Home » If (y propto frac{1}{sqrt{x}}) and x = 16 when y = 2, find x when…

If (y propto frac{1}{sqrt{x}}) and x = 16 when y = 2, find x when…

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})

Related:  Mathematics Theory (a) In the diagram, A, B, C and D are points on the circumference of...