Find the eigenvalues and eigenvectors of the matrix in the following problem

$$\left( \begin{array}{ccc} 2 & -3 & 4 \\ -3 & 2 & 0 \\ 4 & 0 & 2\end{array}\right)$$

As a man walks barefoot along the beach, he steps on a sharp shell. His foot automatically jerks upward, even before he feels pain. What process is this an example of? How does it help protect the man?

Write the statement as an inequality. "6y is no more than 8."

Decide whether the statement is true or false. Give an explanation for your answer. If f(x) is a positive periodic function, then $\int _ { 0 } ^ { \infty } f ( x ) d x$ diverges.

Multiply. Write the product in simplest form. 4/9 x 3.

Amelia bought roast beef for $6.85 per pound. Find the total cost if Amelia bought 4 pounds of roast beef. Justify your answer by using the Distributive Property.

Find each unknown number. Check your work.

$$\frac { b } { 4 } = 12$$

Federal regulations set standards for the size of the quarters of marine mammals. A pool to house sea otters must have a volume of ''the square of the sea otter's average adult length (in meters) multiplied by 3.14 and by 0.91 meter." If x represents the sea otter's average adult length and f(x) represents the volume (in cubic meters) of the corresponding pool size, this formula can be written as $f(x)=0.91(3.14) x^{2}$. Find the volume of the pool for each adult sea otter length (in meters). Round answers to the nearest hundredth. (a) 0.8, (b) 1.0, (c) 1.2, (d) 1.5.

Simplify using the index laws: a. $a^{4} b^{5} \times a^{2} b^{2}$ b. $6 x y^{5} \div 9 x^{2} y^{5}$ c. $\frac{5\left(x^{2} y\right)^{2}}{\left(5 x^{2}\right)^{2}}$

What do the symbols

$$\mu _ { \overline { x } } \text { and } \sigma _ { \overline { x } }$$

represent?

Evaluate the following derivatives. Express your answers in terms of f, g, f', and g'. $\frac { d } { d x } \left( \frac { x f ( x ) } { g ( x ) } \right)$

Suppose that $T$ is linear and

$$\begin{equation*}T\begin{pmatrix}\begin{bmatrix}4\\-2\end{bmatrix}\end{pmatrix}= \begin{bmatrix}-6\\16\end{bmatrix}.\end{equation*}$$

Determine

$$\begin{equation*}T\begin{pmatrix}\begin{bmatrix}-2\\1\end{bmatrix}\end{pmatrix}\text{ and } T\begin{pmatrix}\begin{bmatrix}8\\-4\end{bmatrix}\end{pmatrix}.\end{equation*}$$

Use your book or dictionary to define each term. Chitin _____.

Solve each equation by completing the square. Express square roots in simplest form. $x^{2}-6 x=-6$ _____.