If x varies inversely as y and y varies directly as z, what is the relationship between x and z?
Question 1 Report
If x varies inversely as y and y varies directly as z, what is the relationship between x and z?
Answer Details
The given problem states that x varies inversely with y, which means that as y increases, x decreases and vice versa. Similarly, it also states that y varies directly with z, which means that as z increases, y increases and vice versa.
Now, to find the relationship between x and z, we need to combine these two statements. Since y is the common variable, we can rewrite the second statement as y \(\alpha\) z.
Substituting this value of y in the first statement, we get x \(\alpha\) \(\frac{1}{y}\), which can be further simplified as x \(\alpha\) \(\frac{1}{z}\).
Hence, the relationship between x and z is x \(\alpha\) \(\frac{1}{z}\). is the correct answer.
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