For the following problem, find the area.

The parallelogram determined by $\vec{c}=4 \vec{i}+4 \vec{\jmath}-7 \vec{k}$ and $\vec{d}=-2 \vec{i}+5 \vec{j}-14 \vec{k}$

Factor the polynomial function that is given below.

$$3 x^3+81$$

For the given polynomial function f:

f(x)=$-x^2(x^2-4)(x-5)$

Find the x - and y-intercepts of the graph of f.

How can we find the multiplicity of a polynomial function?

The orbit of Explorer VII and the outline of Earth's surface are shown in the fig. ure at the top of the next column. This orbit can be described by the equation

$$\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}\leq1$$

where a = 4464 and b = 4462. The surface of Earth can be described by $\text{(x - 164)}^\text{2}+\text{y}^\text{2}=3960^2$. Find the maximum and minimum heights of the satellite above Earth's surface if all units are in miles.

How are $\lim _{x \rightarrow a^{-}} p(x)$ and $\lim _{x \rightarrow a^{+}} p(x)$ calculated if p is a polynomial function?

Find the midpoint of the line segment whose endpoints are $(-2, 5)$ and $(4, -9)$.

Choose the word in each row that does not belong in the group.

fresa naranja plátano maíz

Factor the polynomial function that is given below.

$$8 x^3-1$$

Given that the augmented matrix in row reduced form is equivalent to the augmented matrix of a system of linear equations, (a) determine whether the system has a solution and (b) find the solution or solutions to the system, if they exist.

$$\left[\begin{array}{lll|r} 1 & 0 & 1 & 4 \\ 0 & 1 & 0 & -2 \end{array}\right]$$

State one ecological reason why some individuals might support the reintroduction of wolves to the Adirondacks.

A basis $\mathcal{B}$ for $R^3$ is given. If

$$\begin{equation*}v=\begin{bmatrix}x\\y\\z\end{bmatrix} \text{ and }[v]_B=\begin{bmatrix}x'\\y'\\z'\end{bmatrix} .\end{equation*}$$

Write equations expressing $x$, $y$, and $z$ in terms of $x'$, $y'$, and $z'$.

$$\begin{equation*}\mathcal{B}=\begin{Bmatrix}\begin{bmatrix}1\\-1\\1\end{bmatrix}, \begin{bmatrix}-1\\3\\2\end{bmatrix},\begin{bmatrix}-1\\1\\1\end{bmatrix}\end{Bmatrix}.\end{equation*}$$

Determine whether the given set is a generating set for $R^n$.

$$\begin{equation*}\begin{Bmatrix}\begin{bmatrix}1\\-2\end{bmatrix},\begin{bmatrix}-2\\1\end{bmatrix}\end{Bmatrix}\end{equation*}$$

Factor the polynomial function that is given below.

$$27 x^3+8$$