If y varies directly as \(\sqrt{n}\) and y = 4 when n = 4, find y when n = 1\(\frac{7}{9}\)
A
\(\sqrt{17}\)
B
\(\frac{4}{3}\)
C
\(\frac{8}{3}\)
D
\(\frac{2}{3}\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
y \(\propto \sqrt{n}\)
y = k\(\sqrt{n}\)
when y = 4, n = 4
4 = k\(\sqrt{4}\)
4 = 2k
k = 2
Therefore,
y = 2\(\sqrt{n}\)
y = 2\(\sqrt{\frac{16}{9}}\)
y = 2\((\frac{4}{3})\)
y = \(\frac{8}{3}\)
Source: Myschool Past Questions Archive (Record #27222)