A rancher has 4,648 feet of fencing available to enclose a rectangular area bordering a river. He wants to use part of the fencing to create two partitions to separate his cows, horses, and pigs by dividing the enclosure into three equal areas. No fencing is required along the river. Let x represent the length of the partitions. Complete parts a. through d. Create a function, A(x), that describes the total area of the rectangular enclosure as a function of x, where x is the length of a partition. A(x) (Simplify your answer.) b. Find the length of a partition that will yield the maximum area. The maximum area will be yielded when the length of a partition is how many feet? c. Find the length of the side of the fence parallel to the river that will yield the maximum area. The maximum area will be yielded when the length of the side of the fence parallel to the river is how many feet? d. What is the maximum area? The maximum area is?
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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A rancher has 4,648 feet of fencing available to enclose a rectangular area bordering a river. He wants to use part of the fencing to create two partitions to separate his cows, horses, and pigs by dividing the enclosure into three equal areas. No fencing is required along the river. Let x represent the length of the partitions. Complete parts a. through d. Create a function, A(x), that describes the total area of the rectangular enclosure as a function of x, where x is the length of a partition.
A(x)
(Simplify your answer.)
b. Find the length of a partition that will yield the maximum area.
The maximum area will be yielded when the length of a partition is
how many feet?
c. Find the length of the side of the fence parallel to the river that will yield the maximum area.
The maximum area will be yielded when the length of the side of the fence parallel to the river is how many feet?
d. What is the maximum area?
The maximum area is?
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