Points M(a,b) and N(c,d) are dilated by a scale factor k, with the origin as the center of dilation. Show algebraically that MN||M'N'. What are the image points of the dilation? Select all that apply. OA. M'(ka,kb) O B. N'(kc,kd) O C. M' O D. N'

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A: A gasoline tank is an oblate spheroid generated by revoluting the region boundedby graph of…

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Q: at, the graph or ind the area of the region R. d the value of A such that the vertical line al area…

A: The region is bounded by y=x , the line x=4 . The vertical line  x=k divides the region R into two…

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A: Given the curve y2=4x and the lines x=1 and x=4

Q: Ay Use the graph at the right. Find the vertices of the image of QRTW for a dilation with center…

A: The coordinates of a quadrilateral QRWT are: Q(-2,3)R(-3,1)W(2,-1)T(2,4)

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A: We have to find the area bounded by the region between x=1 to 4.

Q: 10. Consider the region R in the first quadrant bounded by the parabolas y = 4x and y 2x. %3D %3D…

A: 10. Consider the given parabolas y2=4x and y=2x2 Fins the intersection point…

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A: According to the problem, we have

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Q: Find the area of the region bounded by the curve y2= 4x and the lines x = 1 and x = 4. A 56/3 square…

A: area of the region will be obtained by taking out the definite integral of the function within given…

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A: AS per our guidelines, we are allowed to answer one question pr query, Please ask next question…

Q: A dilation centered at the origin with a scale factor of is applied to ARST. The result is AR'S 'T',…

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Q: a of the shaded region is. to four decimal places as needed.) z= -0.92 z 1.29

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A: Here we have to describe the dilation of the following figure. Now,  the coordinates of the point A,…

Q: Q1/ Sketch the region defined by <0< sos , -1 <r<1 Ans./

A: 1. Consider the given information. -π4≤θ≤π4, and -1≤r≤1

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A: Scale Factor: k=2

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A: Given that,⇒                 the median of∆PQR are PT,QU, RS⇒                 they meet at a single…

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Q: Qs/ Find the ave of the region R enclosed by the parabola x = - y²) and the line Y. X +2

A: find the shaded area

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A: Solution is here

Q: eering 1/ Find the area of the region enclosed between the curves y= 2x2+10 and y=4x+16 and ,x=-2…

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Q: Sketch the region enclosed by the given curves. x - 6y, x- 20 + y2 VAVA -3 -2 -1 2 -10 15 -25 -15…

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Q: 2 Find the area of the region bounded by the curve y2 =4x and the lines x = 1 and x = 4. A. 24…

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Q: A gasoline tank is an oblate spheroid generated by revolving the region bounded by the graph of = 1…

A: x29+y24=1We have to find the region of integration along yx29=1-y24x2=91-y24 put x=0 ,then y24=1y=±2

Q: Sketch the region enclosed by the given curves. x = 5y2, x = 16 + y? y y 3 -3 -2 -1 1 2 2 - 10 10 15…

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Q: 43 12 %1 40 9- G J. 567 8 I0 11 12 13

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Q: Find the area of the region bounded by the curve y? = x+ 1, both x and y axes, and the line a = 8.…

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Q: 12 AXYZ is dilated using a scale factor of Find the coordinates of point Xif (4, 12) 3 B 2. © (1, 3)…

A: Coordinate of X' after dilation will be calculated as following:-

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Q: Find the area of the region enclosed by the curve y=e¬5x and the lines y=1 and x=2. .e-10 + 으 10 10…

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Q: 2 Figure DEFG is dilated using a scale factor of with a center of dilation at vertex E to form…

A: Given that:

Q: Find the area of the region bounded by the curve y? = x + 1, both æ and y axes, and the line æ = 8.…

A: Double integration: The integration is defined as ∫D∫f(x,y) dA  where D is the region of integration…

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.