Find all the values of x that satisfy the inequality | (3x + 1)/2| < 1?
- MATH
Find lim t–> 1[(t^3 – 1)/ (t – 1)].
We have to find the value of lim t–> 1[(t^3 – 1)/ (t – 1)]. Now merely replacing the values of x with 1 will yield 0/0 which is indeterminate. Here we can use L’Hopital’s rule, but…
1 educator answer
- MATH
Find all the values of x that satisfy the inequality | (3x + 1)/2| < 1?
We have to find all values of x that satisfy the inequality | (3x + 1)/2| < 1. First let us change this to the form -1 < [(3x + 1)/2] < 1 Multiply all the terms by +2 => -2 < (3x +…
1 educator answer
- TO KILL A MOCKINGBIRD
In To Kill a Mockingbird, using Jem and Scout’s experiences show the significance and importance…
Education is important because we have the opportunity to learn quickly what other people have spent more time learning and build on the body of information making our own lives simpler than those…
1 educator answer
- ROMEO AND JULIET
In Romeo and Juliet, what is the significance of the lark in Romeo and Juliet’s conversation?
In this scene, Romeo and Juliet have just spent the night together after their secret marriage. Romeo had during the night climbed into her room. Because no one knew of their marriage except the…
1 educator answer
- THE DEAD
How does Joyce’s portrayal of Women in “The Dead” inevitably affect Gabriel, his growth as a…
This is a great question – perfect for an essay, as you are completely right to focus on how the various female characters in this incredible short story reveal more about Gabriel’s character. It…
1 educator answer
- REFERENCE
I am feeling really stressed. Any advice for me??? How many minutes does it take to commit…
Sometimes life does get stressful, and I understand your pain. Please, please, go and talk to someone about this. A parent, a friend, a counselor or teacher, or you can call this number right…
2 educator answers
- MATH
(3x+7)(x-1) = 24 We will expand the brackets. ==> 3x*x + 7*x + 3x*-1 + 7*-1 = 24 ==> 3x^2 + 7x-3x – 7 = 24 We will combine like terms. ==> 3x^2+ 4x -7 – 24 = 0 ==> 3x^2 + 4x – 31 = 0…
1 educator answer
- MATH
Differentiate y = 2sin(3x+1)cos(3x+1)?
y= 2SIN(3X+1)*COS(3X+1). We will use the trigonometric identities to simplify. We know that sin2x = 2sinx*cosx ==> y= sin2(3x+2) ==> y= sin(6x+4). Now we will use the chain rule to…
- A&P
Does the text of A & P by John Updike have a significant purpose? (Is it a call to action…
Literature is art, and art speaks to different people in different ways. This is my personal response to the short story in question. When I read John Updike’s “A & P,” I don’t necessarily get…
1 educator answer
- A&P
How is the importance of studying literature shown in “A & P” by John Updike?
John Updike’s short story “A & P” demonstrates the importance of reading literature. Sammy is the main character in this story. He is a youngster who works at the grocery store, and the story…
1 educator answer
- A DOLL’S HOUSE
In“A Doll’s House” by Ibsen, and the story “Chrysanthemums” by Steinbeck, talk about the…
[eNotes editors are only permitted to answer one question at a time. Additional questions must be placed in separate postings.] The role of the author of a story, play or poem, is to speak to the…
1 educator answer
- MATH
Calculate z+1/z if z = (-1+i*3^1/2)/2.
Since 1/z = z’ or the conjugate of the complex number z, we’ll put z’ = (-1-i*sqrt3)/2 Now, we’ll add z + z’ = 2Re(z) We’ll identify Re(z) = x: z = (-1+i*sqrt3)/2 for z = x + i*y We’ll compare and…
- A DOLL’S HOUSE
What common theme or idea is being presented in “A Doll’s House” and the story…
In A Doll’s House by Henrik Ibsen, and “Chrysanthemums” by John Steinbeck, the common theme in these two stories revolves around “a woman’s place.” In A Doll’s House, Nora is our protagonist….
1 educator answer
- ADRIENNE RICH
Analyze and evaluate the use of imagery or form in the poems“America” by Claude McKay, and…
In Adrienne’s Rich’s poem, “Song,” and Claude McKay’s poem, “America,” imagery plays an important part. In “Song,” perhaps the title gives the reader its first clue that the poem has little to do…
1 educator answer
- BUSINESS
For a business owner, an acceptable trade-off might includeA. exchanging goods products for…
The best answer of the ones that you have given us is D. This is the trade-off that would be most beneficial to a business owner. The reason for this is that increased productivity can offset the…
1 educator answer
- MATH
Find x if the numbers x, 6, x-5 are the terms of a geometric series.
The numbers x, 6 and x-5 are terms of a geometric series. Therefore we have 6/x = (x – 5)/6 => x(x – 5) = 36 => x^2 – 5x – 36 = 0 => x^2 – 9x + 4x – 36 = 0 => x(x- 9) + 4(x- 9) =0 =>…
1 educator answer
- MATH
f(x) = 5^(tan5x) We will use the chain rule to find the derivative. Let g(x) = tan5x. ==> g'(x) = 5*sec^2 (5x) ==> f(x) = 5^g(x). Let us differentiate using the chain rule. ==> f'(x) =…
1 educator answer
- HISTORY
Is John Brown a freedom fighter or a terrorist? Explain.
The answer to this is “yes.” In other words, John Brown is both. Because he was on the side of the North and because the North won, we see him in a positive light today. However, the things he…
2 educator answers
- HISTORY
How does Frederick Douglass feel about John Brown and his raid?
Frederick Douglass was in awe. He had dinner with John Brown on a couple of occasions, and was utterly impressed with the fact a white man would go to such lengths to fight black slavery. When he…
2 educator answers
- MATH
Find the area bounded by the graphs of the following functions: f(x)=x^2, g(x)=x^3.
Given the functions: f(x) = x^2 g(x) = x^3 We need to find the area bounded by both curves. First we need to determine the intersection points of the functions. ==> f(x) = g(x). ==> x^3 =…
1 educator answer
- MATH
What is the solution of the equation 7^(3x-2)=17 in terms of logarithms?
We know that log ab = log a + log b and log a^b = b*log a. Here these are used on 7^(3x-2) = 17. 7^(3x-2) = 17 Take the log of both the sides => log [ 7^(3x-2)] = log 17 => (3x – 2)*log 7 =…
2 educator answers
- ETHAN FROME
In Ethan Frome what reason does Ethan give for not driving Zeena to the station?
Ethan, who is not very practiced at lying or deceiving people, doesn’t want to take his wife to the station, because he wants to be at home where he can spend more time with Mattie during her…
1 educator answer
- MATH
We have to solve sin x = 1 + (cos x)^2 Let sin x = y. Now we know that (sin x)^2 +(cos x)^2 = 1 => (cos x)^2 = 1 – (sin x)^2 => 1- y^2 Now we can write sin x = 1 + (cos x)^2 as sin x = 1 + 1…
2 educator answers
- MATH
Determine the quadratic if f(-1)=4, f(1)=2, f(2)=7 .
Let the quadratic equation be ax^2 + bx + c. Now f(-1)=4 f(1)=2 f(2)=7 Substitute x = 1 in ax^2 + bx + c => a + b + c = 2…(1) Substitute x = -1 in ax^2 + bx + c => a – b + c = 4…(2)…
2 educator answers
- MATH
What are the roots of the derivative of y=x^2/(2x-1)-2/(2x-1) ?
We’ll have to differentiate the function for finding the roots of the expression of the first derivative. We’ll re-write the function: f(x) = (x^2 – 2)/(2x-1) Since the given function is a product,…
- PHYSICS
What was the initial velocity of a body of mass 10 kg if it sticks to a a stationary body of mass…
When two masses collide and stick to each other it is a perfectly inelastic collision. Here the total momentum is not conserved, but the total energy is conserved. The kinetic energy is given by…
1 educator answer
- MATH
Find the natural number n if 1+5+9+..+n=231.
The series given is an arithmetic progression with the first term 1 and common difference as 4. Now the sum of the first N terms of an AP is given by (N/2)[2a1 + d(N-1)] =(N/2)[ 2 + (N-1)*4] This…
1 educator answer
- SOCIAL SCIENCES
What are some benefits of being a social worker ?
The major benefit of going into the field of social work is nonmonetary. Social workers do not make large salaries, but their jobs can be emotionally rewarding. Social workers generally work with…
1 educator answer
- MATH
Solve the inequality 5*|7n-7|<35
The first step is to simplify the given expression, dividing it by 5 both sides: 5*|7n-7|<35 |7n-7|<7 Now, we’ll discuss the absolute value of the expression 7n-7: Case 1) 7n-7for 7n-7>=0…
- PHYSICS
What is the final velocity in the following scenario?A body of mass 16 kg travelling to the right…
In a perfectly inelastic collision: M1*v1 + M2*v2 = (M1 + M2)*vf Here M1 and M2 are the masses of the bodies colliding, v1 and v2 are their initial velocity and vf is their final velocity. Now, in…
1 educator answer
- BIOLOGY
What is the advances of ferns over bryophytes?
Ferns are seedless plants that possess a developed vascular system. The true ferns have complexleaves (megaphylls) that contain more than one vein. This developed system allows ferns to exist in…
- ROMEO AND JULIET
In Romeo and Juliet, do human beings cause all of their own problems bring out their own fate?a…
This could be analyzed by looking at 3 of the main characters: Romeo, Juliet and Mercutio. Romeo is portrayed from the beginning of the play as a fickle young man. Even the Friar suggests this…
1 educator answer
- MATH
What is the harmonic mean of 6 and 8?
If the harmonic mean of two terms a and c is b, it implies that 1/b is the arithmetic mean of 1/a and 1/c. Now, we are given a = 6 and c = 8. The reciprocals of a and c are 1/6 and 1/8. The…
1 educator answer
- MATH
What are the roots of (3x^3 + 8x^2 + 4x)(x^2 + 3x – 4)?
The expression (3x^3 + 8x^2 + 4x) (x^2 + 3x – 4) has a term with x raised to the power 5. Therefore it has 5 roots. The roots can be found by equating (3x^3 + 8x^2 + 4x) (x^2 + 3x – 4) to 0….
3 educator answers
- MATH
At what points does the curve defined by y = x^3 – 3x + 3 have horizontal tangents.
Horizontal lines have a slope of 0. Therefore to find the points where the curve y = x^3 – 3x + 3 has horizontal tangents we need to find the points where the slope of the tangent is 0. The slope…
2 educator answers
- MATH
Find the point of intersection of the tangents to the curve y = x^2 at the points (-1/2, 1/4) and…
The first derivative of a curve gives the slope of the tangent to the curve at any point. We are given the curve y = x^2 Now y’ = 2x. At the point (-1/2, 1/4), y’ = 2*(-1/2) = -1 The equation…
2 educator answers
- MATH
For f(x) = (x – 1)/x, what is the value of f(x)*f (1 – x)?
f(x) is defined as (x – 1)/x. Therefore f (1 – x) => (1 – x – 1)/ (1 – x) => (- x)/ (1 – x) So f(x)*f (1 – x) => [(x – 1)/x]*[(- x)/ (1 – x)] => [(x – 1)/ (1– x)]…
1 educator answer
- MATH
If f(x) = 2x and g(x) = sin x, what is the range of f (g(x))?
We are given f(x) = 2x and g(x) = sin x. Now f (g(x)) = f (sin x) = 2sin x. Now sin x can take all values in the set [-1, 1] 2*sin x can take all values in the set [-2, 2]. Therefore the range of f…
1 educator answer
- HARD TIMES
What is the behavior of Louisa towards her father in the novel Hard Times?
An excellent chapter to think about and study in depth with regard to this question in Chapter 15, entitled “Father and Daughter,” when Gradgrind relates the proposal he has received to his…
1 educator answer
- MATH
Consider the graph of y=9-x^2. At which point(s) on the graph will the normal line to the curve…
Let (x1,y1) be the point on the curve. Then the y1 = 9-x1^2. The slope of the curve at x1 is dy/dx at x= x1. At x= x1, y1 = 9-x1^2. Therefore dy/dx = (9-x^2)’ = -2x. Therefore the slope m of the…
- PHYSICS
Answer the questions based on the following information.Assume that you are driving along a…
You are travelling at 60 ft/s and at a distance of 1350 ft from you is a vehicle travelling at 30 ft/s. As you just want to touch the vehicle, your speed should be 30 ft/s too. Now let the rate at…
1 educator answer
- PHYSICS
How can a body be charged by induction?
A body can be charged in a process that does not involve charges coming to it from any other source. This is called charging by induction. It can be done in the following way. Let’s assume that…
1 educator answer
- OSCAR WILDE
How is figurative language used in “The Selfish Giant” by Oscar Wilde?
The fairy tale “The Selfish Giant” by Oscar Wilde has a lot of figurative language and figures of speech as it often occurs in this genre. When the giant repeatedly says “My own garden is my own…
3 educator answers
- BRAVE NEW WORLD
In Brave New World, how did the return from the reservation change Bernard’s life?
Having not only braved the world of the savages in the Reservation but also survived and bringing one of them back with him who was sired by the Director of Hatcheries greatly changes Bernard’s…
2 educator answers
- PHYSICS
Find the electric field between the sheets of the capacitor in the following case after the…
The plates of a capacitor carry opposite charges. Here it is given that the charge on the plate is 53.1*10^-8 C. The capacitance of the capacitor is 177 pF and the sheets are 1 cm apart. We can…
1 educator answer
- THE GIFT OF THE MAGI
In “The Gift of the Magi,” what is the situational irony?
Situational irony can be defined as when we as readers are led to believe that one thing is going to happen only to be shocked and surprised when something entirely different or the opposite of…
1 educator answer
- WUTHERING HEIGHTS
Wuthering Heights CharactersSo, I have to summarize the main characters of wuthering heights. The…
Cathy is a split-personality.early in her life she has become conscious of her profound affinity to Heathcliff and yet she marries Edgar Linton.she is drawn towards Edgar because of his social…
- MATH
What is the distance between the point of contact of the line x + 4y + 8 = 0 with the lines x = 4…
We have to first find the point of contact between the line x + 4y + 8 = 0 and x = 4. For this we can substitute x = 4 in x + 4y + 8 = 0 => 4 + 4y + 8 =0 => 4y = -12 => y = -12/4 => y =…
1 educator answer
- MATH
Can the root of a polynomial P(x) =3x^3 – 10x^2 – 5x be equal to -2/3?
The root of a polynomial P(x) is a number that makes P(x) equal to 0. Now we are given P(x) = 3x^3 – 10x^2 – 5x. If we substitute -2/3 for x in P(x), we get P (-2/3) = 3*(-2/3) ^3 – 10 *(-2/3) ^2…
1 educator answer
- MATH
What is the remainder when x^8 + 4x^6 + 3x^3 + x^2 + 7x + 19 is divided by (x + 5)?
This problem can be solved using the remainder theorem. According to this commonly used theorem, the remainder we get when f(x) is divided by (x – a) is equal to f(a). We have the polynomial f(x)…