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Geometry/Direct and Inverse Variation

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Question
hello sir

sir i have not explained my confusion clearly because i was not able to express clealy. Now i had explained below clearly

Sir if in direct variation the value of x increases , value of y increases in such a way that the ratio not change, it remains constant in this case.In such a case y1 y2 are the values of y corresponding to the values of X1 X2 of respectively then X1 BY Y1= X2 Y2.

iN INVERSE VARIATION IF VALUE OF X INCREASES, VALUE OF Y DECREASES IN SUCH A MANNER THAT THE PRODUCT OF THEIR CORRESPONDING VALUES REMAINES CONSTANT. If in this case if y 1, y2 are the values of y coresponding to the values x1 x2 of x respectively then x1y1= x2 y2 0r x1 by y1 = x2 by y2.

Sir in this for me fomuals are confuing please explain them in terms of
d variatiation and i variation.

please.

Answer
Hi Aishwarya,

In direct variation, the ratio of corresponding parts does not change.  As x1 increases, y1 increases as well.  So if you had two poles of heights y1 and y2 that cast shadow of lengths x1 and x2, respectively, you would have the following:

x1/x2 = y1/y2

You could cross-multiply to give (x1)(y2)=(x2)(y1), but then we lose the visual effect of the common ratio.

For inverse variation, as x1 increases, y1 decreases, such that their product is constant ("product" means the result of a multiplication).  So, almost by definition:

(x1)(y1)=(x2)(y2)

Hope this helps,
Azeem

Geometry

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Azeem Hussain

Expertise

I welcome your questions on algebra, 2D and 3D geometry, parabolic functions and conic sections, and any other mathematical queries you may have.

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4 years as a drop-in and by-appointment tutor at Champlain College. Private tutor for dozens of clients over the past 8 years.

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CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry

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Bachelor of Science, Major Mathematics and Major Economics, McGill University, 2014. Diploma of Collegiate Studies; Pure and Applied Science, Champlain College Saint-Lambert, 2010.

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