If y \(\alpha\) x\(^2\) and y = 1\(\frac{1}{4}\) when x = 4, find the value of y when x = \(\frac{1}{2}\)
A
\(2\frac{1}{2}\)
B
5
C
10
D
80
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
y \(\propto x^2\), y = 1\(\frac{1}{4}\), x = 4
y = \(\frac{\text{k}}{x^2}\)
k = y x\(^2\) = \(\frac{5}{4}\) x 4\(^2\) = 20
y = \(\frac{20}{x^2}\) = \(\frac{20}{x^2}\) = \(\frac{20}{(\frac{1}{2})^2}\)
= \(\frac{20}{\frac{1}{4}}\) = 20 x 4 = 80
Source: Myschool Past Questions Archive (Record #26712)