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 \(\alpha\) \(\frac{1}{z^2}\)
waec 2017mathematics

The correct answer is B. x \(\alpha\) \(\frac{1}{z}\)

\(x \propto \frac{1}{y}\), 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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