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WAEC Mathematics 2014 Paper

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Question : 12

Total: 49

F x varies inversely as y and y varies directly as Z, what is the relationship between x and z?

x $\alpha$ z
x $\alpha \; \frac{1}{z}$
x $\alpha z^2$
$x \alpha \; \frac{1}{z^2}$

Solution:

Concept:

Combine inverse and direct variation to find the net relation.

Explanation:

x

varies inversely as

y

, so

x \propto \frac{1}{y}

.

y

varies directly as

z

, so

y \propto z

.

Let

x = \frac{k}{y}

and

y = c z

, where

k

and

c

are constants.

Substitute

y = c z

into

x = \frac{k}{y}

.

x = \frac{k}{c z}

.

Since

\frac{k}{c}

is a constant,

x \propto \frac{1}{z}

.

Answer:

x \propto \frac{1}{z}

, so the correct option is B.

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