If x varies inversely as y and \(x = \frac{2}{3}\) when y = 9, find the value of y when \(x=\frac{3}{4}\)
Question 1 Report
If x varies inversely as y and \(x = \frac{2}{3}\) when y = 9, find the value of y when \(x=\frac{3}{4}\)
Answer Details
The problem statement tells us that x and y are inversely proportional, which means that their product is constant. We can write this relationship as:
xy = k
where k is a constant. We are also given that when y = 9, x = 2/3. Substituting these values into the equation above, we get:
(2/3)(9) = k
k = 6
Now we can use this value of k to find y when x = 3/4:
(3/4)y = 6
y = (6 x 4)/3
y = 8
Therefore, when x = 3/4, y = 8. So the answer is option (D).
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