Estimate by first rounding each number to the nearest 1/2.

3 4/11 x 2 1/10
a. 6
b. 7
c. 9
d. 12

The following division is being performed using multiplication by the reciprocal find the missing numbers is 5/12 divided by x/3 equals 5/12 times x/10 equals 1/x

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) = .

Kayla made observations about the sellin price of a new brand of coffee that sold in the three different sized bags she recorded those observations in the following table 6 is $2.10 8 is $2.80 and 16 is to $5.60 use the relationship to predict the cost of a 20oz bag of coffee.