Precalculus, Chapter 1, 1.3, Section 1.3, Problem 46

Determine an equation for the line with a slope $2$ containing the point $(4,-3)$. Express your answer using the general form or the slope intercept form of the equation of a line, which ever you prefer.

Using the Point Slope Form to find the equation


$
\begin{equation}
\begin{aligned}

y - y_1 =& m(x- x_1)
&& \text{Point Slope Form}
\\
y - (-3) =& 2(x-4)
&& \text{Substitute $m = 2, x = 4$ and $y = -3$}
\\
y + 3 =& 2x - 8
&& \text{Simplify}
\\
y =& 2x - 11
&& \text{Slope Intercept Form}
\\
\text{or} &
&&
\\
2x-y =& 11
&& \text{General Form}

\end{aligned}
\end{equation}
$

Hello tutor. I am doing an assignment on Texas government. It would be great if I can get answers from you so that I can get inspiration to start my assignment. Thank you in advance. Identify an interest group related to your career objectives that has an active chapter in the State of Texas. After providing some background information on that group, explain why you would or would not join that group. Does the group benefit only the group members, or does it provide something of value to the state? Public interest groups often suffer from free riders. In your opinion, what could or should be done to curtail this? Do you consider yourself to be a free rider? Do you participate in volunteer activities? If so, how does your participation benefit you and the community? What would you do to increase civic awareness and participation in community activities?

An example of an interest group that has an active chapter in Texas related to my career would be the Texas Council for the Social Studies. This group is affiliated with the national organization called the National Council for the Social Studies. The Texas Council for the Social Studies works to promote social studies education in the state of Texas. This group lobbies legislators to pass laws and develop policies that promote and support social studies education in Texas. The group also publishes newsletters to keep its members informed and helps teachers gain access to high-quality social studies lessons. The Texas Council for the Social Studies holds an annual conference for social studies teachers each year. At this conference, teachers can meet textbook publishers, network with other social studies teachers, attend sessions to gain ideas that can be applied in the classroom, and hear from well-known speakers about various topics.
If I lived in Texas, I would be a member of this group, and I would be active in it. I am active in my state council, as I hold two important leadership positions in it. I also am active in the national council and have held and currently hold important leadership positions. The Texas Council for the Social Studies benefits all social studies educators in the state of Texas, whether they are or are not members. This group may also work with other professional groups to support issues beneficial to educators in general in Texas or at the national level.
I will very briefly answer the second question since the first question had many parts to it. One way to deal with free riders is to have a password protected, members-only section on the organization’s website. Many groups do this to encourage people to join the group. Some of the more relevant and useful information may be in this section. I am not a free rider. I am a member who pays dues to be in the organization, and I hold two leadership positions in my state council. We communicate with our members to make them aware of legislation that may impact them. We also support social studies activities for students in our state and offer student scholarships to our annual state conference. We work closely with our state education department to promote social studies education in the state. We also work with the national council to promote social studies issues at the national level.
http://www.wcss-wi.org/

https://iowacouncilforthesocialstudies19.wildapricot.org/

https://www.facebook.com/TxSocialStudies/

How and why did the Nullification Crisis almost bring us to the brink of civil war?

The constitutional theory of nullification holds that individual states have the right to nullify, that is to say invalidate, a federal law on the grounds that it is unconstitutional. In practice, however, the theory has never been upheld by a federal court. Nonetheless, in the early nineteenth century, nullification seemed like a live option, and its contemplation by South Carolina precipitated a major constitutional crisis.
It all started with tariffs. Under the presidency of John Quincy Adams, a number of tariffs were introduced to protect American industry from being undercut by cheap foreign imports. Although the measures were widely welcomed in the more industrialized North, they were deeply resented in the South. Due to the imposition of tariffs, Southerners would now have to pay considerably more for imported goods they couldn't produce themselves.
When Andrew Jackson won the presidency in 1828, his fellow Southerners naturally assumed that the hated tariffs would be significantly reduced, if not scrapped altogether. However, when that didn't happen, Southern opinion was outrage at the Jackson Administration's inaction. Even Vice President John C. Calhoun, a native of South Carolina, was at odds with his administration's policy.
Jackson attempted to address these concerns by making some tariff reductions in 1832. But this was far too little, far too late for Calhoun, who resigned the Vice Presidency in December of that year. More ominously still, the new measures were woefully inadequate in appeasing the growing anger of the Southern states at what they saw as a betrayal of their economic interests by an administration they had previously supported.
A month before Calhoun's resignation, a specially convened convention was held in South Carolina, which declared the tariffs of both 1828 and 1832 unconstitutional and unenforceable in the state. Those attending the convention knew that the Ordinance of Nullification which they'd passed would be fiercely resisted by the federal government as it represented a clear challenge to its authority. Military preparations were then made by the state authorities to counter any armed incursions by federal troops.
The situation was tense and highly dangerous; it seemed as if the nation was on the brink of civil war. Both the federal government and the state of South Carolina believed they had the Constitution on their side and were prepared to fight if necessary to prove that they were right. Thankfully, armed conflict was averted by means of a timely concession. President Jackson enacted the Compromise Tariff of 1833, which South Carolina found acceptable. Although civil war had been avoided, it was a close call. And South Carolina's defiance proved to be an eerie portent of events to come in the very same state less than thirty years later.

In the story, "The Metamorphosis", Gregor has morphed from being human to an animal. But what makes him still humane? Please provide a quote with the page number for textual evidence.

After his metamorphosis, Gregor demonstrates he is still humane because he is considerate enough to avoid visibility.
Although his back is slightly crushed and he cannot get in all the way, Gregor scuttles under the couch and remains there out of sight during the night. He feels that he should "lie low" and,

show[ing] his family every possible consideration, help them bear the inconvenience which he simply had to cause them in his present condition. (Ch.2)

One day Gregor's sister, who has taken on the responsibility of feeding him and tending to his needs, enters his room earlier than usual. He is still looking out the window she has pulled a chair beside. At the sight of him, she springs back and locks the door. Consequently, he hides under the couch. When she comes into his room at noon, she still seems uneasy. This uneasiness causes Gregor to decide she is still repulsed by him. So, he puts a sheet over the couch that he can hide under and be completely out of sight:

the job took four hours—and [he] arranged it in such a way that he was now completely covered up and his sister could not see him even when she stooped. (Ch.2)

Single Variable Calculus, Chapter 3, 3.6, Section 3.6, Problem 28

Find an equation of the tangent to the curve $x^{\frac{2}{3}} + y^{\frac{2}{3}} = 4$ at the point $\displaystyle \left(-3\sqrt{3},1\right)$ using Implicit Differentiation.
If $y'= m\text{ (slope)}$ then,
$\displaystyle \frac{d}{dx} \left(x^{\frac{2}{3}}\right) + \frac{d}{dx} \left(y^{\frac{2}{3}}\right) = \frac{d}{dx} (4)$


$
\begin{equation}
\begin{aligned}
\frac{2}{3} (x)^{\frac{-1}{3}} + \frac{2}{3} (y)^{\frac{-1}{3}} \frac{dy}{dx} &= 0\\
\\
\frac{2}{3\sqrt[3]{x}} + \frac{2}{3 \sqrt[3]{y}} y' &= 0\\
\\
\frac{2}{3\sqrt[3]{y}} y' &= \frac{-2}{3 \sqrt[3]{x}}\\
\\
y' &= \frac{-2(3\sqrt[3]{y})}{2(3\sqrt[3]{x})}\\
\\
y' &= \frac{-\sqrt[3]{y}}{\sqrt[3]{x}}
\end{aligned}
\end{equation}
$

For $x = -3\sqrt{3}$ and $y =1 $, we obtain

$
\begin{equation}
\begin{aligned}
y' = m &= - \frac{\sqrt[3]{y}}{\sqrt[3]{x}}\\
\\
m &= - \frac{\sqrt[3]{1}}{\sqrt[3]{3-\sqrt{3}}}\\
\\
m &= \frac{1}{\sqrt{3}}
\end{aligned}
\end{equation}
$


Using the point slope form

$
\begin{equation}
\begin{aligned}
y - y_1 &= m(x-x_1)\\
\\
y - 1 & = \frac{1}{\sqrt{3}} [x - ( -3 \sqrt{3})]\\
\\
y - 1 & = \frac{1}{\sqrt{3}} (x + 3\sqrt{3})\\
\\
y &= \frac{x+3\sqrt{3}}{\sqrt{3}} +1 \\
\\
y &= \frac{x+3\sqrt{3}+\sqrt{3}}{\sqrt{3}}\\
\\
y &= \frac{x+4\sqrt{3}}{\sqrt{3}} && \text{Equation of the tangent line at } (-3\sqrt{3},1)
\end{aligned}
\end{equation}
$

What are two examples of personification in the epic poem Beowulf?

The epic poem Beowulf is the earliest surviving Old English work. It is believed to have been composed between 600-900 A.D., and then later transcribed by Anglo-Saxon monks in what is now known as England. We have no real idea who created the poem, which might very well be based on Norse stories that travelers or storytellers brought from the north.
Personification is the attribution of human qualities to a nonhuman entity. After Grendel's first attack on Herot, the poet (according to the Burton Raffel translation) says that:

Distance was safety, the only survivors
Were those who fled him. Hate had triumphed.

Hate is personified in this line. When the poet says that it "triumphs" he implies that hate is willful, in the sense that it can try to defeat something, like a human being would do.
Later, the poet tells us that as a result of his misery, Hrothgar is miserable. He uses personification when he says:

His misery leaped 
The seas, was told and sung in all
Men's ears.

We know that misery cannot actually "leap." The poet means that the story of Hrothgar's misery was told by travelers, eventually making it to Beowulf's ears. Since Beowulf lived across  the sea from Hrothgar, saying that misery "leaped" gives the reader (or listener, when the story was first being told) a nice image, a sense of action as the story is told, then re-told, until Beowulf hears it. 

Dana's homes are her house in California and the Weylin plantation in Maryland in Kindred. However, the idea of home also applies to the two time periods in which she lives. Where does Dana appear to be more at home?

The complexity of her relationship with each of the time periods is hard to overstate. Her life in the 1970s obviously is much better because she is a free woman with a relatively good and happy life, as well as a caring husband. However, when she is thrust through time and space into the 1800s, she becomes a slave. This would make it easy to assume that she feels much more at home in the present, but it neglects the connections she makes in the past.
In the 1800s, in spite of being a slave, she grows close to Alice, her ancestor, and learns to love several people in that time period. Because of the kinship she feels, she is not quite as alone in the past as one might imagine. Therefore, she feels "at home" in different ways in each time and place. However, in the end, she is more pleased to return to her own time, signifying that she is most at home in her own time period.

If push came to shove, then of course Dana would prefer to remain in 1976, where (though she is still a member of an ethnic minority routinely subjected to racism) she still has her freedom. But the whole point of the story is to show us that such simple binary choices often don't come up in our lives. The present day, like the past that precedes it, is a good deal more complex than we might like to think.
Dana's direct experience of the horrors of slavery has made her understand this, giving her a new perspective on the nature of racial relations. More crucially, it gives her food for thought concerning the complex, multi-faceted nature of American history behind the flag-waving celebrations of the Bicentennial.
Strictly speaking, she's not "at home" anywhere; and perhaps she never will be. But at least now she has a unique perspective on things that allow her to transcend her present condition and see how the past feeds into the present, which in turn can give rise to a more hopeful future: a future free from discrimination and exploitation.

Because Dana is a free woman in 1976 California and a slave on the Weylin plantation in the 1800s, we might assume that she is more "at home" in her modern life and time. However, the novel indicates that Dana's relationship to each of her "homes" is more complicated than that and becomes increasingly so as the novel progresses.
When Dana is first mysteriously plunged back in time and across space, she is obviously frightened and disoriented. As a black woman in the 1800s South, she is automatically considered a slave, despite the fact that in her current life, she is a writer. She is shocked by the racism and the violence of plantation life, and that reality becomes even harsher when she must face it repeatedly.
However, as she goes back and forth from past to present, she learns to survive on the plantation and bonds with the other slaves, especially Alice, who turns out to be one of her ancestors (along with the master, Rufus Weylin). Because she is connected to some of the people on the plantation (through her family line) and forms relationships with her peers, the plantation becomes an odd sort of home for her. Also, because of the abusive interracial relationship between Alice and Rufus, Dana reflects on her own marriage to a white man, Kevin. Although she is happy to return home to her life with Kevin and her freedom, she is forever changed by her experience in the past, and knowing what she now knows about her history, she cannot be truly comfortable in the present either.