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The problem involves two pendulums, with the number of swings per minute for a pendulum of length \( L \) (in inches) given by the formula:

\[
\text{Number of swings per minute} = \frac{375}{\sqrt{L}}
\]

For **Pendulum 1**, the length \( L_1 = 38 \) inches, and for **Pendulum 2**, \( L_2 = 49 \) inches.

We can calculate the number of swings for each pendulum using the given formula.

### For Pendulum 1:
\[
\text{Swings}_1 = \frac{375}{\sqrt{38}} \approx \frac{375}{6.16} \approx 60.88
\]

### For Pendulum 2:
\[
\text{Swings}_2 = \frac{375}{\sqrt{49}} = \frac{375}{7} \approx 53.57
\]

### Difference in the number of swings:
\[
\text{Difference} = 60.88 - 53.57 \approx 7.31
\]

Rounding to the nearest whole number, the difference is approximately **7 swings** per minute.

Would you like a detailed explanation of the steps, or do you have any further questions?

Here are five related questions:
1. How does the length of the pendulum affect the number of swings?
2. What would happen if both pendulums were the same length?
3. How could this formula change for pendulums of different materials?
4. Can you find a way to predict swings for pendulums of much longer lengths?
5. How could you use this formula in a real-world experiment?

**Tip:** The period of a pendulum (and thus the number of swings) depends on the square root of its length, meaning small changes in length lead to relatively smaller changes in swing frequency.

There are 2 pendulums showcased in a museum. The number of swings back and forth of a pendulum of length L, in inches, each minute is 375/sqrt(L). How many more swings can Pendulum 1 make than Pendulum 2 each minute? Round to the nearest whole number. Pendulum 1 has a length of 38 inches and Pendulum 2 has a length of 49 inches.

Explore how to calculate the difference in swings between two pendulums with lengths of 38 inches and 49 inches. The formula used is 375 divided by the square root of the length. Perfect for students in Grades 8-10.

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