Why did Lucy feel comfortable in the faun's cave?

In chapter two of C.S. Lewis' The Lion, the Witch and the Wardrobe, Lucy meets Tumnus, a faun who is in the service of the evil White Witch. In this chapter, Lucy shows her trustingness and naivety by visiting the home of a stranger.
The faun's home is delightful. The text says that "Lucy thought she had never been in a nicer place." It is a little cave with just two rooms: a sitting room and a bedroom. The cave has a carpet on the floor, two little chairs, a table, a dresser, a fireplace with a mantlepiece, and a shelf full of books. This home is cozy and cheery.
Though Tumnus is a spy for the queen, he is a very good and kind fellow. After Lucy becomes queen, she and Tumnus remain friends for the rest of her reign. He serves a simply wonderful tea with an egg, sardines on toast, buttered toast, toast with honey, and a sugar-topped cake. He tells Lucy stories of what life in Narnia is like and plays her music on his flute.
The plot to hand Lucy over to the queen reveals how wrong Lucy was to trust a stranger, but the joy that she enjoys in this cave demonstrates the childlike wonder that Lucy experiences as she explores this new land.

f(x)=log_4(x+2)-1 Graph the function. State the domain and range.

We are asked to graph the function y=log_4(x+2)-1 :
This is a translation of the graph of y=log_4x 2units left and 1 unit down.
The domain is x>-2 and the range is all real numbers. There is a vertical asymptote at x=-2 and the function is increasing and concave down on its domain.
Some points on the graph: (-31/16,-3),(-7/4,-2),(-1,-1),(2,0),(14,1).
The graph:

Discuss the relationship between love and hate in this tragedy.

The love Desdemona and Othello share is pitted against the seething hatred Iago feels toward Othello in this tragedy—and hate wins.
Othello and Desdemona truly love each other, despite their differences in culture, age, and race. Iago, who already hates Othello as someone he doesn't accept as worthy of having command over him, becomes even angrier and more violently hate filled when Othello promotes Cassio over him. The best way Iago can find to hurt Othello is to drive a wedge between him and Desdemona. He grasps that Othello's weak point is his insecurity about being lovable to such a woman, and so Iago goes after that weakness relentlessly.
We see that hate is the enemy of romantic love. A hateful character like Iago can't bear to see Desdemona and Othello contented and in love. But another enemy of love is insecurity. If Othello could have loved himself more—perhaps an impossible hope given the racist culture of Venice—Iago could not have manipulated him into killing Desdemona.
Further, sexism interferes with love. Othello, a military leader, is used to relying on the advice and insight of other men, so he doesn't communicate enough with Desdemona. This contributes to their tragic end.
The play also shows the pitfalls involved when good, pure-hearted people go up against an evil manipulator who will tell any lie or stoop to any level to achieve his ends. Desdemona and Othello fully expect that the people around them will share their own sense of truth and honor. They can't see what a vile person Iago is and are not prepared to defend against him.
The play shows that love is not only an isolated quality shared between two people but plays out in the context of a larger social reality, in which hate can be a destructive force. In this way, the play is similar to Romeo and Juliet, where larger hatreds contribute to the deaths of the main characters.

William Shakespeare explores love primarily through the characters of Othello and Desdemona, and hate primarily through Iago. Othello and Desdemona have a deep, passionate, committed love for one another. Desdemona has defied convention in order to marry Othello. Her father, Brabantio, loves his daughter and wants to see her happily wed. His racial prejudice, however, makes him suspicious of Othello’s motives and methods. While he never grows to love Othello, he begrudgingly accepts him as Desdemona’s husband. Othello’s love for Desdemona leads to such great jealousy that he cannot stand the idea of her being with another man or betraying him. Distraught when he realizes he has killed her, he takes his own life rather than live without her.
Iago seems to be what today would be called a sociopath, and he is possibly also a narcissist. He is incapable of loving anyone and treats his wife, Emilia, with contempt; he is totally self-centered. His motivation for hatred seems to be envy combined with arrogance, along with elements of racism. Iago’s resentment at serving a black superior officer feeds into his negative feelings, which are compounded when Othello rejects him for a promotion. It may be as well that Iago hates the idea of a black man marrying a white woman. Factors that might seem minor to another man seem major to Iago, who develops such hatred for Othello that he is determined to destroy him. Paradoxically for a man who cannot love, he understands the kinds of passions love can stir up and uses them against Othello.

Throughout the play, Shakespeare illustrates the passionate and often misguided emotions of love and hate. Love is illustrated by Othello's strong affection for Desdemona. Despite Othello's passion for Desdemona, his love quickly turns to hate once Iago convinces him that Desdemona is having an affair with Michael Cassio. Othello's capricious disposition emphasizes how easily love and hate can transform into one another. Since both emotions are manifestations of deep desires and unaffected by logic, love and hate are portrayed as interchangeable throughout the play. Othello's unhinged jealousy manifests into hate as he loses the ability to control his emotions. While his strong passion remains constant, Othello alters its direction towards hate as he brutally murders his beloved Desdemona. Overall, both emotions are represented as fickle, unreliable manifestations of passion; they can be easily interchanged and are in no way connected to logic.

Who is Sherrena in Evicted?

Sherrena is one of the landlords in the book Evicted. She houses the author, among many others. After years as a teacher and a failed attempt at starting a daycare business, Sherrena decides to take on real estate, buying up properties in inner-city Milwaukee and renting them out to low-income African Americans.
Because of the nature of real estate in the city of Milwaukee, Sherrena realizes she can make a substantial amount of money renting to impoverished African-Americans, charging exorbitant rates for sub-par housing because the individuals have no other options. Since many of the nicer rental facilities will not accept individuals with criminal histories or low credit scores, Sherrena and renters like her essentially can set prices however they want and don't need to maintain their housing.
Sherrena is like many of the other property managers in the area who make a large profit from the misfortune of their tenants. Because she makes more money from low-quality apartments, she is earning a hefty sum for every renter that she keeps in squalor. She evicts many of her tenants, including Lamar, Arlene, Patrice, Doreen, and Crystal. While she does show some care for those renting from her, in the end she treats the situation as strictly business and doesn't appear to lose any sleep over the evictions.

Published in 2016 and written by American sociologist Matthew Desmond, Evicted: Poverty and Profit in the American City is a work of non-fiction about landlords and tenants in Milwaukee, Wisconsin.
Sherrena Tarver is one of the African American landlords that Matthew Desmond profiles in the book. A former schoolteacher, she originally started a daycare business before realizing she could make more money as a property landlord. Sherrena owns a number of properties on the North Side of Milwaukee, a run-down and principally black neighborhood where white people don’t tend to buy.
Due to the lack of affordable housing, she is able to rent out inferior properties to desperate people who would otherwise be homeless. Safe in the knowledge that she has a steady stream of potential tenants waiting for homes, she is also able to be an uncompromising landlord, and she does not think twice about evicting existing tenants if needed. Sherrena works hard, is very ambitious and, as her property portfolio grows, her husband, Quentin, leaves his job as a police officer to become her property manager. Due to her success, she and Quentin are able to live in the wealthier part of the city and travel for pleasure regularly.

Sherrena is one of the book's main characters. She's an African American woman who makes a good living as a professional landlord. Sherrena owns a string of properties in the run-down black neighborhoods of Milwaukee which she rents out to hard-pressed tenants who have literally nowhere else to go. The chronic lack of affordable housing in the city means that landlords like Sherrena can make a lot of money out of letting sub-standard properties in rough areas where no one would choose to live.
The structural imbalance of the broken housing market gives landlords like Sherrena the whip hand over their tenants. As she can always count on a steady stream of potential clients desperate for a roof over their heads, Sherrena can afford to evict her existing tenants at the drop of a hat, safe in the knowledge that she won't be out of pocket. It's through the character of Sherrena that Matthew Desmond makes one of his key points: the fundamentally broken housing system actually incentivizes evictions and poor housing maintenance. It doesn't matter how dilapidated Sherrena's properties are or how dangerous the surrounding neighborhoods may be; she is guaranteed to make substantial sums of money as a landlord. As Sherrena puts it herself, when trying to encourage white landlords to invest in black neighborhoods: "The 'hood is good."

Sherrena is the ambitious landlord in Evicted. She met her husband, Quentin Tarver, when he pulled her over at a traffic stop. She started off as a schoolteacher but left that job to start a daycare. That did not pan out the way she had planned, so she began buying cheap properties with high rents and found that she was able to make a lot of money that way. She was making so much that her husband quit his job to become her property manager.
As Sherrena continues to make money, she also decides to start rounding out her income by helping her tenants with other professional things—for a fee. She is a very ambitious businesswoman who is always looking for new ways to expand.

Sherrena Tarver is the landlord of several of the individuals in Evicted, including Matthew Desmond, the author. Sherrena was originally a teacher, and she met her husband, Quentin Tarver, when he pulled her over at a traffic stop. After several years together, Sherrena was feeling dissatisfied with her job and attempted to start a daycare business. When her daycare venture failed, Sherrena set her sights on real estate and began purchasing run-down properties in urban Milwaukee. Sherrena quickly discovered that she could make a lot of money renting to poor black individuals. Apartments in the run-down inner city can often be rented at the same rates as properties in nicer areas. However, inner-city apartments do not have to be well maintained, because prospective tenants are poor and desperate for any type of housing. In fact, many poor or black individuals are completely shut out from nicer neighborhoods, where buildings often reject individuals with past evictions or criminal records. Sherrena’s real estate business quickly grew, and she began to manage multiple properties. Her husband, Quentin, eventually left his job as a police officer to become a property manager in their new buildings. Sherrena is not wholly uncaring, but it is impossible to ignore the fact that she profits from the misfortune of her tenants. Ultimately, Sherrena evicts Lamar, Arleen, Patrice, Doreen, and Crystal.

How did Thomas Paine's "Common Sense" help the American Patriots win the war against Britain?

Thomas Paine wrote a pamphlet called Common Sense that was published in January 1776. In this pamphlet, Thomas Paine explained why the colonists should become independent from Great Britain. This pamphlet was an important factor in gaining support for the fight against Great Britain that was about to occur.
Before this pamphlet was written, there were many people in the colonies who thought that the colonists shouldn’t break free from Great Britain. These people felt it was unlikely the colonists would win. Some of them felt that Great Britain was justified in governing the colonies as they saw fit to do. Other people feared there might be chaos if the colonists were to win the war and then to begin governing themselves. This pamphlet changed the narrative.
Thomas Paine wrote this pamphlet in a way that was understandable to the colonists. After reading this pamphlet, more colonists became convinced that they should declare independence from Great Britain. They began to see that the British were really mistreating them. They began to believe that declaring independence was the proper course of action. Without this pamphlet, it is possible the colonists wouldn’t have had enough support from their own people to successfully launch and win the Revolutionary War.
http://totallyhistory.com/common-sense-pamphlet/

https://www.history.com/this-day-in-history/thomas-paine-publishes-common-sense

If the play Twelve Angry Men was set in modern times, what are three ways that it would be different?

This question is very much an opinion based question. It is up to you to decide how this play might be changed for modern day audiences. Some of the changes could be huge, while other changes could be incredibly minor changes. Your main job is going to be to adequately justify why you think those changes would/should be made. Here are a few changes that I think might be changed for modern day audiences.
The jury wouldn't be comprised of only men. The jury would contain women as well. At one point in American history, women were not allowed to be jury members; however, that is not the case anymore. A modernized play would likely go for a balanced jury of 6 men and 6 women.
The previous change would almost assuredly mandate a title change to 12 Angry Jurors.

The jury would be comprised of only women, and the play would be called 12 Angry Women. This is not that far of a stretch. Swapping out the previous all-male foursome of the Ghostbusters crew happened in the recent remake of the film, and all four of the new Ghostbusters are female. A female cast reboot of Ocean's 11 is also currently in the works.
The murder weapon would be a gun. There is no reason that a knife wouldn't still work for modern day audiences, but with as much as gun control is in the media, it makes sense that a director or writer would want to bring gun violence into the spotlight.

How does Achebe vividly convey Obi's changing feelings towards Nigeria in No Longer at Ease?

The answer to your question has to do with Achebe's ability to use both direct and indirect characterization. Achebe uses these methods of characterization to highlight the character of Obi and how he changes throughout the course of No Longer at Ease. Achebe sometimes directly tells us about Obi’s changing feelings about Nigeria (which is part of direct characterization). Other times, Obi speaks and acts accordingly (which is part of indirect characterization). With direct characterization, we are told about the personality of the character. With indirect characterization, we are shown the personality of the character.
Obi is enamored with Nigeria at the beginning of the novel. Achebe uses both indirect and direct characterization to show this to the reader. Obi is happy to be in London studying to better his life and his education; however, he misses his homeland. The narrator directly tells us about Obi’s feelings:

Four years in England had filled Obi with a longing to be back in Umuofia. This feeling was sometimes so strong that he found himself feeling ashamed of studying English for his degree. He spoke Ibo whenever he had the least opportunity of doing so. Nothing gave him greater pleasure than to find another Ibo-speaking student in a London bus. But when he had to speak in English with a Nigerian student from another tribe he lowered his voice.

Through this direct characterization, the reader can see that Obi "longs" to be back in Nigeria. This example of direct characterization is especially pertinent in that Achebe actually uses the word “feeling” multiple times in regards to Obi. Obi even feels "ashamed" when he considers himself to be studying English instead of Law. Obi is so proud of his idealistic Nigerian ideals that he lowers his voice when speaking English to another Nigerian student. This is an example of direct characterization. Achebe tells us of Obi’s exact feelings here. Achebe describes all of this to the reader instead of using Obi's own words. However, there are some examples of indirect characterization when Obi recites his own poetry about Nigeria. These poems reveal Obi’s idealism about Nigeria through Obi’s own word choice. In these poems, Obi focuses on Nigeria's natural beauty and the honorable values among its people. At this point in the book, Obi truly wants to believe that the corruption among the learned in Nigeria can be overcome.
By the end of No Longer at Ease, Obi has lost his idealism completely. Obi has gone back to Nigeria and become one of those corrupt academics by accepting bribes. Obi has set aside his idealistic poetry and has just tried to "get by." Obi tries to convince himself that his financial situation excuses the "necessary" practice of accepting bribes. At one point, Obi tells the reader about his disillusionment and lack of idealism that he once had:

The impatient idealist says: "Give me a place to stand and I shall move the earth." But such a place does not exist. We all have to stand on the earth itself and go with her at her pace.

Obi, in fact, is only an idealist at the beginning of the novel. His poetry and his actions at university prove this. However, here we are shown Obi’s feelings only through his own words instead of being told directly that Obi has lost his idealism. However, with the help of Obi’s own words and indirect characterization, he tells us that this idealistic "place" actually "does not exist." Obi has given up and become a passive character who accepts the corruption as it comes. The rationalization here is that Obi attempts to "stand on the earth" by going "with her at her pace." In this case, the earth's "pace" now requires Nigerian academics to participate in the corrupt practice of bribery.