Give a planar drawing of K2.3 with partition ({v1, v2}, {w1, W2, W3}).

Q: f (x, y) = x² + y² – 2x, D is the closed triangular region with vertices (2, 0), (0, 2), and (0, –2)

A: According to the given information, it is required to find the absolute maximum and minimum values…

Q: Find the projection of d on the plane P if a 4 and P has the equation x + y+ z = 1.

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Q: Find the value of So(4x + y)dy- xydy where C is the path around the triangle in the counterclockwise…

A: The objective is to find the value of the given integral where c is the path around the triangle in…

Q: Find the condition for the points (a, 0). (h, k){0,b) when ab = 0 to be collinear.

A: Find the condition for the given points to be collinear.

Q: 1.Find the area of the triangle in the xy-plane with vertices A(n,,n2, n2),B(m,,m2,m3),C(r,,r2, 13).

A: Please see the explanation below

Q: the distance between the two skew lines L and L2. L: x=3+3t, y=-1-4t, z=4+2t. L2: x=6+5p, y=3-p,…

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Q: Use the transformation u = y – 3x, v = y + 6x to evaluate // (2y + 12x) dA on the parallelogram R…

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Q: 6. Given a rule x2 + y2 = 9, its image rule x2 + y2 – 2x + 6y + 1 = 0 under a translation, state a…

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Q: Find midpoint M of P,P2, which joins P1(5, -7, 2) and P2(2, 5, 6), as shown in Figure 10.46 of…

A: Formula used : Mid-point formula Mx1+x22,y1+y22,z1+z22 Here (x1,y1,z1) and (x2,y2,z2) are the end…

Q: (d) [[x - y dA where R is the triangular region with vertices (3, 10), (3, 0) and (-2, 0).

A: Use double integral

Q: Sketch z =- 2cos y in R3

A: The expression y=cos(x) will give the graph of a cosine curve in the x-y plane, with the value of y…

Q: 4. Evaluate . F.ds , where C is the triangle with vertices (1,0,0), (0,2,0), and (0,0,3) oriented by…

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Q: 2. Find the images of the mapping W= z2 of the line y = 2.

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Q: ZA'B'C' is the image of LABC following the reflec- tion of ZABC across line (. If mZA'B'C'= + 20 and…

A: Given: m∠A'B'C'=x5+20, m∠ABC=x2+5 We know that when we take reflection of a triangle across any line…

Q: Use the Euler Lagrange Multiplier to find three positive integers x, y, and z that satisfy the given…

A: Solution is given below:

Q: 6. Find a plane with the P (3, – 4, 5) and contains the line L:= =*

A: It is given that plane passes through (3,-4,5) and the DR's of a given line is 2,-3,5.

Q: Find the pmf p(x) of X, the number of casts needed to obtain that first six.

A: Let x be the number of times die thrown until 6 appears. Probability that 6 appears on top is 1/6…

Q: (x² +2y) where D is the triangular region with vertices (0, 1), (1,2) and (4,1).

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Q: Find the equation of the line through P = (4, 12) such that the triangle bounded by this line and…

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Q: Evaluate // x² zdS, where S is the part of the S 1 + 4x + 3y above the rectangle plane z = [о, 2] x…

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Q: Y: The set of yellow pieces H: The set of hexagonal pieces L: The set of large pieces B: The set of…

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Q: Find the distance between the planes M: 3x – 4y + z – 17 = 0 and N: 6x – 8y + 2z + 68 = 0.

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Q: 7. If 1x, y2 are the coordinates of a point P in the xy-plane,then x is called the__________________…

A: Given that, x,y are the coordinates of a point P in the xy-plane. The objective is to fill in the…

Q: 3) Find the mZT= %3D

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Q: Compute the Jacobian of the mapping. G(r, s) = (8rs, 4r + 6s)

A: G(r,s)=(8rs,4r+6s). We need to find the jacobian.

Q: 4y² dA, D is the triangular region with vertices (0, 1), (1, 2), (4, 1)

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Q: 2. Find the image of the line y = 5x + 7 under collineation a if a((x, y)) = (2у — х, х — 2).

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Q: 1)calculate xy dxdy D where D is a parallelogram with vertices (0,0) ,(5,-1).(3, 1) and (8,0)

A: We have to evaluate the integral ∬ xy dxdy over D where D is a parallelogram. First we will sketch…

Q: Show that the points D(0, 3), E(−2, 7), and F(2, 9) are the vertices of a right triangle. mDE  =…

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Q: Consider AB in the coordinate plane below. 10 4. 2. A -10-9 -8-7 l0 1 -1 -5-4-3 -2-1 2. 4. 10 -2 -3…

A: Given: AB¯

Q: Find the distance between the planes – 3x + 5y = 32 and – 3x + 5y = 27.

A: Simply use the formula for the distance between two planes.

Q: 9. Find the angle between the two planes 2x + 3y + z = 3 and x + 3y + 2z = -3

A: Given,           2x+3y+z=3    and   x+3y+2z=-3We know that,           Suppose the two equation be…

Q: Find image of a and preimage of b T(v1, v2, v3) = (4v2 – v1, 4v1 + 5v2) v = (2, -3, -1) , w =…

A: Given, T(v1, v2 , v3 ) = (4v2 – v1 , 4v1 + 5v2) v = (2, -3, -1) , w = (3, 9)

Q: H. (7m - 48)° (3m +0)° (14n + 11)° K. Part 1 out of 2 mZG=

A: We properties of parallelogram opposite sides are equal in length opposite angles are equal sum of…

Q: Consider the sphere S given by the equation 2x² + 2y² + 2z² = 3x + 3y Use Lagrange multipliers to…

A: Solution: From P(1, 2, 2), the closest point is (0.8618, 1.309, 0.8944), and the farthest point is…

Q: Find the coordinates of the reflection without using the coordinate plane. P (4,6) over the x-axis.

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Q: 19. y² dA, D is the triangular region with vertices (0, 1), (1, 2), (4, 1)

A: 19. Given D is the triangular region with vertices (0, 1), (1, 2), (4, 1).We find the given double…

Q: Use the given transformation to evaluate the integral. (12x + 12y) dA, where R is the parallelogram…

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Q: Find the general soladtion of y+5y'=5

A: Given equation is y"+5y=5                          (1) Auxiliary equation to the homogeneous…

Q: Hw-2 If A(X, -2,0),B(-lel,=3)_, C(-4,ile2)_and D(3,0,0)are-points-in Slace thenfind value that…

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Q: 1. Determine the exact value(s) of k for which the planes x– 2y + kz + 7= 0 and x– 2y – 2 = 0 have…

A: Note: According to our answering guidelines we have to answer only one question if multiple…

Q: Find the Ker(T) and Rng(T) and their dimensions. T:R →R defined by T(x)= Ax, where 1 -1 27 -3 3 -6

A: The objective is to find ker(T) and range (T) and their dimension.

Q: Find the point of intersection for the following three planes: 3x + 4y + z + 4 =0 x + 2y + 3z +2 = 0…

A: Given Planes:

Q: If C is the square with vertices (+1, ±1) oriented counter- clockwise, then -y dx + x dy =

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Q: Find the coordinates of the point Y that lies 2. along the directed line segment from X(-1,3) to…

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Q: Give Z(G), the center of G, for G = S3 %3D

A: Definition of Center: Let G be a group. The set of all elements which commute with every other…

Q: B. If the two planes ax-4y - 9z = 4 and perpendicular. Find the value of a. x-2xy + 3z = 1 are

A: Topic = Geometry

Q: 10. If mZTSV= (6x + 17) and mSV = (15x + 13)', find mSUV. %3D T

A: A circle

Q: Find the values of w, x, y and z in fraction form using (a)Gauss Elimination, (b)Gauss-Jordan…

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Q: Given z1= j3 and z2 =(4+j2), perform the multiplication for z= z1 · 2. Then, draw the Argand diagram…

A: Since you have asked multiple questions in a single request we will be answering only first question…