How was daily life in the colonies for the minority groups?

I assume by "colony" you are referring to the English colonies of North America. The answer is that it depended on how you define "minority" and what time period you are talking about. 
Jamestown (1607) was the first permanent English colony in North America and it was colonized with English men and boys; only two women arrived a year later. If we consider women as a minority in terms of the rights they had, then the women of the early colonies had roughly the same rights they enjoyed back in England--basically none. They could not vote nor hold public office; however, they did serve a pivotal role in providing stability, without which the colony and later colonies would not have survived.
But by "minorities" you probably mean non-Europeans, which in a colonial context meant Africans (I will not address American Indians here). The first 20 Africans to arrive in North America arrived in Jamestown as indentured servants after being captured from a Portuguese slave ship. Most gained their freedom after several years. However, indentured servitude--even slavery--occurred among Europeans as well, and there were even cases of blacks and American Indians owning indentured whites. The first person to be enslaved for life did not occur until 1640 and it was another 20 years before slavery laws were introduced.
Through most of the mid to late 1600s, blacks and whites enjoyed many of the same freedoms. Free blacks owned land, businesses, and some also owned slaves. But as slavery became more the norm, restrictions on blacks--free and slave--became codified to a greater degree. Firearm prohibitions, prohibitions against congregating in large numbers, as well as restrictions on property were introduced. Laws against intermarriage were also passed by the 1690s. Intermarriage between Europeans and Africans did occur, which also precipitated laws regarding the status of children from such unions. Free black men marrying white women also ran the risk of being sold into slavery beginning in the first quarter of the 1700s.
Over the decades leading up to the American Revolutionary War, the lives of blacks both free and slave became increasingly bifurcated between the southern and northern colonies, particularly as anti-slavery laws were passed in the north. This bifurcation was an immense hurdle in the creation of the US and would ultimately result in the American Civil War. So we can conclude that the rights of blacks went from something similar to whites early on in the colonies, only to become heavily restricted as colonies grew and slavery became more entrenched.
http://www.historyrocket.com/American-History/colonial-america/Women-Rights-During-Colonial-America.html

https://www.nps.gov/jame/learn/historyculture/african-americans-at-jamestown.htm

https://www.nps.gov/jame/learn/historyculture/the-indispensible-role-of-women-at-jamestown.htm

Calculus of a Single Variable, Chapter 5, 5.3, Section 5.3, Problem 27

f(x)=ln(x-3)
Take note that a function is strictly monotonic if it is increasing on its entire domain or decreasing on its entire domain.
For our function,
f(x)=ln(x-3)
to determine if it is strictly monotonic, let's first figure out its domain.
Take note that in logarithm, its argument should be above zero. So to get its domain, set its argument x-3 greater than zero.
x-3gt0
xgt3
So the domain of the given function is (3, oo) .
Then, let's apply the derivative. It will be strictly monotonic if there is no sign change in the value of f'(x).
The derivative of the function
f(x) = ln(x-3)
is
f'(x) = 1/(x-3)
Notice that the derivative of the function can never be zero. Because of that, the function f(x) has no critical numbers. This means that there will be no sign change in the value of f'(x). To verify, assign values to x falls within the domain of the function and plug-in them to f'(x).
x=4
f'(x) = 1/(4-3)=1
x=10
f'(x) = 1/(10-3)=1/7
x=23
f'(x) =1/(23-3)=1/20
x=42
f'(x)=1/(42-3)=1/39
Notice that on the interval (3,oo) , the value of f'(x) is always positive. There is no sign change in the value of f'(x). So the function is entirely increasing on its domain.
Therefore, the function f(x)=ln(x-3) is strictly monotonic on its entire domain.

What is the name of Calpurnia's church?

In chapter 12 of To Kill a Mockingbird, Calpurnia brings Jem and Scout to First Purchase African M.E. Church on Sunday because their father, Atticus, has been summoned to an "emergency session" outside of Maycomb and could not be home to bring the kids to church himself. Calpurnia worries about Jem and Scout going to their church alone because of an earlier incident where the children, unsupervised, tied up a peer in the furnace room of the church and forgot about her:



"Left to its own devices, the class tied Eunice Ann Simpson to a chair and placed her in the furnace room. We forgot her, trooped upstairs to church, and were listening quietly to the sermon when a dreadful banging issued from the radiator pipes, persisting until someone investigated and brought forth Eunice Ann saying she didn’t want to play Shadrach any more—Jem Finch said she wouldn’t get burnt if she had enough faith, but it was hot down there. "



On Saturday night, Calpurnia makes sure Jem and Scout are spotlessly clean, stating that she didn't want anyone to think she didn't care for her children. When Jem and Scout arrive at First Purchase, it's unlike anything they've ever experienced:



"First Purchase African M.E. Church was in the Quarters outside the southern town limits, across the old sawmill tracks. It was an ancient paint-peeled frame building, the only church in Maycomb with a steeple and bell, called First Purchase because it was paid for from the first earnings of freed slaves. Negroes worshiped in it on Sundays and white men gambled in it on weekdays."
The building is old and run-down, and Scout cannot understand why there are no hymnals in the pews, which is an important detail that Lee includes in her character. Scout, because of her youth and naiveté, cannot comprehend that the church is too poor and uneducated to afford (or need) something as luxurious as individual hymnals. This theme of innocence punctuates the novel as Scout grows and learns about her world of racism, oppression, and injustice in fragmented anecdotes, such as First Purchase's lack of hymnals, thus creating for the reader a slow, steady, jarring, and quizzical revelation of 1930 southern America's grand, completed world.
It's also important to note that First Purchase is named such because it was "paid for from the first earnings of freed slaves," and yet "white men gamble in it on the weekdays." The church serves as a poignant symbol of injustice and privilege. Nothing belongs to the black community--not even something that was bought and paid for with money, time, and blood. White men can still do what they wish with this building because they were born with the "correct" skin color.

In chapter 12, Atticus travels to Montgomery, and Calpurnia decides to take Jem and Scout to Sunday service at First Purchase African M.E. Church. Jem and Scout enjoy their experience at First Purchase African M.E. Church and gain valuable insight into the black community of Maycomb. The Finch children are shocked to discover that the majority of the congregation cannot read and use a technique called "lining" to sing hymns in unison. They also notice how Reverend Sykes calls specific individuals out for their sins and locks the church's doors until the congregation raises ten dollars for Helen Robinson's family. Jem and Scout also discover that Calpurnia lives a "modest double life" and is one of the most educated women in her community. Overall, Jem and Scout enjoy their visit to First Purchase African M.E. Church and gain valuable insight into the black community of Maycomb.

How is prejudice to the vulnerable evident in Lord of the Flies?

Prejudice against vulnerable individuals is illustrated by the way Jack and his hunters treat Piggy, Simon, and the littluns. Both Piggy and Simon are vulnerable because they are viewed as outcasts among the group of boys and are easily intimidated by Jack and his hunters. Piggy is overweight, asthmatic, and easily frightened by Jack. Similar to the littluns, Piggy relies on Ralph's protection to survive. Simon is vulnerable because he is known to faint and is considered extremely weird by the group of boys. Simon also has difficulty expressing his feelings, which is one reason he is ridiculed and overlooked. The littluns are not only physically weak but are too young to challenge Jack and his hunters, and they cannot make rational decisions without the help of Ralph and Piggy.
Jack and his hunters continually taunt Piggy, interrupt him during assemblies, and physically threaten him. They understand that Piggy is too weak and afraid to defend himself, which makes him an easy target. Piggy is bullied by the other boys and only becomes close with Ralph after Jack establishes his own tribe of savages. Similarly, Simon is neglected by the group of boys and is labeled an outcast because of his odd behavior. The boys rarely listen to Simon, and he becomes an afterthought among the group. The littluns are essentially left to fend for themselves as Jack demonstrates his lack of sympathy when they cry at night. Unfortunately, Piggy, Simon, and the littlun with the mulberry-colored birthmark lose their lives on the island because they are vulnerable.

How do Valentine and Peter resolve the issue of their disagreement about the politics on Earth?

I am going to assume that the question is asking about events that occur during chapter 9 of Ender's Game.  Near the start of the chapter, Peter approaches Valentine about the state of the world.  He sees a great world war coming.  He's afraid that mankind is on the verge of destroying itself, and he wants to stop it:

"Do you understand? I want to save mankind from self-destruction."
She had never seen him speak with such sincerity. With no hint of mockery, no trace of a lie in his voice. He was getting better at this. Or maybe he was actually touching on the truth.
"So a twelve-year-old boy and his kid sister are going to save the world?" 

Of course Valentine is very skeptical.  She believes that her brother is smart enough and power-hungry enough to make a power play of his own; therefore, she is not immediately willing to help her brother out.  
After some more talking, Peter eventually convinces Valentine to help; however, she still doesn't think they can have any impact on the world: 

"Val, if you don't help me, l don't know what I'll become. But if you're there, my partner in everything, you can keep me from becoming––like that. Like the bad ones."
She nodded. You are only pretending to share power with me, she thought, but in fact I have power over you, even though you don't know it. "I will. I'll help you."

The main reason that Valentine is skeptical is because of their relative ages.  They are kids, and she knows that the world won't listen to a pair of kids:

"Peter, you're twelve years old. I'm ten. They have a word for people our age. They call us children and they treat us like mice."
"But we don't think like other children, do we, Val? We don't talk like other children. And above all, we don't write like other children."

Peter's solution to the age problem is anonymity.  The Internet gives them a way to hide their identity and age.  They can write inflammatory and logical pieces that push and pull public opinion in the desired direction.  Peter and Valentine also agree to write from two different perspectives.  Peter will be Locke and write the more rational and empathetic pieces, and Valentine will be Demosthenes and write more hostile and paranoid pieces.  Basically, they are writing the opposite of their own personality.  This forces Peter and Valentine to be inextricably tied to each other.  They can't write their piece without seeking out the advice of the other person:

Demosthenes began to develop as a fairly paranoid anti-Warsaw writer. It bothered her because Peter was the one who knew how to exploit fear in his writing -- she had to keep coming to him for ideas on how to do it. Meanwhile, his Locke followed her moderate, empathic strategies. It made sense, in a way. By having her write Demosthenes, it meant he also had some empathy, just as Locke also could play on others fears. But the main effect was to keep her inextricably tied to Peter. She couldn't go off and use Demosthenes for her own purposes. She wouldn't know how to use him. Still, it worked both ways. He couldn't write Locke without her. 

What style of poem is "What Lips My Lips Have Kissed" by Edna St. Vincent Millay?

Millay's poem is sonnet, a poem of fourteen lines, written in an elegiac style. An elegy is a lament, usually for the dead or to regret a loss.
In the sonnet, Millay mourns her aloneness, and, implicitly, her aging. In the first octet (eight lines) she is remembering the many loves she once had, so many she can't remember them. She is regretting not remembering them, but more profoundly, that they are "ghosts" who will not come again. As she puts it, she feels a "pain":

For unremembered lads that not again
Will turn to me at midnight with a cry.

In the sestet or last six lines of the poem, she compares herself to a tree in winter that is "lonely." Just as she has gradually lost her lovers, so the tree has one by one lost its songbirds, until it is all alone.

Millay uses conventional metaphors or comparisons to make an emotional point about loneliness and age: winter, for example, is traditionally associated with getting old and dying. But despite the conventional imagery, the stark, simple words carry emotional weight as they convey her pain and loneliness.

This poem is an Italian, or Petrarchan, sonnet. This means that it is written in iambic pentameter: each line has five feet, each foot consisting of two syllables (for a total of ten syllables per line), one unstressed syllable followed by one stressed syllable. It also has fourteen lines, but it is split into an octave (a section consisting of eight lines) and a sestet (a section consisting of six lines). In an Italian sonnet, the octave can present a question and the sestet an answer, or the octave can offer a claim while the sestet offers an example, etc. In this poem, the speaker presents her emotional state in the octave: she is remembering, sadly, "unremembered lads that not again / Will turn to me at midnight with a cry." She is lonely and sad, thinking of her lost loves that will never return. Then, the sestet presents a metaphor that illustrates this feeling: the "lonely tree" is the speaker and the "birds [who] have vanished one by one" are her lost loves. Just as summer passes and the tree becomes lonely, so has the speaker's own "summer" gone by, and she is now alone.

Edna St. Vincent Millay's poem "What Lips My Lips Have Kissed and Where and Why" is a sonnet. A sonnet is a poem with fourteen lines; there are usually ten syllables in each line, and the poem is written in iambic pentameter.
Iambic pentameter refers to how a line of poetry is constructed. In a poem, each line consists of stressed and unstressed syllables: this is the meter of a poem. A foot is made up of either two of three syllables. If the foot has two syllables that proceed in an unstressed/stressed pattern, we call this an iamb. So, a line written in iambic pentameter will have five sets of unstressed and stressed syllables. Let's take a look at the first four lines of the sonnet in question:

What(unstressed) lips (stressed)/ my (unstressed) lips (stressed)/ have (unstressed) kissed (stressed),/ and (unstressed) where (stressed),/ and (unstressed) why (stressed),/
I have/ forgot/ten, and /what arms /have lain/
Under/ my head/ till morn/ing; but/ the rain/
Is full/ of ghosts/ tonight,/ that tap/ and sigh/

So, you can see there are five metrical feet in each line. Each line also proceeds in an unstressed/stressed pattern, which makes this a poem written in iambic pentameter.
Also, it looks like the poem in question is an Italian or Petrarchan sonnet. The Italian sonnet is usually divided into an octave (with eight lines having a rhyme scheme of abbaabba) and a sestet (with six lines having a variable rhyme scheme of either cdecde, cdedce, cdcdcd, or another—the pattern is flexible).
Hope this helps!
http://www.sonnets.org/basicforms.htm

Beginning Algebra With Applications, Chapter 5, 5.4, Section 5.4, Problem 52

Determine the equation of the line through the points whose coordinates are $(14,-1)$ and $(-7,-7)$.

Using the Slope Formula with $(x_1, y_1) = (14,-1)$ and $(x_2, y_2) = (-7,-7)$

$\displaystyle m = \frac{-7-(-1)}{-7-14} = \frac{-6}{-21} = \frac{2}{7}$

The slope of the line is $\displaystyle \frac{2}{7}$.

Using the point slope formula with $\displaystyle m = \frac{2}{7}$ and $(x_1, y_1) = (14,-1)$


$
\begin{equation}
\begin{aligned}

y - y_1 =& m(x - x_1)
&&
\\
y-(-1) =& \frac{2}{7} (x-14)
&& \text{Substitute } m = \frac{2}{7}, (x_1, y_1) = (14,-1)
\\
y+1 =& \frac{2}{7}x - 4
&& \text{Apply Distributive Property}
\\
y =& \frac{2}{7}x - 5
&& \text{Write the slope-intercept form}

\end{aligned}
\end{equation}
$