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September 9th, 2011, 02:43 AM   #1
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Direct and Inverse Variation

DIRECT VARIATION : one quantity increases the other quantity increases or if one quantity decreases the other quantity decreases.

INVERSE VARIATION : one quantity increases the other quantity decreases or if one quantity decreases the other quantity increases.

Applications in Physics
--------------------------

1. V ? I -> Ohm's Law -> Voltage is Directly Proportional to Current. As Voltage increases, Current Increases.

2. Speed = Distance / Time -> Speed is inversely Proportional to Time. As Speed increases, Time Decreases.

Applications in Economics
-------------------------------

1. Law of Supply : As the price of a good or service increases, the quantity of goods or services offered by suppliers increases and vice versa.

Price ? Quantity of Goods Offered by Suppliers.

Price is Directly proportional to Suppliers Supplying Goods.

2. Law of Demand : as the price of a good or service increases, consumer demand for the good or service will decrease and vice versa.

Price is inversely proportional to Consumer Demand for Goods.

Questions
------------

1. In Maths we have the word "Variation". Variation are into two types -> Direct and Inverse.
Is Variation and Proportion are Synonyms ? i.e Different words having same meaning. Or there is a difference interpreted in Maths for Variation and Proportion ?

can we say Direct Variation is Direct Proportion ?
can we say Inverse Variation is Inverse Proportion ?.

i.e are they same ?

2. Other than Applications in Physics and Economics, where we can find applications of Direct and Inverse Variation i.e Chemistry, Physiology etc ?.

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Prashant S Akerkar
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November 6th, 2011, 09:55 PM   #2
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Re: Direct and Inverse Variation

http://en.allexperts.com/q/Advanced-Mat ... iation.htm

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Prashant S Akerkar
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November 10th, 2011, 11:57 AM   #3
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Re: Direct and Inverse Variation

Mathematically, a proportion is an equation with two ratios on each side. It states that two ratios are equal to each other.

A direct variation is a specific type of proportion, where there are two variables, x and y, and one constant k, such that they are related like so:

y = kx, or written in the "familiar proportion form" y/x = k/1.

Inverse variations are another specific type of proportion, with variables x and y, and constant k, such that this relationship ensues:

xy = k, or in the "familiar proportion form" y/1 = k/x.

So to say a direct variation is a direct proportion is kind of like saying that a red apple is a red fruit. I guess it is always better to be specific, but you would not be entirely incorrect in saying that.

Direct and inverse variations only apply to linear equations without a y-intercept. Proportions can involve all different types of equations.

For chemistry, density and volume vary inversely by the proportion given below (when mass is constant).

d = m/v or d/1 = m/v. (as density increases, volume decreases) or (as volume increases, density decreases) when mass is held constant. If I have 20 lb of cheerios, they will take up more space than 20 lb of steel. Steel being more dense than cheerios.

Also, m = dv, so mass and volume vary directly(as mass increases, volume increases) when density is held constant.
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November 14th, 2011, 11:11 PM   #4
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Re: Direct and Inverse Variation

Thank you.

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Prashant S Akerkar
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