How do we use solvents in our lives?

A solvent is a substance that is used to dissolve another substance (called solute) into it. For example, when we mix salt and water together, salt is the solute and the water is the solvent because water dissolves the salt.
Here are some examples of solvents in our daily lives:
1. As nail polish remover: acetone is a commonly used solvent in nail polish removers.
2. Rubbing alcohol: isopropanol is commonly used as rubbing alcohol for degreasing surfaces.
3. Oils, such as turpentine and gasoline (petrol): are commonly used for removing oily deposits.
4. Dry-cleaning chemicals: TCE (trichloroethylene) was the most commonly used chemical for dry-cleaning of clothes. Trichloroethane is another alternative for the same.
5. Water: the most important solvent in our lives. It dissolves minerals and is also used for cleaning purposes (as well as many other uses it serves in our daily lives).
Thus, we commonly use solvents in our day-to-day life for cleaning purposes and also for transport of minerals and nutrients (through water), and so on.

How is masculinity treated in Chopin's 'The Awakening'?

As presented through the main male characters of Leonce Pontellier and Robert Lebrun, masculinity is portrayed in The Awakening as domineering and uncomfortable with challenges to its power.
Leonce Pontellier is a wealthy man with a fairly high social position. He expects his wife Edna to follow all of the rules of social propriety and to fulfill her duties as a wife and mother as well as a member of the upper class. After a somewhat carefree summer in Grand Isle, the family returns to New Orleans and to their "normal" lives. At this point, though, Edna has progressed and evolved as a character and no longer wants to play the role for which she is supposed to be fitted. For example, she goes out on walks and does what she feels like doing when she is supposed to be home receiving visitors from the Pontelliers' social class. Leonce chastises Edna for not following these norms. She becomes bolder and acquires a smaller house—the pigeon house—where she decides to live on her own, disgusted by the extravagance and obligations of Leonce's family house. Leonce is, of course, embarrassed and concerned about his reputation as a man and a husband. He is also told at one point by Edna's father that he needs to crack down on her and control her more, as though she is a piece of property or an animal. Masculinity, through Leonce, is portrayed as not flexible or open to challenges and also domineering in the sense that he feels it is his right to control his wife and force her to fulfill certain duties.
Robert Lebrun is a different character from Leonce in many ways; he seems more sensitive, and maybe even more feminine to an extent. However, it turns out that Robert is not so different from other men of his class after all. It is implied that he has an affair with a young Mexican girl, which is accepted (seemingly by all, other than Edna, who is offended because she loves him), and this points to the double standard that men can have sexual experiences outside of marriage while women cannot (contrast this to the way women are judged when they spend time with Alcee Arobin). The best piece of evidence that Robert is basically like other men of his time and class occurs after he and Edna confess their feelings for one another near the end of the novel. Robert says that he wants to marry Edna; in other words, he wants to possess her. Edna is disappointed that Robert still thinks in such traditional ways about the potential relationships of men and women. She finds marriage and gender roles restrictive, but Robert wants to put her in the role of wife all over again. This shows that the male characters are conservative and enjoy their power over women; they want to maintain control over their wives and still think (if subconsciously) of women as belongings rather than independent people with their own wills and desires.

Masculinity is treated as something that is somewhat fragile, especially in the face of an empowered woman.  In Grand Isle, when Edna does not leap from her sleep to listen to Leonce's tales of the club and that night's game, he seems to feel that his position is threatened by her failure to play her role.  He lies and says that one of their sons is sick, and he reproaches her for her inattention as a mother (when what he is really irritated with is her inattention as a wife).  On another, later evening, Edna will not come inside and prefers to remain in the hammock alone rather than come in and give in to her husband's sexual advances, as she becomes aware that, in the past, she would simply have done as he'd asked.  With his masculinity threatened by her refusal, Leonce comes outside and refuses to go in as well, as if to make it seem like it is he who is refusing Edna and not the reverse.  
Likewise, Robert Lebrun's masculinity cannot handle the unconventional relationship that Edna proposes near the novel's end.  He hopes that Leonce will divorce her and that he and Edna can get married and be accepted by society; however, Edna sees that this can never happen and also expresses her desire that it not happen, even if it could.  Who would Robert be if he could not perform his masculinity in the way that his society tells him it should be performed: as a husband to a conventional wife and not simply the lover of a disgraced woman?  He does not know, and he cannot imagine it, and so he leaves her, this woman he obviously loves.
This seems to be why Edna's failure to be feminine in the proper way is so threatening: it prevents the men in her life from being masculine in what society has dictated to them to be the proper way.  Thus, we see that their masculinity is fairly fragile, because it cannot withstand one woman's deviation from her socially-prescribed role.  Femininity and masculinity seem to be rooted together, and if the former shifts, the latter will crumble.  

Is there justice in Maycomb County?

One would have to say no. Tom Robinson has been falsely convicted of the rape and assault of Mayella Ewell. This wasn't even a borderline case; it was physically impossible for Tom to have carried out the deed. But in Maycomb County, as elsewhere in the Deep South, that doesn't really matter, because the trial of a black man accused of rape has less to do with achieving justice and more to do with reinforcing the dominance of the white race.
As soon as Tom was accused of the crime, the vast majority of people in Maycomb made up their minds that he was guilty as sin. Why? Because Tom is black, and in the South at that time, the prevailing prejudice held that black men were always on the lookout for white women to rape and as such needed to be kept firmly in line by the law.
Mayella's accusation, though patently false, is tantamount to a conviction in such a deeply racist society. The members of the jury—all but one of them, anyway—have already made up their minds as to Tom's guilt before even setting foot inside the courtroom. They know what's expected of them; they know that their deliberations have absolutely nothing to do with any meaningful notion of justice, but everything to do with keeping African Americans firmly in their place.

Judging from the verdict of the Tom Robinson trial, one could argue that there is no justice in Maycomb County. Tom Robinson becomes the victim of racial injustice after being wrongly convicted of assaulting and raping Mayella Ewell. During the trial, Atticus proves that Bob and Mayella's stories were fabricated and shows that Bob had the motivation to assault his daughter. Atticus also proves that Tom Robinson could not have inflicted the injuries to Mayella's face and neck because of his obvious physical handicap. Despite Atticus's efforts, the racist jury wrongly convicts Tom Robinson of assaulting and raping Mayella simply because he is black. This blatant example of racial injustice is enough evidence to state that there is no justice in Maycomb County. In addition to Tom becoming a victim of racial injustice, the Old Sarum bunch is not punished for attempting to lynch Tom before the trial, and Bob Ewell is allowed to freely roam throughout the community after committing obvious perjury.

Calculus of a Single Variable, Chapter 9, 9.10, Section 9.10, Problem 70

From the table of power series, we have:
(1+x)^k = 1 +kx+ (k(k-1))/2! x^2 +(k(k-1)(k-2))/3!x^3 + ...
To apply this on the given integral int_0^0.2 sqrt(1+x^2)dx , we let:
sqrt(1+x^2) =(1+x^2)^(1/2)
Using the aforementioned power series, we may replace the "x " with "x^2 " and "k " with "1/2 or 0.5 ".
(1+x^2)^(1/2) =1 +0.5x^2+ (0.5(0.5-1))/2! (x^2)^2 +...
= 1 +0.5x^2 -0.25/2! x^4 +...
= 1 +x^2/2-x^4/8 +...
The integral becomes:
int_0^0.2 sqrt(1+x^2)dx = int_0^0.2[1 +x^2/2-x^4/8 +...]dx
To determine the indefinite integral, we integrate each term using Power Rule for integration: int x^ndx =x^(n+1)/(n+1) .
int_0^0.2[1 +x^2/2-x^4/8 +...]dx = [x +x^3/(2*3) -x^5/(8*5) +...]|_0^0.2
= [x +x^3/6 -x^5/40+...]|_0^0.2
Apply definite integral formula: F(x)|_a^b = F(b) - F(a) .
F(0.2)=0.2 +0.2^3/6 -0.2^5/40+ ...
=0.2+1.3333x10^(-3)-8x10^(-6)+ ...
F(0) =0+0^3/6-0^5/40+ ...
= 0+0-0+...
All the terms are 0 then F(0)= 0.
We can stop at 3rd term (8x10^(-6) or 0.000008) since we only need an error less than 0.0001 .
Then,
F(0.2)-F(0) = [0.2+1.3333x10^(-3)-8x10^(-6)] -[0]
= 0.2013253
Thus, the approximated integral value is:
int_0^0.2 sqrt(1+x^2)dx ~~0.2013

Why does Mr. White say that Herbert’s death is particularly hard?

The next day after Mr. White uses the monkey's paw to wish for two hundred pounds to pay off their mortgage, he and his wife receive the tragic news that their son Herbert has died in an unfortunate work accident. In Part Two, a messenger from Herbert's place of work visits the White's home and informs them that their son lost his life when he got caught in a piece of machinery. The messenger also mentions that the Whites will receive two hundred pounds as compensation for Herbert's death. After learning about his son's death, Mr. White comments, "He was the only one left to us. . . It is hard" (Connell, 9). These two sentences are significant and indicate that Herbert was not their only child. It is also written that Mr. and Mrs. White have been married for nearly forty years and have apparently endured many hardships. Mr. White's comment also indicates that they have outlived all of their children. Overall, Herbert was their last remaining child alive, which makes his death extremely difficult for Mr. and Mrs. White.

Mr. White says that Herbert’s death is particularly hard because “He was the only one left to us.” Although Mr. White’s explanation is short, the implication is that he is their last remaining child, and their other children have died. Elsewhere in the story we learn that Mr. White and his wife have been married for approximately forty years, and based on the rest of the story, it seems that they have faced many hardships. It appears that Herbert’s death is the death of their last surviving child.
But there is an additional reason that it is particularly hard for Mr. White: Mr. White made the wish that resulted in Herbert’s death. Although this reason is not explicitly provided by Mr. White when he explains that it is hard, it is important to keep in mind that Mr. White is, essentially, responsible for Herbert’s death.

Discuss the difference between acids, alkalis, and bases. Discuss and compare the reactivity of alkali metals with those of alkali earths.

Differences between acids, alkali, and bases:
Acids are chemicals that have a pH of less than 7.0, while bases are substances that have a pH of more than 7.0.
Acids can also be thought of as chemicals that donate protons, while bases are chemicals that accept protons.
An acid can also be thought of as a chemical that can neutralize a base. Similarly, a base can neutralize an acid.
Acids turn litmus paper red, while bases make litmus paper turn blue.
Some examples of acids are sulfuric acid, hydrochloric acid, nitric acid, and so on. Some examples of bases are sodium hydroxide, potassium hydroxide, and so on.
Acids generally taste sour, while bases have a bitter taste.
Alkalis are the bases that are water-soluble, which means that they dissolve in water. In other words, not all bases are water-soluble, and only the water-soluble bases are known as alkalis. An example of an alkali is sodium hydroxide. It is a base because it can neutralize an acid, and because it is water-soluble, it is an alkali. An example of a base that is not alkali is copper oxide. This chemical can neutralize an acid, but it is insoluble in water.
In other words, all alkali are bases but not all bases are alkalis.
Also, an alkali has a hydroxide group, while a base has an oxide group in it.
Reactivity of Alkali metals with Alkaline Earth metals:
Alkali metals are group I (or group IA) elements in a periodic table of elements. These include metals such as sodium, lithium, potassium, and so on. Alkaline earth metals are group II (or group IIA) elements and include metals such as calcium, magnesium, barium, and so on. Both the alkali and alkaline earth metals are very reactive due to the loosely associated valence electrons.
In case of alkali metals, only one electron is present in the outermost shell. It is easier to lose this electron to attain a filled electronic configuration. In case of an alkaline earth metal, there are two valence electrons. Since two electrons are a little more difficult to lose when compared to one electron, alkaline earth metals are less reactive when compared to the alkali metals. For example, it is easier for a sodium atom to lose one electron than it is for a magnesium atom to lose two electrons. This means that sodium is more reactive when compared to magnesium.
If we go down a group in the periodic table, the reactivity increases. This is mostly due to an increase in the size of atoms, which results in less nuclear attraction for the valence electrons. This makes the electrons easier to lose, which results in an increase in the reactivity of the atom.
Hope this helps.

What were Sparta's cultural achievements and legacy?

The cultural achievements of Sparta include a well-organized society, gender empowerment, and military prowess. Sparta was made up of three main communities: Spartans, Perioeci, and Helots. The Spartans held the administrative and military positions. The Helots were Greeks captured from other lands conquered by Sparta. They were used as slaves for menial jobs, such as cleaning, farming, and other house chores. The Perioeci were passers-by, mostly traders that visited Sparta to make money.
In all of Greece, Sparta was one of the few areas where women were given the freedom to go to school, own property, and engage in sports.
The government of Sparta paid for the Spartan's military training. It was compulsory for all able-bodied male children to begin military training when they were 7 years old. The training taught them to be patriotic, obedient, and learn to endure tough times. They would become secret police officers by 13, and then graduate to full-time soldiers by 20.
Sparta's legacy was that they had one of the strongest armies in the world at the time.
https://www.history.com/topics/ancient-history/sparta

Through the years, Hollywood has trumpeted the military acumen of the ancient Spartan people, but the city-state also enjoyed tremendous cultural advancement. The Spartans built a very well organized culture which combined elements of democracy, oligarchy, and monarchy. They were strong architects and builders as seen in their remarkable temples, government buildings, and monuments. While the Athenians are generally regarded as artists, the Spartans were known to be gifted in the musical arts including dancing. Their sculpting ability was the envy of the ancient world, particularly their work with bronze. The Spartans are also on the historical record as being respected poets and the oldest love poem in the world is believed to be one written by a Spartan. The Spartans also created a very unique social structure that granted women a great deal of responsibility and respect.