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The problem requires us to transform the function \( y = 0.000304x^3 \), where \( y \) is the weight of a rainbow trout in pounds, and \( x \) is the length in inches, to a function that relates \( y \) in kilograms and \( x \) in centimeters.

### Step-by-Step Solution:

1. **Convert Weight from Pounds to Kilograms**:
   - 1 pound is approximately 0.453592 kilograms.
   - Thus, the weight \( y \) in kilograms is \( y_{\text{kg}} = 0.453592 \cdot y \).

2. **Convert Length from Inches to Centimeters**:
   - 1 inch is approximately 2.54 centimeters.
   - Therefore, the length \( x \) in centimeters is \( x_{\text{cm}} = 2.54 \cdot x \).

3. **Substitute and Simplify the Function**:
   - Substitute \( y = 0.000304x^3 \) into \( y_{\text{kg}} = 0.453592 \cdot y \):
     \[
     y_{\text{kg}} = 0.453592 \cdot (0.000304x^3) = 0.000137692288x^3
     \]
   - Now replace \( x \) with \( x_{\text{cm}} / 2.54 \):
     \[
     y_{\text{kg}} = 0.000137692288 \cdot \left(\frac{x_{\text{cm}}}{2.54}\right)^3
     \]
   - Simplifying further:
     \[
     y_{\text{kg}} = 0.000137692288 \cdot \frac{x_{\text{cm}}^3}{16.387064} \approx 0.000008404598x_{\text{cm}}^3
     \]

So, the new function in terms of \( y \) in kilograms and \( x \) in centimeters is:
\[
y = 0.000008405x^3
\]
(rounded to nine decimal places).

### Graph Interpretation:
For part **b**, the correct transformation involves a **scaling** change due to the unit conversions, which would affect both the weight and length scaling on the graph.

Would you like further details on any of these steps, or have any questions?

Here are some questions to explore related concepts:
1. How would you verify the accuracy of the unit conversion factors?
2. What would the function look like if the weight was measured in grams instead?
3. How would the function change if we measured length in meters instead of centimeters?
4. Can you explain how scaling affects the graph of a function?
5. What other transformations might you apply to functions to change their units?

**Tip**: When converting units in a function, pay careful attention to how each unit conversion affects both the constant and variable terms.

The weight y (in pounds) of a rainbow trout can be modeled by y = 0.000304x^3, where x is the length (in inches) of the trout. Write a function that relates the weight y and length x of a rainbow trout when y is measured in kilograms and x is measured in centimeters. Round the coefficient of any term in your result to 9 decimal places.

Learn how to convert a weight function for a rainbow trout from pounds and inches to kilograms and centimeters. This problem covers key concepts in unit conversion and function transformation, suitable for high school students.

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