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Mathematics

In the following table, do x and y vary directly:

xy
2781
45180
54216
75225

Direct & Inverse Variations

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Answer

x1y1=2781=13,x2y2=45180=14,x3y3=54216=14,x4y4=75225=13,\dfrac{x1}{y1} = \dfrac{27}{81} = \dfrac{1}{3},\\[1em] \dfrac{x2}{y2} = \dfrac{45}{180} = \dfrac{1}{4},\\[1em] \dfrac{x3}{y3} = \dfrac{54}{216} = \dfrac{1}{4},\\[1em] \dfrac{x4}{y4} = \dfrac{75}{225} = \dfrac{1}{3},\\[1em]

x1y1x2y2=x3y3x4y4\Rightarrow \dfrac{x1}{y1} ≠ \dfrac{x2}{y2} = \dfrac{x3}{y3} ≠ \dfrac{x4}{y4} = not a constant

Hence, x and y are not in direct variation.

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