In the following formula, $f(x)$ is the minimum number of hours of studying required to attain a test score of $x: f(x)=\frac{0.51 x}{100.5-x}$. How many hours of study are needed to score 92?
Answer
Final Answer: The minimum number of hours of studying required to attain a test score of 92 is approximately \(\boxed{5.52}\).
Step 1 ：Given the function \(f(x)=\frac{0.51 x}{100.5-x}\), which represents the minimum number of hours of studying required to attain a test score of \(x\).
Step 2 ：We are asked to find the number of hours needed to score 92, which means we need to find the value of \(f(92)\).
Step 3 ：Substitute \(x=92\) into the function: \(f(92)=\frac{0.51 \times 92}{100.5-92}\).
Step 4 ：After calculating, we find that \(f(92)\) is approximately 5.5200000000000005.
Step 5 ：Rounding to two decimal places, we get \(f(92)\) is approximately 5.52.
Step 6 ：Final Answer: The minimum number of hours of studying required to attain a test score of 92 is approximately \(\boxed{5.52}\).
