2.46=(-4pi(0.023)(90-240)/((1/0.4)-(1/x))

Let's solve the equation:

\[
2.46 = \frac{-4\pi(0.023)(90 - 240)}{\left(\frac{1}{0.4} - \frac{1}{x}\right)}
\]

### Step 1: Simplify the numerator
First, simplify the expression inside the parentheses:

\[
90 - 240 = -150
\]

Now substitute this back into the equation:

\[
2.46 = \frac{-4\pi(0.023)(-150)}{\left(\frac{1}{0.4} - \frac{1}{x}\right)}
\]

### Step 2: Multiply the constants in the numerator
Now calculate the numerator:

\[
-4\pi(0.023)(-150) = 4\pi(0.023)(150)
\]

Let's calculate this value.

\[
4 \cdot \pi \cdot 0.023 \cdot 150
\]

I'll do the calculations next.The value of the numerator is approximately \( 43.35 \).

So the equation now becomes:

\[
2.46 = \frac{43.35}{\left(\frac{1}{0.4} - \frac{1}{x}\right)}
\]

### Step 3: Solve for the denominator
First, isolate the denominator by multiplying both sides by the denominator:

\[
2.46 \left( \frac{1}{0.4} - \frac{1}{x} \right) = 43.35
\]

Next, divide both sides by 2.46 to solve for the expression inside the parentheses:

\[
\frac{1}{0.4} - \frac{1}{x} = \frac{43.35}{2.46}
\]

Let's calculate the right-hand side.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can continue the calculation manually:

\[
\frac{43.35}{2.46} \approx 17.63
\]

Now the equation becomes:

\[
\frac{1}{0.4} - \frac{1}{x} = 17.63
\]

You can solve this by first calculating \( \frac{1}{0.4} = 2.5 \), so:

\[
2.5 - \frac{1}{x} = 17.63
\]

Solve for \( \frac{1}{x} \):

\[
\frac{1}{x} = 2.5 - 17.63
\]

\[
\frac{1}{x} = -15.13
\]

Finally, solve for \( x \):

\[
x = \frac{1}{-15.13} \approx -0.066
\]

If you need further assistance, feel free to ask!

---

Would you like more details on any of the steps?

Here are 5 related questions to expand this topic:
1. How can you solve more complex equations involving trigonometric functions?
2. What are the rules for simplifying expressions with fractions?
3. Can you explain how to handle negative numbers in equations?
4. How do you calculate with π (pi) in different contexts?
5. What are the steps for solving equations with multiple variables?

**Tip:** Always isolate variables step by step to make complex equations easier to handle!

2.46 = (-4π(0.023)(90-240))/((1/0.4)-(1/x))

In this guide, solve the complex fractional equation 2.46 = (-4π(0.023)(90-240))/((1/0.4)-(1/x)). Key concepts include simplifying fractions, using pi in calculations, and solving for unknown variables. This problem is suitable for students in Grades 10-12.

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