Stardollars Coffee hosted a coffee-cup-stacking contest. Anthony noticed a pattern. He told the judges that Figure
100 would have 203 coffee cups stacked up. Was he correct? Use mathematics and a complete explanation to prove or disprove Anthony’s claim

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) = .

Anyone? 15m is what percent of 60m; 3m; 30m; 1.5 km?

Which of the functions graphed below has a removable discontinuity?