x ∝ (1/√y) and when x = 40 then y = 16. If x = 10, find y.

1.	x ∝ (1/√y) and when x = 40 then y = 16. If x = 10, find y.
Answer» x ∝ (1/√y) ∴ x = k x (1/√y) where, k is the constant of variation. ∴ x × √y = k …(i) When x = 40, y = 16 ∴ Substituting x = 40 andy = 16 in (i), we get x × √y = k ∴ 40 × √16 = k ∴ k = 40 × 4 ∴ k = 160 Substituting k = 160 in (i), we get x × √y = k ∴ x × √y = 160 …(ii) This is the equation of variation. When x = 10,y = ? ∴ Substituting, x = 10 in (ii), we get x × √y = 160 ∴ 10 × √y = 160 ∴ √y = 160/10 ∴ √y = 16 ∴ y = 256 … [Squaring both sides]

Answer»

x ∝ (1/√y)

∴ x = k x (1/√y)

where, k is the constant of variation.

∴ x × √y = k …(i)

When x = 40, y = 16

∴ Substituting x = 40 andy = 16 in (i), we get

x × √y = k

∴ 40 × √16 = k

∴ k = 40 × 4

∴ k = 160

Substituting k = 160 in (i), we get

x × √y = k

∴ x × √y = 160 …(ii)

This is the equation of variation.

When x = 10,y = ?

∴ Substituting, x = 10 in (ii), we get

x × √y = 160

∴ 10 × √y = 160

∴ √y = 160/10

∴ √y = 16

∴ y = 256 … [Squaring both sides]

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