Can you please answer this question for me?

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) = .

Jude is making cement for a driveway. the instructions show the amount of each ingredient to make 1 batch of cement. complete each statement to adjust the ingredients for each new situation if jude uses these instructions.

Answer asap and if you do you will get brainliest. catherine buys a gallon of ice cream from the store. after taking it home, she eats a fifth of a gallon of ice cream. her sister eats some of the ice cream as well. if two-thirds of the original amount of ice cream is left, then what fraction of a gallon of ice cream did her sister eat?