Given the function f(x) = x² + 8x + 12, determine the average rate of change of

1 answer:

3 0

The average rate of change of a (continuous) function f(x) over an interval [a, b] is given by the so-called difference quotient,

$\dfrac{f(b)-f(a)}{b-a}$

Here we have f(x) = x² + 8x + 12 and the interval is [-10, -2], so the ARoC of f(x) on this interval is

$\dfrac{f(-2) - f(-10)}{-2 - (-10)} = \dfrac{0 - 32}8 = \boxed{-4}$

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Eight swimmers participate in a race in how many ways can the swimmers finish in first second and third place an it be answered

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Answer:

336

Step-by-step explanation:

To define whether we use permutations or combinations we must define whether or not the order in which we arrange the results matters. If the order matters we use permutations and if the order doesn't matter we use combinations.

In this case, since we are talking about the first places in a competition, order definitely does matter, so we use permutations. Also in permutations it must be indicated if repetition is allowed, in this case not because the same person cannot be in more than one place.

We use the following formula:

$P=\frac{n!}{(n-r)!}$