Combine these radicals

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) = .

2.5 milligrams is equivalent to how many grams

Consider the following estimates from the early 2010s of shares of income to each group. country poorest 40% next 30% richest 30% bolivia 10 25 65 chile 10 20 70 uruguay 20 30 50 1.) using the 4-point curved line drawing tool, plot the lorenz curve for bolivia. properly label your curve. 2.) using the 4-point curved line drawing tool, plot the lorenz curve for uruguay. properly label your curve.