Expert: Sherry Wallin - 9/10/2011

Question
QUESTION: Dear Prof Sherry

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
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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
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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
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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 ?.

Thanks & Regards,
Prashant S Akerkar

ANSWER: Variations involve a constant k. y = kx means y varies directly as x. y = k/x means y varies inversely as x. Both have the constant k in them.
For ohms law we have V = IR. You could say that voltage varies directly as R so then I is the constant. So in that sense the proportionality are the same.

Math Prof

Any formulas that have something equal to a product of two or more other things can be thought of as direct variation. And any formula that has something equal to a quotient of something could be thought of as inverse variation. For example d = rt, solve for r and get r = d/t and you have rate varies inversely as time when distance is constant.

---------- FOLLOW-UP ----------

QUESTION: Dear Prof Sherry

1. Can i conclude saying both

a. Direct Variation and Direct Proportion
b. Inverse Variation and Inverse Proportion

are same. i.e I can use both the terms interchangeably.

2. What could be applications of both other than physics, economics subjects i.e in Chemistry, Physiology (Biology) etc ?

Thanks & Regards,
Prashant S Akerkar

Answer
Direct proportion and direct variation would mean the same thing in this context.
You asked what other applications outside of the sciences, economics etc. Any formula with 3 variables where one variable can be held constant would satisfy the requirement.
Math Prof