Determine the centroid (x, y) of the shaded area. The image depicts a graph on a coordinate plane, illustrating the function \( y = 4 - \frac{1}{16}x^2 \).### Description of the Graph:- **Axes:** - The **x-axis** is horizontal, and the **y-axis** is vertical. - The origin (0,0) is not labeled, but the axes intersect at the bottom left corner of the diagram.- **Function:** - The equation of the curve is given as \( y = 4 - \frac{1}{16}x^2 \). - This equation represents a downward-facing parabola.- **Bounds:** - The parabola spans from \( x = -4 \) to \( x = 4 \). - The vertex, or highest point, of the parabola is at \( (0, 4) \).- **Shaded Region:** - A region is shaded in blue beneath the curve and above the horizontal line at \( y = 0 \) from \( x = -4 \) to \( x = 4 \). - This creates a symmetric, curved region with the parabola serving as the top boundary.- **Dimensions:** - The height of the shaded region is labeled as 4 m. - The total width of the shaded region is labeled as 8 m across the x-axis from -4 to 4.### Educational Context:This diagram is useful in illustrating the concept of a parabolic curve in a real-world context, potentially for solving problems involving area under a curve or discussing the properties of quadratic functions. It visually represents how the parameters in the function \( y = a - bx^2 \) affect the shape and dimensions of a parabola.

Answered: Image /qna-images/answer/827aed52-6f6f-49c2-9b52-1bc6d5e7ae3a.jpg

Answered: 4m y - 4 - 1 16 72

Engineering

Mechanical Engineering

4m y - 4 - 1 16 72

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Free Body Diagram

The system of forces acting on a body tends to either rotate it or make the body undergo motion. In general, when an external agent exerts a force on a body, the body undergoes translational motion and rotational motion. The body has six degrees of freedom under the influence of that force. Here, three degrees of freedom are from the translational motion while the other three are from the rotation motion. However, sometimes the bodies are not allowed to undergo any motion and are fixed, under such conditions the body is said to be constrained.

Question

Determine the centroid (x, y) of the shaded area.

The image depicts a graph on a coordinate plane, illustrating the function \( y = 4 - \frac{1}{16}x^2 \).

### Description of the Graph:

- **Axes:**
- The **x-axis** is horizontal, and the **y-axis** is vertical.
- The origin (0,0) is not labeled, but the axes intersect at the bottom left corner of the diagram.

- **Function:**
- The equation of the curve is given as \( y = 4 - \frac{1}{16}x^2 \).
- This equation represents a downward-facing parabola.

- **Bounds:**
- The parabola spans from \( x = -4 \) to \( x = 4 \).
- The vertex, or highest point, of the parabola is at \( (0, 4) \).

- **Shaded Region:**
- A region is shaded in blue beneath the curve and above the horizontal line at \( y = 0 \) from \( x = -4 \) to \( x = 4 \).
- This creates a symmetric, curved region with the parabola serving as the top boundary.

- **Dimensions:**
- The height of the shaded region is labeled as 4 m.
- The total width of the shaded region is labeled as 8 m across the x-axis from -4 to 4.

### Educational Context:

This diagram is useful in illustrating the concept of a parabolic curve in a real-world context, potentially for solving problems involving area under a curve or discussing the properties of quadratic functions. It visually represents how the parameters in the function \( y = a - bx^2 \) affect the shape and dimensions of a parabola.

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