Friday, August 6, 2010

What is current?

I am assuming that your question refers to electric current.


Electric current is motion of electric charges. The electric charges can move when placed in an electric field. That is, in the region of space where there will be electric force acting on the charges.


Electric charges that are free to move, if placed in an electric field, are found in certain materials called conductors. A metal wire is an example of a conductor. A conductor is used to connect an element where current is needed (such as a light bulb) to a battery, a device that produces potential difference (commonly known as voltage, a measure of change of electric field) between its two terminals. Together, a light bulb, a conductor and a battery can be made into the simplest electrical circuit. The flow of the electric charge around the circuit is electric current.


Electric current is measured as the amount of charge that flows through the cross section of a conductor in a unit of time:


`I = (Delta q)/(Delta t)` . The unit of measurement of the current is Amperes, after the scientist who discovered that the current-carrying wires create magnetic field.

How do you tell the differences between a linear and nonlinear equation?

A linear equation has every variable occurring only to the first power in terms involving only one variable at a time, and possibly constants. Every term has degree one or zero.


Examples include x=3 or y=-2 which are linear in one variable, y=2x+3 or 2x-3y=6 which are linear in two variables, x+y+3z=-10 which is linear in three variables etc...


The graphs of linear equations are lines (hence the name.) For linear equations of two variables, there is a constant rate of change called the slope -- as one variable changes by a fixed increment, the other variable will also change by a fixed increment (not necessarily the same.)


A nonlinear equation has a term or terms with degree greater than one, or a negative or rational (non-integral) power.


Examples include `y=x^2, y=1/x, y=x^(2/3), y=x^3-x ,z=xy` .Note that z=xy is not linear as the xy term has degree two. Transcendental functions (e.g. trigonometric, logarithmic, etc...) are not linear.


The graphs of nonlinear equations involve curves.


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Wednesday, August 4, 2010

general solution cos (4x-60)=sin2x [-90:90]

Solve `cos(4x-60^@)=sin2x ` :


`cos(4x-60^@)=sin2x `


`sin(4x+30^@)=sin2x `


Take the inverse sine of both sides:


1. `4x+30=180-2x+360n ` where n is an integer.


6x=150+360n


x=25+60n


or


2. 4x+30=2x+360n


2x=-30+360n


x=-15+180n


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The general solution is x=25+60n for n an integer or x=-15+180n for n an integer.


On the interval [-90,90] the solutions are x=-35,-15,25,85


Here is the graph: the left side in black and the right side in red:



convert the scale from radian to degrees.

I am currently doing an assignment on apartheid laws. I chose the Separate Amenities Act. In an interview, what would be some good questions to ask...

The Separate Amenities Act was connected to the system of segregation in South Africa. If you were to interview a person who experienced it, I would suggest several questions to ask in this interview.


Below is a pool of questions to consider asking. The goal of these questions is to try to get a picture of what it was like for this person who lived with these segregation laws.


  • How old were you when you first experienced segregation? (Understanding a person’s age should shed some light on that person’s experiences. A younger person may have a different view than an older person.)

  • Can you describe how the system of segregation worked? I would ask the person to focus on some form of public life such as a hotel, movie theater, or restaurant.

  • Explain how segregation worked in the field of education? How did this impact your education?

  • How did these laws impact your family?

  • How do you personally feel about these laws?

  • What, if anything, did you try to do to change these laws?

  • How do you believe these laws have impacted how you view the world today?

  • What do you tell your children or grandchildren about this time in South Africa's history?

  • What message would you like my classmates to take from your experiences?

Monday, August 2, 2010

What are literary conventions? Do you know of any examples?

A literary convention is a commonly used device or aspect of a certain kind of work. If you are reading a certain type of literary work, you can expect it to conform to certain conventions. For example, plays are typically divided into acts and scenes, and characters generally speak to each other with dialogue. In Shakespeare's dramas, characters communicate their inner thoughts through the use of soliloquies. If you do not understand this particular literary convention, it will be difficult for you to make sense of what is going on--you might think that the character is speaking to other characters rather than privately expressing their inner thoughts. Some literary forms, like the novel, for example, have fewer conventions. (For example, some novels are broken up into chapters, and some are not.)

Prove that `sqrt(7)` is irrational.

Hello!


We'll prove this by a contradiction. Let `sqrt(7)` is a rational number, that means `sqrt(7)=m/n` where m and n are natural numbers.


Also let m and n be coprime. If they aren't, divide both by their GCF.


Now we square the equality and obtain `7n^2=m^2.` Therefore 7 is a factor of `m^2.` Because 7 is a prime number, 7 is also a factor of m itself. So `m=7k` for some natural k.


Thus `7n^2=7^2*k^2,` or `n^2=7k^2.` So 7 is a factor of `n^2` and therefore of n. But this means m and n have a common factor 7, which is a contradiction. This contradiction proves that `sqrt(7)` is irrational. 

Why is Jimmy Valentine pardoned?

Jimmy Valentine is pardoned because he has many important friends and connections on the outside. The last sentence of the first paragraph of the story indicates this important fact.



When a man with as many friends on the outside as Jimmy Valentine had is received in the “stir” it is hardly worth while to cut his hair.



Jimmy is characterized throughout "A Retrieved Reformation" as young, intelligent, good-looking, well-dressed, and popular. Everybody, including the Warden, likes him. The name Jimmy, rather than Jim or James, is intended to suggest likeability and popularity. The last name of Valentine suggests affection. Jimmy has "many friends on the outside" because of his winning personality. Since he is very successful in his profession as a safecracker, he is generous with his money. No doubt he contributes handsomely to the right politicians in the days when graft and corruption were so commonplace.


At the same time that Jimmy is portrayed as successful, there are some indications that he may be too successful. Too many people know about him and talk about him. He seems to be in danger of becoming a hardened criminal who keeps getting arrested and spending more and more time behind bars. One indication is contained in the first words Mike Dolan, an apparent cog in a big politician machine, says to him.



“Sorry we couldn't make it sooner, Jimmy, me boy,” said Mike. “But we had that protest from Springfield to buck against, and the governor nearly balked. Feeling all right?”



Jimmy has been incarcerated much longer than he had expected. This must have given him time to think about his future.



He had served nearly ten months of a four year sentence. He had expected to stay only about three months, at the longest. 



Jimmy knows he is in danger of losing all his "friends on the outside" if he keeps getting busted for bank jobs. They will want to forget they ever knew him. He has become too successful, too notorious. When he commits three safecracking jobs right after being released from state prison:



Ben Price investigated the scenes of the robberies, and was heard to remark:




“That's Dandy Jim Valentine's autograph. He's resumed business. Look at that combination knob—jerked out as easy as pulling up a radish in wet weather. He's got the only clamps that can do it. And look how clean those tumblers were punched out! Jimmy never has to drill but one hole. Yes, I guess I want Mr. Valentine. He'll do his bit next time without any short-time or clemency foolishness.”



Jimmy is smart enough to move to an entirely new territory of operations. In Elmore, Arkansas, he falls in love at first sight with Annabel Adams and decides to reform. But she is only the catalyst. He had been sensing the need for a change since spending ten sobering months in prison. He seemed indifferent to the Warden's lecture at the time of his release, but he was really thinking along the same lines as the Warden, who liked him and gave him this sincere parting advice:



“Now, Valentine,” said the warden, “you'll go out in the morning. Brace up, and make a man of yourself. You're not a bad fellow at heart. Stop cracking safes, and live straight.”



Jimmy was beginning to realize that honesty is the best policy, that crime does not pay. A man with all his superior assets--intelligence, skills, good looks, winning personality--can do better by going straight than by following the downward path of a recidivist. His success in Elmore proves it. He is soon engaged to the most beautiful girl in town and has become a prosperous leading citizen.

find square roots of -1+2i

We have to find the square root of `-1+2i` i.e. `\sqrt{-1+2i}` We will find the square roots of the complex number of the form x+yi , where ...