Find the points that are minimum to the origin and lie on the lines of intersection of planes: y + 2z = 12 and x + y = 6 %3D

Q: Find the shortest distance, d, from the point (11, 0, –6) to the plane x + y + z = 6. = p

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Q: Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated…

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Q: Find the minimum distance from the point P with coordinates (1. 2. 1) to the line r = a+Ab, where a…

A: The minimum distance from the point P(1,2,1) to the line r is the perpendicular distance between P…

Q: Find the points on the surface y2 36 + xz that are closest to the origin. (х, у, 2) (smaller…

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Q: Determine the diameter of a hole that is drilled vertically through the center of the solid bounded…

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Q: f(x, y, z) = x² + 3y² + 5z?

A: Let us assume f(x,y,z)=x2+3y2+5z2=k Assume that k≠0 x2+3y2+5z2=k Divide both sides by k,…

Q: mine an equatio

A: Here we have to find the equation of rectifying plane to We have,

Q: Find the aren of the region in the tirst quadrant baunded by the line y=27, e the line X-4, the…

A: We first sketch the region using a graphing calculator.

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 an equation for the set of points equidistant from the a. xy-plane and yz-plane. b. x-axis and…

A: a) Let (x,y,z) be such point that xy-plane and yz-plane are equidistant from it.Distance of (x,y,z)…

Q: Which of the following is the total length of the curve of intersection of the surfaces x2 + y? + 22…

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Q: Find the maximum volume of a rectangular box with faces parallel to the coordinate planes if one…

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Q: Find minimum distance from the surface x² – y? – z² = 1 (Lagrange Multipliers) to the origin.

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Q: Use Lagrange multipliers to find the points on the given surface that are closest to the origin. y2…

A: Use Lagrange multipliers to find the points on the given surface that are closest to the origin.…

Q: Describe the level curves of: (a) f(x, y) = e4x-y (b) f(x, y) = In(4x – y) (c) f(x, y) = 3x² – 4y2…

A: (a) To decribe the  level curvesf(x, y)=e4x-y = 1 , 2 , 3, 4, 5

Q: Determine the location of a point (x, y, z) that satisfies the condition y < 0

A: With the given condition there are 4 scenarios 1) x>0,y<0,z>0 2) x<0,y<0,z<0 3)…

Q: Find the minimum distance from the parabola a – y? = 0 to the point (0, 3). Minimum distance =

A: Find the distance using distance formula and then differentiate to get the minimum value equate the…

Q: Find the shortest distance, d, from the point (4, 0, –4) to the plane x + y + z = 4.

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Q: The area, in square units, bounded by the curves y = x² , y=2 – x and y=1 is ,

A: For a bounded figure, to find the area we need to determine the limits and the curves we need to…

Q: Find the minimum distance from the point to the plane x- y +z = 6. (1, -6, 2)

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Q: Find the two (x, y, z) points on the surface z² = x² + 3y² that are closest to the point (2, 2, 0)…

A: The surface is z2=x2+3y2. Obtain the distance of the point x, y, z to the point 2, 2, 0: Dx, y,…

Q: ди ди + x - Əx %| ду 0 =

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Q: Show that the minimum distance from the origin to a point on theplane ax + by + cz = d is

A: Given: ax+by+cz=d we know that minimum distance p of a point x1,y1,z1 from given equation of plane…

Q: Find the minimum distance from the point (−2, −2, 0) to the surface                     z = √(1 − 2x…

A: We have to find the minimum distance from the point (-2,-2,0) to thesurface z=1-2x-2y

Q: Determine the diameter of a hole that is drilled vertically through the center of the solid bounded…

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Q: Find the minimum distance from the point (-6, -6, 0) to the surface z = O√√559 O 3√61 09 O√773 O√69…

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Q: Graph the first-octant portion of each plane. x + y + z = 15

A: Given a Plane, x+y+z=15 We need to graph the above plane.

Q: What is the minimum vertical distance between the parabolas y = x² + x en y = x – x²?

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Q: Find the shortest distance, d, from the point (6, 0, -4) to the plane x + y + z = 4.

A: The shortest distance of a point from a plane is said to be along the line perpendicular to the…

Q: Sketch the region in the xy  -plane defined by the equation or inequalities. -1 <=y<=3

A: -1≤y≤3

Q: Find the minimum distance from the curve y = 2 to the point P(6,0)

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Q: What kind of surfaces are the level surfaces f(x, y, z) = const? f = 4x - 3y + 2z

A: As per the question we are given a trivatiate function : f(x, y, z) = 4x - 3y + 2z And we have to…

Q: Find the minimum distance from the parabola x − y2 = 0 to the point (0,3) Minimum distance =

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Q: Use Lagrange multipliers to find the points on the given surface that are closest to the origin. y2…

A: Given data:   The given expression is y2=36+xz.   The expression of the distance of a point from the…

Q: Find the distance from the x-axis to the plane z = 3.

A: Given equation of plane - z = 3z-3 = 0       ................(1)General equation of plane is given…

Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y =…

A: Consider M is the mass of the triangular plate bounded by the y-axis and both the lines. To find…

Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y =…

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Q: Determine the location of a point (x, y, z) that satisfies the condition xyz > 0

A: In four of the eight octants xyz>0 1) x>0, y<0, z<0 (2) x<0, y>0, z<0 (3)…

Q: The area bounded by the curve y = 4x and the lines r = 6 ,x = 12 and a – axis is 144 square units O…

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Q: Find the points on the surface y2 = 64 + xz that are closest to the origin. %3D (х, у, 2) 3 (smaller…

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Q: Find the minimum distance from the point to the surface z = V7 - 2x – 2y. (Hint: To simplify the…

A: We need to find the minimum distance from the point A (-2,-2,0) to the surface z = 7-2x-2y…

Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y =…

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Q: Find the point on the line y = x closest to the circle of radius 1 and center (5, 2) using Lagrange…

A: First I have find the function f(x,y) and then decide the constraint.Then using Lagrange multipliers…

Q: . Evaluate the length of the curve, y = x/2, from x = 0 to x = 4. %3D

A: first step differentiate w.r.t to x

Q: Find the absolute maximum and minimum values of f(r, y) = r-3r-y+12y, closed region D, where D is…

A: Given problem:-  Find the absolute maximum and minimum values of f(x, y) = x²-3x-y³+12y, on the…

Q: Q/ Find the points have minimum distance from the origin to the surface. xyz²=1

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Q: What is the maximum vertical distance between the line y -x = 2 and the parabola y = x? in the…

A: We have to find the maximum vertical distance between the line y-x=2 and the parabola y=x2 in the…

Q: nd the minimum distance from the point to the surface z = V7- 2x - (-2, -2, 0)

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Q: Find the minimum distance from the point to the surface z = √4 - 2x - 2y. (Hint: To simplify the…

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