If x varies inversely as y and y varies directly as z, what is the...
MATHEMATICS
WAEC 2017
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 \(\alpha\) \(\frac{1}{z^2}\)
Correct Answer: B. x \(\alpha\) \(\frac{1}{z}\)
Explanation
\(x \propto \frac{1}{y}\), y \(\propto\) z
x = \(\frac{k}{y}\)
y = mz
Since y = mz,
x = \(\frac{k}{mz}\), where k and m are constants. Hence,
x \(\propto\) \(\frac{1}{z}\)
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