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4m y - 4 - 1 16 72

4m y - 4 - 1 16 72

Elements Of Electromagnetics
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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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.
Transcribed Image Text: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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