https://file.aiquickdraw.com/mathbot/file/1730274870829j717kaam.jpg

Let's analyze and solve the equation provided in the image step-by-step.

The equation is:
\[
T = \frac{1}{2 \pi \sqrt{\mu C}}
\]
where \( \mu \) and \( C \) are given values. Based on the second part of your equation, the specific values seem to be:
- \( \mu = 9.3 \times 10^3 \)
- \( C = 10^{-6} \)

Now, let’s substitute these values and calculate \( T \).

### Step 1: Calculate the product inside the square root
\[
\mu \cdot C = 9.3 \times 10^3 \times 10^{-6} = 9.3 \times 10^{-3}
\]

### Step 2: Take the square root
\[
\sqrt{9.3 \times 10^{-3}} = \sqrt{9.3} \times \sqrt{10^{-3}}
\]
\[
\sqrt{9.3} \approx 3.05, \quad \sqrt{10^{-3}} = 10^{-1.5} = 0.03162
\]
\[
\sqrt{9.3 \times 10^{-3}} = 3.05 \times 0.03162 \approx 0.0965
\]

### Step 3: Calculate the denominator \( 2 \pi \sqrt{\mu C} \)
\[
2 \pi \approx 6.283
\]
\[
2 \pi \sqrt{\mu C} = 6.283 \times 0.0965 \approx 0.606
\]

### Step 4: Compute the final value of \( T \)
\[
T = \frac{1}{0.606} \approx 1.65
\]

### Final Answer
\[
T \approx 1.65
\]

Let me know if you need any further details or have any other questions!

---

Here are five questions related to this problem:
1. What physical quantity might this equation represent (e.g., period or frequency)?
2. How does changing \( \mu \) or \( C \) affect the result?
3. What are the units of \( T \) in this case?
4. Can the product \( \mu C \) be interpreted physically?
5. How does this result change if \( C \) is doubled?

**Tip:** Always track units carefully in problems like this to avoid confusion!

Learn how to calculate the period T for an oscillatory system using the formula T = 1 / (2π√(μC)). In this example, values of μ = 9.3 × 10^3 and C = 10^-6 are substituted to find the solution step-by-step. This tutorial covers the multiplication of powers of 10, square root operations, and approximate values for scientific calculations. Suitable for Grades 10-12.

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