Graph your vase. You want to center the base of the vase at the origin so that it is symmetric across the x-axis, and trace half of it in the first quadrant. You need to determine the radius of the glass at regularly spaced height intervals, and generate a table of values. Be precise! Height Radius 3 units 6.5 6. 1.12. 12 8.5 15 9.5 18 10 21 9.5 24 8.5 27 Create a piecewise equation to model your vase. You may use the regression function on your calculator to determine the equation. Once you generate your equation, rotate it about the x-axis to generate a solid.
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.
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