Given that y varies inversely as the square of x. If x = 3 when y = 100, find the equation connecting x and y.
A
\(yx^2 = 300\)
B
\(yx^2 = 900\)
C
y = \(\frac{100x}{9}\)
D
\(y = 900x^2\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
Y \(\alpha \frac{1}{x^2} \rightarrow y = \frac{k}{x^2}\)
If x = 3 and y = 100,
then, \(\frac{100}{1} = \frac{k}{3^2}\)
\(\frac{100}{1} = \frac{k}{9}\)
k = 100 x 9 = 900
Substitute 900 for k in
y = \(\frac{k}{x^2}\); y = \(\frac{900}{x^2}\)
= \(yx^2 = 900\)
Source: Myschool Past Questions Archive (Record #49035)