
ReferenceOur global perspective has expanded over the years for a variety of reasons. One way that our global perspective has expanded is with the growth of businesses beyond our borders. We are realizing...

Little WomenAt the beginning of the book, Meg wears old clothes, but she dreams of the old days, when her family was wealthier and she could wear nicer clothes. Though Meg has to wear poplin to balls, she...

A River Runs Through ItThis quote appears at the end of A River Runs Through It, after Norman has spoken of the death of his brother, Paul, and of his old age, when he fishes alone (though some people warn him he...

The Most Dangerous GameToward the end of Richard Connell's short story "The Most Dangerous Game," the protagonist Sanger Rainsford leaps from a cliff across from General Zaroff's chateau in order to avoid certain death...

HistoryAfter Abraham Lincoln was elected in early November of 1860, the Confederate states began to secede from the country. South Carolina was the first Confederate state to secede, in December of 1860....

HistoryThe Spanish colonized what we now think of as the Southwestern United States, plus Florida, as well as Mexico and much of Central and Latin America, as well as Cuba. The Spanish explorers or...

BusinessWorkforce diversity is a good thing. The question is how to achieve it, and to what ends. If we believe a company has a moral obligation to help society move towards gender and racial justice, we...

Social SciencesStudents fail in school for various reasons. Many school buildings have a student team of concern available for teachers who notice students exhibiting atrisk behaviors. This team will gather...

The NecklaceDramatic irony occurs when the audience (or reader) knows something that one or more of the characters do not. In other words, the audience is one or more steps ahead of the characters in the...

The SniperThe only hint in the beginning of the story about how the sniper feels about the war (in a mostly detached narration of his activities) appears in the second paragraph when the third person...

The Swiss Family RobinsonThe answer to this can be found in Chapter 10 of The Swiss Family Robinson, at least in the version summarized by eNotes. In the version available on Gutenberg, the answer is to be found in...

ScienceA photon of frequency f has the energy E = hf, where h is the Planck's constant: `h = 6.63*10^(34) J*s` . The frequency is related to the wavelength as `f = c/lambda` , where c is the speed of...

HistoryThe legislative branch of government in the United States is made up of the House of Representatives and Senate, which together make up the U.S. Congress. The Congress passes legislation in a...

The Cask of AmontilladoEdgar Allan Poe's short story, "The Cask of Amontillado," is the tale of Montresor describing his revenge upon Fortunato, who insulted him. His family motto is "Nemo me impune lacessit," which is...

HistoryThere is no way to know for sure what things in human history could possibly have happened differently. We cannot run experiments on human history to determine whether the League of Nations could...

ScienceTake note that average speed can be computed using the formula `s_(avg) = (t otal .distance . covered)/ (t otal . time . taken)` Plugging in the given values, the formula becomes `22.4m/s...

Literaturei don't no i need help to. uhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh! i am sad and crying someone help me pleaase.

Social SciencesThe most common reason proposed for why people need government is that people need government in order to protect their rights. This idea is often called the “social contract” and it was made...

HistoryThis answer depends on your political ideas and, to some extent, what your socioeconomic circumstances were. For the most part, people who were strongly involved in the market economy supported the...

The OutsidersDally and Two Bit have grown up on the streets. They have learned how to fight, use switchblades, watch for Socs, hide their emotions (especially fear), and trust no one but Greasers. Dally and Two...

HistoryThere were four plans of Reconstruction that were being considered at different times. President Lincoln proposed his plan before the end of the Civil War. He believed the President should be in...

MathA function `f(x, y)` is called homogeneous if for some integer `n` `f(tx, ty) = t^n f(x, y).` The given function satisfies this condition with `n = 0:` `f(tx, ty) = tan((tx)/(ty)) = tan(x/y) = f(x,...

MathEquation of a tangent line to the graph of function `f` at point `(x_0,y_0)` is given by `y=f(x_0)+f'(x_0)(xx_0).` Since every tangent passes through the origin `(0,0)` we have...

MathThe equation of the tangent line at the point `(t, f(t))` is `y  f(t) = (x  t)f'(t).` For the given point of intersection `(x + 2, 0)` this equation becomes `f(t) = 2f'(t),` or `f'(t) = 1/2...

MathTo find the equation of the graph passing through the point (9,1), we need to solve the given differential equation: `y' = y/(2x)` . First, rewrite it as `(dy)/(dx) = (y)/(2x)` . This equation can...

MathTo solve this equation, multiply by `y` and integrate: `yy' = 9/16 x,` `int yy' dx = int (9/16 x) dx,` `y^2/2 = 9/32 x^2 + C,` or `y = +sqrt(C  9/16 x^2),` where `C` is an arbitrary...

MathWe need to find the equation of the graph that passes through the point (0,2). The slope of the tangent line to the graph of y(x) is the derivative y' and it is given by the equation `y' = x/(4y)`...

MathIn the following answer, I assume that k and `P_0` are constants. Then, the given differential equation can be solved by separation of variables: `dP  kPdt = 0` `dP = kPdt` Dividing by P results...

MathThis differential equation can be solved by separating the variables. `(dr)/(ds) = e^(r  2s)` Dividing by e^r and multiplying by ds results in the variables r and s on the different sides of the...

MathAn ordinary differential equation (ODE) has differential equation for a function with single variable. A first order ODE follows . In the given problem: `(du)/(dv)=uvsin(v^2)` , we may apply...

MathThe given problem: `ysqrt(1x^2)y' xsqrt(1y^2)=0` is written in a form of first order "ordinary differential equation" or first order ODE. To evaluate this, we can apply variable separable...

MathThe given problem: `ysqrt(1+x^2)y' xsqrt(1+y^2)=0` is written in a form of first order ODE (ordinary differential equation). To evaluate this, we can apply variable separable differential...

MathThe problem: `2xy'ln(x^2)=0 ` is as first order ordinary differential equation that we can evaluate by applying variable separable differential equation: `N(y)y'=M(x)` `N(y)(dy)/(dx)=M(x)` `N(y)...

MathI suppose `y(x+1)` means `y(x)*(x+1),` not `y` at the point `x+1.` This differential equation may be expressed as `(y')/y = x  1` and then integrated: `lny = x^2/2  x + C, or y = Ce^(x^2/2...

MathFor the given problem: `sqrt(x)+sqrt(y)y' =0,` we may rearrange this to `sqrt(y)y' = sqrt(x)` Recall that `y'` is denoted as `(dy)/(dx)` then it becomes: `sqrt(y)(dy)/(dx) = sqrt(x)` Apply the...

MathFor the given problem:` yy'2e^x=0` , we can evaluate this by applying variable separable differential equation in which we express it in a form of `f(y) dy = f(x)dx` . Then, `yy'2e^x=0` can be...

MathFor the given problem: `12yy'7e^x=0` , we can evaluate this by applying variable separable differential equation in which we express it in a form of `f(y) dy = f(x)dx` . Then, `12yy'7e^x=0` can...

MathThe general solution:` lny=(lnx^2)^2/2+C` can be expressed as: `y = e^((lnx^2)^2/2)+C` . Let: e^C = C as arbitrary constant.

MathTo be able to evaluate the problem: `sqrt(14x^2)y'=x` , we express in a form of `y'=f(x)` . To do this, we divide both sides by `sqrt(14x^2)` ....

MathThe general solution:` y ^2=16/pisin(pix)+C` can be expressed as: `y = +sqrt(16/pisin(pix)+C)` .

MathThe general solution of a differential equation in a form of `y' = f(x) ` can be evaluated using direct integration. The derivative of y denoted as` y'` can be written as `(dy)/(dx)` then `y'=...

MathAn ordinary differential equation (ODE) has differential equation for a function with single variable. A first order ODE follows y' =f(x,y). The `y'` can be denoted as `(dy)/(dx) ` to be able to...

MathRecall that `y'` is the same as `(dy)/(dx)` . Then in the given problem: `(2+x)y'=3y` , we may write it as: `(2+x) (dy)/(dx) = 3y.` This will help to follow the variable separable differential...

Math`(dr)/(ds)=0.75s` This differential equation is separable since it has a form `N(y) (dy)/dx=M(x)` And, it can be rewritten as `N(y) dy = M(x) dx` So separating the variables, the equation...

MathThe general solution of a differential equation in a form of can be evaluated using direct integration. The derivative of y denoted as `y'` can be written as `(dy)/(dx)` then `y'= f(x) ` can be...

Math`(dy)/dx = (6x^2)/(2y^3)` This differential equation is separable since it can be rewritten in the form `N(y) dy=M(x) dx` So separating the variables, the equation becomes `2y^3dy = (6x^2)dx`...

MathRecall that an ordinary differential equation (ODE) has differential equation for a function with single variable. A first order ODE follows `(dy)/(dx) = f(x,y)` . In the given problem:...

Math`(dy)/dx = 3x^2/y^2` This differential equation is separable since it can be rewritten in the form `N(y)dy = M(x) dx` So separating the variables, the equation becomes `y^2dy = 3x^2dx` Taking the...

Math`(dy)/dx = x/y` This differential equation is separable since it can be rewritten in the form `N(y)dy = M(x)dx` So separating the variables, the equation becomes `ydy = xdx` Integrating both...

MathFormula for compounding n times per year: `A=P(1+r/n)^(nt)` Formula for compounding continuously: `A=Pe^(rt)` A=Final Amount P=Initial Amount r=rate of investment expressed as a percent...
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