What is the primary cause of tidal activity on Earth?

The primary cause of tidal activity on Earth is the relative relationships between our planet, the moon, and the sun. Both the sun and the moon have gravitational pulls that affect the liquid water on Earth. Although the sun is much larger than the moon, and therefore has a greater gravitational pull, it's also much farther away than the moon. The relationship between the sun and Earth is pretty steady, so the sun's part in tidal activity is actually quite minor. Much of the variation we see in tides is the result of the moon's orbit around our planet. In many cases, the gravitational pull of the sun and moon conflict with each other; during an eclipse, however, the pull of the moon and sun combine to create the biggest tides experienced on Earth. 

Tides vary regularly throughout the day as a result of the Moon's orbit around our planet. Over longer periods of time, the Earth's rotation around the Sun affects the relative intensity of tides. 

What were the motives behind American overseas imperialism?

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How is Lady Macbeth cruel to Macbeth?

Lady Macbeth is cruel to Macbeth because she wants him to be cruel, and to abandon both his fears and his sense of morality in order to kill King Duncan and seize the throne of Scotland that she sees as his destiny. Upon receiving word of Macbeth's encounter with the witches, Lady Macbeth says he is too full of the "milk of human kindness" to murder the king. She resolves to be full of "direst cruelty" in her efforts to push Macbeth toward fulfilling the witches' prophecy. When Macbeth resolves, at the end of Act I, to "proceed no further in this business," his wife bitterly excoriates him for wavering:

I have given suck, and know
How tender ’tis to love the babe that milks me:
I would, while it was smiling in my face,
Have pluck'd my nipple from his boneless gums,
And dash'd the brains out, had I so sworn as you
Have done to this.

She implies Macbeth is a coward and challenges his masculinity in an attempt to goad him into the murder. Her remarks to Macbeth are undoubtedly cruel, and no doubt would have been somewhat shocking and unnatural to Shakespeare's audiences. We should note that Lady Macbeth did it out of a sincere desire to help her husband rise to the throne of Scotland. Lady Macbeth is indisputably cruel and evil, but she is also, in a twisted way, a very caring and loving wife to her husband. 

`int sqrt(1 - 4x^2) dx` Evaluate the integral

`intsqrt(1-4x^2)dx`

`=intsqrt(1-(2x)^2)dx`

Now apply the integral substitution,

Let u=2x,

`=>du=dx`

`=intsqrt(1-u^2)du`

Now using the standard integral,

`intsqrt(a^2-x^2)dx=(xsqrt(a^2-x^2))/2+a^2/2arcsin(x/a)+C`

`=(usqrt(1-u^2))/2+1/2arcsin(u/1)+C`

Now substitute back u=2x,

`=(2xsqrt(1-(2x)^2))/2+1/2arcsin((2x)/1)+C`

`=xsqrt(1-4x^2)+1/2arcsin(2x)+C`

What are five examples of satire in Gulliver's Travels, book 4?

One element of satire in Part IV is how long it takes Gulliver to recognize the Yahoos as humans, which makes fun of human pretensions and self-deceptions about what they are: "I never beheld in all my travels so disagreeable an animal," he says of the Yahoos. He simply cannot see the common traits he shares with them, even though they stand on two legs and have no tails.

Second, humans are satirized when Gulliver's Houyhnhnm master suggests castrating the Yahoos, letting them die out, and replacing them with asses. If rational creatures like the Houyhnhnms prefer asses to humans, what does that say about humans?

Third, the humans in England are satirized for eating unnecessarily complicated and unhealthy gourmet food. 

Fourth, Swift satirizes Gulliver for his unthinking devotion to the Houyhnhnm, limited creatures who are dull and lack human emotions, despite their rationality. We as readers are meant to laugh when Gulliver says  "I took a second leave of my master, but as I was going to prostrate myself to kiss his hoof, he did me the honor to raise it gently to my mouth."

Fifth, Gulliver is satirized when he returns home to England and is still so enraptured with the Houyhnhnms that he refuses to speak to his wife and children and goes and stays with the horses, trying to talk them as if they were his beloved Houyhnhnms. "When I thought of my family, my friends, my countrymen or [the] human race in general, I considered them as they really were, Yahoos in shape and disposition, only a little more civilized . . . ," This satirizes people like Gulliver who are so caught up in black and white thinking they cannot see the good around them and try instead to imagine "the perfection of nature." Gulliver is satirized for not seeing the flaws in the Houyhnhnms and for failing to see the good in humans. 

What is an example of personification in Ralph Waldo Emerson's essay, "Nature"?

Emerson uses personification in the introduction of his essay to imbue the era in which he lives with uniquely human characteristics:

"Our age is retrospective. It builds the sepulchers of the fathers. It writes biographies, histories, and criticism."

Here, Emerson attributes sentience, critical thinking and even the ability to erect tombs (sepulchers) to a non-human, intangible idea, “our age,” which most nearly means, “the times in which we live.”

A little later, at the end of the first paragraph of chapter one, when discussing the ability of nature to evoke awe and wonder in humans, Emerson again employs personification to lend human characteristics to the stars in the sky.

“But every night come out these envoys of beauty, and light the universe with their admonishing smile.”

Here, Emerson designates the stars as “envoys,” which in common parlance means diplomatic messengers. This is clearly a human description of a non-human object. Then Emerson describes the stars as wearing an “admonishing smile,” another uniquely human characteristic.

This latter example of personification (the admonishing smile) is part of a larger motif present in much of Emerson’s works; he imparts aspects of human behavior and physicality to the natural world in order to convey his feelings of intense kinship for nature. Again and again throughout Emerson's writings, the reader can see that he views the natural world as his friend and constant companion.

Where does the middle finger raised gesture come from? What is its origin?

It is difficult to say exactly when obscene nature of the middle finger originated, but it is possible to say that it has been used since ancient times.  The earliest documented reference to it being offensive is in Ancient Greece, in 419 BC when the gesture was used in a play.  It is believed that the middle finger being raised is done to mimic the private parts of a man.  The Romans also considered the middle finger to be obscene and had a name for it:  digitus impudicus, or indecent finger.  The first reference to the use of "the bird" in the United States occurred in a newspaper account of a baseball player gesturing it at reporters in 1886.  It also should be mentioned that the middle finger is not obscene in all cultures.  As an example, in Iran, the "thumbs up" sign is similar to what the middle finger means.