f(x) = e^(x/3) , n=4 Find the n'th Maclaurin polynomial for the function.

Maclaurin series is a special case of Taylor series that is centered at a=0. The expansion of the function about 0 follows the formula:
f(x)=sum_(n=0)^oo (f^n(0))/(n!) x^n
 or
f(x)= f(0)+(f'(0)x)/(1!)+(f^2(0))/(2!)x^2+(f^3(0))/(3!)x^3+(f^4(0))/(4!)x^4 +...
We may apply the formula for Maclaurin series to determine the Maclaurin polynomial of degree n=4 for the given function f(x)=e^(x/3) .
Apply derivative formula for exponential function: d/(dx) e^u = e^u * (du)/(dx) to list f^n(x) as:
Let u =x/3 then (du)/(dx)= 1/3
Applying the values on the derivative formula for exponential function, we get:
d/(dx) e^(x/3) = e^(x/3) *(1/3)
         = e^(x/3)/3 or 1/3e^(x/3)
Applying d/(dx) e^(x/3)= 1/3e^(x/3)  for each f^n(x) , we get:
f'(x) = d/(dx) e^(x/3)
          =1/3e^(x/3)
f^2(x) = d/(dx) (1/3e^(x/3))
          =1/3 *d/(dx)e^(x/3)
          =1/3 *(1/3e^(x/3))
          =1/9e^(x/3)
f^3(x) = d/(dx) (1/9e^(x/3))
           =1/9 *d/(dx) e^(x/3)
          =1/9 *(1/3e^(x/3))
          =1/27e^(x/3)
f^4(x) = d/(dx) (1/27e^(x/3))
           =1/27 *d/(dx) e^(x/3)
           =1/27 *(1/3e^(x/3))
           =1/81e^(x/3)
Plug-in x=0 on each f^n(x) , we get:
f(0)=e^(0/3) = 1
f'(0)=1/3e^(0/3) = 1/3
f^2(0)=1/9e^(0/3)=1/9
f^3(0)=1/27e^(0/3)=1/27
f^4(0)=1/81e^(0/3)=1/81
Note: e ^(0/3) = e^0 =1.
Plug-in the values on the formula for Maclaurin series, we get:
f(x)=sum_(n=0)^4 (f^n(0))/(n!) x^n
    = 1+(1/3)/(1!)x+(1/9)/(2!)x^2+(1/27)/(3!)x^3+(1/81)/(4!)x^4
   =1+1/3x+1/18x^2+1/162x^3+1/1944x^4
The Maclaurin polynomial of degree n=4 for the given function f(x)=e^(x/3) will be:
P_4(x)=1+1/3x+1/18x^2+1/162x^3+1/1944x^4

Why did Truman Capote write "A Christmas Memory"?

Truman Capote is known for powerful works of fiction and non-fiction, including his most famous investigative work In Cold Blood, which became a best seller. Capote's talent for observing sensory details and capturing characters makes his writing very compelling.
That talent is obvious in this short memoir, first published in a collection with the novel Breakfast at Tiffany's, Capote's second most famous work. In this story, Capote recounts memories of celebrating Christmas as a young boy with his elderly cousin. Like In Cold Blood, certain details in "A Christmas Memory" are embellished, and that is perhaps what makes the story even more interesting. It has been called "semi-autobiographical" and functions as a window into this interesting writer's background.
Because Capote was fairly openly gay during a time when homosexuality was often kept secret, his sensitive recounting of the events of his childhood helps us understand the writer's deep need to tell his own story. Despite growing up in poverty, Capote went on to know wealth and fame. This story conveys his humble beginnings and the loyalty he feels to his elderly cousin, who understood him better than his closer family members. The story may in part be a memory of this relationship, but also of a way of life that Capote left behind when he became a famous writer who lived a life of luxury and sophistication.

What sign does Melanie say to look for?

When Elizabeth asks what sort of sign she should look for, Melanie answers that she (Elizabeth) should look for a secret omen.
In chapter 9, April tells the rest of the group (Elizabeth, Marshall, and Melanie) that they have been summoned back to Egypt. She mysteriously reports finding a feather on her window sill and concludes that it was a token from the mighty gods.
Meanwhile, Elizabeth is worried about breaking away from the trick-or-treating group; she doesn't believe that it's a good idea to visit Egypt on Halloween, of all nights. So, she is especially nervous when April makes the eerie announcement that the group has been summoned back to Egypt.
Elizabeth is doubly concerned when April also suggests that they should look for a sign to determine the validity of the summons. She then inquires about the kind of sign the children should look out for. At this point, Melanie chimes in to say that everyone should look out for a "secret omen." 
April concurs with Melanie's assessment but suggests that the sign need not necessarily be a pigeon feather (as Marshall suggests).

In the novel Lord of the Flies, what are some quotes/plot events that represent the fight for civilization?

In Chapter 3, Ralph and Jack begin to argue over building shelters and hunting. Jack insists that the boys need meat, while Ralph continues to promote the importance of building shelters and maintaining a signal fire. When Ralph mentions that the best thing they can do is find a way to be rescued, Jack says, "Rescue? Yes, of course! All the same, I'd like to catch a pig first---" (Golding 74). Ralph then says, "So long as your hunters remember the fire----" (Golding 75). Jack replies by saying, "You and your fire!" (Golding 75). The signal fire is a symbol of hope and rescue throughout the novel. Jack expresses his affinity for hunting pigs and dismisses the significance of the signal fire. Ralph's attempt to remind Jack about the importance of maintaining the fire is ignored. This minor disagreement eventually leads to the conflict between civility and savagery.
In Chapter 5, Ralph holds a meeting to discuss why certain tasks and responsibilities are not being carried out by the boys. The boys then discuss the existence of the beast and Ralph says that they need to vote on whether they believe there are ghosts on the island. When no one raises their hand, Golding writes,

"The world, that understandable and lawful world, was slipping away. Once there was this and that; and now---and the ship had gone" (128).

Piggy attempts to regain control by saying,

"What are we? Humans? Or animals? Or savages? What's grown-ups going to think? Going off---hunting pigs---letting fires out---and now!" (Golding 120).

Clearly, the boys are gradually descending into savagery. Ralph and Piggy try their best to argue for civility, but the majority of boys are beginning to neglect their responsibilities and follow Jack.

What were the major causes of war between the Powhatans and the English settlers?

The Powhatan War (1622–1644) was among the first conflicts between European settlers and Native Americans. In general, this warfare was caused by cultural differences and conflicts over land.
Jamestown (1607) was the first permanent English settlement in North America. At the time of its founding, the surrounding area was dominated by the Powhatan Indian Confederacy, led by Chief Powhatan. Relations between the two disparate peoples were problematic from the start, but full-scale war was avoided for fifteen years.
The first couple of years for the Jamestown settlers were hazardous, and the colony almost collapsed. The settlers sought merely to survive, and Indian foodstuffs were badly needed by the colonists. The Indians cultivated corn, fished, and hunted, so they had surplus food. In exchange for food, the Indians received blue beads from the English. But relations were tense, and there were occasional conflicts. Nevertheless, an uneasy cooperation continued for a few years.
One reason why limited cooperation persisted was the role played by Pocahontas. A daughter of Powhatan, she supposedly saved the life of Captain John Smith as he was about to be executed by the Indians. Later, in 1613, Pocahontas was captured by the English, and she married an Englishman in 1614. This marriage helped maintain a delicate peace.
By 1618, both Powhatan and Pocahontas were dead. Opechancanough became the new chief. Tensions were high. The English had started to cultivate tobacco and were seizing land from the Indians. Tobacco was extremely lucrative, so more land was needed by the colonists for planting and for settlements as more Europeans poured into Virginia. In 1622, Opechancanough led a devastating attack, and full-scale war had begun.

When English settlers arrived in Virginia and came into contact with the Powhatan, they were reliant on the Powhatan and their corn for survival. This, combined with the fact that the English settlers were heavily outnumbered, led to early cooperation between the English and the Powhatan. With the development of tobacco as a cash crop, however, things began to change.
The introduction of tobacco to the Virginia colony proved to be very successful. A high demand for tobacco in Europe led to increasing profitability, which led to a strengthening of English settlements in Virginia. With English settlers realizing the value behind the growing demand for tobacco, they attempted to plant more tobacco in order to increase their wealth. This led to the English attempt to gain more land, which encroached upon Powhatan land. This would lead to conflict and violence between the English and the Powhatan, as they both attempted to exert control over the same land.
https://www.britannica.com/event/Powhatan-War

Aside from the cultural differences that contributed to friction between native peoples and Europeans throughout the Americas, the main cause of the Anglo-Powhatan wars in the years following Jamestown's founding was the desire of English settlers for land. When the Jamestown colonists arrived in Virginia, they entered the empire of the Powhatan people, whose chieftain had spent the previous two decades expanding his influence over the region. At first, he probably saw the English as subject peoples and perhaps valuable allies, but after surviving a series of horrific famines, and nearly failing as a business venture, the English began to plant a variety of tobacco that could be easily marketed in Europe. Virginia quickly became a cash crop colony, and the colonists' demands for land increased dramatically. As more and more colonists arrived, they became more of a threat to the Powhatan, and this process led to conflict. The earliest war had actually begun when the Powhatan attempted to starve out the colonists by denying them corn, a response to early English expansion (before tobacco became a factor). But the introduction of tobacco into the colony sped up expansion and intensified conflict with area natives. This process ended in disaster for the Powhatan.
http://www.virginiaplaces.org/nativeamerican/anglopowhatan.html

Intermediate Algebra, Chapter 3, 3.3, Section 3.3, Problem 32

(a) Write the equation $7x - 3y = 3$ in slope-intercept form.


$
\begin{equation}
\begin{aligned}

7x - 3y =& 3
&& \text{Given equation}
\\
\\
-3y =& -7x + 3
&& \text{Subtract each side by $7x$}
\\
\\
y =& \frac{7}{3}x - \frac{3}{3}
&& \text{Divide each side by $-3$}
\\
\\
y =& \frac{7}{3}x - 1
&&

\end{aligned}
\end{equation}
$



(b) Give the slope of the line.

Here the slope is $\displaystyle \frac{7}{3}$. It can be interpreted as $\displaystyle m = \frac{\text{rise}}{\text{run}} = \frac{7}{3}$

(c) Give the $y$-intercept.

The $y$-intercept is $-1$.

(d) Graph the line.

From $(0,-1)$, move 7 units up and 3 units to the right and plot a second point at $(3,6)$. Draw a line through the two points.

What are some impacts of climate change on the Great Barrier Reef? How would these impacts alter biotic/abiotic components of the ecosystem? Are there any further impacts?

The Great Barrier Reef (GBR) off the eastern coast of Queensland, Australia is the world's largest reef. In fact, it's the largest living thing on Earth spanning more than 2500km (GBRMPA). As climate changes in response to human activities, the GBR suffers the indirect effects of increased atmospheric CO2 emissions.
The most pronounced and widespread effect of climate change on the GBR is coral bleaching. Coral bleaching is the visible change in coral appearance as a result of the death (or loss) of symbiotic organisms that give the coral its color. As sea temperatures rise in response to climate change, the marine algae that live within the coral (and on its surface) die off - when they disappear, they leave behind the white coral structure. In small patches, coral bleaching isn't a problem - it can even be a good thing for growing new algae. However, the widespread bleaching resulting from average sea temperature increases that may or may not be permanent in nature highlights real problems for the reef. Currently 97% of the great barrier reef has been bleached or partially bleached. Will it ever restore itself and heal from the impacts of climate change? That's a question scientists are currently working on, and the future doesn't look too bright (link).
Other effects of climate change on the reef include ocean acidification (which impacts calcium carbonate formation of the coral itself) and sea level rise (which changes the location of the reef relative to the coastline).
For more information, check out the links below.
 
https://www.coralcoe.org.au/media-releases/only-7-of-the-great-barrier-reef-has-avoided-coral-bleaching