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08C99-Variation.tex
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08C99-Variation.tex
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\documentclass[12pt]{article}
\usepackage{pmmeta}
\pmcanonicalname{Variation}
\pmcreated{2013-03-22 14:53:49}
\pmmodified{2013-03-22 14:53:49}
\pmowner{drini}{3}
\pmmodifier{drini}{3}
\pmtitle{variation}
\pmrecord{7}{36579}
\pmprivacy{1}
\pmauthor{drini}{3}
\pmtype{Topic}
\pmcomment{trigger rebuild}
\pmclassification{msc}{08C99}
\pmsynonym{Proportion}{Variation}
\pmrelated{HomogeneousEquation}
\pmrelated{GraphOfEquationXyConstant}
\pmrelated{ProportionalityOfNumbers}
\pmdefines{Relationships between two or more variables.}
\endmetadata
% this is the default PlanetMath preamble. as your knowledge
% of TeX increases, you will probably want to edit this, but
% it should be fine as is for beginners.
% almost certainly you want these
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
% used for TeXing text within eps files
%\usepackage{psfrag}
% need this for including graphics (\includegraphics)
%\usepackage{graphicx}
% for neatly defining theorems and propositions
%\usepackage{amsthm}
% making logically defined graphics
%%%\usepackage{xypic}
% there are many more packages, add them here as you need them
% define commands here
\begin{document}
Variation and proportion are defined to be the relationship between two or more variables with regard to a constant of proportionality.
The traditional notation for direct proportionality is $x \propto y$ or, if using regular equality notation, $x = ky$.
Here, $k$ denotes the constant of proportionality.
Similarly, the traditional notation for inverse proportionality is $x \propto 1/y$ or, with regular equality, $x = k/y$.
For direct proportionality, to find the value of an unknown $x$ or $y$, you may use the formula:
$y_{1}/x_{1} = y_{2}/x_{2}$
Similarly, for inverse proportion it would be:
$x_{1}/y_{1} = y_{2}/x_{2}$
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\end{document}