If \(y \propto \frac{1}{x^2}\) and x = 3 when y = 4, find y when x = 2.
Question 1 Report
If \(y \propto \frac{1}{x^2}\) and x = 3 when y = 4, find y when x = 2.
Answer Details
If we have that y is proportional to \(\frac{1}{x^2}\), then we can write:
y = k\(\frac{1}{x^2}\)
where k is a constant of proportionality. To find k, we can use the fact that when x = 3, y = 4:
4 = k\(\frac{1}{3^2}\)
Simplifying:
k = 36
Now we can use k to find y when x = 2:
y = k\(\frac{1}{2^2}\)
y = 9
Therefore, the answer is y = 9.
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