Consider the area shown in graph. Suppose that a=4 m, b=6 m, and k=3/8 m^-1. Locate the centroid y of the shaded area.
Consider the area shown in graph. Suppose that a=4 m, b=6 m, and k=3/8 m^-1. Locate the centroid y of the shaded area.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Consider the area shown in graph. Suppose that a=4 m, b=6 m, and k=3/8 m^-1.
Locate the centroid y of the shaded area.
Transcribed Image Text:### Locating the Centroid of a Shaded Area
In this exercise, you are tasked with locating the centroid \( \bar{y} \) of a shaded area.
#### Instructions:
1. **Express your answer** to three significant figures and include the appropriate units.
2. Use the input box provided:
- **Enter the value** of \( \bar{y} \) in the "Value" field.
- **Enter the units** in the "Units" field.
#### Example of Input Fields:
- **\( \bar{y} = \)**
Value | Units
------|------
- Click the **Submit** button to finalize your answer.
- If you need to **request the answer**, use the "Request Answer" button.
#### Available Tools:
- You can use the special character input tool, depicted by icons showing common mathematical symbols and text formatting commands, to assist in entering your information accurately.
#### Tips:
- Double-check your calculations to ensure precision.
- Make sure to include the correct units, as they are crucial for a complete answer.
> Note: Incorrect entries or missing units may result in the answer being marked as incorrect.
Use the diagram, tools, and instructions to accurately determine the centroid of the shaded area.
![### Area Under a Parabola
The image presents a shaded region representing the area under a parabolic curve. The Cartesian coordinate system is used, with the x-axis and y-axis perpendicular to each other.
#### Diagram Explanation
The diagram displays the following key elements:
1. **Axes**:
- The horizontal axis is labeled as the \( x \)-axis.
- The vertical axis is labeled as the \( y \)-axis.
2. **Parabolic Curve**:
- The equation of the curve is given by \( y = kx^2 \). This represents a parabolic function, where \( k \) is a constant.
3. **Dimensions**:
- The distance along the \( x \)-axis from the origin to the end of the shaded region is denoted by \( a \).
- The distance along the \( y \)-axis from the origin to the height of the shaded region is denoted by \( b \).
#### Purpose of the Diagram
- **Illustrate the Area**: The shaded region represents the area under the curve \( y = kx^2 \), from \( x = 0 \) to \( x = a \).
- **Parameters**:
- \( a \): The length along the \( x \)-axis.
- \( b \): The maximum height of the parabola within the interval \([0, a]\).
This diagram is useful for explaining concepts such as integrations to find the area under curves, the properties of parabolic functions, and the relationship between the variables in the quadratic equation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5838e840-08d6-4f9e-8368-3d89f35487e5%2F2ae8c388-73ab-44ca-96fd-d479008cb702%2F06uv5u_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Area Under a Parabola
The image presents a shaded region representing the area under a parabolic curve. The Cartesian coordinate system is used, with the x-axis and y-axis perpendicular to each other.
#### Diagram Explanation
The diagram displays the following key elements:
1. **Axes**:
- The horizontal axis is labeled as the \( x \)-axis.
- The vertical axis is labeled as the \( y \)-axis.
2. **Parabolic Curve**:
- The equation of the curve is given by \( y = kx^2 \). This represents a parabolic function, where \( k \) is a constant.
3. **Dimensions**:
- The distance along the \( x \)-axis from the origin to the end of the shaded region is denoted by \( a \).
- The distance along the \( y \)-axis from the origin to the height of the shaded region is denoted by \( b \).
#### Purpose of the Diagram
- **Illustrate the Area**: The shaded region represents the area under the curve \( y = kx^2 \), from \( x = 0 \) to \( x = a \).
- **Parameters**:
- \( a \): The length along the \( x \)-axis.
- \( b \): The maximum height of the parabola within the interval \([0, a]\).
This diagram is useful for explaining concepts such as integrations to find the area under curves, the properties of parabolic functions, and the relationship between the variables in the quadratic equation.
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