### Tutorial Exercise Sketch the region bounded by the curves, and visually estimate the location of the centroid. Then find the exact coordinates of the centroid. \[ y = 4 - x^2 \] \[ y = 0 \] ### Step 1 Since the region is symmetric about the y-axis, we know that \( \bar{x} \) = ____. #### Diagram Explanation: The diagram displays a graph of the curves \( y = 4 - x^2 \) and \( y = 0 \). The shaded region represents the area bounded by these curves. - The graph of \( y = 4 - x^2 \) is a downward-opening parabola with its vertex at the point (0, 4). - The parabola intersects the x-axis at points \( x = -2 \) and \( x = 2 \), completing the boundary of the shaded region. - The \( y = 0 \) curve is the x-axis, serving as the lower boundary for the shaded region between \( x = -2 \) and \( x = 2 \). The curve forms a symmetric shape about the y-axis.
### Tutorial Exercise Sketch the region bounded by the curves, and visually estimate the location of the centroid. Then find the exact coordinates of the centroid. \[ y = 4 - x^2 \] \[ y = 0 \] ### Step 1 Since the region is symmetric about the y-axis, we know that \( \bar{x} \) = ____. #### Diagram Explanation: The diagram displays a graph of the curves \( y = 4 - x^2 \) and \( y = 0 \). The shaded region represents the area bounded by these curves. - The graph of \( y = 4 - x^2 \) is a downward-opening parabola with its vertex at the point (0, 4). - The parabola intersects the x-axis at points \( x = -2 \) and \( x = 2 \), completing the boundary of the shaded region. - The \( y = 0 \) curve is the x-axis, serving as the lower boundary for the shaded region between \( x = -2 \) and \( x = 2 \). The curve forms a symmetric shape about the y-axis.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Tutorial Exercise
Sketch the region bounded by the curves, and visually estimate the location of the centroid. Then find the exact coordinates of the centroid.
\[ y = 4 - x^2 \]
\[ y = 0 \]
### Step 1
Since the region is symmetric about the y-axis, we know that \( \bar{x} \) = ____.
#### Diagram Explanation:
The diagram displays a graph of the curves \( y = 4 - x^2 \) and \( y = 0 \). The shaded region represents the area bounded by these curves.
- The graph of \( y = 4 - x^2 \) is a downward-opening parabola with its vertex at the point (0, 4).
- The parabola intersects the x-axis at points \( x = -2 \) and \( x = 2 \), completing the boundary of the shaded region.
- The \( y = 0 \) curve is the x-axis, serving as the lower boundary for the shaded region between \( x = -2 \) and \( x = 2 \).
The curve forms a symmetric shape about the y-axis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcc840c2e-3c91-4264-9dad-5574b6dda8ed%2F9e0a92be-58db-4c0f-bdd0-3738c9339a5d%2Fmtsd2ui_processed.png&w=3840&q=75)
Transcribed Image Text:### Tutorial Exercise
Sketch the region bounded by the curves, and visually estimate the location of the centroid. Then find the exact coordinates of the centroid.
\[ y = 4 - x^2 \]
\[ y = 0 \]
### Step 1
Since the region is symmetric about the y-axis, we know that \( \bar{x} \) = ____.
#### Diagram Explanation:
The diagram displays a graph of the curves \( y = 4 - x^2 \) and \( y = 0 \). The shaded region represents the area bounded by these curves.
- The graph of \( y = 4 - x^2 \) is a downward-opening parabola with its vertex at the point (0, 4).
- The parabola intersects the x-axis at points \( x = -2 \) and \( x = 2 \), completing the boundary of the shaded region.
- The \( y = 0 \) curve is the x-axis, serving as the lower boundary for the shaded region between \( x = -2 \) and \( x = 2 \).
The curve forms a symmetric shape about the y-axis.
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