Locate the centroid x¯ of the shaded area. **Consider the area shown in (Figure 1). Suppose that \( a = 9 \, \text{m} \), \( k = \frac{1}{9} \, \text{m}^{-1} \).**Figure Explanation:**The figure displays a shaded region in the first quadrant of the \(xy\)-plane. The area is bounded by the following components:- **Horizontal Axis (x-axis):** Extends from \(x = 0\) to \(x = a\).- **Vertical Axis (y-axis):** Extends from \(y = 0\) upwards.- **Vertical Line:** \(x = a\), parallel to the \(y\)-axis.- **Curve:** The curve is described by the equation \(y = kx^2\), and it starts at the origin \((0, 0)\) and curves upwards passing through the point \((a, a)\).The shaded region, which resembles a quarter of a parabola, is contained within these boundaries. The curve is a segment of the parabola described by the given equation, and the limits define a square area with side \(a\).

Given: a=9 mk=19 1m Equation of parabolic curvey=kx2 Substitute value of k in the above equation,…

Answered: Locate the centroid x¯ of the shaded…

Engineering

Civil Engineering

Locate the centroid x¯ of the shaded area.

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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Concept explainers

Length and Length related Variables

Length can de defined as the measurement or extent of physical quantities or objects from one terminal to another terminal. Stone age humans used finger length, step length, and so on to measure the size or displacement of an object. Nowadays, depending on how precise the measurement requires to be and the object’s size is measured, we use measuring devices for measurements like rulers and steel tape. Most people have used a ruler or tape measure to measure a particular distance or the size of an object. For more precise measurements of tiny objects, the development of measurement tools such as the Vernier caliper, which permits us to measure dimensions within 1/1000 of an inch. In the last few decades, electronic distance measuring instruments (EDMI) have been implemented that permit us to measure distances from a few feet to many miles with reasonable accuracy.

Question

Locate the centroid x¯ of the shaded area.

**Consider the area shown in (Figure 1). Suppose that \( a = 9 \, \text{m} \), \( k = \frac{1}{9} \, \text{m}^{-1} \).

**Figure Explanation:**

The figure displays a shaded region in the first quadrant of the \(xy\)-plane. The area is bounded by the following components:

- **Horizontal Axis (x-axis):** Extends from \(x = 0\) to \(x = a\).
- **Vertical Axis (y-axis):** Extends from \(y = 0\) upwards.
- **Vertical Line:** \(x = a\), parallel to the \(y\)-axis.
- **Curve:** The curve is described by the equation \(y = kx^2\), and it starts at the origin \((0, 0)\) and curves upwards passing through the point \((a, a)\).

The shaded region, which resembles a quarter of a parabola, is contained within these boundaries. The curve is a segment of the parabola described by the given equation, and the limits define a square area with side \(a\).

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