If 2.5 =(8.0 + DF/2 × 10.0)/(0.375 × 9.81) , what is the value of F

To solve for \( F \) in the equation:

\[
2.5 = \frac{8.0 + \frac{DF}{2} \times 10.0}{0.375 \times 9.81}
\]

We'll follow these steps:

### Step 1: Simplify the equation

Start by multiplying both sides of the equation by \( 0.375 \times 9.81 \) to eliminate the denominator:

\[
2.5 \times 0.375 \times 9.81 = 8.0 + \frac{DF}{2} \times 10.0
\]

Calculate the left-hand side:

\[
2.5 \times 0.375 \times 9.81 = 9.193125
\]

So, the equation becomes:

\[
9.193125 = 8.0 + \frac{DF \times 10.0}{2}
\]

### Step 2: Isolate the \( F \) term

Subtract 8.0 from both sides:

\[
9.193125 - 8.0 = \frac{DF \times 10.0}{2}
\]

\[
1.193125 = \frac{DF \times 10.0}{2}
\]

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

Multiply both sides by 2 to isolate \( DF \times 10.0 \):

\[
2 \times 1.193125 = DF \times 10.0
\]

\[
2.38625 = DF \times 10.0
\]

Finally, divide both sides by 10 to solve for \( F \):

\[
DF = \frac{2.38625}{10} = 0.238625
\]

Thus, the value of \( F \) is \( **F = 0.238625** \).

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Do you want more details or have any questions?

Here are some follow-up questions to consider:
1. What steps can be taken to verify the value of \( F \)?
2. How can this equation be used in practical applications?
3. What does the variable \( F \) represent in this context?
4. Could rounding affect the accuracy of the solution?
5. How would changes to the constants (like 0.375 or 9.81) affect \( F \)?
6. Can this method be applied to solve similar equations?
7. How would you solve for \( F \) if additional terms were added to the equation?
8. What if \( F \) was part of a larger system of equations?

**Tip:** Always perform operations step-by-step and keep track of units when solving equations involving physical quantities.

Learn how to solve the equation 2.5 = (8.0 + DF/2 × 10.0)/(0.375 × 9.81) to find the value of F. This problem involves algebraic manipulation and solving for an unknown variable in a complex equation. Suitable for high school students and those interested in algebraic equations.

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