Question

The force F (in newtons) of a 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, π/3], and F(0) = 700.

Answer 1

`F(x)=700*sec^2(x)`

Explanation:

If the the force F is proportional to the square of sec x, the force F is equal to:

`F(x)=k*sec^2(x)`

Where k is a constant.

Now, to find k, we are going to use:

`F(0)=700`

So, if we replace x by 0 on the first equation, we get:

`F(0)=k*sec^2(0)\\F(0)=k\\F(0)=k=700`

It means that k is equal to 700, so F as a function of x is equal to:

`F(x)=700*sec^2(x)`