y varies directly as square root of x. When x = 16, y = 24. Find the c

1.	y varies directly as square root of x. When x = 16, y = 24. Find the constant of variation and equation of variation.
Answer» Given, y varies directly as square root of x. ∴ y ∝ √4x ∴ y = k √x …(i) where, k is the constant of variation. When x = 16 ,y = 24. ∴ Substituting, x = 16 and y = 24 in (i), we get y = k√x ∴24 = k√16 ∴24 = 4k \(\therefore\,k = \cfrac{24}{4}\) ∴ k = 6 Substituting k = 6 in (i), we get y = k√x ∴ y = 6√x This is the equation of variation ∴ The constant of variation is 6 and the equation of variation is y = 6√x .

y varies directly as square root of x. When x = 16, y = 24. Find the constant of variation and equation of variation.

Answer»

Given, y varies directly as square root of x.

∴ y ∝ √4x

∴ y = k √x …(i)

where, k is the constant of variation.

When x = 16 ,y = 24.

∴ Substituting, x = 16 and y = 24 in (i), we get

y = k√x

∴24 = k√16

∴24 = 4k

\(\therefore\,k = \cfrac{24}{4}\)

∴ k = 6

Substituting k = 6 in (i), we get

y = k√x

∴ y = 6√x

This is the equation of variation

∴ The constant of variation is 6 and the equation of

variation is y = 6√x .