Monday, June 3, 2019

18/(x^2-3x)-6/(x-3)=5/x Solve the equation by using the LCD. Check for extraneous solutions.

18/(x^2-3x)-6/(x-3)=5/x
LCD is x^2-3x=x(x-3)
Multiply all the terms of the equation by LCD and simplify,
x(x-3)(18/(x^2-3x))-x(x-3)(6/(x-3))=x(x-3)(5/x)
18-6x=(x-3)5
18-6x=5x-15
-6x-5x=-15-18
-11x=-33
x=(-33)/(-11)
x=3
Let's check the solution by plugging in the original equation,
18/(3^2-3*3)-6/(3-3)=5/3
18/0-6/0=5/3
Since the solution x=3, yields a denominator of zero, so it's an extraneous solution and the original equation has no solution.
 


LCD is an acronym for least common denominator. It is the product of distinct factors on the denominator side. Basically, find LCD is the same as finding the LCM (least common multiple) of the denominators.
For the given equation 18/(x^2-3x)-6/(x-3)=5/x , the denominators are (x^2-3x) , (x-3) , and x . Note: The factored form of the denominator x^2-3x is  x(x-3) .
Based on the list of factors, The distinct factors are x and (x-3).
Thus, LCD= x*(x-3)  or (x^2-3x) .
To simplify the equation, we multiply each term by the LCD.
18/(x^2-3x)*(x^2-3x)-6/(x-3)*x*(x-3) =5/x*x*(x-3)
Cancel out common factors to get rid of the denominators.
18 -6*x =5*(x-3)
Apply distribution property.
18-6x=5x-15
Subtract 18 from both sides.
18-6x-18=5x-15-18
-6x= 5x -33
Subtract 5x from both sides of the equation.
-6x-5x= 5x -33-5x
-11x=-33
Divide both sides by -11 .
(-11x)/(-11)= (-33)/(-11)
x=3
To check for extraneous solution, plug-in x=3 on 18/(x^2-3x)-6/(x-3)=5/x .
18/(3^2-3*3)-6/(3-3)=?5/3
18/(9-9)-6/0=?5/3
18/0-6/0=?5/3
undefined -undefined=?5/3   FALSE.
Note: Any value divided by 0 results to undefined value.
An undefined result  implies the x value is an extraneous solution.
Therefore, the x=3 is an extraneous solution.
 There is no real solution for the given equation 18/(x^2-3x)-6/(x-3)=5/x .

In what ways, if any, did the Spanish, French, and English differ in their dealings with Indian peoples?

There were actually significant differences in the way that the French, English, and Spanish dealt with Native Americans. These differences had a lot to do with their goals for colonization and use of resources in the Americas.
The Spanish sought to enrich their nation with the resources of the Americas. They had a policy of enslaving the native peoples and forcing them to do dangerous and backbreaking tasks such as mining for precious metals and farming cash-crops. They also sought to bring as many native peoples into the Catholic faith as possible. Consequently, they established missions all over their American empire and forcefully converted many Native Americans.
The French also looked to enrich themselves with the resources of the Americas. However, they did not take as heavy-handed an approach to dealing with Native Americans as the Spanish did. Rather than enslaving them, the French formed trade alliances with many tribes. There were never many French colonists in North America, so direct conquest was never really an option. The French would often take advantage of rivalries between different tribes to negotiate favorable trade deals, usually for furs and pelts. A number of French missionaries did convert a significant amount of Hurons to Christianity, but never on the same scale as the Spanish.
The English had a very different approach to dealing with Native Americans. They sought to displace them, not exploit them. The English wanted to keep the native peoples, who they viewed as inferior, as separate from them as possible. In the early years of English colonialism in the New World, there were a number of violent conflicts between different tribes and English colonists who wanted their land. This, coupled with deadly epidemics, led to a decimation of the native population.
http://nativeamericannetroots.net/diary/1357

https://organpipehistory.com/history-and-people/first-encounters-spaniards-and-native-americans-1540-1848/

Sunday, June 2, 2019

What happens to Snowball during the meeting about the windmill?

During the meeting about the windmill, Snowball is attacked by "nine enormous dogs wearing brass-studded collars." These dogs answer only to Napoleon, and they were likely ordered to kill him. However, the dogs could not catch Snowball during the chase and only managed to run him off the farm.
The meeting was held to discuss whether a windmill should be built. For weeks, Snowball had touted the benefits of a windmill, "which could be made to operate a dynamo and supply the farm with electrical power." Snowball proclaimed that once the farm had electricity, the animals could have light and warmth in their stalls during the winter. Electricity would also make the use of a "circular saw, a chaff-cutter, a mangel-slicer, and an electric milking machine" possible.
With the use of time-saving tools, the work on the farm would be far less labor-intensive. The animals would only have to work three days a week. During the meeting, Snowball further expounded on the benefits of the windmill. His passionate discourse inspired the animals to support his windmill initiative. 
Meanwhile, Napoleon became visibly angry at the turn of events. He called up nine ferocious dogs to kill Snowball. However, because of Snowball's agility and speed, none of the dogs could catch him. Essentially, Snowball was chased off the farm.

One of them all but closed his jaws on Snowball’s tail, but Snowball whisked it free just in time. Then he put on an extra spurt and, with a few inches to spare, slipped through a hole in the hedge and was seen no more.

College Algebra, Chapter 9, 9.1, Section 9.1, Problem 24

a.) Determine the first 10 terms of the sequence given by $a_n = a_{n- 1} - a_{n-2}$ that is defined recursively by $a = 1$ and $a_2 = 3$

$
\begin{equation}
\begin{aligned}
a_1 &= 1\\
\\
a_2 &= 3\\
\\
a_3 &= a_2- a_1 = 3-1 = 2\\
\\
a_4 &= a_3- a_2 = 2-3 = -1\\
\\
a_5 &= a_4- a_3 = -3-(-1) = -3\\
\\
a_6 &= a_5- a_4 = -2-(-3) = -2\\
\\
a_7 &= a_6- a_5 = -2-(-3) = 1\\
\\
a_8 &= a_7- a_6 = 1 - (-2) = 3\\
\\
a_9 &= a_8- a_7 = 3 - 1 = 2\\
\\
a_{10}&= a_9- a_8 = 2-3 = -1
\end{aligned}
\end{equation}
$

b.) Graph the first 10 terms of the sequence

Saturday, June 1, 2019

Which character is able to stand up to Prince Hamlet's cunning use of language, and in which context?

Probably the best answer to this question would be the First Gravedigger, whose blackly comic banter with Hamlet in the "Gravediggers" scene shows that he may work with his hands, but he also (to paraphrase A Midsummer Night's Dream), "labors in his mind."
Consider just this one section of the scene:

HAMLET
Whose grave's this, sirrah?
First Clown
Mine, sir.
Sings
O, a pit of clay for to be made
For such a guest is meet.
HAMLET
I think it be thine, indeed; for thou liest in't.
First Clown
You lie out on't, sir, and therefore it is not
yours: for my part, I do not lie in't, and yet it is mine.

Even Hamlet has to admit at this point that the "knave" has command of his wordplay. Although Hamlet addresses him initially as "sirrah," indicating he is speaking to a person of lesser status, the Prince likely has a sneaking admiration for this man who refuses to be intimidated and boldly answers back. Hamlet is used to being the best master of "words, words, words," and to encounter someone who can thrust and parry with him in this unlikely situation appeals to his well-developed sense of the absurd.

Who is Sonia in Unwind by Neal Shusterman?

Sonia is a vital but briefly involved character in the novel Unwind. When the Unwinds, people who have been labelled to be retroactively aborted after living through their teenage years, are trying to escape, Sonia arrives and helps them flee. In addition to being their savior and helping them escape through her basement to a safe haven in Arizona, she gives the children advice and encouragement to help them through their struggles.
She advises Connor and Risa to become pregnant again, because the government will not unwind pregnant people (although they never were pregnant in the first place, Risa was just carrying a baby she assumed was theirs). She also gives them some hope because she has been fighting the system and helping people escape inevitable death for quite some time.


Sonia is one of the characters in Unwind who provides hope for the future survival of the social misfits. Not only does she help Unwinds escape, but she is also presented as an old woman who has been engaged in this subversive work for some time. She gives him and Rita practical, if slightly off course, advice, as she believes the baby they are carrying is theirs: to get pregnant again, as the authorities will not unwind pregnant women. She is a tough-talking, but tender-hearted survivor, who risks her life to help younger people escape as part of the network with Hannah, the teacher.
Sonia is generally associated with the positive values that the society formerly had in that she operates an antiques shop, which seems to Connor to have things from all phases of American history. She also harks back to a specific time in US history, prohibition, as the secret hideaway in the basement of her shop had been used to hide illegal liquor. Now she keeps it stocked with food and supplies for the escapees who hide there while waiting for transport in the ice cream truck.
https://books.google.com/books?id=W1PXSW4R2xsC&source=gbs_navlinks_s


In the novel Unwind, which takes places in a dystopian, post Second Civil War America, we learn that recent legislation has just been passed that allows parents to "retroactively 'abort' a child" between the ages of 13 and 18 for seemingly minor infractions. The name of the legislation responsible for this law is the Bill of Life. Although this seems an odd moniker, given the nature of this new and brutal law, we learn that this same bill has also simultaneously just outlawed abortion. Sonia is the owner of an antique store who also runs a sort of safe house for "unwinds." The three runaway teens we meet at the beginning of the story (Connor, Risa, and Lev) first encounter Sonia at her home, the safe house. Sonia allows them to stay in her cellar for a week until she can secure transportation to the next safe house for unwinds.


In the book Unwind, Sonia is a fairly minor character.  She is important for sure, but she gets very little page time.  Her background is explored in much greater detail in the sequel book UnWholly.   
In Unwind, Sonia operates an underground railroad of sorts.  Instead of secretly spiriting away slaves, Sonia helps runaway Unwinds make their way to the Graveyard.  She does this by housing the Unwinds in her basement and arranging safe transport to Arizona.  While staying in her basement, Sonia requires each Unwind to write a letter to a loved one.  She keeps the letter until the Unwind turns 18.  At that point, the child is no longer in danger of being unwound.  The child can then return for the letter and personally mail it out or destroy it.   If the child is unwound or does not return for the letter, Sonia mails it out herself.  Connor and Risa both benefit from her work and her protection in the book Unwind. Unfortunately, so does Roland.   

What kind of courses should companies provide for their employees so they can be part of the “lifelong learning” process?

Lifelong learning can be defined as the ongoing pursuit of skills and knowledge by individuals for personal and professional reasons. Gone are the days when individuals would stay on working with the same company for all of their professional life, doing the same kind of tasks. Today, most people want to change companies or even careers during their working life. Lifelong learning, therefore, offers individuals the possibilities of doing this with fewer headaches. For instance, one can learn a new skill on a part-time basis, while fully employed. Businesses, on the other hand, are able to make use of lifelong learning opportunities to train their senior employees on emerging trends within the industry and motivate their teams towards knowledge and skill acquisition throughout their employment. This said it is important to note that lifelong learning programs generally suit industries which have new developments as the years go by or even those that have further areas of study. Examples of such dynamic industries are IT, aviation, engineering, multimedia, etc. For example, programming languages evolve over the years forcing IT specialists to seek new skills in emerging products. Lifelong learning is, however, less attractive in fields that depend on short-term hires such as the fast food industry, cleaning services, or other menial kinds of work.
Companies interested in offering lifelong learning courses to their employees can focus on those areas that are relevant to the operations of their businesses. Some general courses that companies can offer, regardless of their specialization, are leadership strategies, company management, digital marketing strategies, negotiation skills, strategic business management, entrepreneurial skills, leadership communication, and conflict resolution within the workplace. Others are technology and analytical skills development, and career development.
Some examples of companies that have well organized lifelong learning programs within their organizations are Optoro, Digital Ocean, OverDrive, Etsy, Culture Amp, Airbnb etc.

Summarize the major research findings of "Toward an experimental ecology of human development."

Based on findings of prior research, the author, Bronfenbrenner proposes that methods for natural observation research have been applied in ...