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To find the x-component \( V_x \) of the vector \( \vec{V} \), we use the following formula:

\[
V_x = |\vec{V}| \cdot \cos(\theta)
\]

Given:
- \( |\vec{V}| = 9.77 \, \text{m} \)
- \( \theta = 154^\circ \)

Now, calculate:

\[
V_x = 9.77 \cdot \cos(154^\circ)
\]

First, evaluate \( \cos(154^\circ) \):

\[
\cos(154^\circ) \approx -0.8988
\]

Thus:

\[
V_x = 9.77 \cdot (-0.8988) \approx -8.78 \, \text{m}
\]

Therefore, the x-component of the vector is approximately:

\[
V_x \approx -8.78 \, \text{m}
\]

Would you like more details or further clarification on this? 

Here are 5 related questions to extend your understanding:
1. How is the x-component affected by the angle's reference quadrant?
2. What is the y-component of the same vector?
3. How would the x-component change if the angle were in the first quadrant?
4. Can the magnitude of a vector ever be negative?
5. What is the relationship between the x-component and the overall direction of the vector?

**Tip:** The cosine of angles greater than 90 degrees is always negative because they lie in the second or third quadrants.

Find the x-component of the given vector |V| = 9.77 m, θ = 154°.

Learn how to find the x-component of a vector with magnitude 9.77 m and angle 154°. This tutorial uses the formula Vx = |V| * cos(θ) and explains step-by-step trigonometric decomposition. Suitable for high school students in Grades 9-12.

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