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| {{about|proportionality, the mathematical relation|other uses of the term|Proportionality (disambiguation)}}
| | BSOD or the Blue Screen of Death, (sometimes known as blue screen physical memory dump), is an error which happens on a Windows system - when the computer merely shuts down or automatically reboots. This error could happen merely as your computer is booting up or some Windows application is running. When the Windows OS discovers an unrecoverable error it hangs the program or leads to memory dumps.<br><br>Windows Defender - this does come standard with several Windows OS Machines, however, otherwise may be download from Microsoft for free. It might help safeguard against spyware.<br><br>The error is basically a outcome of issue with Windows Installer package. The Windows Installer is a tool selected to install, uninstall and repair the most programs on the computer. Let you discuss a limited things that helped a great deal of folks that facing the synonymous issue.<br><br>Registry cleaners have been crafted for 1 purpose - to clean out the 'registry'. This really is the central database which Windows relies on to function. Without this database, Windows wouldn't even exist. It's so important, that the computer is continually adding plus updating the files inside it, even when you're browsing the Internet (like now). This really is great, however, the problems happen when a few of those files become corrupt or lost. This arises a lot, plus it takes a good tool to fix it.<br><br>Use a [http://bestregistrycleanerfix.com/fix-it-utilities fix it utilities]. This can search your Windows registry for 3 types of keys that can definitely hurt PC performance. These are: duplicate, lost, and corrupted.<br><br>Let's begin with the negative sides first. The initial price of the product is fairly inexpensive. However, it just comes with 1 year of updates. After that we must subscribe to monthly updates. The advantage of that is that ideal optimizer has enough income plus resources to research mistakes. This technique, you're ensured of safe fixes.<br><br>Maybe you may be asking why these windows XP error messages appear. Well, for we to be able to understand the fix, you need to initially understand where those mistakes come from. There is this software called registry. A registry is software which stores everything on the PC from a regular configuration, setting, information, and logs of activities from installing to UN-installing, saving to deleting, along with a lot more alterations you do in the program pass by it plus gets 'tagged' and saved because a simple file for recovery reasons. Imagine it because a big recorder, a registrar, of all your records in the PC.<br><br>If you wish To have a computer with fast running speed, you'd better install a good registry cleaner to clean the useless files for you. As long as we take care of the computer, it will keep in wise condition. |
| {{Unreferenced|date=December 2009}}
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| [[Image:Variables proporcionals.png|thumb|y is directly proportional to x.]]
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| In [[mathematics]], two variables are '''proportional''' if a change in one is always accompanied by a change in the other, and if the changes are always related by use of a constant. The constant is called the [[coefficient]] of proportionality or '''proportionality constant'''.
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| *If one variable is always [[wiktionary:product#|the product]] of the other and a constant, the two are said to be ''directly proportional''. {{nobr|''x'' and ''y''}} are directly proportional if the [[ratio]] <math>\tfrac yx</math> is constant.
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| *If the product of the two variables is always equal to a constant, the two are said to be ''inversely proportional''. {{nobr|''x'' and ''y''}} are inversely proportional if the product <math>xy</math> is constant.
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| If a [[linear function]] transforms {{nobr|0, ''a'' and ''b'' }} into {{nobr|0, ''c'' and ''d'', }} and if the product {{nobr|''a b c d'' }} is not zero, we say {{nobr|''a'' and ''b''}} are proportional {{nobr|to ''c'' and ''d.''}} An equality of two ratios such as <math>\tfrac ac\ =\ \tfrac bd,</math> where no term is zero, is called a [[wiktionary:proportion#Noun|proportion]].
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| __TOC__
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| <p id="i_2" style="clear:both;text-align:right">
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| == Geometric illustration ==
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| [[Image:Academ homothetic rectangles.svg|thumb|upright=2|The two rectangles with stripes are similar, the ratios of their dimensions are horizontally written within the image. The duplication scale of a striped triangle is obliquely written, in a proportion obtained by inverting two terms of another proportion horizontally written.]] When the duplication of a given rectangle preserves its shape, the ratio of the large dimension to the small dimension is a constant number in all the copies, and in the original rectangle. The largest rectangle of [[#i_2|the drawing]] is [[Similarity (geometry)|similar]] to one or the other rectangle with stripes. From their width to their height, the coefficient is <math>\tfrac dc\ =\ \tfrac ba\ =\ \tfrac{d\,+\,b}{c\,+\,a}.</math> A ratio of their dimensions horizontally written within the image, at the top or the bottom, determines the common shape of the three similar rectangles.
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| The common diagonal of the similar rectangles divides each rectangle into two superposable triangles, with two different kinds of stripes. The four striped triangles and the two striped rectangles have a common vertex: the center of an [[Homothetic transformation|homothetic]] transformation with a negative ratio ''−k'' or <math>\tfrac {-1}{k}</math>, that transforms one triangle and its stripes into another triangle with the same stripes, enlarged or reduced. The duplication scale of a striped triangle is the proportionality constant between the corresponding sides lengths of the triangles, equal to a positive ratio obliquely written within the image:<br/><math>\tfrac ca\ =\ k</math> or <math>\tfrac ac \ =\ \tfrac 1k.</math>
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| In the proportion <math>\tfrac ab\ =\ \tfrac cd</math>, the terms ''a'' and ''d'' are called the extremes, while ''b'' and ''c'' are the means, because ''a'' and ''d'' are the extreme terms of the list {{nobr|(''a'', ''b'', ''c'', ''d''), }} while ''b'' and ''c'' are in the middle of the list. From any proportion, we get another proportion by inverting the extremes or the means. And the product of the extremes equals the product of the means. Within the image, a double arrow indicates two inverted terms of the first proportion.
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| Consider dividing the largest rectangle in two triangles, cutting along the diagonal. If we remove two triangles from either half rectangle, we get one of the plain gray rectangles. Above and below this diagonal, [[Area|the areas]] of the two biggest triangles of the drawing are equal, because these triangles are superposable. Above and below the subtracted areas are equal for the same reason. Therefore, the two plain gray rectangles have the same area: {{nobr|1=''a d'' = ''b c.''}}
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| ==Symbols==
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| The mathematical symbol '''∝''' ([[Unicode mathematical operators|U+221D]] in [[Unicode]], <code>\propto</code> in [[TeX]]) is used to indicate that two values are proportional. For example, A ∝ B means the variable A is directly proportional to the variable B.
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| Other symbols include:
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| * ∷ - U+2237 "PROPORTION"
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| * ∺ - U+223A "GEOMETRIC PROPORTION"
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| ==Direct proportionality==
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| Given two [[variable (math)|variable]]s ''x'' and ''y'', ''y is '''directly proportional''' to x'' (''x and y '''vary directly''','' or ''x and y are in '''direct variation''''') if there is a non-zero constant ''k'' such that
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| :<math>y = kx.\,</math> | |
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| The relation is often denoted, using the ∝ symbol, as
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| :<math>y \propto x</math>
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| and the constant ratio | |
| :<math> k = \frac{y}{x}\,</math>
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| is called the '''proportionality constant''', '''constant of variation''' or '''constant of proportionality'''.
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| ===Examples===
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| * If an object travels at a constant [[speed]], then the [[distance]] traveled is directly proportional to the [[time]] spent traveling, with the speed being the constant of proportionality.
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| *The [[circumference]] of a [[circle]] is directly proportional to its [[diameter]], with the constant of proportionality equal to [[pi|π]].
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| *On a [[map]] drawn to [[scale (map)|scale]], the distance between any two points on the map is directly proportional to the distance between the two locations that the points represent, with the constant of proportionality being the scale of the map.
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| *The [[force (physics)|force]] acting on a certain object due to [[gravity]] is directly proportional to the object's [[mass]]; the constant of proportionality between the mass and the force is known as [[gravitational acceleration]].
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| ===Properties===
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| Since
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| :<math>y = kx\,</math>
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| is equivalent to
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| :<math>x = \left(\frac{1}{k}\right)y,</math>
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| it follows that if ''y'' is directly proportional to ''x'', with (nonzero) proportionality constant ''k'', then ''x'' is also directly proportional to ''y'' with proportionality constant 1/''k''.
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| If ''y'' is directly proportional to ''x'', then the graph of y as a [[function (mathematics)|function]] of x will be a [[line (mathematics)|straight line]] passing through the [[Origin (mathematics)|origin]] with the [[slope]] of the line equal to the constant of proportionality: it corresponds to [[linear growth]].
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| == Inverse proportionality ==<!-- This section is linked from [[Poliomyelitis]] -->
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| The concept of ''inverse proportionality'' can be contrasted against ''direct proportionality''. Consider two variables said to be "inversely proportional" to each other. [[Ceteris paribus|If all other variables are held constant]], the magnitude or absolute value of one inversely proportional variable will decrease if the other variable increases, while their product (the constant of proportionality ''k'') is always the same.
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| Formally, two variables are '''inversely proportional''' (also called '''varying inversely''', in '''inverse variation''', in '''inverse proportion''', in '''reciprocal proportion''') if one of the variables is directly proportional with the [[multiplicative inverse]] (reciprocal) of the other, or equivalently if their [[Product (mathematics)|product]] is a constant. It follows that the variable ''y'' is inversely proportional to the variable ''x'' if there exists a non-zero constant ''k'' such that
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| :<math>y = {k \over x}</math>
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| The constant can be found by multiplying the original x variable and the original y variable.
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| As an example, the time taken for a journey is inversely proportional to the speed of travel; the time needed to dig a hole is (approximately) inversely proportional to the number of people digging.
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| The graph of two variables varying inversely on the [[Cartesian coordinate]] plane is a [[hyperbola]]. The product of the X and Y values of each point on the curve will equal the constant of proportionality (''k''). Since neither x nor y can equal zero (if k is non-zero), the graph will never cross either axis.
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| ==Hyperbolic coordinates==
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| {{Main|Hyperbolic coordinates}}
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| The concepts of ''direct'' and ''inverse'' proportion lead to the location of points in the Cartesian plane by [[hyperbolic coordinates]]; the two coordinates correspond to the constant of direct proportionality that locates a point on a [[line (mathematics)#Ray|ray]] and the constant of inverse proportionality that locates a point on a hyperbola.
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| ==Exponential and logarithmic proportionality==
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| A variable ''y'' is '''exponentially proportional''' to a variable ''x'', if ''y'' is directly proportional to the [[exponential function]] of ''x'', that is if there exist non-zero constants ''k'' and ''a''
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| :<math>y = k a^x.\,</math>
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| Likewise, a variable ''y'' is '''logarithmically proportional''' to a variable ''x'', if ''y'' is directly proportional to the [[logarithm]] of ''x'', that is if there exist non-zero constants ''k'' and ''a''
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| :<math>y = k \log_a (x).\,</math>
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| ==See also==
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| * [[Ratio]]
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| * [[Correlation]]
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| * [[Eudoxus of Cnidus]]
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| * [[Golden ratio]]
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| * [[Proportional font]]
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| * [[Rule of three (mathematics)]]
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| * [[Sample size]]
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| * [[Similarity (geometry)|Similarity]]
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| ===Growth===
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| * [[Linear growth]]
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| * [[Hyperbolic growth]]
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| {{DEFAULTSORT:Proportionality (Mathematics)}}
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| [[Category:Mathematical terminology]]
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| [[Category:Ratios]]
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BSOD or the Blue Screen of Death, (sometimes known as blue screen physical memory dump), is an error which happens on a Windows system - when the computer merely shuts down or automatically reboots. This error could happen merely as your computer is booting up or some Windows application is running. When the Windows OS discovers an unrecoverable error it hangs the program or leads to memory dumps.
Windows Defender - this does come standard with several Windows OS Machines, however, otherwise may be download from Microsoft for free. It might help safeguard against spyware.
The error is basically a outcome of issue with Windows Installer package. The Windows Installer is a tool selected to install, uninstall and repair the most programs on the computer. Let you discuss a limited things that helped a great deal of folks that facing the synonymous issue.
Registry cleaners have been crafted for 1 purpose - to clean out the 'registry'. This really is the central database which Windows relies on to function. Without this database, Windows wouldn't even exist. It's so important, that the computer is continually adding plus updating the files inside it, even when you're browsing the Internet (like now). This really is great, however, the problems happen when a few of those files become corrupt or lost. This arises a lot, plus it takes a good tool to fix it.
Use a fix it utilities. This can search your Windows registry for 3 types of keys that can definitely hurt PC performance. These are: duplicate, lost, and corrupted.
Let's begin with the negative sides first. The initial price of the product is fairly inexpensive. However, it just comes with 1 year of updates. After that we must subscribe to monthly updates. The advantage of that is that ideal optimizer has enough income plus resources to research mistakes. This technique, you're ensured of safe fixes.
Maybe you may be asking why these windows XP error messages appear. Well, for we to be able to understand the fix, you need to initially understand where those mistakes come from. There is this software called registry. A registry is software which stores everything on the PC from a regular configuration, setting, information, and logs of activities from installing to UN-installing, saving to deleting, along with a lot more alterations you do in the program pass by it plus gets 'tagged' and saved because a simple file for recovery reasons. Imagine it because a big recorder, a registrar, of all your records in the PC.
If you wish To have a computer with fast running speed, you'd better install a good registry cleaner to clean the useless files for you. As long as we take care of the computer, it will keep in wise condition.