The force f (in newtons) of the hydraulic cylinder in a press is proportional to the square of sec x where x is the distance (in meters) that the cylinder is extended in its cycle. the domain of f is [0, pi/3], and f(0) = 500.
a) find f as a function of x.
f(x)=
b) find the average force exerted by the press over the interval [0, pi/3] (round your answer to 1 decimal place)
f=

Set up a system of 2 equations.
Gallon equation:
x+y = 28
Solution equation:
10x + 17y = (28)(12)

Solve with substitution:
y = 28-x  (From 1st equation)

(Sub into 2nd equation)
10x + 17(28-x) = 336

10x + 476 - 17x = 336

-7x = -140

x = 20

y = 28-20 = 8

Therefore the solution is (20,8)
You need 20 gal of 10% solution mixed with 8 gal of 17% solution to obtain 28 gal of 12% solution.