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

Question
Functions
asked 2021-03-08
y varies inversely as the square root of x,y=6 when x=100. Find yy when x=144.

Answers (1)

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
\(\displaystyle{y}={\frac{{{60}}}{{\sqrt{{144}}}}}\)
\(\displaystyle{y}={\frac{{{60}}}{{{12}}}}\)
\(\displaystyle{y}={5}\)
0

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