Identify a complex number as a vector quantity

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) = .

Someone answer asap for ! the boiling point of water at an elevation of 0 feet is 212 degrees fahrenheit (°f). for every 1,000 feet of increase in elevation, the boiling point of water decreases by about 2°f. which of the following represents this relationship if b is the boiling point of water at an elevation of e thousand feet? a. e = 2b - 212 b. b = 2e - 212 c. e = -2b + 212 d. b = -2e + 212

Which statement shows that 6.24 is a rational number? a. 6.24 = 6.242424 b. 6.24 = 6.24 c. 6.24 = 68⁄33 d. 6.24 = 66⁄25