How does music help us express our feelings in our lives?

To understand how music helps us express feelings, we must take a look at what music is, in the literal sense. Music at its essence, is just organized sound, whether it be our favorite song, or the wind in the trees. To me, as a musician, the music happens whenever I decide to tune in, and call it such.
The shift from mundane sound to music happens when I remind myself that every moment contains sound that has the potential to be music. I've worked as a custodian where all of the sudden the broom I'm sweeping with becomes a brush on a snare drum, with its own rhythm and life. When the shift happens, I let go of conscious attachments, and herein lies the expression.
When the expression happens, I like to think of it as "taking out the trash." It is as though I've supplemented a cleaning agent on whatever ales me, physically, mentally, and emotionally. This is what expression is, our negativity and tension taking the "expressway" out.
I once had a music teacher who gave me the assignment of "listening walks." I would take a walk of at least five minutes, tuning in to each different sound I heard, until it became a symphony. I would start by noticing the birds, then the wind with the birds, then the sound of my feet on the sidewalk with the wind with the birds, and so on, until I was in the place of symphonic bliss. This is where I discovered the "expressway" and I didn't need my instrument to ride it.
Music helps us express our feelings when we decide to have a "musical" moment. When we step back, let go and tune into the sound around us, we are swimming in music. It is accessible 24/7.
FURTHER READING
Victor Wooten's "The Music Lesson"

Music is a powerful force upon our feelings, and I would like to see more research done on the brain chemistry of this. Music does not simply express our feelings. It can enhance them, alter them, and bring them back to us, too.
To say that music expresses our feelings suggests to me the ideas of reflecting and communicating our feelings. When I am happy, I tend to play music in a major key, music that is upbeat, literally and figuratively—happy music. When I am sad, I tend to play music in a minor key, music that is sad or perhaps contemplative. Sometimes I express myself by playing CDs, and sometimes I express myself by playing the piano. I am in either case reflecting my mood. I can also communicate my mood to others with music. If my family came home to rock and roll on the stereo, I imagine they knew I was feeling lighthearted and energetic. If they came home to hear some very sad Nina Simone playing, they probably knew I was low for some reason. Back in the day when there were jukeboxes everywhere, I can imagine a few boyfriends for whom I should have played "Breaking Up Is Hard to Do" to communicate something. This does not mean, of course, that every musical choice we make is laden with meaning, but there is no question that our selections can and do often reflect or communicate our feelings.
Music also intensifies what we feel. A sad song will make me feel sadder. A happy song will make me feel happier. Today, with our playlists, we can put together a collection of music to enhance any mood we like. Sports teams have "fight songs." The national anthem intensifies our feelings of patriotism, as does "This Land Is Your Land." If I am feeling energetic and want to clean my house, music can enhance that feeling of energy, at least for a while. I find show tunes—for example, from Chicago—to be energetic and thus energizing.
Romantic songs enhance our feelings of love, and hymns enhance our feelings of spirituality. 
Music is a way of altering our emotions, too. If I do not want to give in to a sad mood, I can play music that will change my mood. When people go to a supermarket, they might be angry, lonely, or sad. But the music playing can and often does alter their moods. There have been times when I have gone to see a musical and though I was not in a particularly good mood when I arrived—grumbling, for example, over crowds and parking—I was elated by the time I left because of the music. Concerts have this effect upon people, too, but you can make yourself happy at home with your musical selections. You can prime yourself to be in a mood with music.
Most of us have a soundtrack to our lives, and hearing anything from this soundtrack gives us instant access to many of our feelings and memories of the past. People with Alzheimer's remember music when much else has been lost, and it helps put them in touch with a few memories. When I hear a particular song from a particular era, it conjures up for me where I was, what I was doing, and whom I was with. The Vietnam War had a soundtrack, which was the music of the late sixties and early seventies. Vietnam War veterans will tell you that Jimi Hendrix takes them back to where they were. I would imagine every war has its own soundtrack.
I personally think that music is an essential part of a good life. It not only expresses our feelings, but also it can alter and enhance them. And it is like a book of memories, too, bringing back our past to us.
http://www.openculture.com/2016/02/music-in-the-brain-scientists-finally-reveal-the-parts-of-our-brain-that-are-dedicated-to-music.html

Describe the gender discrimination in this play?

Right from the start of the play, we're aware that the society portrayed is structured along traditional gender lines. The women perform housework; the men are the breadwinners. The world outside is the exclusive preserve of men; women are confined to home and hearth. This is rural Irish society at its most traditional.
The whole family suffers as a direct consequence of traditional gender roles. After the death of Michael, there's now only one man about the house, and that is Bartley. Without additional (male) financial support, the family faces an uncertain, potentially impoverished future. The family's travails represent in microcosm the economic and demographic problems of the island in general. The island is wholly dependent on fishing, and this is dangerous work. Inevitably, many young men perish at sea, leaving their families and the community as a whole in financial distress.
And it is the family's economic decline that presages a potentially radical change in gender roles and relations. With Bartley off to try and earn a living, the women of the house must take on the roles traditionally associated with men. For example, Cathleen needs to go to market and sell the family's pig. But Maurya is fiercely dismissive of the very idea: she wonders how will Catherine get a fair price for the animal? The implicit assumption here is that the men at the marketplace won't take Catherine seriously as she is a woman and so won't give her a fair price for the pig. Maurya is instinctively rebelling against what she sees as a desperate, uncertain future. She is too old, too weary, too set in her ways to contemplate any substantial change in social and gender relations. There is no choice, then, but for her to cling to the past with all its certainties, its familiar patterns of social life, and its traditional division of labor between the sexes.

Calculus of a Single Variable, Chapter 9, 9.1, Section 9.1, Problem 55

a_n=n e^(-n/2)
Monotonicity
First five terms of the sequence are
a_1=e^(-1/2)=0.6065
a_2=2e^-1=0.7358
a_3=3e^(-3/2)=0.6693
a_4=4e^-2=0.5413
a_5=5e^(-5/2)=0.4104
We can see that after the second term, the terms are decreasing so it is possible that the whole sequence is monotonically decreasing. Let us verify that.
a_n>a_(n+1)
n e^(-n/2)>(n+1)e^(-(n+1)/2)=(n+1)e^(-n/2)e^(-1/2)
Divide the inequality by e^(-n/2). We can do that because e^(-n/2)>0, forall n in NN.
n>(n+1)e^(-1/2)=n e^(-1/2)+e^(-1/2)
Divide by n. We can do that because n>0.
1>e^(-1/2)+e^(-1/2)/n
Since e^(-1/2)<1, we can find sufficiently large n such that the above inequality holds. In this case n=2.
1>e^(-1/2)+e^(-1/2)/2=0.9098
Therefore, forall n geq 2 (a_n>a_(n+1)) which means that the sequence is monotonically decreasing.
Boundedness
We have shown that the sequence is monotonically decreasing from second term onwards. This means that the second terms is also maximum of the sequence. In other words the sequence is bounded from above by a_2=2e^-1.
On the other hand if we look at the sequence a_n=n e^(-n/2), we see that all of its terms are positive. This is because n>0 and exponential function is always positive so e^(-n/2)>0 and the product of two positive numbers is itself positive.
Therefore, a_n>0, forall n in NN i.e. the sequence is bounded by zero from below.
We can conclude that forall n in NN, a_n in [2e^(-1),0) i.e. the sequence is bounded from both below and above.
The image below shows first 20 terms of the sequence. Both boundedness and monotonicity can clearly be seen on the image.

Is the number theory a complete abstraction or are there real applications of it in the wold?

To answer your question in short: yes and yes.
To answer your question in long . . .
Philosophers have been arguing for literally millennia about whether or not mathematics (and by extension number theory) is merely an abstraction or whether numbers actually exist in a meaningful sense. So, right off the bat, there's that, and it makes it tricky to answer. That being said (and philosophy discussions aside), yes, most people would consider number theory a complete and total abstraction. It's arguably the most important subfield of pure mathematics, so by definition, it only deals in the abstract. It's free of any references to the "real" world, unlike statistics, or computer science, or game theory. Those fields are collectively referred to as applied mathematics. Number theory only deals with the study of integers: nothing more, nothing less.
However, that doesn't mean number theory or pure mathematics in general don't have very real applications. Number theory is extremely important in cryptography, which essentially a cornerstone of modern communication technologies. Further, it has wide-ranging interdisciplinary applications, from differential topology to mathematical physics. Also, while not an example of number theory, Boolean algebra, another branch of pure mathematics, is the basis for modern digital circuits. It was developed a full ninety-nine years before the first digital computer was built in 1946!
To make my point short here: just because a field or discourse is abstract doesn't mean it has no applications, and just because something seems useless doesn't mean it always will be. A nice rule of thumb for pure mathematics is "if there isn't a use for it now, there will be."
https://plato.stanford.edu/entries/platonism-mathematics/

https://uwaterloo.ca/pure-mathematics/about-pure-math/what-is-pure-math

Difference between direct democracy and indirect democracy

An indirect democracy is otherwise known as a "republic" or a "representative democracy." Many countries that are well-known for their democracy, such as the United States, are actually republics and not true direct democracies.
A direct democracy is exactly how it sounds: the people cast votes, and the person with the most votes at the end of the election wins. If my ballot is counted last, and my vote determines if person A or person B wins the election, you can say that my vote "directly matters." This might seem obvious, but when it comes to republics, not all votes directly "matter."
In a republic, people vote for representatives. These are often governors, senators, representatives for the house, and other legislators. In these district elections, the votes of people "directly matter" because the candidate with the most votes wins. However, in political practices one tier above that, the common man does not get to directly vote.
Legislators and senators and the like are tasked with voting for their district. That means that your county has chosen representatives who have beliefs that match with most of yours. Thus, those representative people will vote in congress or court or wherever how you probably would have voted. This simplifies the process and allows for educated legal specialists (senators) to make educated legal decisions instead of leaving it up to you and me.
This also takes place within voting for certain offices, like the presidency. In America, there is an electoral college. That group of educated voters sits in a little office and takes a look at the ballots cast by the common people for the candidates for presidency. The electoral college people then take their votes (the ones that actually count) and cast them probably based off of the votes of their represented districts. So if everyone in Washington votes for the Democratic candidate, the electoral college for that state will cast their (actually important) votes for the Democratic candidate.
Now that is not to say that the common man's vote does not matter; if the common people did not cast their votes for office, then the electoral college would not know who the public wanted them to vote for. It's like telling your mom that you want a green scarf, but she ultimately has the decision and buying power. She might buy you the green one, but she also might see that the scarf is made of a scratchy fabric that might itch you, so she picks an orange one instead. She takes your input into account. So too does the electoral college.
So, a direct democracy allows everyone to participate in the "most votes" contest. An indirect democracy allows everyone to participate in the "most votes" contest to choose educated politicians to make the hard decisions for us.

I need a full summary about The Wonder Spot?

The Wonder Spot is a “chick-lit” coming of age novel by award-winning author Melissa Banks.  At the opening of the book, we are introduced to our protagonist, Sophie Applebaum, who is riding in the car with her family on the way to her cousin’s bat mitzvah in Chappaqua, New York. Sophie has been raised in Pennsylvania, in a suburban Jewish family, where she struggles to find her own identity.  
Throughout the novel, we follow Sophie as she grows and learns on her journey through adolescence and then adulthood.  At the bar mitzvah, she has her first defining moment of adolescence; she meets a cute eighth-grade boy with whom she sneaks cigarettes in the forest. Then, at a seventh grade skating party, Sophie suddenly realizes that no one is looking at her, even though she felt sure that everyone was.  This event sets the tone for the rest of the book and her journey to adulthood. Sophie, in contrast to her seemingly confident younger and older brothers, realizes over the course of her life that she is more of a follower than a doer. She feels disappointed and unsatisfied at almost every turn of her life, from attending Hebrew School to going on dates with men who never seem to satisfy her need for something more.
Meanwhile, she is surrounded by people who seem to know what they are doing; this includes a younger brother whose brilliance gives him an almost-certain direction in life, and an older brother whose charisma and charm make her feel a bit inferior and shapeless. We see her character through her relationship with her magical college roommate Venice, who seems almost unreal. We also see her character through her grandmother, who seems determined to rescue her from “impending spinsterhood” by finding her a nice young man.
Even as her life progresses and she navigates through her defining moments in life, including deciding on which college to attend ("Not Brown but Bowling Green; not Wesleyan but Ohio Wesleyan, not Williams or Smith, but William Smith”), she does not realize how significant her search actually is; she does not feel proud of her grades and her passions in life have either not added up to anything or continue to be nonexistent. She graduates college feeling lost among a sea of people who have already chosen their passions. Sophie, like always, remains maddeningly unsure.
Finally, she ends up in New York, working for her brother’s ex-girlfriend and accepting dates with a neurologist and a biker.  Yet, though she may have chosen a place to go, someone to date, and something to work for, she remains conflicted about what exactly is the right choice for her. Sophie is funny, sarcastic, and deeply critical of herself.  She never seems comfortable with her own choices, her own life, and her own experiences.  In contrast to her brothers, who each find their partners in life and who each have something to work for, she never quite finds her niche.  In the end, The Wonder Spot is not a typical "chick-lit" bildungsroman, but a relatable tale for any modern young woman.

What was the reaction of the Filipinos to being acquired by the United States?

While all the people of the Philippines did not act homogeneously, many Filipinos hated the idea of being acquired by the Americans after the Spanish-American War in 1898.  The Filipinos had been fighting against Spanish colonial rule for years, and they thought that they should gain their independence.  The leader of these rebels, Emilio Aguinaldo, thought that he should be president of the new nation and even thought that he had a deal with the Americans to make him such after the war.  When the war ended and it appeared as though Aguinaldo would not get his nation, he turned against the Americans.  The Filipino War lasted from 1898 to 1902 and killed more Americans than the Spanish-American War.  Both sides committed atrocities, and Aguinaldo's forces attacked both Americans and Filipinos who tried to help the outsiders.  Aguinaldo also had to fight Filipino leaders who also wanted to be the first president of the Philippines.  The war ended only after Aguinaldo's capture.  There would continue to be a Filipino independence movement in the country until independence was granted after World War II.