Ronnie, Bobby, and Mike are singers from the group New Edition. They are raising money for studio time. Ronnie raised $30 more than Mike, and Bobby raised $12 less than Ronnie. They collected $432 in total. How much did Bobby collect? *

Write and solve a real word problem that involves determining distance on a coordinate plane

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) = .

Cd is the perpendicular bisector of both xy and st, and cy=20. find xy.