What is the shortest distance from the surface ry + 15x + z2 = 204 to the origin? distance = (10,5,2)

Q: Find the distance between the point (0,0,0) and the plane 2x – y + 2z = 4

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Q: Explain why the curve of intersection of the surfaces x2 + 3y2 − 2z2 + 2y = 4 and 2x2 + 6y2 − 4z2 −…

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Q: Find the minimum distance from the point (5, 0, 0) to the paraboloid z = x2 + y2. (Give your answer…

A: Given:    z = x2 + y2  Point: ( 5, 0, 0 )

Q: Find the minimum distance from the point to the plane x-y+z=3 at (1,-3,2)

A: We will find the minimum distance from the point to the plane x-y+z=3 at (1,-3,2) in the following…

Q: There is a line through the origin that divides the region bounded by the parabola y = 6x x-axis…

A: We will find the slope

Q: Sketch the surface..........CYLINDERS.............x2 + 4z2 = 16

A: Here we have to draw the surface of cylinder having equation  x2+4z2=16

Q: Find the dimensions of the rectangular box of maximum volume that has three of its faces in the…

A: Let say that(a,b,c) is point in plane 4x+3y+z=12 and it is one vertex of requested rectanglar box.…

Q: 4. At the point (0, 0) the graph of y 4.x2 has greater curvature than does y 2x2.

A: These equation represents parabola,then Radius of curvature: K=  y'' /([1+(y')²]^3/2)

Q: 7. Sketch the surface 15zs9-x' - y² and x'+y' <1

A: To find:

Q: Find the minimum distance from the point to the plane x - y + z = 3.

A: Now, formula of shortest distance of the plane ax+by+cz=d passing through the point (l, m, n) is,

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

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Q: Find the length of the arc of the curve 9y2 = 4x3 from the origin to the point (4,). %3D

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Q: Find the minimum distance from the point (4, 0, 6) to the plane x − y + z = 3.

A: Find the minimum distance from the point (4, 0, 6) to the plane x − y + z = 3.

Q: 6. Find the area of the surface generated when y = v4x + 6 is revolved about the x- axis on the…

A: 80π

Q: Find the minimum distance from the point (8, 3, 4) to the plane x - y + z = 4. (Hint: To simplify…

A: Let ax+by+cz+d=0 is a plane  Then distance from the  a point (xo,yo,zo) is D= |axo +byo +czo…

Q: Find the distance from the point (3, -4, 2) to thea. xy-plane b. yz-plane c. xz-plane

A: The 3D view of the point is as below

Q: What is the total length of the curve of intersection of the surfaces x2 + y2 + z2 = 4 and y2 + 2z2…

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Q: Find the points on the surface xy2z3=2 that are closest to the origin.

A: Given, xy2z3=2We have to find the point on the given surface that are closest to origin.let the…

Q: A metal rain gutter is made from sheets of aluminum that are 12 inches wide by using a machine that…

A: Given that  sheets of aluminum that are 12 inches wide by using a machine that turns up the edges to…

Q: A rectangular field of fixed area is to be enclosed and divided into five lots by parallel to one of…

A: To find the dimensions to obtain minimum fencing

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

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Q: Calculate the point on the surface z =1 - x2 - y2 that has a maximum value for the sum of its…

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Q: Find the minimum distance from point (2, 5, -1) and plane 3x + 4y + z = 10.

A: Given query is to find the minimum distance.

Q: Find the minimum distance from the point to the plane x - y + z = 9. (Hint: To simplify the…

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Q: Find the minimum distance from the point to the plane x - y + z = 6. (Hint: To simplify the…

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Q: 5. What is the maximum vertical distance between the line v1+2 and the parabolh v for

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Q: Find the minimum distance from the point (2, –6, 6) to the plane 2x - y + z = 0.

A: NOTE:- the distance between a plane say px+qy+r z +s=0 and a point say u, v, w is d= p u+q v+r…

Q: Find the distance between the point (0,0,0) and the plane 2x – y + 2z = 4.

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Q: Sketch the surface x = 2y2 +3z2

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

A: To find the minimum distance from the point (6,1,6) to plane x - y + z = 6. By using formula,…

Q: A point moves such that the ratio of its distances from two fixed point is constant, show that its…

A: Let the moving point be P (x, y, z). Let A(a, 0, 0) and B(-a, 0, 0) be two fixed points.

Q: Describe the traces of the curve x2 + 9z2 = 9 in the vertical planes (those parallel to the…

A: The traces of a surface are the cross-sections created when the surface intersects a plane parallel…

Q: What is the distance between the point (4,-&, 1) and the plane 5x-z= 2y+5?

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Q: A piece of wire of length 1 meter is cut into two parts, one of which is bent into the shape of a…

A: A piece of wire of length 1 meter is cut into two parts , one of which is bent the shape of a circle…

Q: Determine the shortest distance from the surface xy+3x+z2=12 to the origin.

A: Given surface equation is

Q: A hydro-company wants to lay cables between sites A, B, and C. If they are drawn on a map xy -plane,…

A: consider the provided question, In your question mention the point B and C are same, which is (0,3).…

Q: There is a line through the origin that divides the region bounded by the parabola y=8x−4x2y=8x-4x2…

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Q: Find the minimum distance from the point (2, 1, 9) to the surface x + y + z = 9.

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Q: Find the minimum distance from the point (0,0,0) to the plane 9x+4y+z=5.

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Q: What is the shortest distance from the surface xy+3x+z^2=12 to the origin?

A: Let (x ,y, z) any point on surface. We have to minimize function f(x,y,z) = x2 + y2 + z2 under…

Q: Find the area of on of the triangle that can drawn between the planes Зх — бу- 2г 15 and 2x + y - 2z…

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Q: Show that the surfaces S1 : 4x + y° + 9z² = 108 and S2 : xyz = 36 are tangent at the point (3, 6,…

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Q: Calculate the point on the surface z =1 - x2 - y2 that has a maximum value for the sum of its…

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Q: Sketch the surfaces ASSORTED 16y2 + 9z2 = 4x2

A: Solution:- We have to  Sketch the surfaces ASSORTED 16y2 + 9z2 = 4x2

Q: Find the minimum distance from the surface x2 -y2 -z2= 1 to the origin.

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Q: Sketch the graph of -x + 9y² – 4z² = 36 and identify the surface. %3D

A: Given a function in terms of x, y and z. Here x and y are independent variables and z is a dependent…

Q: What is the surface generated by a straight line which moves along a fixed curve, and which remains…

A: To determine the name of the surface generated by a straight line which moves along a fixed curve,…

Q: 1 Find the points have minimum distance From the origih to the Surface xyz =1.

A: Using the lagrangian ultiplies Let For critical points,

Q: Find the length of the arc of the curve 9y2 = 4x³ from the origin to the point (4, ). %3D

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Q: Find the minimum distance from the cone z= to the point (6, 6, 0).

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