T = 5000 + 484218.07 * (0.002 * 4560 * (5566.18 - 340) / 340)

Let's solve the equation for \( T \):

\[ T = 5000 + 484218.07 \cdot \left(0.002 \cdot 4560 \cdot \frac{5566.18 - 340}{340}\right) \]

We will follow the order of operations (PEMDAS/BODMAS) step by step:

1. **Calculate inside the innermost parentheses**:
   \[
   5566.18 - 340 = 5226.18
   \]

2. **Division within the parentheses**:
   \[
   \frac{5226.18}{340} \approx 15.371117647058823
   \]

3. **Multiplication within the parentheses**:
   \[
   0.002 \cdot 4560 \cdot 15.371117647058823 = 0.002 \cdot 7003.6988235294115 = 14.007397647058823
   \]

4. **Multiplication outside the parentheses**:
   \[
   484218.07 \cdot 14.007397647058823 \approx 6783157.872681705
   \]

5. **Addition**:
   \[
   5000 + 6783157.872681705 \approx 6788157.872681705
   \]

Therefore, the value of \( T \) is approximately \( 6788157.87 \).

Would you like more details or have any questions? Here are some questions you might want to ask:

1. How do you solve equations with multiple variables?
2. Can you explain how to handle fractional exponents in expressions?
3. What is the significance of the order of operations in solving equations?
4. How do you verify the solution of a complex equation?
5. Can you solve a quadratic equation step by step?

**Tip:** When solving mathematical expressions, breaking down the problem into smaller, manageable steps can help ensure accuracy and reduce errors.

Explore the step-by-step solution to the mathematical expression T = 5000 + 484218.07 * (0.002 * 4560 * (5566.18 - 340) / 340). Learn about order of operations (PEMDAS/BODMAS) and how to apply it correctly in arithmetic operations. Suitable for students in Grades 9-12.

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