If (y propto frac{1}{sqrt{x}}) and x = 16 when y = 2, find x when y = 24
-
A.
(frac{1}{9}) -
B.
(frac{1}{6}) -
C.
(frac{1}{3}) -
D.
(frac{2}{3})
Correct Answer: Option A
Explanation
(y propto frac{1}{sqrt{x}})
(y = frac{k}{sqrt{x}})
When x = 16, y = 2.
(2 = frac{k}{sqrt{16}} implies 2 = frac{k}{4})
(k = 8)
(y = frac{8}{sqrt{x}})
When y = 24,
(24 = frac{8}{sqrt{x}})
(sqrt{x} = frac{8}{24} = frac{1}{3})
(therefore x = (frac{1}{3})^2)
(x = frac{1}{9})