Describe the set of all points that satisfy (x−1)(x−3)(x+5)=0(x−1)(x−3)(x+5)=0 if the solution set is plotted (a) in RR, the xx-axis. (b) in R2R2, the xyxy-plane. (c) in R3R3, 33-space with variables xx, yy, and zz. Explain your answer using complete sentences with correct grammar, spelling, and punctuation

Q: Identify and sketch the surfaces x2 + y2 - z2 = 4

A: Given, The surface is x2 + y2 - z2 = 4

Q: Of all the points on the graph of z = 10 - x^2 - y^2 that lie above the plane x + 2y + 3z = 0, what…

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Q: Sketch the region in the xy-plane defined by the equation or inequalities. (a) -1sys3 (b) |지 < 4 and…

A: Since we only answer up to three sub parts. We’ll answer the first three. Please resubmit the…

Q: Suppose f(x, y, z) = In(7x + 9y+7z). Find an equation for the level surface of f that passes through…

A: Given Data: The level of the curve for fx,y,z=In 7x2+9y+7z2 is of the form,…

Q: Find the equation in the xy-plane whose graph includes x In(6t) and y = t².

A: Given  x= ln(6t) y=t2

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

A: Given : The equation of the planes are x+ 2y + 6z = 1 and x + 2y + 6z = 10 .

Q: Identify and sketch the surfaces 4x2 + 4y2 + z2 = 4

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Q: What is the y-coordinate of any point in the xz-plane?

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Q: Find the maximum value of ƒ(x, y) = 6xye^(-(2x+3y) )in the closed first quadrant (includes the…

A: Given and

Q: Find the intersection of the planes r + 2y - 3z 1 and x -y+ z 1 two different

A: Given: equation of planes We need to find intersection of above two planes.

Q: Find the points on the surfaces z = V² + y? and z = 2 – x/2 having the shortest distance to the…

A: We know that the two given surfaces will intersect at some curve whose equation can be obtained by…

Q: Find the point closest to origin in R³ that is on both the planes 3x+y+z=5 and x+y+z=1.

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

Q: Identify and sketch the surfaces x2 + y2 + z2 = 4

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Q: Find the distance between the parallel planes P and P2 P: 2x-y+ 3z 6 = 0 P2: 6x - 3y+9z+ 6 = 0 8 *…

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Q: Find the intersection of the planes x + y + z = 1 and 3x − 2y +z = 5.

A: Consider two planes which are not parallel to each other and intersect. Since planes are three…

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

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Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x² + y² + z² = 1 is…

A: Let's find lowest and highest temperature by using langrange multipliers.

Q: Use LaGrange multipliers to find the points on the surface 2² = x² + y² which are closest to (4, 2,…

A: Given surface z2=x2+y2 and the point (4,2,0). The objective is to find the points on the surface…

Q: Find the distance between the parallel planes: 3x - 4y + z = 12 6x - 8y + 2z = 2

A: Given, The equation of planes  3x - 4y + z = 12 6x - 8y + 2z = 2   We have to find the distance…

Q: Find the line of intersection between the two planes x+2y-z = 5 and x-4y+z=3

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Q: Q1-)A-) Find the distance from the point (0 ,1,1) to the line of intersection of the planes : x + 2y…

A: To find the distance from the point 0,1,1 to the line of intersection of the planes:…

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 distance between these two planes x + 2y –' 2z = 3 and 2x + 4y - 4z = 7.

A: Devide the equation of 2nd plane by 2 .we get that both planes are parallel so just apply formula…

Q: Find the maximum and minimum values of f(x, y) = x² + 2y² on the quarter circle x² + y² ≤ 4 with r,…

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Q: The graphs of r +y² + 6x – 24y + 72 = 0 and x² - y' + 6x + 16y - 46 0 intersect at four points.…

A: We have to find distance from given point to intersecting points of given equation. And then add all…

Q: Describe the set of points in 3-space defined by the equations x? + y² + z2 - 8z = 9, x = 3. %3D

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Q: Q1-)A-) Find the distance from the point (0 ,1,1) to the line of intersection of the planes : x + 2y…

A: Use equation of plane

Q: 9-The distance d between the parallel planes -2x+y+z 0, 6x-3y-3z-5-0 is: a) V54 b) 54 V5 d) 3 c) e).…

A: Distance between two parallel lines

Q: Find the point closest to the origin on the line of intersection of the planes y + 2z = 12 and x + y…

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Q: Find the points that are minimum to the origin and lie on the lines of intersection of planes: y +…

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Q: Find the distance between the parallel planes P1: 2x – y + 2z +6=0 and P2:6x- 3y+6z- 18 = 0

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Q: Verify Green's Theorem for: f4y³dx-2x²dy where C, oriented anti-clockwise, is composed of the…

A: To find the integral ∮C4y3dx-2x2dy where C is the positively oriented closed curve x2+y2=9, y≥0 and…

Q: Give equations for two distinct planes whose trace in the xy-plane hasequation 4x + 3y = 8.

A: Given information: The xy-plane has equation 4x + 3y = 8. Calculation: The equation of the plane is…

Q: Find the distance between the parallel planes P1: 2x – y+2z + 6 = 0 and P2: 6x - 3y+ 6z – 18 = 0 3y…

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Q: Find the line of intersection of the planes 2x – y + z = 2 and x + 2y – 4z = 1

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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: What points in the xy-plane satisfy the equations and inequalities in Exercises 11–12? Draw a figure…

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Q: Find the maximum value of f(r, y) = 10ry(4 – 8z - 4y) over the triangle with vertices (0, 0), (,0)…

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Q: Find the distance between the planes 4x + 6y – 2z = 4 and –2x – 3y + z = -3.

A: We have to find out the distance between two planes

Q: Find the point on the graph of z = x2 + y2 + 10 nearest the plane x + 2y - z = 0.

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Q: Find the distance between the two parallel planes 2x + 4y + 12z=7 and x + 2y + 6z= 10.

A: We have to find

Q: Q:- find of the the line of interscetion plane given by 3X +6y -S2=-3 f the plane -2x + 79 -2=24

A: 3x+6y-5z+3=0 -2x+7y-z-24=0 Let z=t 3x +6y = 5t-3 -2x+7y = t+24

Q: Reduce the equation x2 − y2 + z2 − 4x − 2y − 2z + 4 = 0 to one of the canonical forms of the…

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Q: Enclosed by the cylinders z= x2 y = x 2 and the planes  z =0 y =4

A: Given: The cylinders z= x2 y = x 2 and the planes  z =0 y =4 The solid enclosed by the surfaces,

Q: Q2:Prove that the line (x-1)/2=(y+1)/3=(z-2)/(4 ) is parallel to the plane x-2y+z=6 ?

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Q: ) Let Z = 3x2 – y². Find all points at which |VZ| = 6

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: What is the center of X x² + y² – 30x + 221 = 0? Show all work for full credit.

A: Topic = Geometry

Q: Find the line of intersection of the planes x + 7y + z = 9 and x − 5y + 4z = 15

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Q: Find the point on the sphere  x2+y2+z2=7056 that is farthest from the point (5,−15,−2)

A: The given question has been solved in detail

Q: Among all the points on the graph of z = 10 - x2 - y2 that lie above the plane x + 2y + 3z = 0, find…

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