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The question in your image asks for the x-component (horizontal component) of a vector that is described as being 48 cm "north of east."

Here's how to solve this:

1. **"North of east"** means that the vector is at some angle northward from the east direction. However, since no angle is given, it's important to assume a likely scenario. If we assume that "north of east" means at a 45° angle (a common assumption when an angle is not specified), we can calculate the x-component using trigonometry.

2. The formula to find the x-component of a vector at an angle is:
   \[
   R_x = R \cdot \cos(\theta)
   \]
   where:
   - \(R_x\) is the x-component of the vector,
   - \(R = 48 \, \text{cm}\) is the magnitude of the vector,
   - \(\theta = 45^\circ\) is the angle north of east.

3. Using \(\cos(45^\circ) = \frac{\sqrt{2}}{2} \approx 0.707\):
   \[
   R_x = 48 \, \text{cm} \cdot 0.707 \approx 33.94 \, \text{cm}
   \]
   
4. The closest whole number answer from the provided choices would be **34 cm**, but this doesn't match the options.

Looking at your options, **the closest one is 42 cm**, which suggests there may be a slightly different assumed angle. For example, an angle of around 30° north of east would give an x-component closer to 42 cm.

Would you like a more detailed exploration of the angle assumptions, or do you have any other questions?

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Here are 5 relative questions for further exploration:
1. What is the y-component of the same vector?
2. How would the x-component change if the angle were 60° north of east?
3. If the resultant vector were 60 cm instead of 48 cm, how would that affect the x-component?
4. Can you find the total displacement if you are given both x and y components?
5. How do you decompose vectors into components for any general angle?

**Tip**: Always check for hidden assumptions like angles when directions like "north of east" are given without a specific degree.

If the resultant, R, of two vectors is 48 cm north of east, what is the x-component (Rx) of that vector?

Learn how to find the x-component of a vector that is 48 cm north of east. This solution uses trigonometric principles and vector decomposition to calculate the x-component. Suitable for high school students learning about vectors and trigonometry.

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