Who is the character that is torn between his/her duty and what he/she feels he/she should do?

Claude Frollo, Archdeacon of Paris, is definitely a character in the story who's torn by conflicting impulses. It is he who discovers the abandoned baby Quasimodo and raises him as his own son. One could say that he does this out of duty. But despite this sense of duty, and despite his position of authority in the church, Frollo frequently finds himself torn between what he ought to do and what he really wants to do.
As part of his duty as an Archdeacon, Frollo must remain celibate. However, the demands that this imposes on him conflict with his passionate desire for Esmeralda. Indeed, it is this desire that causes Frollo to act in ways that he knows he really shouldn't. He orders Quasimodo to abduct Esmeralda after she spurns the Archdeacon's advances; he does nothing to intercede on Esmeralda's behalf when she's tortured on a trumped-up charge of being a witch; he stabs Phoebus in a jealous rage as Phoebus is about to make love to Esmeralda.
Yet deep down, Frollo knows that he really shouldn't be acting this way; this is not how a senior member of the church hierarchy should behave. His inner conflict between his burning passions and his sense of duty drives him to madness. Even when he does the right thing, such as by rescuing Esmeralda from the cathedral, he only does so for purely selfish reasons. His final abandonment of Quasimodo, the man he brought up as if he were his own son, represents the point of no return for Frollo. The battle between duty and desire is now over, and desire has finally prevailed.

In the novel The Bronze Bow, what does Hezron say is stronger than all the power in Rome?

Hezron, Joel's father, is a Rabbi, or teacher of the Jewish Law. He is also a Pharisee, a member of a strict sect of Jewish leaders whom Jesus said valued outward observance of the law over inward qualities such as mercy, justice, and faith. When Daniel visits Joel at his home, he stays for their meal and engages in an uncomfortable conversation with Hezron.
The man actually knew of Daniel's father and his fate at the hands of the Romans. Instead of showing sympathy, he states coolly, "He was a good man, your father, but a rash one." The conversation turns to the one topic that is always uppermost in Daniel's mind: the Roman occupation of Israel. Hezron states that he is grieved about the captivity of the Jews just as Daniel is. However, he views the Roman presence as a punishment from God on the Jewish nation and believes that they must bear it patiently. He compares the ineffectiveness of the Zealots to "buzzing mosquitoes."
He then tells Daniel what he thinks is more powerful than Rome, namely, "the Law, given to Moses and our fathers." Long past the day when the Romans have "vanished from the earth," he says, the Law will remain. This is small consolation to Daniel since it envisions a lifetime of subservience to people he despises. Hezron tells Daniel to "go in peace" but commands him to never return to their home. He has given Daniel no hope to help him deal with his inner turmoil.

When Hezron says that the Law of Moses is more powerful than the whole might of the Roman Empire, he is emphasizing the enormous spiritual strength that the Jews derive from their religion, which sustains them throughout the period of Roman occupation. Here on earth the Romans may enjoy military superiority, but theirs is merely a temporal authority, which, like all the things of this world, is transient. Contrast that to the Law of Moses, whose authority is truly timeless and transcendent. Hezron is scathing of the zealots because they adopt the same attitude as the Romans. They think that what really matters in this world is the attainment and exercise of earthly power. As well as being wrong-headed from a practical standpoint, this attitude diverts the attention of zealots away from the most important thing of all for any Jew: fidelity to the Law.

In Chapter 5, Daniel gets permission from Rosh to travel to Capernaum to recruit Joel to join Rosh's band. Daniel visits Joel's beautiful home in the middle of the city and is invited to have dinner with his family. During dinner, Daniel expresses his hate and bitterness towards the Romans in front of Joel's father, Hezron. Hezron scolds Daniel for openly criticizing the Romans and tells him that he must learn to keep his thoughts to himself. Hezron then explains to Daniel that the Zealots do not take into account the numerous troops and massive force that Rome possesses. Hezron proceeds to tell Daniel that Israel has one great strength mightier than Rome: "the Law, given to Moses and our fathers" (68). Hezron believes the Law will remain even after the Roman Empire is reduced to nothing and that the Jews must remain loyal to the Law. 

How was Reverend Hale portrayed in the movie vs play?

In the 1996 film version for which Arthur Miller wrote the screenplay, Reverend Hale is portrayed pretty closely to the way the playwright wrote his part for the stage. In the scene when Hale arrives in Salem, he is smug and seems to enjoy showing off his prowess in detecting the presence of witchcraft. When the girls confess and then begin naming witches at the close of the first act, he is quite triumphant in the film version.
The chief difference in the stage and screen versions comes after he visits the Proctors' farm and hears that the court has ordered the arrests of Martha Corey, Rebecca Nurse, and Elizabeth Proctor. He tries to remain calm, but it is quite clear in Rob Campbell's acting in the film version that his frustration with Hathorne and Danforth mounts. He raises his voice quite loudly when he protests in open court that Abigail has "struck him [as] false."
Also in the film version, it is clear that Hale intends to abandon the court when he rides away on horseback following John Proctor's arrest at the end of act 3. The look he gives the townspeople and officials is both withering and regretful. This scene is not part of the stage play, and so his feelings about the proceedings are only declaimed as "I quit this court" as act 3 ends onstage.
In both the stage play and the film version, Hale is subdued in the fourth act. He understands that John and Elizabeth will not allow themselves to become pawns of a theocratic government desperate to be seen as infallible, and his demeanor is much quieter and resigned to the injustice.

There is not a notable difference between Reverend Hale in the play and the depiction of Reverend Hale in the 1996 film. Both characters embody a Reverend who seeks to do the Lord's work by removing Satan's presence in the world. Hale's additional education in witchcraft allows the residents of Salem to acknowledge him as a capable and credible source. His confidence in his work is apparent in both the play and the film. As the play (and the film) progress, Hale is increasingly troubled by the personal motives that drive the accusations. His doubt in the court and in the over-reliance on spectral evidence causes him great strife. Miller's description of Hale's epiphany is strong, but it is best seen in the film as the film provides the audience the opportunity to observe the facial reactions (bewilderment, scorn, condemnation) up close.

In the text, Reverend Hale comes to Salem believing so thoroughly in his own education and knowledge that he never believes for a moment that he could be taken in or tricked. This arrogance makes him vulnerable. He doesn't realize why Tituba might lie to him, what motives Abigail and the other girls might have for making up stories, and so he is taken in by their dishonesty. He is not a bad man, but he was a little too confident in himself and his abilities. Later, in Act Four, when Hale returns to Salem to counsel the convicted to confess a lie, he agonizes over his role in the trials, how his confidence amounted to complicity. In the 1996 movie, directed by Nicholas Hytner, Rob Campbell portrays Reverend Hale, and he does a good job of capturing these most important elements of Hale's character. He is portrays Hale's confidence well, the confidence that crumbles as the play progresses, and he allows Hale to continue to be sympathetic while, simultaneously, showing how even his behavior helped to permit the tragedy to occur.

Different readers and movie viewers are perhaps going to feel differently about how Hale's character compares between Miller's version and Hytner's film version. Personally, I feel that the movie version of Hale sticks quite closely to the play's version of the character. Hale shows up in both versions as an incredibly confident and self-righteous person. He believes in witchcraft, and he believes that he is one of the men than can and should purge Salem of witches. By the end of the play, he is a broken and cynical man. He has lost all faith in the law, and he counsels the accused to confess to a lie in order to save their lives. This happens in the movie as well, and I believe that actor does a great job at conveying Hale's passion for valuing life as God's most precious gift. It's really good that the movie got this character right because, after John Proctor, I believe he is the most complex character.

What is the meaning of the play in a feminist context?

Susan Glaspell's play Trifles is charged with feminist meaning. Its feminist themes come through in the condescension of the male characters towards the female characters, the gender roles, and the dilemma of justice in a patriarchal society.
The men in the play, especially the county attorney, speak to the women with condescension. All three men mock the women for being concerned about Mrs. Wright's jars of preserves that have frozen and cracked. Mr. Hale observes that they worry about "trifles" regularly, and the county attorney says, patronizingly, "And yet, for all their worries, what would we do without the ladies?" He then observes that Mrs. Hale is "loyal to your sex." The men laugh at the women's discussion about Minnie's plan for her quilt.
The play presents the clearly defined gender roles of the early 1900s. The men have occupations—farmer, attorney, sheriff. The women keep house and raise the children. When Mrs. Hale suggests that "farmers' wives have their hands full," the attorney responds by criticizing Minnie's poor "homemaking instinct." Women are also expected to be helpers to their husbands: The attorney remarks that "a sheriff's wife is married to the law." Despite the presumed superiority of the males, the women succeed where the men do not. Throughout the play, the men are the ones who are tasked with solving the crime, yet the women, by using their special intuitive skills and emotional intelligence, actually find the critical evidence the men overlook.
The most disturbing feminist theme of the play is the question of whether a woman can receive true justice in a male-dominated society. As the picture of Minnie Wright's lonely and oppressed life with John Wright becomes clear to Mrs. Hale and Mrs. Peters, they find it harder to reveal the evidence of Minnie's motive for murder that they have discovered. Although they know that "the law is the law," they also know that twelve men on a jury will not treat Minnie with understanding—they are not the "jury of her peers" that the Constitution guarantees. (Glaspell later wrote a short story version of this play titled "A Jury of Her Peers." At the time in which the play and story were written, women didn't serve on US juries.) It seems clear that Mrs. Wright did murder her husband, possibly because she feared that his temper would result in her neck being broken like the bird's if she didn't. In her patriarchal society, battered or abused women had few options for protection. Any concerns she might have expressed to law enforcement about her safety would probably have earned her a condescending laugh and pat on the head like those the county attorney so liberally doled out to women. At least if Minnie's case were to be tried in front of a jury of half women, she might have a chance of a reduced sentence. But Mrs. Hale and Mrs. Peters know she will appear before a male judge and an all-male jury and that she won't receive justice, so they take justice into their own hands.
Glaspell's short play brims with feminist insights about patronizing male attitudes toward women, rigid gender roles, and the lack of justice toward oppressed women.

Calculus of a Single Variable, Chapter 5, 5.2, Section 5.2, Problem 27

Solving for indefinite integral using u-substitution follows:
int f(g(x))*g'(x) dx = int f(u) du where we let u = g(x) .
In this case, it is stated that to let u be the denominator of integral which means let:
u = 1+sqrt(2x).
This can be rearrange into sqrt(2x) = u -1
Finding the derivative of u : du = 1/sqrt(2x) dx
Substituting sqrt(2x)= u-1 into du = 1/sqrt(2x)dx becomes:
du = 1/(u-1)dx
Rearranged into (u-1) du =dx
Applying u-substitution using u = 1+sqrt(2x) and (u-1)du = du :
int 1/(1+sqrt(2x)) dx = int (u-1)/u *du
Express into two separate fractions:
int (u-1)/u *du = int ( u/u -1/u)du
= int (1 - 1/u)du
Applying int (f(x) -g(x))dx = int f(x) dx - int g(x) dx :
int (1 - 1/u)du = int 1 du - int 1/udu
= u - ln|u| +C
Substitute u = 1+sqrt(2x) to the u - ln|u| +C :
u - ln|u| +C =1+sqrt(2x) -ln|1+sqrt(2x) |+C

What are the achievements of the United Nations Organization?

The United Nations (UN) has had a long and somewhat controversial history. Its supporters laud its accomplishments. Its detractors, including the United States, have sometimes excoriated it. Nevertheless, the UN has achieved quite a lot over the past seventy years, and it has been a positive influence.
One achievement of the UN is that it has endured since 1945. Its predecessor, the League of Nations, failed within two decades. But the creators of the UN learned from the League's unhappy experience and created a more robust and effective institution.
The Cold War was an impediment to the UN's effectiveness for its first half century. The world was divided into East and West, and agreement on any issue was problematic. The Soviet Union frequently used its veto in the Security Council. After the Cold War ended around 1990, the UN became more assertive and active.
In spite of East-West divisions, the UN took an active role in both the Korean War and the Suez Crisis (1956). Soldiers from many nations fought under the UN flag in Korea. The UN mediated the crisis that resulted from the Anglo-French attack on Egypt in 1956.
The UN has been active in peacekeeping operations, especially since the 1990s. The organization won the Nobel Peace Prize for its peacekeeping efforts in 1988.
A UN climate conference in 2015 produced the Paris Agreement. Signed by nearly two hundred nations, the accord seeks to reduce greenhouse gas emissions. President Donald Trump took the United States out of the Paris Agreement in 2017.
Today, it is hard to conceive of a world without the UN.

Since its inception back in 1945, the United Nations (UN) has accomplished innumerable successes across the world, especially through coordination with its agencies and other similar organizations. Some of its notable achievements include:
Maintaining Peace and Security
Through peacekeeping and conflict resolution initiatives across the world, UN has managed to restore peace and stability as well as reduce the casualties of war. One such case is that of Sierra Leone where UN peacekeepers between 1999 and 2005 contributed greatly to the end of the decade-long civil war.
Global Food Security and Aid
In addition to changing climate and weather patterns that affect food production, an ever-increasing global population faces the threat of food shortage. The World Food Program (WFP) has however been on the forefront with global food security initiatives. It is estimated that the UN feeds approximately 104 million people from 80 nations annually due to natural disasters, war, poverty, or health emergencies.
Fight against AIDS
Even though it cannot receive full credit for the strides made in the fight against this epidemic, the UN has played a critical role in the achievements made. The World Health Organization, Global Fund to Fight AIDS, and UNAIDS have initiated awareness, prevention, and treatment programs which have significantly reduced the number of deaths from AIDS and related opportunistic diseases. Between 2010 and 2016, the number of new infections in adults and children reduced by 11% and 47% respectively. Also, the number of HIV related deaths since the peak of the epidemic in 2005 had reduced by 48% by 2016.
UN’s achievements span across all the facets of humanity whether politics, economy, health, environment, protection of children, women empowerment or human rights.
https://www.telegraph.co.uk/news/worldnews/europe/switzerland/11700969/UN-at-70-Five-greatest-successes-and-failures.html

https://www.unaids.org/en/resources/fact-sheet

There are several successes of the United Nations. One success was keeping South Korea independent after North Korea attacked them without provocation in 1950. The United Nations put together a fighting force of soldiers from several countries, led by the United States, to force North Korea out of South Korea. South Korea remains independent today.
The United Nations helped save the pyramids in Egypt. When there was a proposal to build a highway that would endanger the pyramids, the United Nations acted to divert the building of the highway so the pyramids would remain safe.
The United Nations has worked to eliminate some diseases and to protect the environment. The United Nations worked to wipe out smallpox with a vast immunization campaign. The United Nations also worked to get countries to work together to protect the ozone layer by getting countries to sign an agreement to reduce carbon emissions.
The United Nations has also worked to help children. The Children’s fund of the United Nations works to protect the rights of kids.
The United Nations has had many successes.
https://time.com/4085757/united-nations-achievements/

I am writing a paper on how the KKK of the 1920s influenced the Charlottesville Rally. I need a specific thesis and am having some trouble pinpointing a specific way the KKK influenced white supremacist protestors at the rally.

First, let us provide some contemporary context for the rally. Then, we can examine its historical antecedents in the revived Ku Klux Klan of the Twenties. While comparing history to the present, I will provide some topic ideas that you can consider.
The Charlottesville rally was mainly influenced by contemporary identitarianism—that is, the belief that white Christian people should define national character in Europe, Canada, and the United States. In the United States, these specifications also extend to the insistence that citizens should also be Anglophone. Identitarianism is prevalent throughout Europe and North America, and many of its current ideas are derived from French writers, such as Renard Camus, Guillaume Faye, and Jean Raspail. The participants at Charlottesville and their sympathizers, such as Richard Spencer, are believed to be largely influenced—directly or indirectly—by these writers' ideas.
The United States is an ethnically complex nation that has long drawn its population from immigrants, but that has not stopped some groups from trying to define native identity.
The Ku Klux Klan of the 1920s was rooted not only in racism, but also in nativist ideologies. Nativism, like identitarianism, seeks to exclude immigrants, particularly those who do not fall into the racial or religious mainstream. The KKK of the 1920s had sympathetic legislators in Congress who passed The Immigration Act of 1924 (The Johnson-Reed Act), which provided quotas determining how many people of a particular ethnic group could enter the United States. The legislation excluded Asians altogether.
For your paper, you could write specifically about how the KKK of the 1920s, along with the racist policies of the period, fostered some of the nativist, anti-immigrant ideas that we see today. It might also be helpful to connect this to Islamophobia, the fear of Muslims. The KKK of the 1920s was also anti-Catholic. The Charlottesville protesters are hostile to Islam and probably dislike any organized faith that is not Christian.
It is also important to note that the revival of the KKK in the 1920s was directly influenced by the popularity of D.W. Griffith's film The Birth of a Nation. Griffith's dexterity as a filmmaker helped him reinvent history, recreating the Confederates as heroes and the antebellum South as a great, lost civilization. The Charlottesville protesters also value this reinterpretation of history and rallied to protest the intended removal of a statue of Robert E. Lee, believing that the removal of such monuments negates a key aspect of American culture—symbols that validate white supremacy.
The revival of the Klan in the Twenties was a response to the increasing visibility and cultural influence of black people, and the passage of the Nineteenth Amendment, which allowed women the right to vote. The increasing emancipation of women stoked fears of miscegenation, or racial-mixing. The KKK particularly disliked the idea of white women coupling with black men. As a result, there was a sharp increase in the lynchings of black people, particularly black men, in the South. The increased visibility and power of white women in politics today has stoked a backlash from white men, though one much less violent than what occurred in the 1920s.
Furthermore, the activism of the NAACP during that period is similar to that of Black Lives Matter today. Just as the KKK of the 1920s was a response to the NAACP, which specifically addressed the lynchings in the South, the Charlottesville protesters were reacting to Black Lives Matter and its protest of police brutality.
What is key to remember is that both the revival of the Klan in the 1920s and the Charlottesville protest were reponses to fears about the fall of white male supremacy. They were reponses to cultural and demographic changes that threaten white male supremacy. Though these organizations responded specifically to threats against white male hegemony, I do not want to diminish the presence of white women in these groups and their support of racist, nationalist principles. Both the KKK of the 1920s and the white nationalist groups of today have prominent white women as spokespeople and supporters. Generally, they tout the importance of traditional gender roles, in addition to white supremacist values. In the Twenties, some white women supported women's suffrage specifically in the interest of expanding the nativist voting bloc.
https://www.splcenter.org/hatewatch/2015/10/12/american-racists-work-spread-%E2%80%98identitarian%E2%80%99-ideology