What is the natural number x if C(x,2) + P(x,2) = 30?

# What is the natural number x if C(x,2) + P(x,2) = 30?

• MATH

What is the natural number x if C(x,2) + P(x,2) = 30?

C(x, 2) = x!/ ( 2! *(x – 2)!) P(x , 2) = x! / (x – 2)! Now C(x,2) + P(x,2) = 30 => x!/ ( 2! *(x – 2)!) + x! / (x – 2)! = 30 => x*(x – 1)/2! + x*(x – 1) = 30 => x*(x – 1)/2 + x*(x – 1) =…

• MATH

Prove that the number (cospi/4+i*sinpi/4)^2008 is real.

(cospi/4 + i*sinpi/4)^ 2008 Let us find the values for the numbers inside the brackets. ==> cospi/4 = sqrt2/2 ==> sinpi/4 = sqrt2/2 ==> ( sqrt2/2 + (sqrt2/2)*i ) ^ 2008. Let us rewrite the…

• A ROSE FOR EMILY

In “A Rose for Emily,” what are some of the feminist elements?

In William Faulkner’s strange and haunting short story, “A Rose for Emily,” there are several feminist elements. The first example can be seen when Miss Emily goes out riding with Homer Baron. She…

• MATH

What are x and y? x(1+2i)+y(2-i)=4+3i

x(1+ 2i) + y( 2-i) = 4 + 3i Let us expand the brackets. ==> x + 2xi + 2y – yi = 4 + 3i. ==> We will combine real terms and complex terms together. ==> (x+ 2y) + (2x -y) i = 4 + 3i. Now we…

• THE COLOR PURPLE

What important events happen in the second half of The Color Purple?

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• SILENT SPRING

What point was Rachel Carson trying to get across to the general public in Silent Spring?

In her 1962 book, Silent Spring, Rachel Carson was trying to alert the public to the dangers of pesticides. She was trying to make people more environmentally aware. At the time that Carson wrote…

What is the difference between a budget deficit and the national debt?

The basic difference between these two things is that a budget deficit is only about one year while the national debt is cumulative. The budget deficit is the difference between the amount the…

• MATH

I need to find the recurrence for integral from 0 to pi/2 sin^n(x) * cos(x) dx.I made int 0-pi/2…

(sin x)^n = sin ^n (x) are the same thing

What are the major steps in developing effective marketing communications?

As a college senior and probably a business or marketing major, this is a question that sounds like it is directed towards specific class or textbook information, so keep that in mind as you read…

• MATH

Determine the perimeter of triangle ABC if AB=6, B=pi/4, C=pi/6.

Given ABC is a triangle such that: B = pi/4 = 45 degree. C = pi/6 = 30 degrees. Then, the third angle A = 180 – B – C = 105 ==> A = 105 degrees. Now we know that: AB / sinc = AC / sinB ==> 6…

• MATH

Find n if (n+1), (n-1), 4 are the terms of n arithmetic sequence.

Given that (n+1), (n-1), and 4 are terms in an arithmetic sequence. Let (r) be the common difference between the terms. Then, we know that: ==> (n-1) = (n+1) + r ==> n-1 = n+1 + r ==> -1=…

• MATH

Given that sina + sinb =1 and cosa + cosb = 1/2 calculate cos(a-b)

We’ll note the given relations as: sina + sinb = 1 (1) cosa + cosb = 1/2 (2) We’ll raise to square (1), both sides: (sina + sinb)^2 = 1^2 We’ll expand the square: (sin a)^2 + 2sina*sinb + (sin…

• MATH

What is x if cos(2x+pi/2)=cos(x-pi/2)?

To find x if cos(2x+pi/2)=cos(x-pi/2). If cosa = cos b, then a = 2npi+b or 2npi-b. Therefore if cos(2x+pi/2)=cos(x-pi/2), then (i) 2x+pi/2 = 2npi+x-pi/2 or (ii) 2x+pi/2 = 2npi-x+p/2. 2x-x =…

• HARD TIMES

In Hard Times, how does Louisa Gradgrind’s marriage to Bounderby set an example of patriachal and…

This is a great question! It is clear that Dickens presents Bounderby and Louisa’s marriage as an unhappy one. Note how it is juxtaposed in the text with another unhappy marriage – that of Stephen…

• MATH

Solve for x . log3 (x+1) + log3 (x+3) = 1

log3 (x+ 1) + log3 (x+ 3) = 1 We will use the logarithm properties to solve for x. We know that log a + log b = log a*b. ==> log3 (x+1) + log3 (x+3) = log3 ( x+ 10/(x+3) ==> log3 (x+1)/(x+3)…

• MATH

evaluate the integral of x^3-x if x=-1 and x=1

Let f(x) = x^3 – x We need to find the integral of f(x) on the interval [ -1, 1]. Let us assume that F(x) = integral f(x). Then the integral is : A = F(1) – F(-1). Let us integrate f(x). ==>…

• TO KILL A MOCKINGBIRD

What are are some quotes that support the theme of racism (or racist quotes)?

There are too many examples of racism and “racist” quotes in the book to count. I will try to give you a few broad examples that will allow you to choose specific quotes. Considering the…

• MATH

Evaluate the integral using the fundamental theorem of calculus for y=4x^t + 5x^-1 + 6sinx

The fundamental Theorem of Calculus states that: Int f(x)dx = F(b) – F(a) for x = a to x =b. In our case, the limits are not given, so we could only calculate the indefinite integral: Int (4x^t +…

• MATH

How do you work our 3x=4-Y Please help .. if you could explain it in quite a simple way, thanks.

You need to isolate the variable y to one side, hence, you need to subtract 4 both sides, such that: 3x−4=4−4−y⇒3x−4=−y3x-4=4-4-y⇒3x-4=-y You need to multiply by -1 both sides, such that:

• SOCIAL SCIENCES

What makes an act good or bad, right or wrong, just or unjust?In his Existentialism is a…

This is one of those all-time great questions that everybody has to think about at least once in their lifetime. How does one define “good” and “bad?” This is hard because it is so subjective….

• MATH

find the exact value: sin[arccos(3^(1/2) / 4]

sin(arccos(3^(1/2)/4] We will simplify starting from inside of the brackets out. Let us rewrite 3^/12. We know that …………. 3^1/2 = 1.7321 ==> 3^1/2 / 4 = 0.4230. ==> arccos(3^1/2)/4 =…

• A DOLL’S HOUSE

Speak about gender roles regarding character vs society in A Doll’s House.Note the symbolism in…

During Nora’s costume change, in Henrik Ibsen’s A Doll’s House, the reader symbolically sees Nora and Torvald throw off the conventions of society to become—temporarily—different people….

• ANTIGONE

In Antigone, what are some lessons that we can learn from Antigone’s act of bravery?

You might want to post this question in the discussion postings for this group to gain a wide range of responses. For me, this play is all about the conflict between our duties to the state of…

• THE HELP

In The Help what did Minny do to Hilly that she said she could never tell anyone when she was fired?

When Minny was working for Hilly’s mother’s, Hilly treated Minny poorly and always accused her of trying to steal things from the home. Minny was fed-up with Hilly’s disrespectful attitude, so she…

• SILAS MARNER

What hope does Silas have?

All of Silas Marner’s hope in life lies in his adopted daugher Eppie. Prior to her unusual arrival on his doorstep, he was a hermit and a miser — only happy by himself when he could get out all…

• SILAS MARNER

In Silas Marner, when had he sought comfort before from this same source?

Silas Marner had always sought comfort from the same source: His loom. When he weaves he is able to concentrate in one thing instead of letting his thoughts and emotions go astray. When he lived in…

• THE SKY IS GRAY

In “The Sky Is Gray,” how are passivity and active agency used to work out problems?

This is an interesting perspective on this short story. “The Sky is Gray,” by Ernest J. Gaines, is set in the South (Louisiana) during the 1940s. This is a time and place in which both racism and…

• SILAS MARNER

To what does Silas turn for comfort?

Silas Marner turns to his weaving for comfort. We cannot say that the kindness of his neighbors did not touch his heart at all. In fact, he began to appreciate all the warm treatment he began to…

• SILAS MARNER

How are Silas’s reactions realistic when he found out that something terribe had happened to him?

When Silas realized that his gold was gone and that someone had basically welcomed himself into his house for the purpose of stealing from him, his reaction was quite realistic, and very similar to…

• THE GIFT OF THE MAGI

Jim and Della were the richest couple on earth. This is paradox. Explain why?

The paradox is that Jim and Della are actually poor. His job earns only enough to eke out an existence while she is a housewife. What did it mean that they were the richest people on earth? Riches…

• SILAS MARNER

What were Silas’s actions after finding his gold missing?

Upon finding out that his gold was missing, Silas had a series of reactions that became a chain of events which led to Silas’s ultimate breakdown. Interestingly, this horrible moment was also the…

• TO KILL A MOCKINGBIRD

Attics and objectsIn To Kill a Mockingbird what specific object/things/words help describe who…

In terms of objects, I see his dress or attire, the 3-piece suit worn tight demonstrating the professionalism he employs with both his work and his children. A gun might represent Atticus because…

• SCIENCE

in computer programing c++ how can one make the program fordiscount and profit?c++ is computer…

Please send any specific program and I’ll send you the codes.

• SCIENCE

What is the name of the part of the brain which processes language?also name of the man on which…

The brain is composed of the cerebrum, cerebellum and the medulla oblongata. The cerebrum is where all the sensory organs register. Also, thought and learning is processed there. Language is…

• THE STRANGER

Describe Camus’s use of imagery at the climactic moment? This question is at…

In Part II of The Stranger, Camus uses a mix of visual and auditory imagery that is connected violently to nature and the body in order to show the gun shoots itself instead of Meursault…

• HAMLET

What would you consider the possible theme behind Hamlet and Ophelia’s relationship?I see Ophelia…

You have an interesting take on Ophelia’s character and the question I would ask you and I think you need to answer to create you “theme” is: What do you mean when you say that she “shows her true…

Define the term “sociocultural environment” with regard to business.

Every business firm operates in a given type of environment. The environment is the firm’s surroundings. Some aspects of the environment have the ability to affect how the firm will need to…

• THE KITE RUNNER

In The Kite Runner, how would you write a personal response to the letter from Hassan?

This would be a great assignment! You have a good teacher. The letter that Rahim Khan delivers to Amir is to be found in Chapter Seventeen of this amazing novel. In this letter, Hassan makes it…

• THE KITE RUNNER

In The Kite Runner, what shocking news does Amir learn when Rahim contacts Amir and tells him to…

It is in Chapter 17 that Amir finds out two pieces of shocking news. Firstly, Rahim Khan tells him about Hassan’s death. However, by far the most shocking piece of news concerns the real father of…

• SCIENCE

What things are formed during the fetal period?

The medical community divides the fetal growth and development stages (which occur during pregnancy) into three trimesters. A completely full-term pregnancy lasts a total of 40 weeks, and these 40…

• THE GIVER

What are the two main themes of The Giver?

I think that one major theme in the book comes down to the role of the individual and their place in society. I believe that Jonas’ initial acceptance of his place in the social order has to be…

• OEDIPUS REX

In Oedipus Rex, how does Oedipus struggle with free will?

A key theme in this remarkable play is the conflict between fate and free will. In so many works of literature this is a massive issue, as characters try to exert their independence and…

• HAMLET

I’m writing a paper on a theme of Hamlet that is difficult to understand. Here is the paper…

One suggestion would be to focus on the “To be or not be” soliloquy — especially the last 6 lines. It is here that Hamlet is summing up his thoughts, and where I think the play becomes very…

• MACBETH

Analyze: Who suspects Macbeth? Support your answer with lines from Act 2.

MacDuff suspects Macbeth of having something to do with Duncan’s death. This is clear in the last scene of Act II when he and Ross are speaking about Macbeth’s coronation at Scone. Ross asks…

• MACBETH

What examples of the motifs of blood and sleep are in Act 2 of Macbeth?

In Act 2 of Macbeth, the motifs of blood and sleep are seen after Macbeth murders King Duncan. Specifically in Scene 2, Macbeth runs back into his chamber to meet Lady Macbeth, and he is sure that…

• TO SIR, WITH LOVE

Describe with 4 or 5 examples how Braithwaite gained the respect and admiration of his students…

Most of what was done to gain Braithwaite’s students’ respect revolves around being more effective in working with them and not against them. When he decides to break out of traditional modes of…

• COMPUTER/TECHNOLOGY

How important is it to know PowerPoint and access it in our life? And why?How important is it to…

It really depends a lot on what you are going to do with your life. But Powerpoint (or something like it that might come around in the future) is important for a lot of professions. Teachers, of…

• BIOLOGY

What are the most important microbes responsible for the creation of fermented soybean products?

There are many fermented soybean products that are consumed all over the world. Though all of them differ in taste, texture and use, there are only a few microbes are used to ferment them. Most of…

• JUDE THE OBSCURE

How can you describe Jude from Jude the Obscure?

Jude, the protagonist of the novel, is a conflicted person. However, the conflicts that exist within his character at the outset of the novel appear to be very different from those that conflict…