**Problem 1**A force, \( f \), varies inversely with the square of the distance, \( d \), from an object.a. Write down the function, \( f \), that describes this situation. Use \( k \) as the constant of variation. \( f(d) = \_\_\_ \)b. When the distance from the object is 6, the force is 144. What is the constant of variation? \( k = \_\_\_ \)c. When the distance is 9, what is the force? \( f(9) = \_\_\_ \)**Answers**- Explanation of answers goes here.(No graphs or diagrams are present in the image.) ### Direct Variation Analysis**Table of Values:**| \( x \) | \( y \) ||---------|---------|| 0 | 0 || 0.5 | 1 || 1 | 3 || 1.5 | 6 || 2 | 8 |**Question:**According to the table, does \( y \) vary directly with \( x \)? Why or why not?**Options:**- **A.** No - the ratio \( \frac{y}{x} \) is not constant- **B.** Yes - the product \( y \cdot x \) is constant- **C.** Yes - the ratio \( \frac{y}{x} \) is constant- **D.** No - the product \( y \cdot x \) is not constant- **E.** Not enough information**Explanation of Concepts:**In a direct variation, \( y \) varies directly with \( x \) if the ratio \( \frac{y}{x} \) is constant for all values. Alternatively, if \( y = kx \) for some constant \( k \), then \( y \) is directly proportional to \( x \).### Analysis:Examine the ratio \( \frac{y}{x} \) for each pair:- For \( (0.5, 1) \): \( \frac{1}{0.5} = 2 \)- For \( (1, 3) \): \( \frac{3}{1} = 3 \)- For \( (1.5, 6) \): \( \frac{6}{1.5} = 4 \)- For \( (2, 8) \): \( \frac{8}{2} = 4 \)These ratios are not constant, indicating \( y \) does not vary directly with \( x \).### Conclusion:The correct answer is:- **A.** No - the ratio \( \frac{y}{x} \) is not constant.This table serves as a tool for understanding direct variation by analyzing the constancy of the ratio \( \frac{y}{x} \).

Name: **Problem 1**A force, \( f \), varies inversely with the square of th
Uploaded: 2024-03-05T11:52:21.000Z
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Description: **Problem 1**A force, \( f \), varies inversely with the square of the distance, \( d \), from an object.a. Write down the function, \( f \), that describes this situation. Use \( k \) as the constant of variation. \( f(d) = \_\_\_ \)b. When the dis