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In mathematics, a rate is the quotient of two quantities, often represented as a fraction. [1] If the divisor (or fraction denominator) in the rate is equal to one expressed as a single unit, and if it is assumed that this quantity can be changed systematically (i.e., is an independent variable), then the dividend (the fraction numerator) of the rate expresses the corresponding rate of change ...
Galois theory has been used to solve classic problems including showing that two problems of antiquity cannot be solved as they were stated (doubling the cube and trisecting the angle), and characterizing the regular polygons that are constructible (this characterization was previously given by Gauss but without the proof that the list of ...
This result also holds for equations of higher degree. An example of a quintic whose roots cannot be expressed in terms of radicals is x 5 − x + 1 = 0. Numerical approximations of quintics roots can be computed with root-finding algorithms for polynomials. Although some quintics may be solved in terms of radicals, the solution is generally ...
A common form for the rate equation is a power law: [6] = [] [] The constant is called the rate constant.The exponents, which can be fractional, [6] are called partial orders of reaction and their sum is the overall order of reaction.
Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication.
The term algebra is derived from the Arabic word al-jabr meaning 'the reunion of broken parts' that he used for naming one of these methods in the title of his main treatise. [31] [32] Algebra became an area in its own right only with François Viète (1540–1603), who introduced the use of variables for representing unknown or unspecified ...
For example, y = x 2 fails the horizontal line test: it fails to be one-to-one. The inverse is the algebraic "function" x = ± y {\displaystyle x=\pm {\sqrt {y}}} . Another way to understand this, is that the set of branches of the polynomial equation defining our algebraic function is the graph of an algebraic curve .
The most common way to approach related rates problems is the following: [2] Identify the known variables, including rates of change and the rate of change that is to be found. (Drawing a picture or representation of the problem can help to keep everything in order)
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related to: algebra rate problems examples worksheet answers 5th edition