Suppose that y varies inversely with the square root of x and y=50 when x=4, how do you find y when x=5?

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Suppose that y varies inversely with the square root of x and y=50 when x=4, how do you find y when x=5?

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Answer 1 · 2015-05-28T11:59:54

If $y$ $y$ varies inversely with $\sqrt{x}$ $sqrt(x)$
then
$y \cdot \sqrt{x} = c$ $y*sqrt(x) = c$ for some constant $c$ $c$

Given $(x, y) = (4, 50)$ $(x,y)=(4,50)$ is a solution to this inverse variation
then
$50 \cdot \sqrt{4} = c$ $50*sqrt(4) = c$
$\to c = 100 xxxxxxxxxx$ $rarr c = 100 color(white)("xxxxxxxxxx")$ (see note below)
and the inverse variation equation is
$y \cdot \sqrt{x} = 100$ $y*sqrt(x) = 100$

When $x = 5$ $x = 5$ this becomes
$y \cdot \sqrt{5} = 100$ $y*sqrt(5) = 100$

$\sqrt{5} = \frac{100}{y}$ $sqrt(5) = 100/y$

$5 = \frac{10^{4}}{y^{2}}$ $5 = 10^4/y^2$

$y = \sqrt{5000} = 50 \sqrt{2}$ $y = sqrt(5000) = 50sqrt(2)$

Note: I have interpreted "y varies inversely with the square root of x" to mean the positive square root of x (i.e. $\sqrt{x}$ $sqrt(x)$ ) which also implies that y is positive. If this is not the intended case, the negative version of y would also need to be allowed.

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Suppose that y varies inversely with the square root of x and y=50 when x=4, how do you find y when x=5?

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