Tennyson wrote both "Ulysses" and In Memoriam in response to the death of a friend. Do you think writing a poem or a story or producing other kinds of art would be an effective way of responding to difficulty or loss? Explain your answer.

The general probability density function has the form $f(x)=\frac{1}{\sigma \sqrt{2 \pi}} e^{-(x-\mu)^{2} / 2 \sigma^{2}}$ where $\mu$ and $\sigma$ are constants, with $\sigma > 0.$ a. Show that f(x) has an absolute maximum at $x = \mu$ and inflection points at $x = \mu + \sigma$ and $x = \mu - \sigma.$ b. Show that $f(\mu + c) = f(\mu - c)$ for every number c. What does this tell you about the graph of f(x)?

Find the region on which the function is continuous. $f(x, y)=\sqrt{4-4 x^{2}-y^{2}}$

evaluate the trigonometric function of the quadrant angle, if possible. cot π

Old Faithful geyser in Yellowstone Park erupts at approximately 1-hour intervals, and the height of the fountain reaches 40.0 m. What is the pressure (above atmospheric pressure) in the heated underground chamber 175 m below the vent? You may assume the chamber is large compared with the geyser vent.

A light ray is incident on a layer of oil floating on water. The index of refraction of oil is greater than that of water, which is greater than that of air. Call the angle of incidence in air $\theta _ { \mathrm { a } }$, the angle of refraction in oil $\theta _ { \mathrm { o } }$, and the angle of refraction in water $\theta _ { \mathrm { w } }$. (a) Draw a diagram showing all three layers and all angles. (b) Show that $n _ { \mathrm { a } } \sin \theta _ { a } = n _ { \mathrm { w } } \sin \theta _ { \mathrm { w } }$. (c) The result in part b implies that in calculating the final direction $\left( \theta _ { w } \right)$ of a light ray passing from medium 1 into medium 2 and then into medium 3, all having different n values, we can ignore the presence of medium 2. Can you also ignore medium 2 if what you are calculating is the location where the ray strikes the bottom of the container of water?

Use De Moivre's Theorem to find the indicated power.

$$\left( \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } i \right) ^ { 20 }$$

Choose the word from the list that completes each statement. The subset of all elements in the universal set that are not elements of a given set is the ------?---- of the set.

Show that the zero vector 0 is uniquely determined by the property in axiom A4.

Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of O and a standard deviation of 1. In each case, draw a graph, then.find the probability of the given bone density test scores. If using technology, round answers to four decimal places. Between and -2.55 and -2.00

How did innovation change literature, the visual arts, and music in the late 1800s?

Let $\gamma_{1}$ be a curve in $R^{k},$ defined on $[a, b] ;$ let $\phi$ be a continuous $1-1$ mapping of $[c, d]$ onto $[a, b],$ such that $\phi(c)=a ;$ and define $\gamma_{2}(s)=\gamma_{1}(\phi(s)) .$ Prove that $\gamma_{2}$ is an arc, a closed curve, or a rectifiable curve if and only if the same is true of $\gamma_{1}$ . Prove that $\gamma_{2}$ and $\gamma_{1}$ have the same length.

Two useful organic compounds that contain Cl atoms are drawn below. Vinyl chloride is the starting material used to prepare poly(vinyl chloride), a plastic used in insulation, pipes, and bottles. Chloroethane (ethyl chloride) is a local anesthetic. Why is the C – Cl bond of vinyl chloride stronger than the C – Cl bond in chloroethane?

$$\begin{array} { c } { \mathrm { CH } _ { 2 } = \mathrm { CHCl } } \\ { \text { vinyl chloride } } \end{array} \quad \quad \begin{array} { c } { \mathrm { CH } _ { 3 } \mathrm { CH } _ { 2 } \mathrm { Cl } } \\ { \text { chloroethane } } \\ { \text { (ethyl chloride) } } \end{array}$$

Solve the equation, if possible. 2x - 14 = -3x + 6