When did the Union Pacific and Central Pacific railroads came together?

As the United States expanded from the Atlantic Ocean to the Pacific Ocean, the need for transportation across the country grew. In 1862, Congress passed the Pacific Railway Act. This law authorized the Central Pacific to begin building the transcontinental railroad eastward from Sacramento, California, and the Union Pacific to begin building westward from Omaha, Nebraska. The goal was to have these two railroad companies meet, which would complete the building of the transcontinental railroad.

Building the transcontinental railroad was a difficult task. There were several obstacles to overcome. The mountains made it hard to build the railroad. Unfriendly Native American tribes presented problems. The climate wasn’t always great for building a railroad. The hot summers and cold winters presented challenges.

Eventually, both companies completed laying the track, and they met at Promontory Point, Utah on May 10, 1869. The final spike was driven into the tracks. The building of the transcontinental railroad was now completed.

How is the injustice that Garrett faces in Boot Camp by Todd Strasser similar to the injustice faced by Aibileen and Minny in The Help by Kathryn...

In Boot Camp by Todd Strasser, the main character, Garrett, is treated with paternalism that is cruel in its intent. As he is being taken to a militaristic boot camp called Lake Harmony in upstate New York, the man transporting him tells him, "Your parents sent you to Lake Harmony because they love you" (page 2). His captors, or "transporters," tell him that they are bringing him to the boot camp for his own good, but his detention in the boot camp is a form of cruelty and imprisonment.

In a similar way, Aibileen and Minny, black maids in The Help, are robbed of their own free will and controlled by whites who state that they have Aibileen's and Minny's best interests in mind. As Aibileen says, "Sides stealing, worse thing you'n do for your career as a maid is to have a smart mouth" (page 17). Like Garrett, whose parents dislike his choosing his own relationships and charting his own course, Aibileen and Minny are supposed to do what their employers want and are supposed to keep their true thoughts to themselves. The white women who employ Aibileen and Minny decide on a Home Help Sanitation Initiative, which involves building outhouses for their black domestic help to use, because, as they state, "99% of all colored diseases are carried in the urine" (page 158). This is another form of paternalism. The white employers are treating their maids with disrespect but tell them it is for everyone's best interest. In this way, the white employers are similar to Garrett's parents in Boot Camp. 

`int_3^6 1 / (25 + (x-3)^2) dx` Evaluate the definite integral

To be able to solve for definite integral, we follow the first fundamental theorem of calculus: `int_a^b f(x) dx = F(x) +C`

 such that f is continuous and F is the antiderivative of f in a closed interval `[a,b]` .

 The `[a.b]` is the boundary limits of the integral such as lower bound=a and upper bound = b.

 For the given problem:` int_3^(6) 1/(25+(x-3)^2)dx` ,

it resembles the basic integration formula:

`int (du)/(a^2+u^2) =(1/a)arctan(u/a)+C` .

 By comparison: `(du)/(a^2+u^2) vs(1/(25+(x-3)^2))dx` , we may apply

u-substitution by letting:

`u^2=(x-3)^2` then `u = x-3`

where `a^2=25 or 5^2` then `a=5`

Derivative of u will be `du = 1 dx` or `du = dx` .

`int_3^(6) 1/(25+(x-3)^2)dx =int_3^(6) 1/(25+(u)^2)du`

Applying the formula:

`int_3^(6) 1/(25+(u)^2)du =(1/5)arctan(u/5)|_3^6`

Plug-in `u = x-3` to express the indefinite integral in terms of x:

`(1/5)arctan(u/5)|_3^6 =(1/5)arctan((x-3)/5)|_3^6`

Recall `F(x)|_a^b = F(b) - F(a)` then:

  `(1/5)arctan((x-3)/5)|_3^6 = F(6)-F(3)`

                 ` = (1/5)arctan((6-3)/5) -(1/5)arctan((3-3)/5)`

                `= (1/5)arctan(3/5) -(1/5)arctan(0/5)`

                ` =(1/5)arctan(3/5) -0 `  

                  `=(1/5)arctan(3/5) `   as the Final Answer.

Note: `arctan(0/5) = arctan(0)= 0 `  

since `tan(theta) = 0` when `theta=0`

How does Jane Austen use Lady Catherine to highlight the theme of prejudice?

Lady Catherine's wealth and status entitle her, in her own opinion, to order others around and judge them as she pleases.  When she learns of the rumored engagement between her nephew, Mr. Darcy, and Elizabeth Bennet, she immediately sets out to confront Elizabeth about the unsuitability of the match based on Elizabeth's lower social status.  While the rumor isn't true, it also isn't too far from the truth.  Lady Catherine doesn't care if Elizabeth would make her nephew happy; she doesn't care if he loves her.  Her main concern is what a degradation it would be for Darcy to marry Elizabeth, a prejudice she has based on her knowledge of Elizabeth's family and connections. Lady Catherine had heard about the behavior of Elizabeth's sister, Lydia, as well as her mother's lack of family status, and thus she believes that she can accurately judge Elizabeth based on that knowledge, without really knowing Elizabeth or what her relationship with Darcy is like.  Lady Catherine's prejudice against Elizabeth eventually alienates her from her nephew and his household after he and Elizabeth are married. 

How can you tell from the story that the policeman is Jimmy in "After Twenty Years"?

Jimmy's letter shows he was the policeman who conversed with Bob in the beginning of the story.

In the letter, Jimmy mentions he was on time to meet Bob. While speaking with him, however, he recognized Bob as a criminal wanted by Chicago cops. Jimmy asks a plainclothes officer to impersonate him because he can't bring himself to arrest a man he used to call a friend.

I didn’t want to arrest you myself. So I went and got another cop and sent him to do the job.

The contents of the letter make it clear Jimmy was the police officer. As we look back at the story, the letter explains why Jimmy asked how long Bob was willing to wait:

“I’ll go on my way,” he said. “I hope your friend comes all right. If he isn’t here at ten, are you going to leave?” “I am not!” said the other. “I’ll wait half an hour, at least. If Jimmy is alive on earth, he’ll be here by that time. Good night, officer.”

Based on Bob's answer, Jimmy may have concluded half an hour was plenty of time for another officer to impersonate him and meet with Bob.

Bob's answer also shows he still has some affection for his old friend, Jimmy. The men may not be close now, but past memories and shared experiences are often difficult to forget. This is perhaps the reason Jimmy sends another officer to do his job.

What are two main reasons the narrator of the first part of Frankenstein gives for why he is adventuring into the frozen north?

Robert Walton is attempting to reach the North Pole and he gives at least three reasons for doing so. He is curious to see a part of the world never seen by others, he hopes his discovery will benefit mankind, and he wants to gain glory for his discovery.

In a letter to his sister, Walton writes, "I shall satiate my ardent curiosity with the sight of a part of the world never before visited, and may tread a land never before imprinted by the foot of man." This desire to gain knowledge and explore untraveled land mirrors Victor Frankenstein's desire for knowledge and his unprecedented creation of human life. 

Walton goes on to say that this discovery will have an "inestimible benefit" for "all mankind." Victor Frankenstein also believed that his scientific discoveries will benefit humanity as his goal is to "banish disease from the human frame, and render man invulnerable to any but a violent death!"

Finally, Walton asks his sister, "do I not deserve to accomplish some great purpose? [...] I preferred glory to every enticement that wealth placed in my path." Similarly, Victor Frankenstein states, "Wealth was an inferior object; but what glory would attend the discovery."

Interestingly, both Walton and Frankenstein are traveling North, Walton to gain knowledge and fame, and Frankenstein to destroy that which he hoped would bring him the same.

What did Helen mean when she said, "Knowledge is love and light and vision" in The Story of My Life?

As a young girl, Helen Keller became deaf and blind due to an illness. Her life was plunged into darkness. Her parents were determined to seek help for her. They wanted Helen to get an education and to learn how to communicate. They sought expert after expert to find help. They were eventually told to contact Mr. Anagnos, who ran a school for the blind. It was through him that they found Annie Sullivan, the woman who became Helen's teacher. Miss Sullivan helped lift Helen from the darkness she had lived in for years. Helen looked back on this and described it using a metaphor:

Thus I came up out of Egypt and stood before Sinai, and a power divine touched my spirit and gave it sight, so that I beheld many wonders. And from the sacred mountain I heard a voice which said, "Knowledge is love and light and vision."

Helen compared her emergence from darkness to the Hebrew people escaping from Egypt. She also referred to Moses, who encountered God on Mount Sinai. She metaphorically heard a voice speaking to her. Through knowledge, Helen discovered "love and light and vision."