Enclosing a Rectangular Field Beth has 3000 feet of fencingavailable to enclose a rectangular field.(a) Express the area A of the rectangle as a function of x,where x is the length of the rectangle.(b) For what value of x is the area largest?(c) What is the maximum area?

Q: David has available 480 yards of fencing and wishes to enclose a rectangular area. (a) Express the…

A: Given:

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A: a).

Q: Beth has 3000 feet of fencing available to enclose a rectangular field.(a) Express the area A of the…

A: It is given that Beth has 3000 feet of fencing available to enclose a rectangular field. Let the…

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A:

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Q: The absolute maximum of the function f(x) = 3x2 + 3x + 14 over [1, 7].

A: We first find the critical points using the f'(x)=0 f(x)=3x2+3x+14f'(x)=6x+30=6x+36x=-3x=-36x=-0.5

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A: David has 400 yards of fencing and he wishes to enclose a rectangular area.

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Q: Optimizati a) If a and b are positive numbers, find the maximum value of f(x)=x"(1–x)°, 0<xs1.

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A: Here we have,  differentiate with respect to x

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A: The given function is f(x)=x8ex, x&gt;0

Q: absolute maximum and minimum

A: We have the given function : f(x)=xe-x2…

Q: Question attached in PICTURE

A: Consider the give statement: "A function of two variables with at least two points of local minimum…

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A: (a) First of all, consider the formula for the surface area of the rectangle as fencing area is…

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A: Given that a rain gutter is formed by bending up the sides of a 42 in. wide rectangular metal sheet.

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A: We have to check

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Q: The absolute maximum of the function f(x) = 3x² + 3x + 12 over [1, 6].

A: f(x)=3x2+3x+12    over  1,6firstly, we have to find critical pointsf'(x)=6x+3=0⇒6x=-3   ⇒x=-36=-12

Q: A rain gutter is formed by bending up the sides of a 52-in.-wide rectangular metal sheet as shown in…

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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.