis it means it has a multiplicity of 2. if an intercept goes through the axis it has a multiplicity of 1 true false

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) = .

8. kelly wants to buy a magazine that is $25. later the magazine was marked up an additional 20%. what is the new price?