y. y:3x- 31 to
Optimization
Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.
Integration
Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.
Application of Integration
In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.
Volume
In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).
Area
Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.
Find the x and y centroid of the shape.
![The image depicts a coordinate plane with two lines and a triangle formed by these lines and the axes.
1. **Axes**:
- The vertical axis is labeled as the y-axis.
- The horizontal axis is labeled as the x-axis.
2. **Lines**:
- The first line is labeled \(y = 3x\). This line is a straight line passing through the origin with a positive slope of 3.
- The second line is labeled \(y = -x\). This line also passes through the origin but with a negative slope of -1.
3. **Triangle**:
- The triangle is positioned in the first quadrant of the graph.
- The vertex at the origin (0,0) is where the two lines intersect.
- The top point of the triangle on the y-axis is at (0, 9').
- The bottom right point of the triangle touches the x-axis at (3', 0).
- The height of the triangle, indicated as 9', is measured on the y-axis.
- The base of the triangle, indicated as 3', is measured on the x-axis.
This setup visually demonstrates the intersection and arrangement of lines with different slopes and helps in understanding the geometric properties and dimensions of the triangle.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F69d20337-9c03-46da-b4bb-59860d913981%2Fe3f0a28a-058b-492b-945a-2dcd96813021%2Fznaqfid_processed.png&w=3840&q=75)
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