What is the minimum value of the objective function, C with given constraints? C=5x+6y

James adds two numbers a + b. sally adds the same two numbers but reverse the order b + a what property of addition assures us that james and sally will get the same sum

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) = .

12 out of 30 people chose their favourite colour as blue caculate the angle you would use for blue on a pie chart