To solve the problem, we need to analyze how the x-coordinate of point B changes as the radius of the circle changes. It looks like you provided a table with some values missing. However, I only see the header and a partial value set. It's necessary to define how the x-coordinate relates to the radius for better calculation.

### Break Down the Problem
1. Identify the relationship between the radius and the x-coordinate of point B.
2. Create or complete the table with the values provided.

### Relevant Concepts
1. For a circle centered at the origin with radius $ r $, the x-coordinate can be represented as:
$$
x = r \cdot \cos(\theta)
$$
where $ \theta $ is the angle in radians.

### Analysis and Detail
1. Assume a specific angle $ \theta $ or a uniform distribution to fill in the x-coordinate values corresponding to the given stages.
2. Calculate the x-coordinate for each given radius if enough information is provided.

From the partial table, let's assume you want to fill out the missing values based on the corresponding radius or stage.

Given the values:
- Stage (n): 1, 2, 4, 3, 0.25
- If these stages represent corresponding x-coordinates, we need to identify the values missing.

### Verification and Summary
1. Fill in the missing values based on logical progression or provided relationships.

### Final Answer
To fill in the values in the table, I need more information regarding the relationship between the changing radius and x-coordinate. Based on the common trigonometric angle for a circle with different stages, here is an approach to suggest some values:

| Stage (n) | x-coordinate (B) |
|-----------|------------------|
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 4 |
| 0.25 | 0.25 |

Please confirm or provide additional context or data about how the x-coordinates are generated for a complete and verified table.

Question

To solve the problem, we need to analyze how the x-coordinate of point B changes as the radius of the circle changes. It looks like you provided a table with some values missing. However, I only see the header and a partial value set. It's necessary to define how the x-coordinate relates to the radius for better calculation.

### Break Down the Problem
1. Identify the relationship between the radius and the x-coordinate of point B.
2. Create or complete the table with the values provided.

### Relevant Concepts
1. For a circle centered at the origin with radius $ r $, the x-coordinate can be represented as:
   $$
   x = r \cdot \cos(\theta)
   $$
   where $ \theta $ is the angle in radians.

### Analysis and Detail
1. Assume a specific angle $ \theta $ or a uniform distribution to fill in the x-coordinate values corresponding to the given stages.
2. Calculate the x-coordinate for each given radius if enough information is provided.

From the partial table, let's assume you want to fill out the missing values based on the corresponding radius or stage.

Given the values:
- Stage (n): 1, 2, 4, 3, 0.25
- If these stages represent corresponding x-coordinates, we need to identify the values missing.

### Verification and Summary
1. Fill in the missing values based on logical progression or provided relationships.
  
### Final Answer
To fill in the values in the table, I need more information regarding the relationship between the changing radius and x-coordinate. Based on the common trigonometric angle for a circle with different stages, here is an approach to suggest some values:

| Stage (n) | x-coordinate (B) |
|-----------|------------------|
| 1         | 1                |
| 2         | 2                |
| 3         | 3                |
| 4         | 4                |
| 0.25      | 0.25             |

Please confirm or provide additional context or data about how the x-coordinates are generated for a complete and verified table.

Knowee AI · Accepted Answer