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If yα1x2 and y=114 when ...

If yα1x2 and y=114 when x = 4, find the value of y when x=12

A.

212

B.

5

C.

10

D.

80

Correct answer is D

y \propto \frac{1}{x^2} \Rightarrow y = \frac{k}{x^2} \Rightarrow k = yx^2\\ k = 1\frac{1}{4} \times 4^2 \Rightarrow k=\frac{5}{4}\times \frac{16}{1}=20\\ ∴y = 20 \div \left(\frac{1}{2}\right)^2=20\times \frac{4}{1}=80