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Sara needs to take a taxi to get to the movies the taxi charges $4.00 for the first mile and then $2.75 for each mile after that if the total charge is $20.50 then how far was sara’s taxi ride to the movie

Si la base de un triángulo isósceles mide 70 m y el ángulo opuesto a ésta mide 58°; entonces ¿cuánto mide la altura de dicho triángulo? a) 21.87 m. b) 40.01 m. c) 43.74 m. d) 63.14 m.

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) = .