# Prove that arctan (2+sqrt3)+arctan (2-sqrt3)=pi/2!

**MATH**

x^ (lgx + 1)/lgx = 100 First let take log for both sides: lg x^(1gx+1)/lgx = lg 100 We know that log a^b = b log a ==> [(lgx +1)/lgx]*lg x = lg 10^2 Reduce similar: ==> lg x + 1 = 2log 10…

1 educator answer

**MATH**

**Prove that arctan (2+sqrt3)+arctan (2-sqrt3)=pi/2!**

Let us assume that: arctan (2+ sqrt3) = x arcttan (2-sqrt3) = y ==> tanx = 2+ sqrt3 ==> tany = 2-sqrt3 Now we know that: tan (x+y) = (tanx + tany)/[1- tanx*tany] ==> tan (arctan (2+…

1 educator answer

**SOCIAL SCIENCES**

**What are five causes that will make you not trust the goverment, and what are five causes that…**

The actual answer to this is going to depend a lot on what country you are asking about. I cannot tell where you are from… I’m from the United States so my answer will reflect that. In general,…

3 educator answers

**MATH**

**Solve the equation (3+2sqrt2)^x + (3-2sqrt2)^x=34**

3+ 2sqrt2)^x + (3-2sqrt2)^x = 34 We know thta: 3+2sqrt2 = 1/(3-2sqrt2) Now substitute: ==> (1/(3-2sqrt2)^x + (3-2sqrt2)^x = 34 ==> (3-2sqrt2)^-x + (3-2sqrt2)^x = 34 Let y= (3-2sqrt3)^x ==>…

1 educator answer

**MATH**

**Determine x if 6^x – 5^x = 4^x – 3^x .**

6^x – 5^x = 4^x -3^x Let us substitute with c=0: ==> 6^0 – 5^0 = 4^0 – 3^0 ==> 1- 1 = 1-1 = 0 Then: x1= 0 is one of the solutions: Now subsotute with x=1: ==> 6^1 – 5^1 = 4^1 – 3^1…

1 educator answer

**POSTCOLONIALISM**

**What is and what are the “Poco Issues”?**

One of the main concerns of postcolonialism is the way in which the Western urban world is taken for the universal and anything other than that is exotic or strange. Joseph Conrad’s “Heart of…

1 educator answer

**MATH**

**Given that x^2 – 2*f(x) = f(1/x) determine f(2)**

x^2 – 2*f(x) = f(1/x) Let us substitue with x= 2: 2^2 – 2f(2) = f(1/2) 4- 2f(2) = f(1/2) ==> f(1/2) = 4-2f(2) ……..(1) Now subsitute with x= 1/2 ==> (1/4) – 2f(1/2) = f(2) ==> f(1/2) =…

1 educator answer

**AS YOU LIKE IT**

**Critical analysis of As You Like It?**

When a teacher/professor asks you for a critical analysis of a text, he/she does not want you to actually criticize the play in terms of looking for errors or mistakes. What a critical analysis of…

1 educator answer

**MATH**

**Solve the equation 2iz/(1 – i) + 2i = 2z(1 – i) – 3 + i**

2iz / (1-i) + 2i = 2z (1-i) -3 + i Let z = a+ bi ==> 2i(a+bi)/ (1-i) + 2i = 2(a+bi)(1-i) -3 + i Multiply by (1-i): ==> 2i(a+bi) + 2i(1-i) = 2(a+bi)(1-i)(1-i) -3(1-i)+ i(1-i) ==> 2ai – 2b…

1 educator answer

**SCIENCE**

**Does the personal health ever intersect with public health?**

Personal health can intersect with public health in a variety of different ways. Say for example a person is sick with strep throat which is contagious. Perhaps they have to work that day. Knowing…

2 educator answers

**MATH**

**If the points A(2,3+a), B(a-1,2a), C(3,5) are on the line calculate a.**

A (2, 3+a) , B(a-1, 2a) C (3, 5) The point are on the same line, Then slope AB = slope BC = slope (AC slope AC = ((5-(3+a)/(3-2)= (2-a) slope BC= (5-2a)/(3-(a-1) = (5-2a)/ (4-a) We know that…

1 educator answer

**WHERE ARE YOU GOING, WHERE HAVE YOU BEEN?**

**Why do you have to count backwards from the last book of the old testament to find Judges when…**

pbull88, Check out this link below. There are a lot of interesting comments regarding the meaning….

**MATH**

**Calculate |[(3-4i)/(5+12i)]^2|.**

The line numbers vary depending on what translation of Beowulf you are studying, so I can’t refer you to specific lines. Beowulf says he is as brave and fearless as Grendel, so he will use no…

3 educator answers

**POETRY**

**How do I do a reader response to “Sailing to Byzantium” by William Butler Yeats?Can you refer to…**

Reader response is a type of critical literary interpretation that ignores author intentions as unknown or even unknowable and emphasizes the “I” of the reader, without whom no literature can ever…

1 educator answer

**THE HOUND OF THE BASKERVILLES**

**How does Watson regard Holmes? and What is the function of a sidekick?**

Watson regards Holmes as an incredibly gifted detective but he also acknowledges his weaknesses and in many ways looks at him as a child or at least as someone that needs a great deal of care in…

1 educator answer

**HENRY**

**What is the climax of the story “The Last Leaf ” by O.Henry?**

In my opinion, the climax of this story comes when Johnsy decides that she is going to live. This comes after she sees the “leaf” still there on the second day and she starts to talk to Sue about…

2 educator answers

**POETRY**

**Analyze “The Whipping” by Robert Hayden utilizing either a biographical or historical…**

In “The Whipping,” we can assume something that we normally should not: The speaker is the poet. The transition from the use of the words, “the boy” and “him,” to “I” and “my” in the middle of the…

1 educator answer

**MATH**

**Solve the equation (3-2*sqrt2)^x + 2(sqrt2-1 )^x = 1**

This is an exponential equation and we’ll use the substitution technique to solve it. We notice that we’ll raise to square (sqrt2-1 )^2, we’ll get: (sqrt2-1 )^2 = 2 – 2sqrt2 + 1 = 3 – sqrt2 So,…

**POETRY**

**How do I do formalist criticism of “Spring and All” by William Carlos Williams, and how can it be…**

In formalist literary criticism, the important thing is the process by which the work is created. Formalism doesn’t engage in evaluating the work in terms of truth or morality. On the other hand,…

1 educator answer

**1984**

**What actions in 1984, by George Orwell, signals the end of Winston’s humanity?**

In my opinion, the event that signals the end of Winston’s humanity is when he betrays Julia. I think that this shows him giving up his human emotions so as to just be able to get along in his…

2 educator answers

**MATH**

**Solve for x sqrt(2x+5) = sqrt(x+2) + sqrt(2x-3).**

sqrt(2x+5) = sqrt(x+2) + sqrt(2x-3) Let us square both sides: ==> (2x+5) = (x+2) + 2sqrt(x+2)(2x-3) + (2x-3) ==> (2x+5) = x+2 + 2x -3 + 2sqrt(2x^2 +x -6) ==> (2x+5) = 3x -1 + 2sqrt(2x^2 +…

1 educator answer

**LAW AND POLITICS**

**Why do you think the 4th Amendment is important?**

I would say that one of the reasons the 4th Amendment is so important is that it is reflective of the Colonists’ own experiences. The Colonists were outraged on many levels that British soldiers…

4 educator answers

**THE BLUEST EYE**

**Why does Frieda seem to handle sexual abuse better than Pecola??**

The answer most probably lies with the difference in the Breedlove and Macteer families. While the Macteer family is poor, and the girls often feel that their parents treat them harshly, there is…

1 educator answer

**MATH**

**Solve log 1/2 (2x^2 + x + 1) >= -1**

log 1/2 (2x^2 + x + 1 ) >=-1 ==> 2x^2 + x +1 >= (1/2)^-1 ==> 2x^2 + x + 1 >= 2 Now subtract 2 from both sides: ==> 2x^2 + x -1 >= 0 Now let us factorise: ==> (2x -1)(x+1)…

1 educator answer

**MATH**

**Determine the roots of f”(x) if f(x)= x/(x^2+1) .**

f(x) = x/(x^2+1) First let us assume that: f(x) = u/v such that: u= x ==> u’ = 1 v= x^2 + 1 ==> v’= 2x f'(x) = (u’v-uv’)/v^2 = (x^2+1) – 2x^2]/(x^2+1)^2 =…

1 educator answer

**MATH**

**Solve for x and y 4x+ 5y = 10, 6x – 5y = 5.**

4x + 5y = 10…….(1) 6x -5y = 5………..(2) Using the elimination method, add (1) and (2): ==> 10x = 15 ==> x = 15/10 = 3/2 ==> x= 3/2 Now to calculate y, let us substitute with (2):…

1 educator answer

**MATH**

**Calculate f'(x) = 0 if f(x) = x/(1+x^2)**

f'(x) = 0 f(x) = x/(1+x^2) assume that: f(x) = u/v such that: u = x ==> u’=1 v= 1+x^2 ==> v’ = 2x f'(x) = (u’v- uv’)/v^2 = 1(1+x^2) – x(2x)]/(1+x^2)^2 = (1+ x^2 -…

1 educator answer

**MATH**

**Determine the function f=ln(x+1) – a*x if the function is increasing on the interval (-1;infinite).**

f(x) = ln (x+1) – ax The function is increasing on the interval (-1, infinite) Then, the first derivative ‘f'(x)” is positive on the interval (-1, inf.) Let us calculate first derivative: f'(x) =…

1 educator answer

**ANIMAL FARM**

**How does Orwell indicate that Frederick and Pilkington are “thoroughly frightened” by the events…**

I think that you can find the answer to this at the start of Chapter 4. Orwell shows that these two men are frightened by the revolution by showing that they are worried about what their own…

1 educator answer

**SCIENCE**

**Which is the recomended daily zinc intake?**

Recommended daily zinc intake ranges according to age and gender. Generally, infants (both males and female) need approximately 2mg of zinc daily. Children, 7 months to 3 years of age, need 3mg of…

1 educator answer

**A PORTRAIT OF THE ARTIST AS A YOUNG MAN**

**Who is the little boy that Moocow meets in James Joyce’s “A Portrait of the Artist as a Young…**

Yes – Stephen is the moocow. In the first section of the first chapter, we get the first glimpse of Stephen’s observation. The narrator says “he was baby tuckoo” meaning that his father always told…

2 educator answers

**LITERATURE**

**What are the themes of Dairy Queen by Catherine Gilbert Murdock?Is there another theme to Dairy…**

You could expand the communication theme into an idea about how communication affects relationships. Look at DJ’s father – and how he communicates differently with his children and then with his…

1 educator answer

**SCIENCE**

Cranial nerves are nerves which rise directly from the brain unlike nerves which rise from the spinal chord. They are twelve in number. They are: 1. Olfactory. The sense of smell is carried by the…

**SOCIAL SCIENCES**

**In democracy who governs and what is the citizen participation?no**

In a democracy, the people are the ones who ultimately have the power, but I suppose you would say that it is the government (elected by the people) that governs. In a democracy, the people elect…

2 educator answers

**SCIENCE**

**Calculate the density of any metal and explain how you did it.**

Density is easily calculated if you know the mass of the object and its volume. To find the mass, you simply need to weigh the item on a triple beam balance or a digital scale. Usually, in science,…

1 educator answer

**ARMS AND THE MAN**

**What is the main theme of Shaw’s Arms and the Man?**

Shaw’s title of his play, Arms and the Man is taken from the opening line of Virgil’s epic The Aeneid – “Of arms and the man I sing.” The play was first produced on April 21st 1894 and was a huge…

**SCIENCE**

**What is the basic principle of holography?I mean the main terms and a short reasonable explanation.**

Holography is the technique of creating holograms – that is special kind of images on 2-dimensional surfaces that create the effect of 3 dimensional objects. The basic principle of holography is to…

**ANIMAL FARM**

**Are the characters in Animal Farm stereotypes?If so, explain the usefulness of employing…**

When creating an allegorical story, the author–to a certain degree–must employ stereotypes to make the characters fit into symbolic molds. If Animal Farm is to be a satire of the Russian…

2 educator answers

**ANIMAL FARM**

**Discuss each character in terms of its animal and human nature in Animal Farm.**

One group of characters that represents both its animal and human characteristics is the group of dogs that Napoleon gathers as his guards. Dogs are well known as loyal animals, and they protect…

2 educator answers

**SCIENCE**

**Using scientific terminologyI am looking for new ideas on improving student’s science vocabulary….**

Word Walls are a particularly effective strategy, but only if you draw students’ attention to the Word Wall on a regular basis. Written activities can reference the Word Wall. Encourage students to…

9 educator answers

**ELIZABETHAN DRAMA**

**What are the secular influnces on the Early English Drama?**

The earliest English Drama that we note as wholly English would be the Mystery, Miracle and Morality plays of the Middle Ages. Though they were meant as teaching tools of the Church, meant to…

1 educator answer

**SCIENCE**

**Give three examples from our daily life to show how important it is for gases to diffuse quickly.**

Diffusion is the process by which molecules of a gas move from a more concentrated state to a less concentrated state because they are constantly in motion. All gases are constantly in motion and…

2 educator answers

**LORD OF THE FLIES**

**What are some good high level questions for Lord of the Flies?I am doing a project for Lord of…**

Since I’m not sure what kind of questions you’ve already come up with, some of my suggestions might be redundant. What textual evidence might lead readers to compare Simon to Christ or a…

4 educator answers

**SCIENCE**

**Molecular mass of chlorine, nitrogen, sulphur dioxide & carbon dioxide are 71, 28, 64, 44…**

Diffusion is the process by which gases spread out when released into a larger space. This larger space can be into a vacuum or into a container which already contains other gases. Kinetic…

1 educator answer

**ROMEO AND JULIET**

**How are hate and revenge displayed in Romeo and Juliet?What actions and quotes are said to prove…**

There are many quotes and points of action in the play that reveal the hatred between the Capulets and Montagues and cries for and actions of revenge. So, I will focus on a main character whose…

1 educator answer

**BUSINESS**

**What do you think about age discrimination at the workplace?What do you think about age…**

The economy has caused an age discrimination problem in two ways. First of all, older people make higher salaries so companies cutting costs often cut them first. Then, it is even harder for them…

1 educator answer

**BUSINESS**

**What do you think about gender discrimination at the workplace? Examples please.What do you think…**

Discrimination of any type and in any form is wrong and should not be tolerated by anyone. Gender discrimination is showing favoritism or granting special work conditions based on whether someone…

2 educator answers

**CANDIDE**

**Drawing from the passage, describe what you see as Voltaire’s vision of human nature in…**

In this satirical piece, the ridiculous nature of man is exposed. The philosophy Pangloss teaches Candide is that whatever happens, it is all for the best, and whatever happens, it is the “best of…

1 educator answer

**TARTUFFE**

**In Tartuffe what specifically do you think Moliere’s contemporaries found so objectionable about…**

I can answer the first part of your question which should help you with second part. It would be helpful for you to refer to eNotes’ historical context and introduction to help with a better…

3 educator answers

**SCIENCE**

**Out of sublimation, condensation, evaporation, boiling, melting & freezing: classify these…**

The underlying concept behind changes of state is kinetic molecular theory – the idea that all particles in substances are constantly in motion. Two factors determine the physical state of any…