To solve the equation \( 1.24 = \frac{2L}{427.8 \times 1.148 \times (104.4)^2} \), we'll start by simplifying and isolating \( L \).

### Step 1: Simplify the denominator

First, compute the expression in the denominator:

\[
427.8 \times 1.148 \times (104.4)^2
\]

### Step 2: Simplify the equation

Once the denominator is simplified, the equation becomes:

\[
1.24 = \frac{2L}{\text{(result from step 1)}}
\]

### Step 3: Solve for \( L \)

Multiply both sides by the denominator to isolate \( L \):

\[
L = \frac{1.24 \times \text{(denominator result)}}{2}
\]

Let's compute this step by step.The value of \( L \) is approximately \( 3,318,756.24 \).

Do you want more details on the steps or have any questions?

Here are some related questions you might explore:
1. What happens if we change one of the constants in the equation?
2. How would the equation change if \( L \) was in terms of another variable?
3. How can we verify the solution using the original equation?
4. What are the units for \( L \) based on the given equation?
5. How would a small error in one of the constants affect the value of \( L \)?

**Tip:** When solving equations with large numbers, be mindful of rounding errors, especially in scientific and engineering calculations.

1.24 = 2(L) / [427.8 * 1.148 * (104.4)^2]

This guide provides a detailed solution for the rational equation 1.24 = 2(L) / (427.8 * 1.148 * (104.4)^2). Learn how to simplify and solve for L using algebraic manipulation techniques, ideal for high school students in Grades 10-12.

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