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If x is inversely proportional to y and x = 2\(\frac{1}{2}\) when y = 2, find x ...


Question

If x is inversely proportional to y and x = 2\(\frac{1}{2}\) when y = 2, find x if y = 4

Options

A) 4

B) 5

C) 1\(\frac{1}{4}\)

D) 2\(\frac{1}{4}\)

The correct answer is C.

Explanation:

x \(\alpha\) \(\frac{1}{y}\) .........(1)
x = k x \(\frac{1}{y}\) .........(2)
When x = 2\(\frac{1}{2}\)
= \(\frac{5}{2}\), y = 2
(2) becomes \(\frac{5}{2}\) = k x \(\frac{1}{2}\)
giving k = 5
from (2), x = \(\frac{5}{y}\)
so when y =4, x = \(\frac{5}{y}\) = 1\(\frac{1}{4}\)

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Dicussion (1)

  • x \(\alpha\) \(\frac{1}{y}\) .........(1)
    x = k x \(\frac{1}{y}\) .........(2)
    When x = 2\(\frac{1}{2}\)
    = \(\frac{5}{2}\), y = 2
    (2) becomes \(\frac{5}{2}\) = k x \(\frac{1}{2}\)
    giving k = 5
    from (2), x = \(\frac{5}{y}\)
    so when y =4, x = \(\frac{5}{y}\) = 1\(\frac{1}{4}\)

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