To solve the equation \(130 = \frac{k(1.6)}{(0.005)^2}\) for \(k\), follow these steps:

1. **Simplify the denominator:**
   \[
   (0.005)^2 = 0.000025
   \]

2. **Substitute back into the equation:**
   \[
   130 = \frac{k(1.6)}{0.000025}
   \]

3. **Multiply both sides by \(0.000025\) to isolate the term with \(k\):**
   \[
   130 \times 0.000025 = k(1.6)
   \]

4. **Calculate the left side:**
   \[
   130 \times 0.000025 = 0.00325
   \]
   So the equation becomes:
   \[
   0.00325 = 1.6k
   \]

5. **Solve for \(k\) by dividing both sides by 1.6:**
   \[
   k = \frac{0.00325}{1.6} \approx 0.00203125
   \]

Therefore, \(k \approx 0.00203125\).

Would you like any further details or have any questions about this solution?

Here are five related questions:

1. How do you solve equations involving fractions and variables?
2. What are the properties of exponents, and how do they apply to solving equations?
3. How would you solve the equation if the denominator was a different value?
4. Can this method be used to solve equations with different forms?
5. What are common mistakes to avoid when solving similar equations?

**Tip:** When solving equations involving small decimals or fractions, consider using scientific notation to simplify calculations and reduce errors.

Learn how to solve the equation 130 = (k * 1.6) / (0.005)^2 step-by-step. This problem involves solving a fractional equation, using algebraic manipulation and scientific notation for precision. Suitable for high school students.

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