Write the coordinates of the vertices after a translation 8 units right. 101r K -10 10 -10 J(-6, -6) → J'( K(-6, 4) → K'( L(-5, 4) → L'( M(-5, -6) → M'(

Q: 3. [For students with ID # ending in 4 or 5.] Through the point (4, 2, -5) and perpendicular to the…

A: Given, through the point (4, 2, -5) and perpendicular to the plane…

Q: 5. Square JKLM with vertices J(-3, 5), K(0, 8). L(3, 5), and M(0, 2); 90° clockwise about P(-4, 0)…

A: If the point (-y,x) rotate 90 degrees clockwise about the point (a,b), then the coordinates of the…

Q: 5) s how that the line af intersection f the Planes X+24-22= 5 and 5x-2y-73D0 is Parallel to theline…

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Q: 1. The plane containing the point (1,-5,8) and orthogonal to the line given b x=-3+15t, y=14-t,…

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Q: Two lines have equations L1: (0,0,1) + s(1,-1,1), s e R and L,: (2,1,3) + (2, 1,0), e R. 10. What is…

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Q: Determine the intersection of 3x – 4y – 5z = 0 with [x, y, z] = [3, 1, 1] + t [2, -1, 2].

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Q: 14. The plane passes through (2, 2, 1) and (-1, 1, -1) and is perpendicular to the plane 2x-3y+z=3.

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: For 3 and 4given the translation rule: T(x,y) (x+2,y-3)

A: Find the image of (5,-1) and preimage of (-6,7)

Q: What kind of conic section is given by the quadratic form ? -11x,2 + 84x,x2 + 24x,2 = 156 Transform…

A: Given Quadratic Equation is, -11x12+84x1x2+24x22=156 Matrix Representation form is, A=-11424224 Find…

Q: Which of the given points are the points on the hyperboloid x2-y?+4z2 = 4 where the normal line is…

A: Solution is in step 2

Q: Graph the image of AUVW after the following glide reflection: Translation (x, y) ► (x - 15, y)…

A: We first find the coordinates of U,V and W U=(3,6), V=(6,3), W=(12,6) Then we apply (x,y)→(x-15,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: 49. The line through the point t (0, 1, 1) that is orthogonal to both (0, -1, 3) and (2, –1, 2).

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Q: L' M' Which describes how the transformation affects the coordinates of the vertices of trapezoid…

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Q: 45. Find the distance from the plane x + 2y + 6z = 1 to the plane x + 2y + 6z = 10.

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Q: Find the work done by the Öeld F = yzi + (xz + 3)j + xyk along the line joining the point A(1, 2, 0)…

A: Given field is,  F = yz i^ + xz+3 j^ + xy k^   The given points is A(1, 2, 0) and B(2, 0, 3). So,…

Q: Find the linearization L(z, y, z) of the f(x, y, z) = 2,/z° + y° + z° at the point (1, 2, 3). %3D…

A: Consider the provided function, fx,y,z=2x3+y3+z3 At the point 1,2,3 find the linearization. The…

Q: 11. Determine whether the lines L₁ given by x=t, y = 1+ 2t, z = 2 + 3t, (with x < t < oo) and L₂…

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Q: 39. The plane that passes through the point (1, 5, 1) and is perpendicular to the planes 2x +y - 2z…

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Q: 3. When origin is shifted to (3,4) by translation of axes, find the transformed equation of 2x² +…

A: We have to solve given problems:

Q: 4 and the plane Find the point on the curve of intersection of the paraboloid x- + y- x - y + 2z = 0…

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Q: 12) Find the intersection of the plane: x – z = 6, and the line r(t) = (1,0, -,1) + t(4,9,2)

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Q: A point moves in the (x, y) plane on the line 2x+ 3y −4 = 0. Where will it be when the sum of the…

A: We have to find a point from where the sum of square of its distances from 1,0 and -1,0 is smallest.

Q: 10. The distance between the point (3,-2,5) and the plane 2x+2y+z=5 is NONE

A: Given: The distance between (3,-2,5) and the plane 2x+2y+z=5

Q: with the guldin's proposition 1 get the contents of the rotating object that occurs if the land…

A: As per the question we are given a 2d region bounded by the curve : y = 6 - 3x - x2 and the straight…

Q: Graph the image of AUVW after the following glide reflection: Translation (x, y) (x- 15, y)…

A: Given: The △UVW has done two transformations 1) x,y→x-15,y 2) Reflection across x-axis

Q: 2. Trapezoid QRST with vertices Q(3. 1), R(5, 2), S(10, 0), and T(4, -3); 270° counterclockwise…

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Q: (10) Find the distance of (3,-1,2) from each of the following: a) line: x = 1+ 2t, y = -t, z = 1-t…

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Q: 1. 2. The area bounded by y = = -(x - 1)² + 4 , and the lines x =1, y = 2, and y = 4 rotated about…

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Q: 4. Find an equation for the plane in R spanned by the points (1, 5, 1) and (1,4, 2).

A: Given v1 = (1 , 5 , 1)v2 = (1 , 4 , 2) Let xyz be a point in spanv1 , v2 , so there exist m , n…

Q: Z is a complex variable, z=x+iy

A: The z is complex variable with z = x + i y , and the given vertices are (0,0),(1,0),(1,1) and (0,1).

Q: find the pole and resuidue of 3z + 1 (z + 1)(2z – 1)

A: Poles and residue of the given function are given below ;

Q: 2. Let C be the closed path constructed by joining the segment [-2, 2] on the real axis with y(t) =…

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Q: 5. Find a plane through the points P(1,2, 3), P2(3, 2, 1) and perpendicu- lar to the plane 4x – y+…

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Q: Plot the points on the same three-dimensional coordinate system. (a) (3, 4, 1) (b) (-2, 3, 7) 10. O…

A: Given Data: Plot the points on the same three dimensional coordinate system. (a) (3,4,1) (b)…

Q: -6 3 Let y = -5 and u = -4 -2 Compute the distance d from 3y to the line through u and the origin.

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Q: 8) Rectangle GHJK with vertices G(2,3), H(2, 5), J(6, 5) and K(6, 3) is rotated 180° about the…

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Q: -4 -8 Let y = 9 and u = -2 -8 7 Compute the distance d from y to the line through u and the origin.…

A: I have appended the formula used in the solution part of the question

Q: 9. The line through (0,-7, 0) perpendicular to the plane x + 2y + 2z = 13

A: Given point is (0,-7,0) and plane equation is x+2y+2z=13 here we have to find the parametric…

Q: 2. 22 – x2 1 By sketching the traces on the ry-, rz- and yz-plane a.

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Q: 2. Thàngle LMN with vertices L(6, 6), M(8, 8), and N(8, 3): a) reflection in the linex = 5 b) 270°…

A: As per our guidelines we are supposed to answer only one question. Please repost another question as…

Q: In Exs. 19-24, find the points of in tersection and trace the curves. 19. z 3y, 3z +- y-24y +36 = 0.…

A: we have given two equations of circle and ellipsex2+y2-4ax =0…

Q: The equation of the plane that passes by P(-1, 2, 1) and that is perpendicular to the line x - 3 1-…

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Q: -:Q1 Evaluate , (x- 2y) dA, where R is the parallelogram in the xy-plane with vertices (0,0), (4,1),…

A: The objective is to evaluate ∫∫Rx-2ydA where R is the parallelogram in the xy plane with vertices…

Q: Build a computation graph for Z = 2 (X *Y) – Max (S, 0) and calculate forward/backward pass. when X…

A: Solution Given  Z = 2 (X *Y) – Max (S, 0) ,when X = 3, Y= 2, S = -1  we need to build a computation…

Q: Find the linearization L(x, y, z) of the f (x, y, z) = 2/³ + y³ + z³ at the point (1, 2, 3 Answer:…

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Q: (5) Let 8. u = 6. --(:)- and y = 1 What is the orthogonal projection of y to the line through u and…

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Q: 1. F = [2², -x², 0], S the rectangle with vertices (0, 0, 0), (1, 0, 0), (0, 4, 4), (1, 4, 4)

A: As given that,  F→=z2i^-x2j^+0k^ Calculating curl F,…