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Find the equation of the circle that represents the range of the volcano and sketch the circle. Which among the cities are in outside the 14-km radius of the volcano?

The new image appears to provide another view or additional information related to the problem. Let's use this new image to confirm or refine the previous analysis of the cities' positions relative to the circle's radius.

Upon further inspection, we should:

1. **Identify and confirm the coordinates of the cities on the grid.**
2. **Verify which cities are within or outside the 14-km radius based on the new grid details.**

Let's go ahead and refine the analysis using the updated coordinates.Upon reviewing the updated image and reconfirming the coordinates, cities **C** and **D** remain outside the 14-km radius of the volcano. The equation of the circle, \( x^2 + y^2 = 196 \), still represents the volcano's range accurately.

Would you like further details or have any questions?

Here are some related questions:

1. How can you verify the accuracy of plotted points on a grid?
2. What steps would you take to plot a circle given its equation and a set of points?
3. How can real-world distances be accurately represented on a grid or map?
4. What are common applications of using circles to represent ranges in real-life scenarios?
5. How can technology assist in determining geographic locations within a certain radius?
6. What role does scale play in interpreting distances on maps?
7. How can you use mathematical equations to model natural phenomena?
8. What methods can be used to visually differentiate areas inside and outside a defined range?

**Tip:** Double-checking the coordinates and calculations, especially in graphical representations, is crucial for accurate results.

Discover how to find the equation of a circle that represents the range of a volcano and sketch it with detailed step-by-step analysis. This problem involves identifying coordinates, verifying distances, and applying the circle equation (x - h)^2 + (y - k)^2 = r^2 to determine which cities are within or outside the 14-km radius.

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