# Discuss the question of sin and penance in The Scarlet Letter.

**THE SCARLET LETTER**

**Discuss the question of sin and penance in The Scarlet Letter.**

Clearly your question focuses very closely on two very important themes that are self-evident from the very beginning of Hester’s account. However, what is interesting, as in much of Hawthorne’s…

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**MATH**

**Write the trigonometric form of the complex number z = 3 + 4i.**

The given complex number is 3+4i. To express the number in the polar form. If z = x+iy, Then r = sqrt(x^2+y^2) x = rccost and y = rsint y/x = tant, or t = arctan (y/x) So z = r(cost + isint ) is…

**MATH**

**What is the distance between the point (0;1) and the line that passes through the points (1;2)…**

To find the distance from (0,1) to the line joining (1,2) and (-1,-2). We know that the line through any two points (x1, y1) and (x2, y2) is: y-y1 = {(y2-y)/(x2-x1)}(x-x1). Therefore the line…

**JANE EYRE**

**How gender affects the plot and character development in the novel?Just describe the differences…**

During the Victorian times, women were restraint to few roles in society. Thus, the upper class women ought to be the angels in the house, the perfect wives and mothers, submissive to the patriarch…

**MATH**

**What are the solutions of the equation 48/(2x+2)=2x+6?**

To find the solutions of 48/(2x+2) = 2x+6. We multiply both sides by 2x+2 . 48 = (2x+2)(2x+6) 48 = 2(x+1)(2)(x+3) 48 = 4 (x+1)(x+3) We divide both sides to keep the equation lower terms. 12 =…

**TO KILL A MOCKINGBIRD**

**What does “If he held his mouth right, Mr. Cunningham could get a WPA job” mean?**

To Kill a Mockingbird is set during the Depression. The WPA (Works Progress Administration) was created in 1935 in order to provide assistance to those suffering because of the economic disaster at…

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**MATH**

**Differentiate the function f(x)=(3-1/x)/(x-1).**

To differentiate the function f(x) = (3-1/x)/(x-1)/ We multiply both numerator and denominator on right side by x and then we get: f(x) = (3x-1)/(x*2-x) f(x) is in u(x)/v(x) form. (u(x)/v(x))’ =…

**MATH**

**Find the function y = mx + n if the points (1;2) and (-1;-1) are on the graph of the function.**

y = mx+n, the points (1,2) and (-1,-1) are on the graph. Since points are on the graph, the coordinates of the two given points should satisfy the graph. Point (1,2) is on y = mx+n. So m*1+n= 2….

**MATH**

**What is x if 14*| 3x – 2 | = 28**

We’ll solve the equation, expressing first the modulus. Case 1: l 3x-2 l = 3x – 2 for 3x-2 >= 0 3x >= 2 x >= 2/3 Now, we’ll solve the equation: 14(3x-2) = 28 We’ll divide by 14: 3x-2 = 2…

**MATH**

**Solve the binomial equation : z^5 – 243 = 0 .**

We’ll add 243 both sides: z^5 = 243*1 We’ll re-write the equation writing the value 1 as the polar form of a complex number: 1 = 1 + 0*i (rectangular form) r = sqrt(1^2 + 0^2) r = 1 tan a = y/x tan…

**MATH**

**Prove that the system have solutions x^-1+y^-1=1 3*x^-1+y^-1=2**

For the beginning, we’ll re-write the equations of the system, using the rule of negative power. a^-b = 1/a^b According to the rule, we’ll have: x^-1+y^-1 = 1/x + 1/y 1/x + 1/y = 1 x + y = xy (1)…

**HARD TIMES**

**How does Dickens paint the picture of utilitarianism through his novel Hard Times?**

Interestingly, I think the theme of utilitarianism that you have highlighted is very closely linked to the theme of the mechanisation of the human soul, that is discussed at length through the…

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**MATH**

**What are a and b if the points (1,3) and (3,7) are on the line f(x) if a*f(x+2) + b*f(2-x) = 6x + 25**

If the points belong to the graph of f(x), their coordinates verify the expression of f(x). f(1) = 3 and f(3) =7 We’ll put x = 1 in the expression of condition from enunciation: a*f(1+2) +…

**MATH**

**Find the point of intersection of the lines (x-1)/2 – y=5 and x + (1-y)/4=6**

To determine the intercepting point, we’ll have to solve the system formed by the equations of the given lines. (x-1)/2 – y=5 We’ll multiply by 2: x – 1 – 2y = 10 We’ll add 1: x – 2y = 11 (1) We’ll…

**AN OCCURRENCE AT OWL CREEK BRIDGE**

**What is Ironic about the fact that Farquhar agrees with the saying, “all is fair in love and war?”**

There is a great deal of irony in Peyton Farquhar’s agreement with the idea that “all is fair in love and war.” It is evident that Farquhar does feel that he is justified in doing whatever he is…

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**MATH**

**Calculate Sn (x) = x + 2x^2 + 3x^3 +…+nx^n if x is real and n is natural.**

We’ll calculate Sn (x) for x = 1. Sn (x) = 1 + 2 + 3 + …. + n We recognize the sum of the first natural n terms: Sn (1) = n(n+1)/2 Now, we’ll multiply Sn (x) by x: xSn (x) = x^2 + 2x^3 + 3x^4 +…

**THE ADVENTURE OF THE SPECKLED BAND**

**What events happen in the exposition of “The Adventure of the Speckled Band.”**

In Sir Arthur Conan Doyle’s “The Adventure of the Speckled Band,” the exposition introduces Holmes’ and Watson’s newest mystery to be solved. A woman arrives early from the train, one Helen Stoner….

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**THE GREAT GATSBY**

**I need some information about Daisy for an essay I need to write for F. Scott Fitzgerald’s The…**

Daisy is female. She is married to Tom Buchanan (though she loved Jay Gatsby before he went off to war). She is wealthy, born into money, and therefore, does not work. Daisy is attractive and wears…

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**THE GREAT GATSBY**

**In The Great Gatsby, what are some quotes about the lavish parties that he throws?**

A great chapter for descriptions of the kind of parties that Gatsby throws is chapter 3. On the one hand this account presents us with the social elite of the day who frequent his parties, but on…

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**MATH**

**A rectangular playground is to be enclosed by a fence, and divided into three sections with…**

Let x and y be the length of the rectangle. We assume the parallel to width , the rectangle is trisected. So the required fencing is x+x+x+2y = 800 meter. So y = (800-3x)/2. Therefore the area A(x)…

**GUIDE TO LITERARY TERMS**

**“The contrast between what is expected or assumed, and what actually happens” is: foil,…**

Of the choices that are provided, irony is the answer you want (third choice). Irony is the difference between what you expect to happen and what actually takes place. There are different kinds of…

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**CINEMA**

**Can anyone tell me how sexism was present at the movie Casablanca?**

It should be noted that I think one would find it a challenge to really make a substantive argument that the message of the film is one of sexism. One can find elements that might contribute to…

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**THE CRUCIBLE**

**How does John Proctor’s great dilemma change during the course of The Crucible?**

At the beginning of the play, the reader learns that John Proctor has had an affair with his house keeper, the much younger Abigail Williams. Though he has decided to end it, his original dilemma…

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**MATH**

**Two numbers have a difference of 28. What is the sum of their squares if it is a minimum?thanks!!**

We know that the two numbers have a difference of 28. Let one of the numbers be x. The other is x+ 28. Now the square of x is x^2 and the square of x+ 28 is (x+28)^2. The sum of the squares is x^2…

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**MATH**

**Determine the equation of the the circle whose center is (3,-2) and the diameter is 8.**

We have the center (3, -2) and diameter = 8 We know that the formula for the circle is: (y-y1)^2 + (x-x1)^2 = r^2 where (x1,y1) is the canter and r is the radius: we hav teh diameter = 8 ==> the…

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**REFERENCE**

**Why is Jamaican Creole so well-researched? Although there is so little historical data available….**

This is an interesting question and probably deserves an entire book devoted to it. I would suggest two reasons for the amount of research on Jamaican creole. Firstly, it is the most populous of…

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**MATH**

**Find the coordinate of the point m(0,a) if m is midpoint between A(3,2) and B(b,-4)**

m(0,a ) is midpoint between A(3,2) and (B(b, -4) We know that if m is midppoint of AB , then the coordinates of the mid point m is: xM = (xA+xB)/2 xy = (yA+yB)/2 Let us subsitute : For the x…

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**MATH**

**Find b value if log (b+2)^2- 2log b = log 3**

log (b+2)^2- 2log b = log 3 We will use the algorethim properties to solve: First we know that: a*log b = log b^a ==> 2log (x+2) – 2log b = log 3 Now factor 2: ==> 2(log(b+2) – log b) = log…

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**MATH**

**-5126 = -6 – 5(x+ 22)^(5/3) solve the equation.**

-5126 = -6 – 5(x+ 22)^(5/3) First we will add 6 to both sides: ==> -5120 = -5(x+22)^(5/3) Now divide by -5: ==> 1024 = (x+ 22)^(5/3) Now we know that 1024 = 2^10 ==> 2^10 = (x+22)^5/3 Now…

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**MATH**

**A charter bus company provides a bus trip for a fare of $80 each for 30 or fewer passengers. For…**

There is no way to answer this question without some additional restraint, for example the number of available buses. Or, for example, if there are only two buses and a mostly empty bus does not…

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**MATH**

**Find the zeros of f(x) = x^3 +9x^2 + 23x + 15**

f(x) = x^3 +9x^2 + 23x + 15 To solve, we will subsitute with the 15 factors which are: 1, -1, 3, -3, 5, -5, 15, -15 let us subsitute with x= -5: f(-5) = 5^3 + 9*5^2 + 23*5 + 15 = -125 + 225…

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**MATH**

**Find the inverse function of g(x) = -2/(x+1)**

let y= -2/(x+1) Now we will multiply by (x+1) both sides: ==> y(x+1) * -2(x+1)/(x+1) Now eliminate similar: ==> y(x+1) = -2 Now we will diustribute y: ==> yx + y = -2 Now we will subtract…

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**MATH**

**Find the value of the discriminant of 6p^2 – 2p – 3 = 0**

6p^2 – 3p – 3 = 0 The discriminant is the value of delta: delta = (b^2 – 4ac) = 9 – 4*6*-3 = 9 + 72 = 81 ==> delta = 81 Since delta is a positive perfect square then the function has two…

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**MATH**

**The polynomial f is divisible by g . Calculate p=f(0)*f(1)*…*f(2009) if f=x^3-4x^2+x+6 and…**

f(x) = x^3-4x^2+x-6 and g(x) = x^2-x-2. To find the product f(1) f(2)f(3)… f(2009). Since f(x) = x^3-4x^2+x+6 is divisible g(x) = x^2-x-2, f(x) has the same factors as that of g(x). But x^2-x-2…

**MATH**

**Simplify the expression: (-10 – 5i) / (-6+6i)**

Let z= (-10-5i)/(-6+6i) First we need to eliminate the complex denominator by multiplying by its inverse: ==> z= (-10-5i)(-6-6i)/(-6+6i)(-6-6i) Let us simplify each: (-10-5i)(-6-6i) = 60 + 60i +…

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**MATH**

**Profit or loss?Prem buys two kinds of lemons at the rate of 6 and 9 for a rupee. He mixes them…**

Let the number of the first kind of lemon Prem buys be x, and the number of the second kind of lemon be y. Prem’s cost is then: C = 1/6 x + 1/9 y = 0.167x + 0.111y Prem mixes them together to get x…

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**MATH**

**Solve the inequality : 3(6b-1) > 18 – 3b**

3(6b-1) > 18 – 3b First we will factor 3 from the right side: ==> 3 ( 6b -1) > 3 ( 6-b) Now divide both sides by 3: ==> (6b -1) > (6-b) Now add b to both sides: ==> 6b -1 + b >…

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**ILIAD**

**What is the importance of arete in the Iliad?**

Arete is the term given to excellence or honour that was won by heroes by achieving feats of great skill or bravery. Arete is a central theme to this book as the warriors all are striving to gain…

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**MATH**

**Simplify the expression : 7(9k + 8) + 3 ( k-10)**

Let E =7(9k+8) + 3(k-10) First we will expand the brackets: we will distribute 7: ==> E = 7*9k + 7*8 + 3*k + 3*-10 = 63k + 56 + 3k – 30 Now will group similar terms: ==> E = 63k +…

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**MATH**

**Solve the equation sin^6x + cos^6x = 1 .**

To solve sin^6x+cos^6x = 1. We know a^3+b^3 = (a+b)(a^2+b^2-ab) Therefore, LHS= sin^6x+cos^6x = (sin^2x+cos^2){sin^4x+cos^4x+sin^2-cos^2x) . sin^6x +cos^6x = (sin^4x+cos^4x -sin^2cos^2x), as…

**MATH**

**What is m if det A = 0? A is matrix of coefficients of variables from equations: x+y+z=2…**

First we will write the coofficient matrix: det (A)= 1 1 1 2 -1 -2 1 4 m Now we will us ethe formula to calculate the determinant: ==> det(A) = 1*-1*m + 1*-2*1 + 1*2*4…

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**MATH**

**Solve in Z*Z the system (x-3)*y=2 (x-y)o4=10 x*y=x+y-3 xoy=xy-3(x+y)+12**

We’ll re-write the equations of the system, using the given laws of composition. (x-3)*y=2, where x*y=x+y-3 We’ll substitute x by (x-3). (x-3)*y = x – 3 + y – 3 We’ll combine like terms: x + y – 6…

**CHEMISTRY**

**What is meant by nitrogen dioxide dimerizes? How is it related to paramagnetism?**

The Lewis structure of nitrogen dioxide requires that the central atom nitrogen be bonded to one oxygen through a double covalent bond and to another oxygen through an unusual ‘three electron…

**MATH**

**Verify if 2x – 1/( x^2 + 1 ) = f(x) if f(x) = ( 2x^3 + 2x – 1 )/ ( x^2 + 1 )**

2x – 1/(x^2 + 1) = f(x) f(x) = (2x^3+ 2x -1)/(x^2 + 1) We will subsitute f(x) in the expression to verify : ==> 2x – 1/(x^2 + 1) = (2x^3+ 2x -1)/(x^2 + 1) Now we will resrite the left side with…

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**LORD OF THE FLIES**

**How does the third death on the island differ from the other two deaths?**

The deaths in the novel can be categorized in much the same way that our legal systems distinguishes them: first degree, second degree, and third degree murder. The first death occurs when the…

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**MATH**

**Solve the equation: 3^( 3x^2 + 5x – 4) = 9^-3**

We have to solve 3^ (3x^2 + 5x – 4) = 9^-3 for x. First we convert both the sides as terms to the power 3 Therefore 3^ (3x^2 + 5x – 4) = 9^-3 => 3^ (3x^2 + 5x – 4) = (3^2) ^-3 => 3^ (3x^2 +…

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**MATH**

**The abscisa and the ordinate of a point in the cartesian plane is (3 ,- 4). What is the distance?**

To determine the abscisa and the ordinate of a point, we’ll draw perpendiculars from the given point to the x and y axis. We’ll form a right angle triangle, whose hypotenuse is the distance from…

**MATH**

**Calculate the area of the surface between the graph of f and the lines x=1, x=2. f(x)=1/(x+2)(x+3)**

f(x) = 1/(x+2)(x+3) and x=1 and x=2 Let F(x) = intg f(x) Then the area between f , x=1, and x= 2 is: A = F(2) – F(1) First we will integrate f(x): F(x) = ing (1/(x+2)(x+3) We will rewrite using…

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**POLITICAL SCIENCE**

**falsification and realismhey,, i would like to ask a basic question about the falsification to…**

Are you asking how you could falsify the theory of realism — prove that it is false? Personally, I do not think that you can falsify it. Popper says that any scientific theory must be…

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**MATH**

**What are a,b,c if f(0) = 2 , f'(1) = 26 and the definite integral of f(x) for x = 0 to x =1 is…**

f(x) = ax^4 + bx^2 + c Given : f(0) = 2 f'(1) 26 intg f(1) – intg f(0) = 4 We start from f(0) = 2 Let us subsitute: f(x) = ax^4 + bx^2 + c f(0) = 0 + 0 + c = 2 ==> c= 2 ==> f(x) = ax^4 + bx^2…