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y x = ky2 1.65 b - x

y x = ky2 1.65 b - x

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Determine the coordinates (in terms of b) of the centroid of the shaded area. [Answer: x = .6b, y = .619b] Note: you will first need to find k by using a known point on the curve and plugging the x and y coordinates of that point into the x = f(y) equation.

The image features a graph illustrating a geometric shape bounded by a curve and straight lines. Here's a detailed explanation: - **Axes**: The x-axis and y-axis are labeled. The horizontal axis is denoted as "x", and the vertical axis as "y". - **Curve**: The curve is defined by the equation \( x = ky^2 \). This represents a parabolic shape opening to the right. - **Boundaries**: - The shape is bounded on the right by a vertical line at \( x = b \). - The top boundary extends horizontally from the y-axis, reaching a distance of \( 1.65b \) along the x-axis. - **Shaded Area**: The region under the curve and above the x-axis, up to the line \( x = b \), is shaded. This is the area of interest within the graph. - **Dimensions**: - Horizontal extent (base of the region): \( b \). - Vertical height at the farthest right point: \( 1.65b \). The graph visually demonstrates the relation between these variables, illustrating a specific segment of a parabola dictated by the given equation.
Transcribed Image Text:The image features a graph illustrating a geometric shape bounded by a curve and straight lines. Here's a detailed explanation: - **Axes**: The x-axis and y-axis are labeled. The horizontal axis is denoted as "x", and the vertical axis as "y". - **Curve**: The curve is defined by the equation \( x = ky^2 \). This represents a parabolic shape opening to the right. - **Boundaries**: - The shape is bounded on the right by a vertical line at \( x = b \). - The top boundary extends horizontally from the y-axis, reaching a distance of \( 1.65b \) along the x-axis. - **Shaded Area**: The region under the curve and above the x-axis, up to the line \( x = b \), is shaded. This is the area of interest within the graph. - **Dimensions**: - Horizontal extent (base of the region): \( b \). - Vertical height at the farthest right point: \( 1.65b \). The graph visually demonstrates the relation between these variables, illustrating a specific segment of a parabola dictated by the given equation.
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