What is the center of x² + y² – 6x = -4y + 68?

Q: Find the point on the plane x+5y+2z=14 closest to the point​ (1,1,1).

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Q: Find the point on the plane x − 2y + 3z = 6 that is closest to the point (4,2,0).

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Q: Find the point on the plane x – 2y + 3z = 6 that is closest to the point (0,1,1).

A: First we find out normal vector to the given plane than find out the point that is closed to the…

Q: Find the point on the plane x – 2y + 3z = 6 that is closest to the point (0, 1, 1).

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Q: - Reduce the equation x2 + y2 - 5xy + 8x- 20y + 15 = 0 to the standard form. %3D

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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: draw the solid x² + y² +2²=2 2 = √3x² + 3√²

A: Given equation is x2+y2+z2=z → Equation of spherez=3x2+3y2→Equation of cone Use GeoGebra graphing…

Q: (4D4 - 4D3 - 3D2 - 2D + 1)y = 0

A: We have to solve the given equation.

Q: Find the trace of the plane 8x – 9y + 2z = -11 in the coordinate xz-plane.

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Q: 4x – y – z = 4 - 2х + бу +2%3D7 - 1х + у +72 %3 3

A: Given: 4x-y-z=4-2x+6y+z=7-x+y+7z=3

Q: find δƒ/δx and δƒ/δy. ƒ(x, y) = 5xy - 7x2 - y2 + 3x - 6y + 2

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Q: Find the line of intersection of the planes 3x+2y-z=7 and x-4y+2z=0.

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Q: Find the distance from the point (3,-7,-1) to the plane -x + 5y + 2z = 34.

A: Here is the solution:

Q: Find the extreme values of ƒ(x, y) = x2 + y2 - 3x - xy on the disk x2 + y2= 9.

A: We have to find the extreme values of ƒ(x, y) = x2 + y2 - 3x - xy subject to x2 + y2= 9

Q: Find the point in the plane 2x − y + 4z = 16 that is closest to the origin.

A: Given:     Plane 2x-y+4z=16 Distance of point P(x1,y1,z1) from plane Ax+By+Cz=D is…

Q: %3D by the paraboloid z 4-x2-12 =4-x- c.m. R. x +y = 4

A: Given, Solid of constant density δ bounded by R: x2+y2≤4 in plane z=0 and paraboloid z=4-x2-y2 To…

Q: Find the point on the sphere x2+y2+z²=900 that is farthest from the point (14,-5,-1).

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: Find the coordinates of the reflection without using the coordinate plane. Q(-3,5) over the y-axis.

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: perpendicukar to the plane 3x- 4y+ 2z = 7

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Q: 7. -x-y-3z = -9 z = -3x- 1 %3D x = 5y- z+ 23

A: given is x - y - 3z = -9 z = -3x-1 x = 5y -z + 23 -x-y-3z = -9 ------(1) 3x + z= - 1 --------(2) x -…

Q: find the Domair y=3+ +Vx X-3

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Q: (i) 6y" – 5y – y = 0, y(0) = 2, y'(0) = 1. %3D %3D -

A: Note: As per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Use the Disk Method Y= x^(3/2) , Y = (3/2)x , revolved around X = 5

A: First we have to design the integral using the given conditions,  and for that obtain functions of…

Q: Find all planes in R3 whose intersection with the xz-plane is theline with equation 3x + 2z = 5.

A: Find all planes in ℝ3 whose intersection with the xz-plane is the line with equation 3x + 2z = 5.

Q: oy=x²+6x+ 5 a = %3D %3D %3D

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Q: Find the point on the plane 4x+7y+8z−19=0 closest to the point (−2​,1​,3​).

A: Given,

Q: Find all planes in R^3 whose intersection with the xz-plane is the line with equation 3x + 2z = 5.

A: To find all planes in ℝ3 whose intersection with the xz-plane is the line with equation 3x + 2z = 5.…

Q: find the engle of intersection between 2x - 4y + 4z = 7 and 6x + 2y – 3z = 2 .

A: Consider the given planes: 2x-4y+4z=7So,n1→=2,-4,46x+2y-3z=2So,n2→=6,2,-3

Q: Determine the center of the sphere x2+y2+z2+8x+6y+10z=0.

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Q: What are the perpendicular generators on (D) 좋 =3 %3D2 (P) 16 2. of the surface

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Q: 1.y" + у %3D Зе2x

A: We have to solve the characteristic equation first.

Q: 5.) y = x3 + 1, y = 0, x = 1 around the a axis.

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Q: Find the point on the plane 2x + 3y + z = 7 that is nearest to​ (2,0,1).

A: NOTE: Refresh your page if you can't see any equations. . the given point is . the given plane is…

Q: Sketch the fol 2 -4y a-. b- y2 -4y 3(y - 5)2 C-

A: As per guidelines, we will solve first three subparts: a. Given equation is  y2-4y+8-4x2=0 Rewriting…

Q: y" + 3y' + 2y = 2x – 1, y(0) = 0, y' (0) = 0. %3D -

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 2x + y -4 %3D -2y + 4z = 0. 3x - 2z = –11 %3D -

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Q: Determine the x coordinate of the point on the plane Π:−3x−2y+2z=2 closest to the point (2,5,−5).

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Q: Find the point on the sphere x2 + y2 + z2 = 4 farthest from the point (1, -1, 1).

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Q: 5. x + y 10x + 8y + 16 = 0 %3D -

A: Consider the following equation of curve:…

Q: (бх - Зу +2)dk - (2xх - у -1) dy 3D0 |

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Q: The surface 2x2 -2y² – 2z² =1 is identified as

A: The given surface is qudratic surface. Different qudratic surfaces 1)Ellipsoid 2)Hyperboloid in one…

Q: Q3/ The distance between the plane 2x+4y-4z-22%-0 and the point(1,-2.2) will be ?

A: Basic 3d geometry problem

Q: Q1: - find dylax for y = 5cscx³

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Q: 2x y'' – 3y' – 10y = 7e y(0) = 1, y'(0) = - 17 - %3D %3D

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Q: esents the center. 105° (4y +14) (7y +1)° (7x +1)°

A: We can see that this is a quadrilateral which is inscribed in a circle. Such a quadrilateral is…

Q: Solve the system

A: x-2y+3z=4.......(1)2x+y-4z=3.......(2)-3x+4y-z=-2.......(3)

Q: dy Calculate y = -6x2 + 2x %3D

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Q: Let z = x + y*- 4x'y2. Find %3D

A: Find the partial derivative of the function z = x5 + y4 -4 x3 y2 z=x5+y4−4x3y2Find ∂2z∂x2 and ∂2z∂y2