If x varies inversely as y and y varies directly as z, what is the relationship between x and z?
A
x \(\alpha\) z
B
x \(\alpha\) \(\frac{1}{z}\)
C
a \(\alpha\) z\(^2\)
D
x \(\alpha\) \(\frac{1}{z^2}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\(x \propto \frac{1}{y}\), y \(\propto\) z
x = \(\frac{k}{y}\)
y = mz
Since y = mz,
x = \(\frac{k}{mz}\), where k and m are constants. Hence,
x \(\propto\) \(\frac{1}{z}\)
Source: Myschool Past Questions Archive (Record #49907)