Determine the function f(x)=(x^3-6x^2+m)/(x-2) if the graph of f is tangent to x axis.

# Determine the function f(x)=(x^3-6x^2+m)/(x-2) if the graph of f is tangent to x axis.

• MATH

Determine the function f(x)=(x^3-6x^2+m)/(x-2) if the graph of f is tangent to x axis.

If the curve that represents the graph of f(x) is tangent to x axis, then the first derivative of numerator is 0. We’ll note the numerator as g(x) = x^3-6x^2+m. We’ll impose the constraint of…

• MATH

(2square root2-square root7)^x+(2square root2+square root 7)^x=<4square root2

We notice that 2sqrt2 + sqrt7 = 1/(2sqrt2 – sqrt7). We’ll raise to x power both sides: (2sqrt2 + sqrt7)^x = 1/(2sqrt2 – sqrt7)^x We’ll note (2sqrt2 + sqrt7)^x = a. We’ll re-write the inequality in…

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What were the expectations of children during the 1930s?I am trying to tie the act of children…

Most children were expected to go to school–unless they were farmers, and sometimes they were needed by their fathers in the fields. So many farmers lost their land (750,000) during the…

• MATH

Factorize the polynomial f=x^3+4x^2-7x-10

We have to factorize f=x^3 + 4x^2 – 7x – 10 f=x^3 + 4x^2 – 7x – 10 => x^3 + 6x^2 – 2x^2 + 5x – 12x – 10 => x^3 + 6x^2 + 5x – 2x^2 – 12x – 10 => x(x^2 + 6x +5) – 2(x^2 + 6x + 5) => (x -…

• MATH

What is x if log2 (x^2+x+1)=logsquare root2 (x+1)?

We have to solve log (2) (x^2+x+1) = log (sqrt 2)(x+1) If y = log (2) (x^2+x+1) = log (sqrt 2)(x+1) => 2^y = x^2 + x + 1 and (sqrt 2)^y = x + 1 taking the square of both the sides of (sqrt 2)^y…

• MATH

What is x if E(x)=(x^2-4)/(x^2+2x-35) is positive?

We are given that E(x)=(x^2-4)/(x^2+2x-35) is positive. E(x)=(x^2-4)/(x^2+2x-35) => (x – 2)(x +2)/ (x^2 + 7x – 5x – 35) => (x – 2)(x +2)/ (x(x + 7) – 5(x + 7)) => (x – 2)(x +2)/ (x – 5)(x…

• MATH

Determine a if the lines (a-3)*x + 2y-7=0 and x+(a+1)*y+2=0 are parallel.

Two parallel lines have the same slope. So we have to find the slope of (a-3)*x + 2y-7=0 and x+(a+1)*y+2=0 (a-3)*x + 2y-7=0 => 2y = -(a – 3)x + 7 => y = -(a – 3)/2* x + 7/2 The slope is (3 -…

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Why do Gothic writers use madness/insanity as a topic?

Gothic writers have often appealed to topics such as insanity and madness as part of the stylistic licenses that are natural to the genre. Gothic literature is a darker branch of Romanticism that…

• MATH

What are the solutions of equation : square root (5x-4)+square root(11x+4)=4square rootx?

We have to solve sqrt (5x-4) + sqrt(11x+4) = 4*sqrt x sqrt (5x-4) + sqrt(11x+4) = 4*sqrt x square both the sides => (5x – 4) + (11x + 4) + 2*sqrt (5x-4)*sqrt(11x+4) = 16x => 16x + 2*sqrt…

• THE ADVENTURES OF TOM SAWYER

Who is the “Model Boy” in The Adventures of Tom Sawyer (chapter 5)?

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How was sharecropping a cycle of debt?

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• MATH

If f(x)=log(15-x) (x+5) solve the equation f(x)=2 15-x is the base of log.

We have the log to the base (15 – x) f(x) = log(15-x) (x+5) = 2 => (x + 5) = (15 – x)^2 => x + 5 = 225 + x^2 – 30x => x^2 – 31x + 220 = 0 => x^2 – 20 x – 11x + 220 =0 => x( x – 20) -…

• MATH

Calculate f'(x) if 0<x<infinite , f(x)=(x+1)^-1 – ln(x+1)/(x+2).

We have to find f'(x). f(x) is given as (x+1)^-1 – ln(x+1)/(x+2). [(x+1)^-1 – ln(x+1)/(x+2)]’ we can write ln (x +1)/(x +2) = ln (x+1) – ln(x+2) => [(x+1)^-1 – ln (x+1) + ln(x+2)]’ =>…

• MATH

Solve for x (4*16)^x+(4*2)^x=79.

To solve for x: (4*16)^x+(4*2)^x=79. Solution: Given equation is rewritten as: 64^x +8^x = 79. Let 64^x = (8^x)^2 = t^2, where t = 8^x. Therefore the equation becomes: t^2+t – 79 = 0 t^2 +t -79 =…

• MATH

What is the slope of the line 6x+3y-15=0 ?

The line ax + by + c = 0 can be written as y = mx + c, where m is the slope of the line and c is the y-intercept. 6x + 3y – 15 = 0 => 3y = -6x + 15 => y = -2x + 5 Therefore the slope is -2.

• MATH

What is the equation of ellipse if the major axis is 10 and the distance between focci is 2c=8?

The equation of the ellipse with major axis 2a and minor axis b i given by: x^2/a^2+y^2/b^2 = 1. Given major axis = 10.Therefore 2 a= 10 , or a = 10/2 = 5. The distance between the focii 2c =…

• LITERATURE

What are at least 3 ways an author develops a character?

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• HISTORY

What form of government or political structure was prevalent in America prior to the American…

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In Romeo and Juliet, does Friar Lawrence believe in Fate?The Friar believe that God has…

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• ROMEO AND JULIET

Are there quotes from Juliet (Romeo and Juliet) that suggest she believes in Fate?i’m trying to…

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• SCIENCE

Acetic acid,methane,chloroform are examples of which type of compounds & why ??Is it…

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what are some similaities and differences between twilight by stephanie myers and beowolf…

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• FRISBY AND THE RATS OF NIMH

In Mrs. Frisby and the Rats of NIMH, whom does Mrs. Frisby meet on her way home in Chapter 2?…

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• CAT IN THE RAIN

What is the theme of Hemingway’s short story “Cat in the Rain”?

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• TEACHERS

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• MATH

a circular cylinder is inscribed in a circular cone of a radius r and height h. what relation…

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• THE STRANGER

What themes are present through out The Stranger?

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• HISTORY

Is nationalism a stabilizing or destabilizing force?Is nationalism a stabilizing or destabilizing…

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• HISTORY

How did poverty policy come about?

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• MIDNIGHT’S CHILDREN

Comment on the language of Midnight’s Children.

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• KATE CHOPIN

Share your ideas about the main characters in Kate Chopin’s “Ripe Figs.”

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• DEATH OF A SALESMAN

How significant is the character of the woman in Arthur Miller’s Death of a Salesman?The woman…

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• GUIDE TO LITERARY TERMS

which literary devices are employed to make ‘defamiliarization’?

In order to understand the literary devices used to create the effect of “defamiliarization” some scholars use the term of foregrounding. It refers to the variety of figurative devices at the…

• SOCIAL SCIENCES

What do you believe is the main contributor to crime rates in the United States? What do you…

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• THE CANTERBURY TALES

What is the theme in “The Wife of Bath” in The Canterbury Tales?Can anyone tell me what’s the…

In the Wife of Bath’s tale a young man must set out on a journey in order to find out what women truly want. After his travels, he comes to the conclusion that: A woman wants the self-same…

• MACBETH

What are the actions of love in Macbeth?I need to compare the type of love between Macbeth and…

Provided that your definition of “love” is a little broad and not aimed specifically at romantic love, then there are several cases when the characters show loving feelings towards each other….

• TEACHERS

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what things in the way of the world we can enjoy without studying the age in which the play was…

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• THE FALL OF THE HOUSE OF USHER

How does both irony and symbolism support the theme of The Fall of the House of Usher?

Excellent question. Of course, when we think of the theme of any given work of literature there are an entire range of answers that can be given. However, certainly when we consider this excellent…

• PHYSICS

Light is incident on plastic at an angle of 72.7 degree and the angle of refraction is 57.1…

Here, we have light moving from vacuum into transparent plastic. The angle of incidence is 72.7 degrees and the angle of refraction is 57.1 degrees. As the refractive indexes of vacuum and plastic…

Please discuss this with real life example if possible How can country move from producing inside…

A country is producing inside the PPF when it is not producing as much in the way of goods and services as it could given the resources it currently has. This typically happens when a country is…

• ECONOMICS

How can the PPF be moved in one direction or another?

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• SOCIAL SCIENCES

Predicting state of the U.S. family?Can you look ahead 50 years and predict the State of the U.S….

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What are possible essay questions that can be asked about Monopolies (apart from the good and bad…

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• TRIGONOMETRY1

Given cos (x+y)-1=0, verify if sin(2x+y)-sinx=0?

We’ll start by expanding the cosine of the sum: cos (x+y) = cos x*cos y – sin x*sin y From enunciation, we know that: cos x*cos y – sin x*sin y – 1 = 0 We’ll add sin x*sin y + 1 both sides: cos…

• TRIGONOMETRY1

Determine all the angles a if 2-cos a=2sina?

We’ll recognize a linear equation and we’ll solve it using the substitution technique. We’ll write sin a and cos a with respect to tangent of the half-angle. sin a = 2 tan(a/2)/[1+(tan a/2)^2] cos…

• MATH

Differentiate y = (3-square root x)+ln(3-square root x)^2

To differentiate y = (3-square root x)+ln(3-square root x)^2. Solution: dy/dx = d/dx {3-sqrtx)+d/dx{ln(3-sqrtx)^2}….(1). d/dx(3-sqrtx) = d/dx(-sqrtx) = -1/(2sqrt x)….(2) d/dx ln{3-sqrtx)^2 =…

• MATH

Evaluate the antiderivative of s(t)=1/(t^2+4t+4)?

To find the anti derivative of s(t)=1/(t^2+4t+4). Solution: s(t) = 1/(t^2+4t+4). => s(t) = 1/(t+2)^2. Therefore Int s(t) dt = Int {1/(t+2)^2} dt +C= Int (t+2)^(-2) dt +C= {(t+2)^(-2+1)}/(-2+1)…

• MATH

What are the solutions of the exponential 2*2025^x-(3*15)^x=1?

To find the solution of 2*2-25^x-(3*15)^x = 1. We know that 2025 = (3*15)^2 = 45^2. So 2025^x= (3* 15)^2x = 45^2x. Therefore the given equation becomes: 2* 45^2x – (45)^x -1 = 0 1. 2t^2-t-1 = 0,…