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

# 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…

• 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 +…

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• 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…

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I am feeling really stressed. Any advice for me??? How many minutes does it take to commit…

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• MATH

Solve for x: (3x+7)(x-1)=24.

(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…

• 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…

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Does the text of A & P by John Updike have a significant purpose? (Is it a call to action…

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• A&P

How is the importance of studying literature shown in “A & P” by John Updike?

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• A DOLL’S HOUSE

In“A Doll’s House” by Ibsen, and the story “Chrysanthemums” by Steinbeck, talk about the…

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• 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…

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Analyze and evaluate the use of imagery or form in the poems“America” by Claude McKay, and…

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• 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 =>…

• MATH

Find f'(x) if f(x)=5^tan5x.

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) =…

• HISTORY

Is John Brown a freedom fighter or a terrorist? Explain.

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• 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…

• 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 =…

• 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 =…

• 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…

• MATH

Solve in R sinx=1+cos^2x

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…

• 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)…

• 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…

• 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…

• 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…

• 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…

• 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…

• 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…

• 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….

• 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…

• 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…

• 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)]…

• 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…

• HARD TIMES

What is the behavior of Louisa towards her father in the novel Hard Times?

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• 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…

• 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…

• OSCAR WILDE

How is figurative language used in “The Selfish Giant” by Oscar Wilde?

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• 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…

• 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…

• THE GIFT OF THE MAGI

In “The Gift of the Magi,” what is the situational irony?

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• 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 =…

• 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…