\(\begin{array}{c|c} x & 1 & 4 & p \\ \hline y & 0.5 & 1 & 2.5\end{array}\). The table below satisfies the relation y = k\(\sqrt{x}\), where k is a positive constant. Find the value of P,
A
2
B
4
C
10
D
25
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
From y = \(\frac{1}{2} \sqrt{x}\)
when y = 2.5 or \(\frac{5}{2}\), x = P
\(\frac{5}{2} \times \frac{1}{2} \sqrt{P}\)
\(\sqrt{P} = \frac{10}{2} = 5\)
P = \(5^2\)
= 25
Source: Myschool Past Questions Archive (Record #36168)