Beginning Algebra With Applications, Chapter 5, Review Exercises, Section Review Exercises, Problem 26

Determine the equation of the line through the points whose coordinates are $(4,14)$ and $(-8,-1)$.

We let $(x_1, y_1) = (4,14)$ and $(x_2, y_2) = (-8,-1)$

Using Slope of the line Formula,


$
\begin{equation}
\begin{aligned}

m =& \frac{y_2 - y_1}{x_2 - x_1}
\\
\\
m =& \frac{-1-14}{-8-14}
\\
\\
m =& \frac{-15}{-12}
\\
\\
m =& \frac{5}{4}


\end{aligned}
\end{equation}
$


Using the point slope form, where $\displaystyle m = \frac{5}{4}$ and $(x_1, y_1) = (4,14)$



$
\begin{equation}
\begin{aligned}

y - y_1 =& m(x - x_1)
&&
\\
\\
y - 14 =& \frac{5}{4}(x-4)
&& \text{Substitute } m = \frac{5}{4} \text{ and } (x_1, y_1) = (4,19)
\\
\\
y-14 =& \frac{5}{4}x - 5
&& \text{Apply Distributive Property}
\\
\\
y =& \frac{5}{4}x + 9
&& \text{Add } 14

\end{aligned}
\end{equation}
$

What are some examples of kidney diseases, and what variables influence how they function?

The kidneys are a pair of vital organs that remove toxins, waste, and extra water from your blood.  After substances are filtered out of blood, they travel through the ureter to the bladder for storage until they can be passed through urine.
Diseases that progressively damage the kidneys and impair their ability to function are referred to as Chronic Kidney Disease (CKD).  If the kidneys are malformed during fetal development, they won't function as efficiently as fully formed kidneys.  Genetic diseases, such polycystic kidney disease, can impair kidney function because it damages the organ's tissue.  Lupus, an immune disorder, can reduce kidney function by causing inflammation in the kidney's filtration system.  This is referred to as lupus nephritis.   Kidney stones are accumulations of minerals that can become lodged in renal tissue, causing damage.  Individuals with diabetes often experience hypertension which can decrease the functioning capabilities of the kidney.  It is unclear why, but occurrence of diabetes varies depending on a persons' ethnicity. 
If a person's kidney disease progresses to the point where the damage is irreversible, they may experience kidney failure. At this point, they may like dialysis or transplantation, to help their body remove toxins and waste from their blood stream.
https://www.kidney.org/atoz/content/about-chronic-kidney-disease

https://www.lupus.org/resources/how-lupus-affects-the-renal-kidney-system

College Algebra, Chapter 2, 2.1, Section 2.1, Problem 46

Show that the triangle with vertices $A(6,-7), B(11,-3)$, and $C(2,-2)$ is a right triangle by using the converse of the Pythagorean Theorem. Find the area of the triangle.

By using distance formula,

$
\begin{equation}
\begin{aligned}
d_{AB} &= \sqrt{(-3-(-7))^2 + (11-6)^2} &&& d_{AC} &= \sqrt{(-2-(-7))^2 + (2-6)^2}\\
\\
d_{AB} &= \sqrt{4^2 + 5^2} &&& d_{AC} &= \sqrt{5^2 + (-4)^2}\\
\\
d_{AB} &= \sqrt{16+25} &&& d_{AC} &= \sqrt{25+16}\\
\\
d_{AB} &= \sqrt{41} \text{ units} &&& d_{AC} &= \sqrt{41} \text{ units}\\
\\
\\
d_{BC} &= \sqrt{(-2-(-3))^2 + (2-11)^2}\\
\\
d_{BC} &= \sqrt{1^2 + (-9)^2}\\
\\
d_{BC} &= \sqrt{1+81}\\
\\
d_{BC} &= \sqrt{82} \text{ units}
\end{aligned}
\end{equation}
$

Next, by using the converse of the Pythagorean Theorem if the sides $\sqrt{82}$, $\sqrt{41}$ and $\sqrt{41}$ forms a right triangle.

$
\begin{equation}
\begin{aligned}
(\sqrt{82})^2 &= (\sqrt{41})^2 + (\sqrt{41})^2\\
\\
82 &= 41+41\\
\\
82 &= 82
\end{aligned}
\end{equation}
$

Since both sides are equal, then the three sides form a right triangle.
Thus, the area is $\displaystyle A = \frac{1}{2} bh = \frac{1}{2} (\sqrt{41}) (\sqrt{41}) = 20.5$ square units

What brave thing does Atticus do in chapter 10?

In Chapter 10, Atticus does something that Jem and Scout believe is completely out of character--he shoots and kills a rabid dog.

In an earlier scene, Scout and Jem ironically complain to Miss Maudie that their father is old and boring. Miss Maudie responds by saying, "You'd be surprised [...] there's some life in him yet." Atticus lives up to her praises by swiftly taking down the rabid dog with one shot from a rifle when it begins charging up the street at him. Even the Sheriff, Heck Tate, is too poor of a shot to take down the dog.
After the dog is killed, Miss Maudie says, "I think maybe [Atticus] put his gun down when he realized that God had given him an unfair advantage over most living things. I guess he decided he wouldn't shoot till he had to, and he had to today." Jem and Scout learn a pivotal lesson about their father here: real bravery is using stepping up when nobody else will.

SOURCES:
https://cleveracademy.vn/wp-content/uploads/2016/10/To-Kill-a-Mockingbird.pdf

In chapter 10, Jem notices a sick dog staggering down the middle of the street and runs to tell Calpurnia about it. When Calpurnia sees the sick dog, she immediately recognizes that the dog has rabies. Calpurnia instructs the children to stay inside and calls the operator to inform the community that a rabid dog is walking through town. When Sheriff Tate and Atticus arrive on the scene, Sheriff Tate gives his rifle to Atticus and asks him to shoot the rabid dog. While the other citizens are safely behind closed doors, Atticus courageously stands in the middle of the street aiming his rifle at the rabid dog. Atticus demonstrates his bravery by shooting the dog while it walks in his direction. After Atticus kills the dangerous animal, Jem is speechless, and Scout is astonished at her father's marksmanship abilities. The fact that Atticus never told his children that he was a talented marksman also reveals his humility.

Calculus of a Single Variable, Chapter 9, 9.5, Section 9.5, Problem 7

To determine the convergence or divergence of the series sum_(n=1)^oo (-1)^n/3^n , we may apply the Ratio Test.
In Ratio test, we determine the limit as:
lim_(n-gtoo)|a_(n+1)/a_n| = L
Then, we follow the conditions:
a) L lt1 then the series converges absolutely
b) Lgt1 then the series diverges
c) L=1 or does not exist then the test is inconclusive.The series may be divergent, conditionally convergent, or absolutely convergent.
For the given series sum_(n=1)^oo (-1)^n/3^n , we have a_n =(-1)^n/3^n .
Then, a_(n+1) =(-1)^(n+1)/3^(n+1) .
We set up the limit as:
lim_(n-gtoo) | [(-1)^(n+1)/3^(n+1)]/[(-1)^n/3^n]|
To simplify the function, we flip the bottom and proceed to multiplication:
| [(-1)^(n+1)/3^(n+1)]/[(-1)^n/3^n]| =| (-1)^(n+1)/3^(n+1) *3^n/(-1)^n|
Apply the Law of Exponent: x^(n+m) = x^n*x^m . It becomes:
| ((-1)^n (-1)^1)/(3^n *3^1)*3^n/(-1)^n|
Cancel out common factors (-1)^n and (3^n) .
| (-1)^1/ 3^1 |
Simplify:
| (-1)^1/ 3^1 | =| (-1)/ 3 |
= |-1/3|
=1/3
Applying |[(-1)^(n+1)/3^(n+1)]/[(-1)^n/3^n]|= 1/3 , we get:
lim_(n-gtoo) | [(-1)^(n+1)/3^(n+1)]/[(-1)^n/3^n]|=lim_(n-gtoo) 1/3
lim_(n-gtoo) 1/3 = 1/3
The limit value L=1/3 satisfies the condition: L lt1 .
Therefore, the series converges absolutely.

What are some adjectives and examples to describe the relationship between Ruth and Beatrice in Paul Zindel's The Effect of Gamma Rays on Man-in-the-Moon Marigolds?

Paul Zindel's play contains a powerful central metaphor in the title and to what it refers. The experiment Tillie conducts to determine if radiation creates mutations in marigolds symbolizes the effect that negative energy and dysfunction has on her own family. The impact of negative emotions like anger, regret, and cruelty strongly affect the family unit.
The relationship between Beatrice and her daughter Ruth is particularly problematic. The outgoing Ruth shows some promise of being socially accepted—unlike Tillie, whose shyness prevents her from engaging with people. Beatrice thinks of herself as attractive and outgoing, but people in her community mock her behind her back and suggest she is mentally ill. This creates a problem with Ruth seeing her mother as a role model. Like Betty, Ruth is very aware of other peoples' opinions of her and is vulnerable to them.
An example is that people have been known to call Beatrice "Betty the Loon," and this remark is overheard by Ruth at school. Ruth repeats it to insult her mother when the two are arguing over the science fair. Ruth's illness makes her dependent on others, though. This causes her to feel resentment, and she may be worrying she'll turn out like her mother, as her condition makes her vulnerable to taunting like Betty was. Some adjectives to describe their relationship might include problematic, toxic, complicated, dysfunctional, dependent, antagonistic, intense, and volatile.

What is Malcolm Gladwell's argument in the book Outliers? How can I write a five-paragraph essay on it?

Malcolm Gladwell argues that the reality behind any success story is very different from the long-held assumptions that many people possess around the notion of success. Success involves a highly complex set of circumstances, argues Gladwell, and though luck and hard work can often contribute to success, other conditions must also be met for a success story to take place.
When formulating your own thesis statement about success, make sure your argument is debatable; re-stating Gladwell's argument as your own will not work for a five-paragraph argumentative essay. Some ideas you might consider exploring in your own argument include the role of race and/or class, whether or not education is as important as people make it out to be, or even the potential of a role model's ability to impact a person's chances of success. Plenty of evidence around these issues is available to you in Gladwell's book.
Once you formulate an original and debatable thesis statement, create a brief outline of your three body paragraphs. Each of these paragraphs must start with a topic sentence that addresses some aspect of your overarching thesis statement; each topic sentence should also summarize the argument contained in that particular body paragraph. Every sentence in the paragraph must connect back to the topic sentence. Once you have your outline ready, look for quotes that support your ideas. Paraphrase them so that you know you understand the quotes you are using as evidence, and organize your quotes so that you have two to three quotes per body paragraph.
Finally, write your conclusion and introductory paragraphs. Many writers struggle when they try to write their introductions before their body paragraphs; writing the introduction after the body paragraphs ensures that you know what you are introducing and streamlines the whole process. Your conclusion can make a point about your essay that leaves your reader with a final interesting thought—but be careful not to end your essay with a new argument or angle to your argument.

The main argument of the book is the idea that successful people are made, not born. Gladwell analyzes the lives and habits of numerous successful individuals from different fields and professions to analyze what has made them successful. In the end, he came to the conclusion that the majority of success is earned, not inborn, even if there is a certain amount of luck or fair fortune that plays a part in their success.
Gladwell coins the concept of the “10,000 hour” expert—the idea that if you spend 10,000 hours on any activity, you will become an expert on it. In the end, he reasons that if you become an expert in a marketable area, you will be successful by putting forth the necessary effort. You can apply this to an essay by analyzing the aspects of success that he discusses—the small amount of luck that takes place, the selection of a marketable skill, and the dedication to honing one’s trade.

Outliers by Malcolm Gladwell is a book that attempts to demythologize the notion of the extraordinary individual by showing the structural factors behind individual success. He argues that individual success stories can be explained by a combination of hidden advantages, cultural advantages, and extensive practice.
A five-paragraph essay consists of an introductory paragraph asserting a thesis, three body paragraphs, each supporting some aspect of the thesis, and a concluding paragraph showing how the body paragraphs confirm the thesis set out in the introduction.


Introduction: Summarize the overall argument of the book concerning "outliers" being explicable through a combination of external preconditions and extended practice.

Body Paragraph 1: Discuss the structural advantages that contribute to success, such as the birth dates of Canadian hockey players.

Body Paragraph 2: Discuss the cultural legacies which can affect success or failure.

Body Paragraph 3: Summarize Gladwell's account of how a minimum of 10,000 hours of practice affects success.

Conclusion: Conclude by showing how the three factors covered in the body paragraphs can explain the success of outliers.

Outliers is a study of extraordinarily successful people. In very simple terms, its author, Malcolm Gladwell, is attempting to explain why these people have been able to achieve as much as they have. His argument is that very successful people are not born that way, but rather made by hard work. This is the famous "10,000 hour" concept that he introduces; only through 10,000 hours of practice, training, hard work in short, can people achieve that level of success. But at the same time, and this is the most important argument of the book, people have to have the means to put in this kind of effort. Brilliant athletes, musicians, and inventors have to have supportive parents and live in societies that support this kind of effort. One can't spend 10,000 hours practicing on guitar if one is hungry, after all. This is Gladwell's thesis in his words:

People don't rise from nothing. We do owe something to parenting and patronage. The people who stand before kings may look like they did it all themselves. But in fact they are invariably the beneficiaries of hidden advantages and extraordinary opportunities and cultural legacies that allow them to learn and work hard and make sense of the world in ways that others cannot. 

One way to go about writing about it (i.e. coming up with three body paragraphs) would be to look at some of the specific examples he uses (Bill Gates, the Canadian hockey players, the Beatles, or Robert Oppenheimer) of people who have been recognized as "outliers." Focus on the ways that he uses them to illustrate his thesis. You might also use some "negative" examples, such as Chris Langen, the man with a 195 IQ who works on a ranch and has not achieved the fame and success of someone like Oppenheimer or Einstein. He did not have the encouragement or have the same family support and education that these men had.
https://books.google.com/books/about/Outliers.html?id=3NSImqqnxnkC&printsec=frontcover&source=kp_read_button