Answer:
Concept: Modeling expressions
- We are given the equation

- We want to find the time after 0.75 seconds given that t is represented in seconds.
- Hence we do

- Hence we get the answer to 191 feet
(a) If <em>f(x)</em> is to be a proper density function, then its integral over the given support must evaulate to 1:

For the integral, substitute <em>u</em> = <em>x</em> ² and d<em>u</em> = 2<em>x</em> d<em>x</em>. Then as <em>x</em> → 0, <em>u</em> → 0; as <em>x</em> → ∞, <em>u</em> → ∞:

which reduces to
<em>c</em> / 2 (0 + 1) = 1 → <em>c</em> = 2
(b) Find the probability P(1 < <em>X </em>< 3) by integrating the density function over [1, 3] (I'll omit the steps because it's the same process as in (a)):

The difference quotient of the function that has been presented to us will turn out to be 5.
<h3>How can I calculate the quotient of differences?</h3>
In this step, we wish to determine the difference quotient for the function that was supplied.
To begin, keep in mind that the difference quotient may be calculated by:
Lim h->0 
Now, for the purpose of the function, we need this:
Then we will have:

j(x) = 5x - 3
Then the following will be true:
Therefore, 5 is the value of the difference quotient for j(x) is %
Read the following if you are interested in finding out more about difference quotients:
brainly.com/question/15166834
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