a college student only saves quarters and dimes in her piggy bank. she empties out her piggy bank at the end of each month. this month there are 28 quarters and dimes. the total value of the coins is $4.05. how many quarters and dimes does the college student have?

The ratio of the measures of the three angles in a triangle is 2: 9: 4. find the measures of the angels

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) = .

Opposite angles in a parrellelogram are