Graph each rational function.

$$f ( x ) = \frac { x + 2 } { x ^ { 2 } - x - 6 }$$

What inductance must be connected to a 25 pF capacitor in an oscillator capable of generating 410 nm (i.e., visible) electromagnetic waves? Comment on your answer.

We are interested in the probability of rolling a 1,4 , or 5. (a) Explain why the outcomes 1, 4, and 5 are disjoint. (b) Apply the Addition Rule for disjoint outcomes to determine P(1 or 4 or 5).

Express each rational number as a decimal.

$$\frac { 7 } { 20 }$$

How does the function of the digestive system contribute to homeostasis?

Determine whether the following is true or false.

All integers of the form $2^{\left(2^k\right)}+1$ for nonnegative integers $k$ are Fermat primes.

Identify the excluded value of each rational function.

$$y = \frac { - 1 } { x }$$

What is an important industry in your area?

Alicia: Estoy de acuerdo con Elena. En casa estamos tomando ________ cafés que nos compraron mis padres en San José el año pasado, y creo que los de Costa Rica son más sabrosos.

Suppose $\mathbf{f}$ is a differentiable mapping of $R^{1}$ into $R^{3}$ such that $|\mathbf{f}(t)|=1$ for every $t$ Prove that $\mathbf{f}^{\prime}(t) \cdot \mathbf{f}(t)=0$ Interpret this result geometrically.

Consider the function $f(x)=\frac{\sqrt{4+x}-2}{x}$. (a.) Use the decimal format with six significant digits (apply rounding at each step) to calculate (using a calculator $) f(x)$ for $x=0.001$. (b.) Use MATLAB (format long) to calculate the value of $f(x)$. Consider this to be the true value, and calculate the true relative error due to rounding in the value of $f(x)$ that was obtained in part (a.). (c.) Multiply $f(x)$ by $\frac{\sqrt{4+x}+2}{\sqrt{4+x}+2}$ to obtain a form of $f(x)$ that is less prone to rounding errors. With the new form, use the decimal format with six significant digits (apply rounding at each step) to calculate (using a calculator) $f(x)$ for $x=0.001$. Compare the value with the values in parts (a.) and (b.).

Use the following matrices to evaluate the given expression.

$$A=\left[\begin{array}{lll}{0} & {3} & {-5} \\ {1} & {2} & {6}\end{array}\right]$$

$$B=\left[\begin{array}{rrr}{4} & {1} & {0} \\ {-2} & {3} & {-2}\end{array}\right]$$

$$C=\left[\begin{array}{rl}{4} & {1} \\ {6} & {2} \\ {-2} & {3}\end{array}\right]$$

CA

Elasticity expresses a relationship between the percentage change in ? and the resulting percentage change in ?.

From the following list: comply, placate, ingratiate, inundate, lament, beseech, infirmity, scoff, embody, cauterize, write the vocabulary word that is closest in meaning to the underlined word or phrase in the sentence. The conquistadors gave away bells and beads to g̲a̲i̲n̲ ̲f̲a̲v̲o̲r̲ ̲f̲o̲r̲ themselves with the Indians.

Let U={0, 1, 2, 3, 4, 5}, A={6, 9}, B={6, 9, 10}, C={0, 1, 6, 9, 11}, D={2, 5, 11}. Determine whether each statement is true or false. Explain your reasoning. $D \subset U$