Equations are given whose graphs enclose a region. Find the area of the region. (Give an exact answer. Do not round.) f(x) = x2; g(x) + 6) * (9 + x); x = 0; x = 3 = - -1

Q: Find all x-intercepts and y-intercepts of the graph of the function. f(x) = 2x°+8x- 8x- 32

A: The given function is fx=2x3+8x2-8x-32. It is known that the y coordinate is zero for the x…

Q: Factor to find all x-intercepts of the function. 2 f(x) = x² - 2x + 1 −

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Q: 2. If the area (A) of the rectangle is (4x³ + 5x + 7) and the width (W) is (x + (Z + 4)). Find the…

A: Given the area of rectangle is (4x³+5x+7) and width is (x+6),  To find the length of rectangle in…

Q: Find the vertex of the graph. f(x) = 2x2 − 3x + 5 (x, y) =

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Q: Factor to find all x-intercepts of the function. 4 x5 f(x) = x³ - 8x¹ + 16x³

A: The given function is .The aim is to find the all intercepts of the function.

Q: Given a function and one of its factors, find the remaining factor complete factorization of the…

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Q: Solve using the method of undetermined coefficients: y" + 3y" – 10y' = 2 + xe* %3D

A: Given: y''' + 3y'' - 10y' = 2 + xex

Q: Find the domain and range of the function. f(x) = 7x² + 5

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Q: 6x r(x) = бх — б x + 2

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Q: Graph the quadratic function f that is given . f(x) = x2 + 4x − 3

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Q: Determine the x- and y-intercepts for the given function. B(x)=5x+8

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Q: and g(x) = 1,, write the composite function (fog) (x). 12 4x+3 4x+6 4x+3 x+3 4x x 31 - 3

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Q: f(x) = 5x3 +17x2 – 14x – 8

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Q: f(x) ---²-(x + 2)²-2 4

A: A quadretic function of the form f(x)=ax-h2+k  where the pair (h,k) is the vertex of the function.

Q: If a field K is algebraically closed, then every polynomiel with co efficients in k has a root in K.…

A: A field K is said to be algebraically closed if every polynomial with coefficients in K has a root…

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.