4. In the diagram below, FD is parallel to GC.Which mapping of AGEC described below would justify that it is similar to AFED? 20 15 (1) a dilation by a factor of centered at E 16 (2) a dilation by a factor of centered at E F 12 (3) a dilation by a factor of centered at E G (4) a dilation by a factor of centered at E 3/44 37144t

Q: A natural cubic spline S for a function fis defined by 1+(x-2) +(*- 2)* S(x) = } la+2(x-3) +(x- 3)*…

A: for x = 3 both conditions of f(x) are true. 1+12(3-2)+12(3-2)3 = a + 2(3-3) +0-01+12+12 = a a = 2

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A: We have to find the slope

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A:

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A: here i am giving you a geometrical proof.

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A:

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Q: 8. On a graph of f(x) = x², (a) draw the tangent line to the graph of f at the point (2, f(2)); (b)…

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A: Givenf(x)=x2-9x-3+m, x≠3           mx+3k ,    x=3To check f is continuous at x=3.

Q: 11. The temperature in OF a heated bar at position x Cin cCkn) at time t Cin Seconds) is given by…

A: We will find out the required value.

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A:

Q: (C) fof 3 Find the f netions (a) fog (9) gog (b) gof A- f (x) = x² – 1 g (x) = 2x + 1 %3D 8- f(x) =…

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A:

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A: (A) To approximate the value of f'(4.5) using the given data from the table.

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A: Application of derivatives

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Q: This is very complex. I need help and would appreciate answers and help to answer this question.…

A: Given hyperbolic functions are,

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A: I am going to solve the given problem by using some simple algebra to get the required result.

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A: Given functions are f(x)=7x6+ex2-8x+1g(x)=x33-5x22+4x+2 So graph of function is

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A: Given the table is

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A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

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A: Area under the velocity-time graph is called total displacement of a particle in that time interval.

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A:

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A: Use the following formula, to obtain the cubic spline for the given data.…

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A: The given function is: f(x)=x3-x2-x+1

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.