Find the y-coordinate of the centroid of the sector in the figure below. Assume that R = V34 and e = 1 (0. y) R
Find the y-coordinate of the centroid of the sector in the figure below. Assume that R = V34 and e = 1 (0. y) R
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![**Problem Statement:**
Find the \( y \)-coordinate of the centroid of the sector in the figure below. Assume that \( R = \sqrt{34} \) and \( \theta = \frac{\pi}{4} \).
\( \bar{y} = \) [ ]
**Diagram Explanation:**
The diagram shows a sector of a circle with:
- The origin \((0,0)\) as its center.
- A given angle \( \theta \).
- A radius \( R \).
The sector is bounded by two radii forming an angle \( \theta = \frac{\pi}{4} \) and an arc forming the top boundary. The coordinates of the centroid are marked as \((0, \bar{y})\).
**Axes:**
- The x-axis is labeled and extends horizontally.
- The y-axis is vertical.
- The endpoint of the sector on the x-axis is marked at \( R \).
**Coloring:**
- The sector area is shaded in beige.
- The arc above the sector is outlined in blue.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F71469e61-2ae3-431f-826d-cc2a14e0ebcf%2Fcfb6f82d-164a-4c90-855a-09aa78442967%2F4c7q56c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the \( y \)-coordinate of the centroid of the sector in the figure below. Assume that \( R = \sqrt{34} \) and \( \theta = \frac{\pi}{4} \).
\( \bar{y} = \) [ ]
**Diagram Explanation:**
The diagram shows a sector of a circle with:
- The origin \((0,0)\) as its center.
- A given angle \( \theta \).
- A radius \( R \).
The sector is bounded by two radii forming an angle \( \theta = \frac{\pi}{4} \) and an arc forming the top boundary. The coordinates of the centroid are marked as \((0, \bar{y})\).
**Axes:**
- The x-axis is labeled and extends horizontally.
- The y-axis is vertical.
- The endpoint of the sector on the x-axis is marked at \( R \).
**Coloring:**
- The sector area is shaded in beige.
- The arc above the sector is outlined in blue.
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