How to find the critical numbers of a function.

Mathematics

1 answer:

Semmy [17]2 years ago

5 0

It maybe help how to find critical number

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A publishing company has just published a new college textbook. Before the company decides the price at which to sell this textb

Kobotan [32]

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3 years ago

A pool is filled with 2,980 quarts of water. How many gallons of water are in the pool?.

Vladimir [108]

Answer:

B. 745 gallons

Step-by-step explanation:

<em><u>4 quarts = 1 gallon</u></em>

There are may ways to solve this, the easiest way is to divide the number of quarts by 4 (there are 4 quarts in a gallon).

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3 years ago

Write an equation in standard form of the hyperbola described.

marishachu [46]

Check the picture below, so the hyperbola looks more or less like so, so let's find the length of the conjugate axis, or namely let's find the "b" component.

$\textit{hyperbolas, horizontal traverse axis } \\\\ \cfrac{(x- h)^2}{ a^2}-\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2} \end{cases} \\\\[-0.35em] ~\dotfill$

$\begin{cases} h=0\\ k=0\\ a=2\\ c=4 \end{cases}\implies \cfrac{(x-0)^2}{2^2}-\cfrac{(y-0)^2}{b^2} \\\\\\ c^2=a^2+b^2\implies 4^2=2^2+b^2\implies 16=4+b^2\implies \underline{12=b^2} \\\\\\ \cfrac{(x-0)^2}{2^2}-\cfrac{(y-0)^2}{12}\implies \boxed{\cfrac{x^2}{4}-\cfrac{y^2}{12}}$