F x varies inversely as y and y varies directly as Z, what is the relationship between x and z?
Question 1 Report
F x varies inversely as y and y varies directly as Z, what is the relationship between x and z?
Answer Details
The statement "F x varies inversely as y" can be mathematically written as x = k/y, where k is the constant of proportionality. Similarly, "y varies directly as Z" can be written as y = kz, where k is again the constant of proportionality. Substituting y in the first equation, we get x = k/(kz), which simplifies to x = 1/z. Therefore, we can conclude that x varies inversely with z, which is mathematically represented as x \(\alpha\) 1/z. So, the correct answer is: x \(\alpha \frac{1}{z}\).
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