<h2>C. components: (-28,-25), actual distance about 37.54 meters</h2>
Answer:
See Below.
Step-by-step explanation:
We want to show that the function:

Increases for all values of <em>x</em>.
A function is increasing whenever its derivative is positive.
So, find the derivative of our function:
![\displaystyle f'(x) = \frac{d}{dx}\left[e^x - e^{-x}\right]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28x%29%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%5Be%5Ex%20-%20e%5E%7B-x%7D%5Cright%5D)
Differentiate:

Simplify:

Since eˣ is always greater than zero and e⁻ˣ is also always greater than zero, f'(x) is always positive. Hence, the original function increases for all values of <em>x.</em>
Let be "x" the number of colored pencils in the box.
According to the information given in the exercise, there are 84 pencils in the box and 53 of them are regular pencils.
Knowing this information, you can set up the following equation:

Finally, you have to solve for the variable "x" in order to find its value. In order to do this, you can apply the Subtraction property of equality by subtracting 53 from both sides of the equation:

The answer is: There are 31 colored pencils in the box.