According to Thoreau, how can the government sometimes hinder the people?

Thoreau wastes no time getting to his feelings about government in Civil Disobedience:

I heartily accept the motto, ‘That government is best which governs least.'"

Thoreau writes that the scope of the government can be misused much in the way of the standing army:

The government itself, which is only the mode which the people have chosen to execute their will, is equally liable to be abused and perverted before the people can act through it.

Thoreau believes it is too easy for a few corrupt individuals to decide the course of the nation without the input of the people.

It has not the vitality and force of a single living man; for a single man can bend it to his will.

It’s not that he believes there should be no government but that there must be "a better government.” He believes that conscience should prevail over law.

Must the citizen ever for a moment, or in the least degree, resign his conscience to the legislator? Why has every man a conscience, then?

He goes on to say that men march off to war feeling it is wrong:

Now, what are they? Men at all? or small movable forts and magazines, at the service of some unscrupulous man in power?

Thoreau believes that our government set-up doesn’t leave much room for the individual to have autonomy, which allows for decision-making based on right and wrong.

All voting is a sort of gaming, like checkers or backgammon, with a slight moral tinge to it, a playing with right and wrong. . . The character of the voters is not staked.

He mentions slavery as an example of the ways a government can get something wrong and the majority must not prevail:

I do not hesitate to say, that those who call themselves Abolitionists should at once effectually withdraw their support, both in person and property, from the government of Massachusetts, and not wait till they constitute a majority of one. . . . I think that it is enough if they have God on their side, without waiting for that other one. Moreover, any man more right than his neighbors constitutes a majority of one already.

As with many of Thoreau’s writings, he emphasizes the importance of independent thought to a functioning society.

According to Thoreau, the government can hinder the people when it governs too much. He says, "That government is best which governs not at all." He uses the Mexican-American War as an example of this. The war, to him, is unjust, and he believes that the majority of individual citizens would not have consented to the war. Yet the government still moved forward and engaged the country in it.  
Further, he points out that the government itself never actually "furthered any enterprise": it does not keep the U.S. free, settle the western territories, or educate citizens.  Everything that has been done for the good of the country has been done by the American people—by individuals who sought to improve things—and not by the government. If anything, he thinks, the government has actually gotten in the way, in part because it can be influenced by a "single man" who seeks to "bend it to his will." 

Write 87% as a decimal.

The definition of a percent is in its name: per cent, where cent stands for a hundredth of a whole. (Much like a cent or penny is 1/100 of an American dollar, or a centurion was one of a hundred Roman soldiers, etc...)
So 87% is 87 parts of a whole comprised of a hundred parts.
87%=87/100 =0.87
 
http://mathworld.wolfram.com/Percent.html

Analyze the woman's position in "To George Sand: A Desire," "To George Sand: A Recognition," and "Sonnets from the Portuguese" by Elizabeth Barrett Browning. In the sonnets, how does Browning subvert patriarchy for her own benefit? Use explanations from the article "Regendering Petrarch" by Marianne Van Remoortel.

The two poems written in honor of George Sands (Amantine-Lucile-Aurore Dupin) openly question the gender binary norms of the 19th century, while "Sonnets from the Portuguese" uses subtler means to achieve this objective.
In "George Sand: A Desire," Browning subverts the natural order of male and female identity from the very first lines of the poem:

Thou large-brained woman and large-hearted man,
Self-called George Sand! whose soul, amid the lions
Of thy tumultuous senses, moans defiance
And answers roar for roar....

The woman assumes a cerebral persona typically associated with the masculine nature, while the man is imbued with the conventional feminine attributes of compassion or emotionalism. George Sands is portrayed as a courageous iconoclastic figure in a den of lions. She challenges the conventions of her time, answering "roar for roar." Browning's hope is that history will regard George Sands as "a pure genius sanctified from blame" for subverting the natural order of gender identity.
The poem "George Sands: A Recognition" is equally bold. Browning commends George Sands for being a "true woman" and "true genius" who denies her "woman's nature with a manly scorn." Later in the poem, Browning ponders the paradox of discarding "the gauds and armlets worn / By weaker women in captivity" while keeping one's hair "unshorn." Browning's poetry exposes the innate strength of feminine proclivities in even the most vocal of rebels. She ends her poem with a prayer that her heroine will burn ever brighter in heaven, where God will "unsex" her on the heavenly shores. 
Browning's exhortation parallels her call for her heroine to be "sanctified from blame" beside the "angel's grace" in "George Sands: A Desire." In these two poems, Browning subverts the patriarchy by arguing that since both men and women are equal in the heavenly realms, they should be equals on earth as well. Browning uses this analogy to draw attention to the plight of female poets and authors, who she felt were largely marginalized in the 19th century.
Meanwhile, "Sonnets from the Portuguese" is more subtle in tone. In her article "Regendering Petrarch," Marianne Van Remoortel explains why this subtlety works:

"Sonnets from the Portuguese" is a collection of 44 poems. In these poems, Browning transposes male love-sickness onto a female psyche. The female protagonist in the poems takes on the previous deprecatory stance of the male supplicant in a romantic courtship. Browning proclaims that it is her lover who now has the ultimate "power" and "grace" to unmask her true self. 


In the anthology, Browning does not resort to the use of synecdoche to reduce a woman to the sum of her body parts (as Petrarch did in his poems). Browning presents the woman in love as a whole person who has a passionate nature and who does not need to resort to artifice to keep her lover's interest.


I love thee freely, as men strive for Right;I love thee purely, as they turn from Praise.I love thee with the passion put to useIn my old griefs, and with my childhood’s faith. 


In her anthology, Browning chooses not to focus on the state of a typically emotional 19th century male lover. Instead, she highlights the idealized femininity of the Victorian era, when women were largely confined to the domestic sphere.


In Petrarchan sonnets, the focus is often on the male response to unrequited love. In a Victorian anthology such as Browning's however, the focus is on the frail, sickly woman, who is the object of a male lover's affections. Browning cleverly exposed 19th-century gender issues by calling attention to the woman's position in society.


Browning's "Sonnets from the Portuguese" delighted Victorian sensibilities (with its erotic portrayal of a refined and modest female protagonist) while it simultaneously drew attention to the plight of middle-class Victorian women, who were largely confined to "fashionable" indoor living. With little exercise and few outlets to channel their physical and emotional energies, women eventually became pale and sickly.


Browning's submission to her lover's courtship also illuminates the reality of 19th-century life for women. Remoortel contends that this submission was an economic and social necessity on Browning's part. However, she also acknowledges the fact that Sir William Blackstone's Commentaries on the Law of England emphasized the responsibility of husbands to provide for and to protect their wives.


In the 44th sonnet, Browning mentions eglantine and ivy. Remoortel points out that the eglantine is a symbol of poetic independence, while the ivy is a symbol of the objectifying forces that threaten female agency. At the same time, the eglantine is also a symbol of poetry, while the ivy is a symbol of marriage. Browning's mention of the two symbolic plants highlights her hope that harmonious and egalitarian relationships will flourish within the realm of marriage and the literary sphere. 

Source: (Re)gendering Petrarch: Elizabeth Barrett Browning's "Sonnets from the Portuguese" by Marianne Van Remoortel, Tulsa Studies in Women's Literature, Vol. 25, No. 2 (Fall, 2006), pp. 247-266

Precalculus, Chapter 4, 4.5, Section 4.5, Problem 20

Anytime you are given 2 functions f(x) and g(x) where the argument of g is an "adjustment" within the expression in parentheses in the form (x + h, where h is any real number) the graph of the parent function f(x) is shifted h units in the opposite direction to the sign. An example would be if f(x) = x^2 and g(x) = (x-5)^2, then the graph of g is simply the graph of f shifted 5 units to the right, as there is a - sign after x. With trigonometric functions, h represents a phase shift of h units in the opposite direction of the sign in front of it. Therefore g(x) = cos (x + pi) implies a shift of pi units to the left from the graph of parent function f(x) = cos x.

How did Henry V portray the themes of heroism and honor?

But if it be a sin to covet honor,
I am the most offending soul alive. [Henry, in Henry V, 4.3.31-32]

Honor is of the utmost importance to King Henry V in Shakespeare's Henry V. Henry views honor as something to be won but not something to be won for himself. He believes that honor must be won on behalf of something that is larger than himself. For Henry, achieving honor is the result of achieving glory for England.
Henry learned about honor from his companion Sir John Falstaff in an earlier play, Henry IV, Part 1. Falstaff considered the pursuit of personal honor, glory, and recognition as pure vanity and ultimately worthless.

FALSTAFF: Therefore
I’ll none of it. Honor is a mere scutcheon [Henry IV, Part 1, 5.1.140-141]

Falstaff believed that honor was not something a person sought, or fought, to attain but that honor was something that came to a person as a result of their unselfish heroic deeds.

FALSTAFF: I like
not such grinning honor as Sir Walter hath: give me
life: which if I can save, so; if not, honor comes
unlooked for, and there's an end. [Henry IV, Part 1, 5.3.62-65]

On the battlefield before the Battle of Agincourt, one of Henry's military leaders, Westmoreland, wishes aloud that England had more soldiers for the battle. Henry explains to him how honor is more important than victory in the battle, or ultimate victory for England.

WESTMORELAND: O, that we now had here
But one ten thousand of those men in England
That do no work today.
KING HENRY: . . . No, my fair cousin.
If we are marked to die, we are enough
To do our country loss; and if to live,
The fewer men, the greater share of honor. . . .
No, faith, my coz, wish not a man from England:
God's peace! I would not lose so great an honor
As one man more, methinks, would share from me [4.3.18-25, 33-35]

The word "hero" doesn't appears in Henry V, but heroism, like honor, is always on Henry's mind. For Henry, honor comes to a person, and glory comes to England, as a result of heroism. You can't have honor without behaving heroically.
Henry demonstrates to his army exactly what heroism is. Henry rouses his troops to bravely charge back into battle, and, despite overwhelming odds against military success, and against even emerging alive, Henry heroically charges into the battle himself.

KING HENRY: Once more unto the breach, dear friends, once
more . . .
Follow your spirit, and upon this charge
Cry “God for Harry, England, and Saint George!” [3.1.1-2, 36-37]

"Prince Hal" from Henry IV has matured into the brave and honorable King Henry in Henry V. In fact, the "wild" days of his youth prepared him for his finest hour: the Battle of Agincourt.
Henry lays the groundwork for this heroic victory by disguising himself and visiting his troops the night before the battle in order to get a feel for what his common soldiers are really feeling. This ability to interact with commoners, which he began back in the days when he drank and caroused with Falstaff, now helps him to be a compassionate leader.
He then inspires his troops with brave words:

But when the blast of war blows in our ears,Then imitate the action of the tiger;Stiffen the sinews, summon up the blood,Disguise fair nature with hard-favoured rage.

He heeds his own advice and doesn't hold back or try to save himself. He fights beside his troops valiantly. In fact, he is so caught up in the fighting that he doesn't even know at first that his army has won.
As the chorus expresses, Henry is an exemplary king. He shows heroism on the battlefield and honor in his mercy to the French. He also marries a French princess in order to unite the kingdoms.

Henry V, one of Shakespeare's history plays, centers on the Battle of Agincourt during the Hundred Years' War, in which the English, led by King Henry V, fight and defeat the French army against all odds—despite having much smaller numbers. As both a monarch and a military leader, the character of Henry V demonstrates courage, heroism, and honor throughout the play. These character traits are also themes of the play, which is primarily a celebration of the British victory, and Henry is the embodiment of these virtues.
For evidence, look at Henry's famous monologue in act 3, scene 1, which begins, "Once more unto the breach, dear friends, once more," and The Saint Crispin's Day speech in act 4, scene 3. Both of these rousing speeches, spoken to restore morale to his disheartened troops, make Henry's heroism and honor plainly apparent. That he can embolden his troops to action through his words and deeds, because they aspire to be like him and to be praised by him, prove that he is a great leader and a noble man.
Henry also demonstrates his heroism and honor in the mercy that he shows to his enemies. After the battle at Harfleur early on in the play, he spares the inhabitants of the town in a generous and honorable move.

In "One Thousand Dollar" what problem does Gillian face?

Young Gillian faces the immediate problem of spending the $1,000 inheritance he's just received from his uncle's will, of which he needs to account for every last penny. For most people, it sounds like a nice problem to have, but for Gillian it turns into a nightmare. He travels all over New York, trying to figure out a way to relieve himself of what's becoming a growing burden. On his travels he even asks a number of complete strangers what they would do with the money, but all to no avail.
Gillian finally hits upon an ingenious idea. He's going to give the money to his uncle's ward, Miss Hayden, who received only a negligible sum from his inheritance. Gillian doesn't yet know it, but he'll receive $50,000 if he's found to have spent the money wisely. However, if Gillian is discovered to have squandered his inheritance on vice, then that money will go to Miss Hayden instead. When Gillian hears about this provision of his uncle's will, he immediately pretends that he lost all the money at the racetrack, and so is not entitled to his share of the estate.
The problem for Gillian is that he just didn't know what to do with all that money. And that was only $1,000, a relatively small amount. He must've thought how much worse it would've been for him to have $50,000 instead, and all the additional problems that would've created. Gillian has learned that sometimes money can be a burden, whether it's too much or not enough. And as the story closes, Gillian's merry whistling convinces us that he's glad to be relieved of it.

Precalculus, Chapter 9, 9.4, Section 9.4, Problem 69

You need to remember what a quadratic model is, such that:
a_n = f(n) = a*n^2 + b*n + c
The problem provides the following information, such that:
a_0 = 3 => f(0) = a*0^2 + b*0 + c => c = 3
a_1 = 3 => f(1) = a*1^2 + b*1 + c => a + b + c = 3
a_4 = 15 => f(4) = a*4^2 + b*4 + c => 16a + 4b + c = 15
You need to replace 3 for c in equation a + b + c = 3 :
a + b + 3 = 3 => a + b = 0
You need to replace 3 for c in equation 16a + 4b + c = 15 :
16a + 4b + 3 = 15 => 16a + 4b = 12 => 4a + b = 3
Subtract a + b = 0 from 4a + b = 3 , such that:
4a + b - a - b = 3
3a = 3=> a = 1
Replace 1 for a in equation a + b = 0 such that:
1 + b = 0 => b = -1
Hence, the quadratic model for the given sequence is a_n = n^2 - n + 3.