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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)`...

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...

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...

MathFor the given problem: `yln(x)xy'=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` . to able to apply direct...

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 of a differential equation in a form of` f(y) y'=f(x)` can be evaluated using direct integration. We can denote `y'` as `(dy)/(dx) ` then, `f(y) y'=f(x)` `f(y)...

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'=...

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`...

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...

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 decimal n=number of...

MathThe formula in compounding interest is `A = P(1 + r/n)^(n*t)` where A is the accumulated amount P is the principal r is the annual rate n is the number of compounding periods in a year, and t is...

MathThe formula in compounding interest is `A = P(1 + r/n)^(n*t)` where A is the accumulated amount P is the principal r is the annual rate n is the number of compounding periods in a year, and t is...

MathThe formula in compounding interest is `A = P(1 + r/n)^(n*t)` where A is the accumulated amount P is the principal r is the annual rate n is the number of compounding periods in a year, and t is...

MathThe formula in compounding interest is `A = P(1 + r/n)^(n*t)` where A is the accumulated amount P is the principal r is the annual rate n is the number of compounding periods in a year, and t is...

MathFormula: `y=Ce^(kt)` `1/2C=Ce^(k*1599)` `1/2=e^(k*1599)` `ln(1/2)=1599klne` `ln(1/2)=1599k` `ln(1/2)/1599=k` `k=4.3349x10^4` `y=Ce^(kt)` `y=Ce^[(4.3349x10^4)(100)]` `y=.9576C` Final...

Math`(dy)/dx=58x` 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...

Math`(dy)/dx = x + 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 `dy = (x+3)dx` Integrating both...

MathIn order to use integration to solve this differential equation, multiply both sides of the equation by dx: `dy = (10x^4 2x^3)dx` . Now we can integrate both sides, using the formula for the...

HealthWhat are some new healthcare technologies and how can healthcare communications can be changed as...Many of the new advances in technology provide an opportunity to transform healthcare in radical ways through changing the models for medical data communication. One type of advance generally falls...

HistoryFirst, European nations developed or acquired, earlier than other peoples around the world, many of the technologies necessary for colonization. These included nautical innovations like the caravel...

ScienceThe most obvious evidence of cell theory is to look at cells themselves. Some cells are large enough to be seen with the bare eye; amoebas, for example, can be seen with a backlight. Using a...

The Ransom of Red ChiefRed Chief terrorizes his kidnappers by sitting in the entrance of the cave where they are hiding out and asking one of the kidnappers if he dares to enter what is Red Chief's camp. He also calls...

HistoryWhat are some examples of international incidents since World War II where America has taken on a...The United States military has taken a "policing" role in several conflicts since World War II. When the United States intervened in the Korean War, President Truman stated that "We are not at war"...

HistoryThere were several causes that led to the launching of the New Deal. Prior to the beginning of the Great Depression, a laissezfaire attitude existed regarding the involvement of the government in...

By the Waters of BabylonI like the second sentence of the story for a good quote. It is forbidden to go to any of the Dead Places except to search for metal and then he who touches the metal must be a priest or the son...

BusinessManagers might overcome the challenges of using Organizational Behavior (OB) by adapting their management style to one that conforms more with the relevant challenge they face, like switching from...

The Merchant of VeniceIt is their friendship that gets Antonio into serious trouble with Shylock, and it is also their friendship that rescues him from that trouble. The main plot of the play has to do with Antonio's...

ScienceTrees and shrubs both have wood parts, while other kinds of plants, such as herbs, do not. A tree has a single perennial straight trunk that is, at the height of 4.5 feet above the ground, is at...

HistoryThe answer to this question can be found at the end of the Declaration of Independence. It is at that point that the signers actually come around and say that they are breaking away from England....

Three Men in a Boat (To Say Nothing of the Dog)After J., George, and Harris decide to go on a boat trip along the River Thames (in Chapter I), they must determine how they are going to travel and what supplies they will take along. In Chapter...

HistoryThe origins of the Cold War actually start during WWII. During the war against Germany, Stalin's armies suffered massive casualties as they pushed Hitler's army out of the Soviet Union and across...

Guy de MaupassantIn Guy de Maupassant's short story "The Necklace," the dramatic irony—if, in fact, it is dramatic irony—rests in Mathilde's desire to have more than she does, and the lengths to which she is...

Marriage Is a Private AffairThere are basically only three characters in Chinua Achebe's short story "Marriage is a Private Affair," Nnaemeka, Nene and Nnaemeka's father Ugoye. Of the three it could be argued that Nene is...

HamletIn Act 3, Scene 1 of Hamlet, the main character utters what would become one of the most common allusions in all of literature: "to be or not to be." This line is written by Shakespeare, but...

RikkiTikkiTaviThe motto that is stated in the question comes from Rudyard Kipling's short story "RikkiTikkiTavi." The motto perfectly embodies the central character, Rikkitikki. "Run and find out" is...

Robert FrostRobert Frost was in American poet Born in San Francisco, California at the end of the 19th century. He wrote a number of his most famous poems, including "Stopping by Woods on a Snowy Evening,"...

The Road Not TakenThis phrase comes at the beginning of the last stanza of the poem: I shall be telling this with a sigh Somewhere ages and ages hence … The poet has told us that he encountered two roads – a...

The NecklaceIn “The Necklace” by Guy de Maupassant, Madame Forestier seems more astonished than angry at Madame Loisel's revelation. Many years after the incident with the necklace, the women meet each...

HistoryThe Louisiana Purchase was very important to the early history of the United States. The western farmers depended on using the port of New Orleans to ship their goods to market. They also needed to...

HistoryReconstruction had a major impact on AfricanAmericans. AfricanAmericans were better off as a result of Reconstruction, even if some of the improvements were temporary. Before the Civil War, most...

The Kite RunnerIn The Kite Runner, the kite is both a positive and negative symbol. As such, kite flying and kite fighting simultaneously trace the themes of betrayal, generational conflict, and redemption as the...

ReferenceThe Bermuda Triangle covers an area in the Atlantic Ocean that goes approximately from Miami to Puerto Rico to Bermuda, making a triangular shape. There have been several instances where...

To His Excellency General WashingtonIn Phillis Wheatley's homage to George Washington, commander of the Continental Army, the poet creates a goddess she calls Columbia to personify the American colonies. The goddess wears olive and...

Of Mice and MenSteinbeck conveys the message that the American Dream—which can be defined in the context of this book as people's ability to control their own land and destiny—is not available to the American...

An Astrologer's DayThe protagonist in "An Astrologer's Day" is an interesting character because he is a survivor. He came to the big city from one of the many little villages in India and had to find some way to...