• MATH

Prove that the number a is natural.a = (2^(2n+3)*3^(n+2)*5^(2n+1) + 3^(n+3)*4^(n+2)*5^(2n))/792…

We have a = (2^(2n+3)*3^(n+2)*5^(2n+1) + 3^(n+3)*4^(n+2)*5^(2n))/792 => (2^3*2^2n*3^2*3^n*5^1*5^2n + 3^n*3^3*4^n*4^2*5^2n)/792 => (8*9*5*2^2n*3^n*5^2n + 27*16*3^n*4^n*5^2n)/792 =>…

1 educator answer

• MACBETH

In Act IV, Scene III, Malcolm deliberately lies to Macduff. What do this behavior and the reason…

This is a rather curious scene in this play where Malcolm shows his own character and ability to manipulate and test his subjects. In response to Macduff’s claims that Macbeth must be deposed,…

2 educator answers

• MATH

Solve the equation 0.2*[0.2*(x-0.2)-0.2]-0.2=0.2.

We have to solve the equation 0.2*[0.2*(x-0.2)-0.2]-0.2 = 0.2 0.2*[0.2*(x – 0.2) – 0.2] – 0.2 = 0.2 divide all the terms by 0.2 => 0.2*[0.2*(x – 0.2) – 0.2]/ 0.2 – 0.2/0.2 = 0.2/02. =>…

1 educator answer

• MOBY DICK

Is Moby Dick still relevant today ?

There’s a fairly cool advertisement for AT&T’s Blackberry Torch mobile device that makes the case for its relevancy in the modern setting. Even outside of that, I think that a case can be made…

1 educator answer

• THE SCARLET LETTER

What is The Scarlet Letter about in chapter 3?chapter 3 scarlet letter

Chapter 3 of the Scarlet Letter is titled “The Reveal” and it is a very important moment in the story of Hester Prynne. In this chapter we are taken back to when Hester Prynne had just been…

1 educator answer

• MATH

What is the quantity of tomatoes eaten in two days in the following case?A family eats tomatoes…

It is given that the family has eaten 1.5 kg on the first day and the next day they ate 0.35 kg more than they did on the first day. So they ate 1.5 + 0.35 = 1.85 kg on the second day. If we add…

2 educator answers

• MATH

Given that f:[a,b] –>R is continuous and f(x)=f(a+b-x) prove that (a+b)/2*integral of…

So, we’ll have to prove that: Int x*f(x)dx = (a+b)/2*Int f(x)dx We’ll calculate the integral from the left side substituting x = a + b – t. By definition, f(a + b – t) = f(t), so the integral will…

• MATH

Determine the expression of antiderivative of f(x)=1/cos^4(x)

The question states that f(x) = 1/ (cos x)^4. We have to find the integral of f(x) = 1/ (cos x)^4. (cos x)^-4 = (sec x)^4 = (sec x)^2 * (sec x)^2 => ((tan x)^2 + 1)* (sec x)^2 => ((tan…

2 educator answers

• MATH

Verify if f'(x)=g(x) . f(x)=x^3+ln(x), g(x)=1/x+3x^2.

The question gives f(x)=x^3+ln(x) and g(x)=1/x+3x^2. Differentiating f(x), we use the relations that the derivative of x^n is n*x^(n-1) and the derivative of ln x is 1/x. These five f'(x) = 3*x^2 +…

2 educator answers

• MATH

What is the angle y if sin^2y=5siny-6 ?

The question states that (sin y)^2 = 5* sin y – 6. let x = sin y => x^2 = 5x – 6 => x^2 – 5x + 6 = 0 => x^2 – 3x – 2x + 6 = 0 => x(x -3) – 2( x – 3) =0 => (x – 2) (x -3) = 0 x has…

2 educator answers

• MATH

Where does the extreme value of y = -3x^2 + 2x + 5 lie?

Given the function: y= -3x^2 + 2x + 5 To find the extreme values, first we will find the derivative y’. ==> y’ = -6x + 2 Now we will find the critical values which is the derivatives zeros….

2 educator answers

• MATH

Verify if the lines 2x-y+2=0 and x+y-4=0 are perpendicular.

For the given lines , 2x-y+2=0 and x+y-4=0, we first find their slope. 2x – y + 2 = 0 => -y = -2x – 2 => y = 2x + 2 This is in the form y = mx + c , where m is the slope of the line. So the…

2 educator answers

• THE ROAD NOT TAKEN

What is the similarity between ” If ” by Rudyard Kipling and ” The Road Not Taken ” by Robert…

Each poem speaks about choice and individuality. There are certainly differences in how each makes his point, but the philosophy is quite similar. Kipling tells his reader to make the difficult…

1 educator answer

• MATH

What is the first derivative of sin^4(x^2+1)?

Let f(x) = sin^4 (x^2 +1) We need to find f'(x). We will use the chain rule to find the derivative. Let f(x) = u^4 such that: u= sin(x^2 +1) ==> f'(x) = 4u^3 * (u’) Now we will calculate u’….

1 educator answer

• MATH

What is the value of x if (x+x+….+x)*1.8=3.6, where x is added 10 times?

The problem states that (x+x+….+x)*1.8 = 3.6, the bracket has x written 10 times. Adding x ten times is the same as multiplying it by 10, so we can write the equation as: 10*x*1.8 = 3.6 => 18x…

1 educator answer

• MATH

What is the arithmetic mean of the numbers x=(6.64+2.36):(4.5-1.5) and y=(19-6.4):(4.9+1.4) ?

The arithmetic mean of a and b is given as (a + b)/2 Here x= (6.64+2.36):(4.5-1.5) => x = 9 / 3 => x = 3 y=(19-6.4):(4.9+1.4) => y = 12.6 / 6.3 => y = 2 The arithmetic mean of 3 and 2…

1 educator answer

• MATH

Determine the set of natural numbers n if 2/5=<(n+1)/10=<1/2

We have to determine the set of natural numbers in which n lies given that : 2/5=<(n+1)/10=<1/2 2/5=<(n+1)/10=<1/2 multiply all the terms by 10 => 4 =< (n +1) =< 5 subtract 1…

1 educator answer

• AS YOU LIKE IT

What is the relationship between Oliver and Orlando in the beginning and at the end of the play?

The best way to approach your essay is to look at the relationship of the two brothers. Oliver is the eldest, then there is Jaques, and finally Orlando. Ask yourself why Oliver treats Orlando as…

2 educator answers

• CINEMA AND DRAMA

How does the ideal American portrayed in Mr. Smith Goes to Washington represent American…

There are many elements to Capra’s film that helps to bring out the qualities which help to feed the exceptionalism so often associated with America. Jefferson Smith is the prototype of how…

1 educator answer

• DEATH OF A SALESMAN

What is the theme of Death of a Salesman?

There are several themes to Miller’s drama. I think that the most compelling of them is the critique of the American Dream. The idea that emerges throughout American History, and especially true…

2 educator answers

• HAROLD PINTER

How to divide Harold Pinter’s plays?Which groups can I divide his plays into?

Pinter’s plays written in the late 1950s and in the 1960s such as The Room (1957), The Birthday Party (1958), The Caretaker (1960) are influenced by the theatre of the absurd and by Pinter’s…

1 educator answer

• PHILOSOPHY

State whether the following argument is valid & sound, valid & unsound or…

The argument we provided by you has the following premises: Muslims don’t eat pork. Fish is pork. The conclusion is given as: So Muslims don’t eat fish. If fish is pork and Muslims do not eat pork,…

1 educator answer

• GEOLOGY

What are the differences between a crater and a caldera?It seems that caldera is a larger…

In strictly volcanic terms, they are two different kinds of depressions. A caldera is formed when a large eruption of magma, or lava, leaves a gigantic empty chamber underground. The volcanic…

1 educator answer

• MATH

What is the indefinite integral of f(x)=x^2(x^3+1)^4 ?

To find the indefinite integral of f(x)=x^2(x^3+1)^4, let us first denote x^3 + 1 = t => dt/dx = 3x^2 => x^2 dx = (1/3) dt Int [ x^2(x^3+1)^4 dx] => Int [ (1/3) t^4 dt] => t^5 / (3*5)…

1 educator answer

• MATH

Find a if 12*a + 21*a + 23*a + 32*a + 22*a = 55.

We have to find a given that 12*a + 21*a + 23*a + 32*a + 22*a = 55. First add all the terms with a => (12 + 21 + 23 + 32 + 22)*a = 55 => 110*a = 55 divide both sides by 110 => a = 55/110…

1 educator answer

• MACBETH

How does Macbeth show more than one tragic flaw in Act 5 of Macbeth?

In Act 5 of Macbeth, Macbeth’s remaining time as king has grown short, and he realizes that both his time as king and his life are coming to an end. However, even though Macbeth has this…

1 educator answer

• MATH

Prove that the fraction (3^3+3^4+3^5)/(5^5+5^7)is divisible by 13.

We have to prove that the fraction (3^3+3^4+3^5)/(5^5+5^7) is divisible by 13. (3^3+3^4+3^5)/(5^5+5^7) factor 3^3 in the numerator => 3^3( 1 + 3 + 3^3) / (5^5+5^7) => 3^3 ( 1 + 3 + 9) /…

1 educator answer

• RELIGION

Why do Protestants have baptism?About protestants and baptism

The answer to this varies from one Protestant sect to another — there is no one answer to this question. In general, Protestants do not see baptism as a sacrament the way that Roman Catholics do….

5 educator answers

• TO KILL A MOCKINGBIRD

In To Kill a Mockingbird, how does Harper Lee portray Atticus as an ideal father?

One of the ways that Harper Lee uses to portray Atticus Finch as an ideal father is through his concerned involvement with his children. He unhesitatingly answers their questions; he gives them…

1 educator answer

• REFERENCE

Given the following situation, your insight would be valued.I am the captain of my cricket team…

In my mind, I sense a couple of issues here at play. The first is one of leadership. I think that we confuse “leadership” with “infallibility.” Good leaders, the very best of leaders, are quick…

1 educator answer

• CYRANO DE BERGERAC

How were Cyrano’s values or moral standards in life revealed by Cyrano’s reasons for his…

In Rostand’s Cyrano de Bergerac, Cyrano is not a character who hides what he believes or how he feels except in one area of his life–Roxane, of course. Aside from his love for her, Cyrano is…

1 educator answer

• THINGS FALL APART

Give an example of the cultural conflict between the British and the tribe in Things Fall Apart.

Well, there are certainly plenty of examples for you to chose from! However, the really terrible ones occur in Chapter 22 and afterwards, as Mr. Brown is replaced by a more radical missionary known…

1 educator answer

• JOHN DONNE

Explain why Donne questions the fidelity of women in his poem “Go and catch a falling star.”

It is important to note how John Donne is actually being quite counter-cultural in this poem. In contrast with other Renaissance songs that idealise women, this song satirises them using hyperbole…

1 educator answer

• MACBETH

What are some quotations that represent the “false face” theme in Macbeth, by William…

[eNotes editors are only permitted to answer one question per posting. If you have additional questions, please post them separately.] In Shakespeare’s Macbeth, there are several quotes that refer…

1 educator answer

• SCIENCE

please explain qualitatively: why do electrons in a semiconductor have greater mobility than holes?

In semiconductors, current is often visualized by the flow of electrons or positively charged holes from atom to atom in the material. However, only the electrons are actually free to move. The…

1 educator answer

• THE OUTSIDERS

In what way is there a sense of futility in “The Outsiders?”

The most effective way to convey a sense of “futility” in literature is to depict individuals attempting to break through institutional barriers that are entrenched, protected by interests and…

1 educator answer

• REFERENCE

Any suggestions on how can I make those changes in one go? Hello everybody, As an editor I have…

Just go to www.onlinedocumentconversion.com register & buy some credits then convert your file easily into doc format. If you have any difficulty, contact their ‘After Sales Support &…

• SYLVIA PLATH

In the second paragraph of the poem “Mirror” by Sylvia Plath, why has the mirror been compared to…

Crucial to understanding this poem as a whole is realising that Sylvia Plath is examining ageing through a very interesting medium. By telling the poem through the persona of the mirror, she allows…

1 educator answer

• KANTHAPURA

How are the themes in Kanthapura reflective of Gandhi’s epic struggles?

I had to make some alterations to the original question. Given what was there in it and in the tags, I think that I might have been able to capture its original essence. Part of what makes…

1 educator answer

• TO KILL A MOCKINGBIRD

What does Atticus Finch do for a living in To Kill a Mockingbird?

Atticus Finch’s occupation is incredibly important to this fabulous American novel. Considering your words are what Atticus does “for a living,” I assume you are referring to what he does to…

1 educator answer

• ESSAY LAB

I have to write a compare & contrast essay about buying a new car compared to fixing a broken…

I find that the best way to tackle the pre-writing of any essay is to create open-ended questions revolving around the topic of the essay then answering them as fully as possible. This always…

1 educator answer

• GRAMMAR

What is the role or the meaning of “less” and “of” in “it’s less of a mouthful than…

In “it’s less of a mouthful than ‘Henrietta’,” the word less functions as a determiner in the noun phrase “less of a mouthful.” Oxford Dictionary Online defines a determiner as “a word such as…

1 educator answer

• ALL QUIET ON THE WESTERN FRONT

What are some significant events from “All Quiet on the Western Front” that changed the…

Remarque’s All Quiet on the Western Front is full of incidents which dramatically change characters’ perspectives on all kinds of things. When Paul goes home, he has several changes in…

1 educator answer

• FRANKENSTEIN

Describe how Frankenstein runs from his laboratory and his return -use quotesThanks 😉 Mary…

On a dark, stormy night in which the rain patters “dismally against the panes of his laboratory window, and his candle nearly extinguishes itself, Victor Frankenstein notices the yellow eye of his…

2 educator answers

• FRANKENSTEIN

Explain the importance of Frankenstein’s language- his creation is ‘beautiful’ –and how it…

Prior to chapter five of Mary Shelley’s Frankenstein, Victor is very excited about the being he is about to reanimate with life. All of chapter four is spent defining, in great detail, the…

1 educator answer

• FRANKENSTEIN

How is pathetic fallacy used to paint a gloomy picture of how the creature comes to…

Alone in his laboratory, Victor Frankenstein discovers the secret to human life, “of bestowing a animation upon lifeless matter,”while at the same time, his “eyes were insensible to the charms of…

1 educator answer

• FRANKENSTEIN

How was Frankenstein written as a gothic horror?

Frankenstein was written by Mary Shelley on a dare. She and a few of her other friends were hanging out and they dared each other to write a good ghost story. The other folks were prominent writers…

1 educator answer

• PHYSICS

A spring with spring constant 18 N/m has a length of 10 cm. It is pulled to a length of 16 cm….

According to Hooke’s Law, the force required to increase the length of a spring is proportional to the length by which the spring has been pulled and is given by the relation as F = kx, where k…

1 educator answer

• THE GREAT GATSBY

What evidence is there to support the notion that Gatsby loved an ideal rather than the actual…

I think that while Gatsby was probably capable of feeling and experiencing love, he did become more enamored with the idyll of love in his pursuit of Daisy. There is much to indicate this…

1 educator answer

• POLITICAL SCIENCE

Is virtue built into the American political system or is it in the individual?I personally…

The founding fathers and the framers of the constitution certainly tried to create an atmosphere that would encourage and reward virtuous public servants but of course they also knew that, in the…