JAMB - Mathematics (1983 - No. 4)
If x is jointly proportional to the cube of y and the fourth power of z. In what ratio is x increased or decreased when y is halved and z is doubled?
4:1 increase
2:1 increase
1:1 no change
1:4 decrease
3:4 decrease
Explanation
\(x \propto y^{3} z^{4}\)
\(x = ky^{3} z^{4}\)
If y is halved and z is doubled, we have
\(x = k (\frac{1}{2} y)^{3} (2z)^{4}\)
\(x = k (\frac{y^{3}}{8}) (16z^{4})\)\)
\(x = 2k y^{3} z^{4}\)
\(\therefore \text{x is increased in the ratio 2 : 1}\)
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