
ReferenceIn each Englishspeaking country, there are varieties of English used, mainly for spoken communication. To write a formal letter to the Minister of Education, you would want to use the Standard...

MathHello! Probably we need to find all the terms of this progression. Recall that each next term of a geometric progression is obtained by multiplying the previous term by the quotient, denote it as...

ReferenceContext Context includes the time period the writing is set in, the prevailing social and political conditions at the time of publication, and specific influences that inspired the writer to pen...

Law and PoliticsI notice that in this question you ask why the Declaration “is” an important document. Therefore, I will address its importance today, not at the time when it was written. The Declaration of...

ArabyThe priest left the following books on the shelf:The Abbot, by Walter Scott, The Devout Communicant, and The Memoirs of Vidocq. The first book is about Mary Queen of Scots, blends Romanticism and...

Raymond's RunOne characteristic that Squeaky uses to overcome her problems is her toughness. She protects her brother, Raymond, who is developmentally disabled. As she says, "But now, if anybody has anything to...

ScienceA process that can change the size and shape of mountain ranges is weathering and erosion. While once among the tallest peaks in the world, the Blue Ridge Mountains of Virginia have been...

Dramatic GenresThese terms, adopted from Aristotle’s Poetics, serve as both dramatic taxonomy and as general terms for aesthetic judgments. As genres, they differ in their motives and their “rules” of...

ReferenceTo analyze the audience, purpose, and context of this speech, we actually need a bit more background information. We can find this speech both published and analyzed in Jon Steel's book Perfect...

Sinners in the Hands of an Angry God"Sinners in the Hands of an Angry God" is a sermon. Who preached this sermon in the mid 1700's in..."Sinners in the Hands of Angry God" is a sermon that was written and delivered by Jonathan Edwards. The sermon was originally preached in July of 1741. It is Jonathan Edward's most famous piece....

The GiverIn The Giver (Lowry), as Jonas watches his father release one of the newborn twins, he finally comes to understand what release is, and the horror of this, seeing a newborn put to death by his own...

A Separate PeaceI believe that this question is asking to describe what is physically different about the Devon School in chapter 13. The answer to this question can be found in the early parts of the chapter....

Tuck EverlastingThe Tuck family has not been aging for 87 years. At the beginning of chapter 7, the Tuck family narrates the origins of their immortality to Winnie Foster. They tell her that they were heading...

A Midsummer Night's DreamI personally believe that Hermia is right to disobey her father's commands, as doing so constitutes a rebellion against oppressive patriarchal laws. In the world of Shakespeare's A Midsummer...

ReferenceThe field of the text is its topic; in this case, the topic is the ceremony to congratulate the seniors who have achieved high results because of their hard work. The mode is both written and oral,...

LanguageWhen asking about "which variety of English would be appropriate," you are asking about which linguistic "register" would be appropriate to use in a given situation among given participants. To...

ReferenceIf you address your colleagues at a youth club meeting, you would use more formal language, meaning you would not likely use slang or incomplete sentences. Instead, if you are chairing the meeting,...

LiteratureThe Great Irish Elk and butter description serves to illustrate the archaeological value of the bog in terms of Irish identity, culture, and history. In the poem, the reference to the Great Irish...

Grammar and speechIt can sometimes be difficult to discern the differences between informal and formal language, which so often comes down to a single case of word choice or order, small syntactical adjustments,...

LiteratureIn the story, Okonkwo is Ezekiel's brother; after Ezekiel's death, he takes Ezekiel's widow, Ma Blackie, as his fourth wife. Even in postcolonial Nigeria, the traditions are such that a woman's...

Law and PoliticsThomas Jefferson wrote the Declaration of Independence. In the Declaration of Independence, there are many ideas about the role of government and about the rights the people should have. A big part...

Death, be not proud"Death, be not proud" is a sonnet by the iconic English metaphysical poet John Donne. The fourteenline poem, which is also referred to as "Holy Sonnet X,"deals with the fear of death, overcoming...

GrammarThe primary reason this sentence is ambiguous is because of the unclear placement and use of the word "right." In the English language, the word "right" can mean two very different things. The...

Reference'Ambiguity' means a lack of clarity or concrete detail, which can make it difficult to discern meaning. In the case of these two sentences, the lack of context and detail make it possible to...

MathGiven `\frac{dy}{dx}=\frac{1}{\sqrt{4x^2}}, y(0)=\pi` , we have to find y. So we can write, `dy=\frac{dx}{\sqrt{4x^2}}` Integrating both sides we have, `y=\int \frac{dx}{\sqrt{4x^2}}+C` Now...

MathComplete the square at the denominator: `x^4 + 2x^2 + 2 = (x^2)^2 + 2x^2 + 1 + 1 = (x^2 + 1)^2 + 1.` Now we see the substitution `y = x^2 + 1,` then `dy = 2x dx,` and the integral becomes `int...

MathBy completing the square and making simple substitution, we will reduce this integral to a table one. `x^24x = (x^2 + 4x + 4) + 4 = (x+2)^2 + 4 = 4  (x+2)^2.` Now make a substitution `y =...

MathTo evaluate the given integral: `int_(2)^(2)(dx)/(x^2+4x+13)` , we follow the first fundamental theorem of calculus: If f is continuous on closed interval [a,b], we follow: ` int_a^bf(x)dx =...

MathRecall that `(arccos(x))' = 1/sqrt(1x^2)` and make the substitution `y = arccos(x),` then `dy = 1/sqrt(1x^2).` The limits of integration are from `arccos(0) = pi/2` to `arccos(1/sqrt(2)) =...

MathWe have to evaluate the definite integral: `\int_{0}^{1/\sqrt{2}}\frac{arc sinx}{\sqrt{1x^2}}dx` Let arc sinx=t Differentiating both sides we get, `\frac{1}{\sqrt{1x^2}}dx=dt`...

MathMake the substitution `u = sin(x),` then `du = cos(x) dx.` The integration limits for `u` are from `sin(0) = 0` to `sin(pi/2) = 1,` and the integral becomes `int_0^1 (du)/(1 + u^2) = arctan(1) ...

MathMake the substitution `y = e^(x),` then `dy = e^(x) dx` and `e^(2x) = y^2.` The limits of integrations for `y` become from `e^(ln2) = 1/e^(ln2) = 1/2` to `e^(ln4) = 1/e^(ln4) = 1/4.` The...

MathTo be able to solve for definite integral, we follow the first fundamental theorem of calculus: `int_a^b f(x) dx = F(x) +C` such that f is continuous and F is the antiderivative of f in a closed...

MathMake the substitution `u = sqrt(4x^2  9),` then `du = (4x)/sqrt(4x^2  9) dx.` Inversely, `dx =sqrt(4x^2  9)/(4x) du = u/(4x) du` and `4x^2 = u^2 + 9.` The limits of integration become from...

MathMake a substitution `y = 2x,` then `dy = 2 dx` and the limits of integration for `y` are from `0` to `3.` The integral becomes the table one: `int_0^3 1/(1+y^2) (dy)/2 = 1/2 (tan)^(1)(y) _(y=0)^3...

MathWe have to evaluate the integral : `\int_{0}^{\sqrt{2}}\frac{dx}{\sqrt{4x^2}}` let `x=2sin t` So, `dx=2cos t dt` When x=0, t=0 `x=\sqrt{2}, t=\pi/4` So we have,...

MathMake a substitution `x = 3y,` then `dx = 3 dy` and the limits of integration for y are from 0 to 1/18. The integral becomes a table one: `int_0^(1/18) (9 dy)/(sqrt(99y^2)) = int_0^(1/18) (3...

MathThis integral may be taken by dividing into two parts: `int (x dx)/(x^2 + 1)  3 int (dx)/(x^2 + 1).` The second integral is obviously `3arctan(x) + C.` The second requires the substitution `u =...

MathWe have to evaluate the integral : `\int \frac{sec^2x}{\sqrt{25tan^2x}}dx` Let `tanx =t` So, `sec^2x dx=dt` Therefore we have, `\int \frac{sec^2x}{\sqrt{25tan^2x}}dx=\int...

MathGiven the integral: `\int \frac{2}{x\sqrt{9x^225}}dx` Let `x=\frac{5}{3}sect` `` So, `dx=\frac{5}{3}sect tant dt` Hence we have, `\int \frac{2}{x\sqrt{9x^225}}dx=\int \frac{\frac{10}{3}sect...

MathMake the substitution `u = t^2/5,` then `du = (2t dt)/5,` `t dt = 5/2 du` and `t^4 = 25u^2.` The integral becomes `int (5/2)/(25u^2 + 25) du = 1/10 int (du)/(1 + u^2) = 1/10 arctan(u) + C =...

MathGiven the integral : `\int \frac{1}{4+(x3)^2}dx` let `x3=t` So, `dx=dt` therefore we have, `\int \frac{1}{4+(x3)^2}dx=\int \frac{1}{4+t^2}dt` `=\int \frac{1}{2^2+t^2}dt`...

MathIndefinite integral are written in the form of `int f(x) dx = F(x) +C` where: f(x) as the integrand F(x) as the antiderivative function C as the arbitrary constant known...

MathRecall that the indefinite integral is denoted as: `int f(x) dx =F(x)+C` There properties and basic formulas of integration we can apply to simply certain function. For the problem `int...

MathWe have to evaluate `\int \frac{dx}{\sqrt{14x^2}}` Let `x=\frac{1}{2} sint ` So, `dx= \frac{1}{2}cost dt` Hence we have, `\int \frac{dx}{\sqrt{14x^2}}=\int \frac{\frac{1}{2}cost...

MathWe have to evaluate the integral: `\int \frac{dx}{\sqrt{9x^2}}` let `x=3sint` So, `dx=3cost dt` Hence we have, `\int \frac{dx}{\sqrt{9x^2}}=\int \frac{3cost}{\sqrt{99sin^2t}}dt`...

MathFirst, check that the given point satisfies the equation: `arctan(1 + 0) = 0 + pi/4` is true. The slope of the tangent line is `y'(x)` at the given point. Differentiate the equation with respect to...

MathThis function is defined on entire real axis and is differentiable everywhere. Its derivative is `f'(x) = 1/(1+x^2)  1/(1 + (x4)^2) = (1 + (x4)^2  1  x^2)/((1+x^2)(1 + (x4)^2)) =` `= (8x +...

MathThe derivative of y with respect to is denoted as` y'` or `(dy)/(dx)` . For the given equation: `y = arctan(x/2) 1/(2(x^2+4))` , we may apply the basic property of derivative: `d/(dx) (uv)...

MathRecall that the derivative of y with respect to is denoted as `y'` or `(dy)/(dx)` . For the given equation: `y = arctan(x) +x/(1+x^2)` , we may apply the basic property of derivative: `d/(dx)...
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