Single Variable Calculus, Chapter 3, 3.6, Section 3.6, Problem 11

Determine $\displaystyle \frac{dy}{dx}$ of $x^2y^2 + x \sin y = 4$ by Implicit Differentiation.

$\displaystyle \frac{d}{dx} (x^2 y^2) + \frac{d}{dx} (x \sin y) = \frac{d}{dx} (4)$

$
\begin{equation}
\begin{aligned}
\left[ (x^2) \frac{d}{dx} (y^2) + (y^2) \frac{d}{dx} (x^2) \right] +\left[ (x) \frac{d}{dx} (\sin y) + (\sin y) \frac{d}{dx} (x) \right] &= \frac{d}{dx} (4)\\
\\
(x^2)(2y) \frac{dy}{dx} + (y^2)(2x) + (x) (\cos x) \frac{dy}{dx} + (\sin y)(1) &= 0

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}
2x^2yy'+2xy^2+xy' \cos y + \sin y &= 0\\
\\
2x^2yy' + xy' \cos y &= -2xy^2 - \sin y\\
\\
y'(2x^2y+ x \cos y) &= -2xy^2-\sin y\\
\\
\frac{y'\cancel{(2x^2+ x \cos y)}}{\cancel{2x^2y + x \cos y}} &= \frac{-2xy^2 - \sin y}{2x^2y + x \cos y}\\
\\
y' &= \frac{-2xy^2 - \sin y}{2x^2 y + x \cos y}

\end{aligned}
\end{equation}
$

What are the disadvantages of globalization?

Globalization can be described as process of integrating cultural, financial, environmental and economical system on worldwide basis. It is a scenario where nations and countries from all around the world gets inter-connected for meeting their needs. These needs might be external or internal. It includes easy migration, advance transportation system, movement of capital between different countries and flow of services, finished goods and raw material.
The disadvantages of Globalization are listed below:
Globalization have created a gap between the rich and the poor. Poor people doesn't have that much access to the resources of the country because of the lack of science and technology in their lives on the other hand rich people are taking good advantage of globalization by application of technology and science.

Globalization has contributed greatly in increasing air pollution because of heavy traffic between countries. Poisonous gases are continuously releasing in the atmosphere and making it polluted.

Natural resources of earth also get affected because of the Globalization. There are large areas of forests and lands that are no more rich in minerals and other nutrients. Farming in those places are almost become impossible.

Small scale industries and local businesses have affected and suffered a lot as multinational national companies have taken place in their own country. The local companies are failed to compete with multinational companies and their counterpart.

The demand for skilled labour has increased in this global environment. Good opportunities for unskilled labour has decreased to a big extent.

Globalization is the interaction and connection of people from different parts of the world. It is encouraged by things such as international trade and information technology.
Some of the disadvantages of globalization are:
While globalization pushes for free trade, there still exist many barriers to free trade between countries. For example, many countries have taxes that are imposed on imports. These taxes increase the prices of imported commodities, thereby rendering them more expensive than the locally produced alternatives. This being said, however, if all barriers to trade were to be lifted, most poor countries would suffer as there would be an influx of higher quality commodities from the developed world into these countries, resulting in unfair competition.
Some multinationals take advantage of globalization to evade tax by exploiting tax havens that exist in other countries.
The increased use of technology that comes with globalization, while good in many ways, has had the counter effect of reducing the number of jobs that can be done by people.
Globalization has contributed to the erosion of local cultures in regions all over the world. For example, local African foods are fast being replaced by western fast foods like chicken and fries; western dressing styles trend over local styles in various communities. This has the effect of reducing the diversity of cultures.
Some multinationals misuse their workers in poor countries by offering them unfair pay or generally unfair working conditions.
Globalization can lead to the spread of infectious diseases across countries.

Example of Cassius being fearful.

As the leader of the audacious plot against Caesar, it is hard to call Cassius "fearful." He is a brave, if also conspiratorial and somewhat cynical, character. Perhaps one instance in the play where Cassius says that he feels fear is when Antony asks to be allowed to speak after the murder of Caesar. Cassius says to Brutus, "I know not what may fall, I like it not." He fears that Antony will in some way use the opportunity to speak against the conspirators. As it turns out, this fear is entirely justified; Antony does exactly that. Cassius also fears a series of omens before the battle of Philippi, which takes place on his birthday and is itself a bad sign. But he resolves, despite these concerns, to fight anyway. As it turns out, again, he was right to be afraid, and the army of Octavian and Antony emerges victorious. So Cassius's fears are, throughout the play, perhaps better described as legitimate concerns. Nevertheless, he follows through on his actions until the bitter end.

What is the author's message (theme) about family?

By juxtaposing the sympathetic character, Maggie, with her deep knowledge and respect for her family members and their traditions and stories, and the misguided Dee, with her lack of understanding of her family's importance in terms of her heritage, Walker shows that familial heritage is as, if not more, important as one's racial heritage. Dee is anxious to embrace her racial heritage, changing her name so that she is not named for her oppressors, but she fails to internalize the fact that her name is a family name. She is named after generations of strong and respected women in her own family, but she isn't interested in those stories because they do not fulfill her need to have artifacts of her history. She cares about material objects more than she cares to learn family traditions, like quilting, or family stories, like who made what, when, and why. Maggie, with her humble knowledge of these things actually honors her heritage more than Dee can conceive.

Alice Walker examines the themes of family conflict and how individual family members understand their relationship with heredity differently. In the story, Dee is ashamed of her family and looks down on her mother and Maggie for their lack of material wealth and success. She views Mama and Maggie as backward rural folks who do not fully appreciate their African heritage. She ends up changing her name to Wangero Leewanika Kemanjo and attempts to take her family's traditional handmade quilts in order to display them in her home.
Maggie is intimidated by her successful, attractive sister, and Mama recognizes that she is not as intelligent or accomplished as Dee. Despite Dee's natural advantages and accomplishments, Mama and Maggie have a deeper and genuine appreciation of their family's heritage and cultural roots. Their differences are revealed by Mama's interpretation of Dee's name, which has been passed down through generations, as well as their feelings towards the traditional quilts. Dee criticizes Maggie for putting the quilts to "everyday use" and believes they should be displayed as cultural pieces of art.
Walker sympathizes with Maggie and Mama's characters and suggests that their interpretation and appreciation for their heritage is more genuine and sincere than Dee's. In regards to family conflict, she illustrates that differences can exist and there are a variety of ways in which people can honor and value their heritage. Family members can also disagree about various things and it is often required for someone to step outside of their character to restore order.

Alice Walker's short story "Everyday Use" is about a rural African American family involved in a struggle over interpersonal roles. 
The narrator is the mother of the family. The two daughters are Dee and Maggie.
Maggie suffers with burn wounds from a fire in her youth. These injuries have affected her self esteem, particularly with regard to her sister Dee. Dee is the outgoing sister, and at the time of the story she is home from college for a brief visit. 
College has changed Dee. She views her sister and mother as hopelessly backward, and treats their household items like museum pieces. When she asks for a particular quilt, one that has been in the family for years, Maggie is disappointed, because it is supposed to be hers when she marries. However, in her timidity, she agrees to let Dee have it.
The narrator-mother, however, has had enough of Dee's uppity attitude and finally stands up to her, telling her that the quilt will stay with Maggie. 
The theme is that family members can lose track of each other's needs and desires. Dee cares nothing for the family's daily needs, and so does not see the value of the quilt in terms of its "everyday use." Sometimes a person, like the mother in this story, has to step out of character to set things right again. 

Beginning Algebra With Applications, Chapter 5, 5.6, Section 5.6, Problem 28

Illustrate the solution set $2x -3 (y + 1) \geq y - (7 - x)$

$
\begin{equation}
\begin{aligned}
2x - 3y - 3 &\geq y - 7 + x
&& \text{Solve the inequality for } y \\
\\
-3y - y &\geq -2x + x + 3 - 7
&& \text{Group terms}\\
\\
-4y &\geq -x - 4
&& \text{Evaluate}\\
\\
\frac{-4y}{-4} &\leq \frac{-x}{-4} - \frac{4}{-4}
&& \text{Remember that if you divide or multiply negative numbers ,the inequality symbol reverses}\\
\\
y &\leq \frac{x}{4} + 1
&& \text{Simplify}
\end{aligned}
\end{equation}
$


To graph the inequality, we first find the intercepts of the line $\displaystyle y = \frac{x}{4} + 1$.
In this case, the $x$-intercept (set $y = 0$) is $(-4,0)$

$
\begin{equation}
\begin{aligned}
0 &= \frac{x}{4} + 1 \\
\\
\frac{x}{4} &=- 1\\
\\
x &= -4
\end{aligned}
\end{equation}
$


And, the $y$-intercept (set $x = 0$) is $(0,1)$

$
\begin{equation}
\begin{aligned}
y &= \frac{0}{4} + 1 \\
\\
y &= 1
\end{aligned}
\end{equation}
$


So, the graph is



Graph $\displaystyle y = \frac{x}{4} + 1 $ as a solid line. Shade the lower half-plane.

What is a narrative version of the poem "The Highwayman" by Alfred Noyes?

There are various ways to approach the assignment of a "narrative version" of this poem, which was written in 1947 but set during the 1800s. The student can re-tell the storyline of this poem as a type of plot summary, or the re-telling can become a narrative that includes a few interpretations of the poem (e.g. the student can mention and explicate important lines or vary details). 
The narrative version can also easily become a song as there is a definite rhythm to this poem that is actually based upon Old English folksongs. Here is a website that has songs that tell stories.
Here is another idea:
The poem could be rewritten in narrative form as a ghost story. It could begin with people sitting in Spaniard's Inn on Hampstead Heath in England (where the highway is thought to have stopped in Noyes's poem) as an old man sits with his tankard and is joined by some younger men who have stopped for the night. The old man tells the tale of the ghost of the highwayman. In this case, the narration could begin with a version of the last stanza. For example, the old man could say,

It was a night just like this winter night with the wind blowing and eerie sounds whistling through the trees. The road was a blue ribbon-like trail under the moon when the ghost of the highwayman came up to this very inn's door.
He rode a handsome steed and his boots were....

At this point the student can pick up the narrative of the poem from the beginning, rewording in prose as though telling a story through the voice of the old man. For instance,

There are those who say they have seen him--a ghostly dandy lad with his claret jacket and French-cocked hat....

Still another idea is to create a narrative that reads like a fairy-tale: "Once upon a time, there was a handsome young man who some called...."

Where can the following quote be found: "Elizabeth saw with admiration for his taste, that it [the furniture] was neither gaudy nor uselessly fine; with less of splendour and more real elegance"?

The quote you mentioned can be found in chapter 43 of the novel. In this chapter, Elizabeth visits Mr. Darcy's Pemberley estate with Mr. and Mrs. Gardiner. For her part, Elizabeth feels a little nervous about visiting Darcy's home.
However, she comforts herself with the thought that she isn't likely to see him there. After all, Darcy has other properties, and he is a well-traveled gentleman of means. Despite her feelings about Darcy, Elizabeth can't help but admire his taste in furniture. She notes with admiration that the furnishings are neither gaudy nor "uselessly fine." Instead, they are elegant and tasteful.
It is interesting that the chapter begins by highlighting Darcy's taste in home furnishings. This focus foreshadows a change in Elizabeth's opinion of Darcy as the chapter ends. Mrs. Reynold's warm praise of Darcy also plays a major role in changing Elizabeth's mind.
The coup de grace occurs when Darcy himself shows up at Pemberley. In behavior, he is the personification of dignity and grace, and he manages to charm everyone. Additionally, his awkward but charming request to introduce his sister to Elizabeth immediately disarms the latter. By the end of the chapter, Elizabeth is not quite sure whether Wickham has been completely honest with her (about Darcy's bad character).