X ∝ 1 √ Y and When X = 40 Then Y = 16. If X = 10, Find Y. - Mathematics

Sum

x ∝ $\frac{1}{\sqrt{y}}$  and when x = 40 then y = 16. If x = 10, find y.

Solution

It given that $x \propto \frac{1}{\sqrt{y}}$ .

∴ $x = \frac{k}{\sqrt{y}}$ , where k is constant of variation

⇒ $x \times \sqrt{y} = k$

When x = 40, y = 16.
∴ $k = 40 \times \sqrt{16} = 40 \times 4 = 160$

So, the equation of variation is $x\sqrt{y} = 160$

When x = 10,

$10\sqrt{y} = 160$

$\Rightarrow \sqrt{y} = 16$

$\Rightarrow y = {16}^2 = 256$

Concept: Inverse Variation
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APPEARS IN

Balbharati Mathematics 8th Standard Maharashtra State Board
Chapter 7 Variation
Practice Set 7.2 | Q 5 | Page 39