How did King Leopold's real goal in the Congo differ from his purported goal?

In short, Leopold said he wanted to help the Africans, but he truly wanted to exploit them.  King Leopold attempted to describe his intentions in Congo as philanthropic to the international community.  Using the racism that was common in the 19th Century, Leopold describes a people in this rain forest region that were incapable of caring for themselves. He claims to be able to protect the Africans from Arab slave runners.  Leopold also feels that the region is to be converted to Christianity and opened for capitalist development.  He is able to convince other imperialist powers to operate Congo as his own private plantation.  Using military tactics and brutal enforcement of his policies, Leopold made the entire population his private slaves.  He forced them to harvest rubber until there was none left, all to personally benefit himself.  It has been estimated that Leopold was responsible for ten million deaths in the Congo.  

`int sec^2(3x) dx` Find the indefinite integral

Indefinite integral are written in the form of `int f(x) dx = F(x) +C`

 where: `f(x)` as the integrand

           `F(x)` as the anti-derivative function 

           `C`  as the arbitrary constant known as constant of integration

For the given problem: `int sec^2(3x)dx` , the integrand function: `f(x)=sec^2(3x)` is in a form of trigonometric function.

To solve for the indefinite integral, we may apply the basic integration formula for secant function:

`int sec^2(u)du=tan(u)+C`

We may apply u-substitution when by letting:

`u= 3x` then `du =3 dx` or` (du)/3 = dx` .

Plug-in the values of `u =3x` and `dx= (du)/3` , we get:

`int sec^2(3x)dx =int sec^2(u)*(du)/3`

                          `=int (sec^2(u))/3du`

Apply basic integration property: `int c*f(x)dx= c int f(x)dx` .

`int (sec^2(u))/3du =(1/3)int sec^2(u)du`

Then following the integral formula for secant, we get:

`(1/3)int sec^2(u)du= 1/3tan(u)+C`

Plug-in `u =3x` to solve for the indefinite integral F(x):

`int sec^2(3x)dx=1/3tan(3x)+C`

What is the main problem in Unwind by Neal Shusterman, and how is Connor affected by it?

I would say that the main conflict that is affecting Connor, Risa, Roland, and other Unwinds is their struggle for survival.  

The book opens by telling readers that the "Bill of Life" allows parents to retroactively abort their child during the teenage years.  The child is "unwound."  This means that every single body part, organ, tissue, etc. is harvested and used for spare parts.  This allows the child to "live" forever in a divided state.  

Connor secretly discovers that his parents are having him unwound.  This is the story's inciting incident.  Connor doesn't want to be unwound, so that is the central conflict surrounding Connor.  He wants to avoid going to a harvest camp because he doesn't want to be unwound.  His desire to live causes him to take all kinds of drastic actions.  The first action is his running away from home and going AWOL.  Along the way he becomes friends with various other Unwinds that are also looking to avoid being unwound.  Connor eventually makes his way to the Graveyard, which is a safe haven of sorts for runaway Unwinds.  As the novel comes to a close, Connor has been given a new identity, which shows him as being too old to be unwound.  He then uses his newfound freedom to become the new head of the Graveyard and help other Unwinds find safety. 

What is the theme of the poem "Lucy Gray" by William Wordsworth?

William Wordsworth's "Lucy Gray" tells the story of an innocent young girl who is lost in the wild and never found again. The suggestion is that she dies, although at the end Wordsworth suggests Lucy might still dwell in the wilderness somewhere far from civilization. It's unclear whether he's implying that Lucy is still alive, or if he's merely suggesting that her spirit lives on in the natural world. 

"Lucy Gray" is part of Wordsworth's "Lucy" poems, a group that includes the famous "She Dwelt Among the Untrodden Ways." All of these poems meditate upon a similar theme: the death of some unimportant and unknown person who lived in relative isolation in the midst of natural beauty. In general, these poems depict a young girl called Lucy who lives in close proximity to the wild and is gradually absorbed by the wild lands she inhabits, either through death or simply by disappearing. "Lucy Gray" follows this theme, as it shows the young, innocent Lucy disappearing into the vast world of nature.

In "A Retrieved Reformation" by O. Henry, what is Jimmy's attitude toward the warden?

Jimmy's attitude towards the warden is dismissive. He playfully mocks the warden by displaying nonchalance and faux innocence when the warden gives him some unsolicited advice.

According to the story, Jimmy has only served 'ten months of a four year sentence.' Because Jimmy has influential friends, his stints in prison always appear to be short. In Jimmy's eyes, he can afford to disregard the warden's impassioned advice. For his part, the warden thinks that Jimmy is a good man who just needs to buckle down and to 'live straight.'

In the conversation with the warden, Jimmy never takes the bait. He refuses to engage the warden in a discussion of his future. Each time the warden questions him about his motives or his part in a previous heist, Jimmy resorts to humor to distract the warden. In the end, the warden can only dismiss Jimmy with a blunt 'Better think over my advice, Valentine.' When Jimmy is released the next day, the warden shakes Jimmy's hand and hands him a cigar. With Jimmy's confident stance, we know that we haven't heard the last of this enigmatic character.

In The Sign of the Beaver by Elizabeth George Speare, how does Matt win Attean's respect?

Matt won Attean's respect in a very unexpected way. When Attean invited Matt to leave with his tribe, Matt refused. Even though both Saknis and Attean reiterated their joint desire to have Matt with them as the tribe moved further north, Matt held steadfast to his decision to stay.

It was Matt's steadfast loyalty to his father and family that earned him respect in Attean's eyes. When Matt realized that his integrity had won him Attean's respect, he was initially shocked. After all, he had previously tried in numerous ways to earn his Indian brother's respect, but to no avail. It was only when he made his decision to keep his word to his father that Attean finally respected him as an equal.

There was no amusement and no scorn in Attean's eyes. How very strange, Matt thought. After all the brave deeds he had dreamed of to win this boy's respect, he had gained it at last just by doing nothing, just by staying here and refusing to leave.

`f(x) = tanh(4x^2+3x)` Find the derivative of the function

`f(x) = tanh(4x^2+3x)`

The derivative formula of hyperbolic tangent is

• `d/dx [tanh(u)] = sec h^2(u)*(du)/dx`

Applying this formula, the derivative of the function will be

`f'(x)=d/dx[tanh(4x^2+3x)]`

`f'(x) = s e c h^2(4x^2+3x)*d/dx(4x^2+3x)`

`f'(x) = sec h^2(4x^2+3x)*(8x+3)`

`f'(x)=(8x+3)sec h^2(4x^2+3x)`

Therefore, the derivative of the given function is `f'(x)=(8x+3)sec h^2(4x^2+3x)` .