(Score for Question 1: ___ of 6 points) 1. Explain whether each following example is proportional or non-proportional.
(a)
(b)

(c) A gallon of milk costs $1.99. A half-gallon of milk costs $3.89.
(d)
x y
2 13
3 19.5
4 26
5 32.5

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) = .

Two farmers pay a total rent of $140 for a pasture. the first farmer placed $4 oxen in the pasture, and the second farmer placed $30 sheep in the pasture. the farmers split the rent based on the proportion of the pasture eaten by their own animals that month. how much should the first farmer pay, if 1 ox eats as much as 10 sheep in a month?

Look at the figure xyz in the coordinate plane. find the perimeter of the figure rounded to the nearest tenth.