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# proportion

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The value of y varies inversely as sqrt(x) and when x=2, y=4. What is x when y=16?

May 14, 2022

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y varies inversely as sqrt(x) means that y = k / sqrt(x) for some non-zero constant k.

Substitute x = 2 and y = 4 into y = k / sqrt(x),

$$4 = \dfrac k{\sqrt 2}\\ k = 4 \sqrt 2$$

So k is 4 * sqrt(2). When y = 16 and k = 4 * sqrt(2), we have

$$16 = \dfrac{4\sqrt 2}x\\$$

Can you take it from here?

May 14, 2022