Finding the power in an inverse proportion from a table
Finding the power in an inverse proportion from a table
IP 2
9 marks
It is known that \(y\) is inversely proportional to \(x^n\), where \(n\) is a positive integer. Some corresponding values of \(x\) and \(y\) are shown in the table.
| \(x\) | \(2\) | \(3\) | \(6\) |
|---|---|---|---|
| \(y\) | \(81\) | \(24\) | \(p\) |
- Find the value of \(n\) and the value of \(p\).[4]
- Find the value of \(x\) when \(y=\dfrac{3}{8}\).[2]
- Without further calculation, explain why \(y\) cannot be directly proportional to any positive power of \(x\).[1]
- The same \(y\) is also inversely proportional to \(w^2\), where \(w>0\), and \(w=4\) when \(x=2\). Express \(w\) in terms of \(x\).[2]
Solution:
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Answer:(a) \(n=3\), \(p=3\) (b) \(x=12\) (c) \(y\) decreases as \(x\) increases, but \(kx^m\) with \(k,m>0\) increases (d) \(w=\sqrt{2x^3}\)
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