Phil is riding his bike. he rides 50 miles in 4 hours, 62.5 miles in 5 hours, and 75 miles in 6 hours. find the constant of proportionality and write an equation to describe the situation. let x represent the number of hours.

Ab based on the given diagram, if m_1 = 60° then m 2 = 30 60 90 180

You are designing a rectangular pet pen for your new baby puppy. you have 30 feet of fencing you would like the fencing to be 6 1/3 feet longer than the width

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) = .