Find equations for the tangents to the curve y = x^2 at the points (-1/2 , 1/4) and (1,1).

# Find equations for the tangents to the curve y = x^2 at the points (-1/2 , 1/4) and (1,1).

• MATH

Find equations for the tangents to the curve y = x^2 at the points (-1/2 , 1/4) and (1,1).

We have the function y = x^2. Now the derivative of a curve at a particular point gives the slope of the tangent at that point. Now, we use the relation that the derivative of x^n is n*x^ (n-1)…

• MATH

What is |z| if i – iz = 2 ?

i – iz = 2 First we need to rewrite the function as a function oin the following format: z = a + bi Let us isolate z on the left side: We need to subtract i from both sides: ==> -zi = 2 – i Now…

• THE CONSERVATIONIST

What are the main issues in Gordimer’s The Conservationist?

The Conservationist by Nadine Gordimer is a story about Mehring, a wealthy, white South African industrialist. Symbolically, Mehring represents the attitude of white South African society. The…

• MATH

Find dy/dx as a function of x for y= x^3*(x+1)/(3x-2)^4

y= x^3*(x+1)/(3x-2)^4 Let us simplify the function first: y = (x^3(x_1)/ (3x-2)64 = (x^4 + x^3)/ (3x-2)^4 Now we will assume that: y = u/v such that: u = x^4 + x^3 ==> u’ = 4x^3 + 3x^2 v =…

• MATH

Evaluate sum (3n + 2) for n = 0 to n = 100 .

We have to find the sum ( 3n +2) for n = 0 to 100. Now we can write the given expression as 3* sum ( n=0 to 100) + 2 + 100 – 0. Here we use the standard forms of summation. The sum of the series of…

• MATH

Find the solution in the simplest form lgx/(1-lg2) = 2.

We have to use the equation lg x / (1 – lg 2) = 2 to find the solution in the simplest form. Now lg x / (1- lg 2) = 2 => lg x = 2*(1- lg 2) => lg x = 2 – 2 lg 2 => lg x + lg 2^2 = 2 =>…

• MATH

Find the values of x that satisfy the inequality |(3x + 1)/2| < 1.

We have the inequality | (3x + 1)/2| < 1 to solve for x. Now as the absolute value of (3x+1)/2 is less than 1, we can convert the inequality to the following form: -1 < (3x+1)/2 < 1….

• THE LOTTERY

What do you think the story of “The Lottery” symbolizes?

The story “The Lottery” symbolizes inhumanity and the inability to question the status quo. You have here a group of people who, for no reason they can actually explain, have continued a morbid…

• MATH

Given that x=3 is a solution of x^3-x^2-8x+6=0 find all the other solutions of this equation.

Since an equation could be written as a product of linear factors, when knowing it’s roots, we’ll write the given equation as: x^3-x^2-8x+6=(x-3)(ax^2 + bx + c) We’ll remove the brackets from the…

• OTHELLO

Who is more naturally suspicious–Othello or Iago?

Even Iago from the beginning of the play describes Othello as a trusting man “who thinks men honest that but seem to be so.” Othello’s trusting nature is perhaps his greatest vulnerability, and it…

• SCIENCE

Biology study guide question about heredity.Some biology students wanted to determine whether a…

The answer to this problem is that you could perform a test cross. It is a way of determining if the parents are homozygous for brown fur color or heterozygous. If you cross the parents with a…

• HAMLET

If you are to compare Gertrude with an animal in symbolic form, what will it be?In my opinion,…

Before I clicked on this and saw your answer to your own question, I was thinking “sheep.” As it turns out, you and I are thinking along the same lines — different animal, but same reason. Our…

• GUIDE TO LITERARY TERMS

Describe the main elements of the novel?detailed answer

All novels have to have some essential features. Most notable is a structure that usually follows a pyramid form and includes other elements — I have bolded the most common elements of fiction….

• RELIGION

What does a sanctuary symbolize for the Seventh Day Adventist?

For most Seventh Day Adventists, consecrated objects on earth represent their heavenly counterparts. Seventh Day Adventists believe that Jesus ministers from a heavenly sanctuary. The church…

• MATH

Solve the equation: |2x – 3| = 7.

We have the equation |2x – 3| = 7 which we have to solve for x. Now |2x – 3| = 2x – 3 for 2x – 3 > 0 and is equal to (3 – 2x) for 2x – 3 < 0 Let’s assume 2x – 3 > 0 => 2x…

• SOCIAL SCIENCES

Why is racism a problem that should be handled by government?Why is racism a problem that should…

Racism is a problem that should be handled by government only when it is manifested in discriminatory actions. In other words, the feelings of racism cannot and should not be a governmental issue…

• MATH

For the functions f(x) = x^2 and g(x) = (x-7), are f (g(x)) = g (f(x)). Also, what is g (f (2))?

We are given that f(x) = x^2 and g(x) = (x-7). Now, to determine g (f(x)), we find the value of f(x) and substitute it in g(x). f(x) = x^2. substituting this in g(x) we get g (f(x)) = x^2 -7. To…

• MATH

Find the domain and range of the following: y = x^2 , y = sqrt(1 – x^2), y = 1/x, y = sqrt(x) ,…

First, let me tell you that you can only post one question at a time. I will answer your questions this time, but keep this in mind the next time you post a question here. For a function y = f(x),…

• 1984

What similarities are there between the 1984-society, the Nazi-regime and the Soviet regime, on…

As you know, 1984 is a dystopian novel which satirizes the totalitarian governments of the extreme left (U.S.S.R.) and extreme right (Nazism). The political spectrum is not linear, but circular:…

• MATH

If log 9 = 2, how to find the value of log 27

In this problem we are given that log 9 = 2. Here we will solve the problem without the need for the base of the logarithm arising. We only use the relation that states: log a^x = x*log a. Now log…

• WILFRED OWEN

What are some of the themes and techniques of Wilfred Owen’s poem titled “Futility”?

Wilfred Owen’s poem titled “Futility” is a work worth examining in some detail in order to understand how its techniques contribute to its themes and meanings. Here are some noteworthy…

• MATH

What is the value of a and b, given that 4+a, 8, 10b and a+2b are terms of AP

In an arithmetic progression, the difference between consecutive terms is the same. We use this property to build up two equations that can be solved to arrive at a and b. 10b – 8 = 8 – (4+a) =>…

• ROMEO AND JULIET

Examine and explore the development of Juliet in Romeo and Juliet.Does Juliet mature and change?

I would say that some things about Juliet’s character seem to remain steady, but that she also changes in at least one very significant way from beginning to end. Let’s begin with the ways that she…

• THE MONKEY’S PAW

How does the author use symbolism in “The Monkey’s Paw”?

Remember that a symbol in literature is defined as an object, action or person that stands for something beyond their literal meaning. So, thinking about symbols, a dove is a common symbol for…

• LAW AND POLITICS

BULLYING (please give your opinions)What is causing bullying? What is being done for it?

I think that bullying is caused by two things: First, I think it is caused by a lack of empathy for others. They think that only their own feelings are important. Second, I think that it is caused…

• MACBETH

UGH!!! why do we study macbeth? i mean i understand yes he kills people big woop? but serioulsy…

I believe that the play is supposed to make you think about (among other things) the roles of fate and ambition in determining what our lives come out like. For example, you’re supposed to think…

• WILLIAM SHAKESPEARE

how can we undustand that shakespeare had very creative mind in himself?

well look at how complicated his plays are they have amazed scholars take hamlet, wonderful what a beauty!!

• THE PAINTED BIRD

What are important themes, and issues, and societal views in The Painted Bird?I need information…

The Painted Bird, Jerzy Kosinski’s powerful novel about survival during World War II, is based on his own experiences in Poland. It deals with many themes, particularly the horrors of war, ethnic…

• CRITICISM FROM PLATO TO ELIOT

How is New Historicism an attempt to grasp simultaneously the historicity of text and the…

The answer to this question — which recycles the famous phrase of Stephen Greenblatt, commonly seen as the founder of New Historicism — can be seen clearly, I think, in the methods of that…

• HAMLET

How does Shakespeare use language to convey Hamlet’s madness throughout the play?Thanks in…

First, if you believe Hamlet in Act I, scene v, when he speaks with Horatio and Marcellus after his meeting with the Ghost, then he is only pretending to be mad, he is not actually mad. He says:…

• GUIDE TO LITERARY TERMS

For my next assignment, could someone explain in ONE sentence the meaning of the following poetic…

(eNotes editors are only allowed to answer one question; this posting contains multiple questions. I’ll address this posting to sonnets, and summarize with one sentence.) Literary terms are usually…

• SHOOTING AN ELEPHANT

How does this story comment on an imperial government sustaining political power and controlling…

I have put this question in the “Shooting an Elephant” group because the original wording of the question made clear that it referred to this story. One of the major points in this story is that an…

• LORD OF THE FLIES

Would you mind explaining the causes of aggressive behavior that overtakes all of “the kids” in…

No better question could be asked concerning Lord of the Flies. Why indeed would a bunch of civilized children turn to such savagery? First, no adults survived the plane crash, for the children…

High School ProjectMy son has a project for 10th grade literature. I will narrow down the…

This assignment which doesn’t seem to be unreasonable, should be discussed as much as possible with the teacher who gave him the assignment. There can be all sort so of problems if you start down a…

• HAMLET

What are Gertrude’s goals, passions, and worst fears?I am guessing her goals are: her son,…

In Hamlet, Gertrude wants: …Hamlet to stay with her: Let not thy mother lose her prayers, Hamlet:I pray thee, stay with us; go not to Wittenberg. …to obey her husband Claudius: I shall obey…

• A MIDSUMMER NIGHT’S DREAM

Discuss the fairies in A Midsummer Night’s Dream

A question this general can lead you in a number of directions. What about the fairies do you want to discuss? Why they’re in the play? Their personalities? Their function? A good place to start…

• THE ABSOLUTELY TRUE DIARY OF A PART-TIME INDIAN

What are the summaries for chapters 13-16 of “The Absolutely True Diary of a Part-Time Indian”?

Please see the links below: Chapter 13 Chapter 14 Chapter 15 Chapter 16

• REFERENCE

What does this mean? “If all else fails, immortality can always be assured by spectacular error”

This quotation is from the famous economist John Kenneth Galbraith. What it means is that people become just as famous for making huge mistakes as they do for being hugely successful. I do not…

• MATH

How do I write sigma notation for a sequence and then find the partial sum?I’m given the…

If you see the series that you have been given 1, 3, 9, 27, 81, 243…, you see that each term is 3 times the earlier term. This is a geometric progression. The nth term of a geometric progression…

• GOING AFTER CACCIATO

What is the climax of the story?

The climax in a narrative is part of the plot – specifically the point of most intense drama and the point of highest emotion. After the climax, the action falls away and the tension reduces. Let’s…

• MATH

ax^2 + bx + c = ( x-2)(x+5) find the values of a, b and c:

ax^2 + bx + c = ( x-2)(x+5) First we will expand the brackets of the right sides: ==> ax^2 + bx + c = x^2 +5x – 2x – 10 ==> ax^2 + bx + c = x^2 + 3x – 10 Now we will move all terms to the…

• HAMLET

In act III of Hamlet, why is Hamlet so upset about his mother’s marriage?

Act III, Sc. 4 of Hamlet is the famous “closet” scene. Hamlet is invited to meet with with his mother in her “closet,” a small private room (perhaps her bedroom). In this scene, Hamlet gives full…

• MATH

solve for x and y : x-y = 5 2x + y = 4

x-y = 5 ………..(1) 2x + y = 4…………..(2) We will use the elimination method to solve: We will add equation (1) to equation (2): ==> x – y + 2x + y = 5 + 4 ==> x +2x = 9 ==> 3x =…

• THE ADVENTURES OF HUCKLEBERRY FINN

In The Adventures of Huckleberry Finn, in Chapter 32 how did “providence” help Huck?

This Chapter is a very important one for a number of reasons. Huck Finn is going to the Phelps’s house because he knows that this is where Jim is because the Duke and the King sold him to Mr….

• MATH

What are the solutions for the function : f(x) = (x^2 – 5x + 6) / (x -3)

f(x) = (x^2 – 5x + 6) / (x-3) To determine the solution of the function first we need to determine the points such that f(x) is defined. we know that the function f(x) is not defined when the…

• RAPPACCINI’S DAUGHTER

In “Rappaccini’s Daughter” is there any symbolism tied to Giovanni’s struggle while dealing with…

Recalling Nathaniel Hawthorne’s being a Dark Romanticist, the character of Giovanni can be interpreted as symbolic of the human artist in conflict with science in the form of Dr. Rappaccini, the…

• MATH

if 3, b, -1, c are terms of an A.P, then find b and c

3, b , -1 , c are terms of an Arthematical progression. Let r be the common difference: Then we know that: b = 3 + r………(1) -1 = 3 + 2r……..(2) c = 3 + 3r………..(3) Let us solve…

• MATH

f(x) = x^2 – 3x + b find b velue if the function has only one root.

f(x) = x^2 – 3x + b If the function f(x) has only one root, then we know that delta is zero. We know that: delta = b^2 – 4*a*c ==> a = 1 b = -3 and c = b ==> delta = 9 – 4*1*b = 0 ==>…

• MATH

Find the absolute value for z = (2-i) / -i

z= (2-i)/ -i First we need to rewrite the complext number z in the standard form which is z = a+ bi Let us multiply and divide by the denominator inverse which is i ==> z = (2-i)*i / -i*i…