# y varies inversely as the square root of x,y=6 when x=100. Find yy when x=144.

Question
Functions
y varies inversely as the square root of x,y=6 when x=100. Find yy when x=144.

2021-03-09
Write the inverse variation equation: $$\displaystyle{y}={\frac{{{k}}}{{\sqrt{{x}}}}}$$
Solve for k, the constant of variation, using y=6 when x=100: $$\displaystyle{6}={\frac{{{k}}}{{\sqrt{{100}}}}}$$
$$\displaystyle{6}={\frac{{{k}}}{{{10}}}}$$
$$\displaystyle{60}={k}$$
The equation will be: $$\displaystyle{y}={\frac{{{60}}}{{\sqrt{{x}}}}}$$
When x=144,ZSK
$$\displaystyle{y}={\frac{{{60}}}{{\sqrt{{144}}}}}$$
$$\displaystyle{y}={\frac{{{60}}}{{{12}}}}$$
$$\displaystyle{y}={5}$$

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