Find the points on the cone z + y that are closest to the point (2, 2, 0). (x, y, z) = (smaller z-value) (x, y, z) = Carger z-value)

Q: The surface z=f(x,y) intersects the plane x-2 along the curve C which has equation of dy Find at the…

A: Given Data: The equation of the curve is: z=13y3-y2 The point at which derivative is required is: x,…

Q: A point moves along the intersection of the elliptic paraboloid z = 10x + 11y and the plane y = 1.…

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Q: Use Lagrange multipliers to find the points on the cone z2 = x2 + y2 that are closest to (8, 2, 0)…

A: Given: Equation of the cone: z2 = x2 + y2 Given point: (8, 2, 0)   To find: The points on the cone…

Q: Find the lateral (side) surface area of the cone generated by revolving the line segment y =x,…

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Q: Compute the area of the portion of the cone x2 +y = z2 with z z 0 that is inside the sphere x y z…

A: Given the area of the cone is x2+y2 = z2 and the sphere is x2+y2+z2 = 2Rz.

Q: Find the surface area cut from the cone 2x2 + 2y2 = 5z2, z > 0, by the cylinder x2 + y2 = 2y

A: To find the surface area cut from the cone 2x2 + 2y2 = 5z2, z > 0, by the cylinder x2 + y2 = 2y

Q: Find the angle between the planes 3x – 2y + z + 4 = 0 and x + 4y – 3z – 3 = 0. Express your answers…

A: The angle between two planes is equal to the angle between their normals.

Q: 4. Find the volume of the wedge cut from the first octant by the cylinder z = 12 - 3y2, and the…

A: We have to find volume.

Q: The tangent plane and the normal line of the surface y = x² + z – 6 at the point (2, -1, 1) have the…

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Q: Use Lagrange multipliers to find the highest point on the curve of intersection of the surfaces.…

A: Use Lagrange multiplies we find heighest point on the curve ofintersection of the surface cone:…

Q: Find the volumes of the regions. The wedge cut from the cylinder x2 + y2 = 1 by the planes z = -y…

A: Given Data The equation of a cylinder is x2+y2=1. z=-yz=0   Determine the interval of x and y,…

Q: A solid is formed by revolving about the y-axis, the area bounded by the curve x^3=y, the y-axis,…

A: Solution :-

Q: . The solid bounded by z = 1 – x², z = 5 – 2x², y = 0, and y – z = 6. |

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Q: under the cone Z =Vx²+y² and above the region bounded by the semicircle X=-V 4-y and the y-axis.

A: The circle and a cone is given as,

Q: Find a formula for a functionf(x, y, z) whose level surface f= 3 is a cylinder of radius 5 centered…

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Q: 3. Calculate the centroid of the given illustration below. y-axis 7.5ft- 4ft 2ft 5ft- х-ахis 2ft

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Q: The diagram shows a small block B, of mass 0.2kg, and a particle P, of mass 0.5kg, which are…

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Q: the voulme of the region are  bounded by the paraboloid x= y^2+z^2 and the half cone x=…

A: The volume of the region bounded by the paraboloid x= y2+z2 and the half cone x= 8y2+z2

Q: A region R consists of a square bounded by the lines x = -1, x = 1, y = 0, and y = -2 and a half…

A: The given region is as follows: The area of region is  A=∬RdA  =Area of semi-circle of radius…

Q: (2) The distance from the point (1, 2, -1) to the plane 3x - y + 2z = 6 is. (3) Consider the…

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Q: Find the lateral (side) surface area of the cone generated by revolving the line segment y = x/2, 0…

A: The given line segment is y=x2 where 0≤x≤4. The line segment is revolved around x-axis, thus it…

Q: Find all points on the isometric dot plane, Ax,1 yl, with x and y integers, that are ex- actly V133…

A: a)The distance from origin to point x,y is 133. b)The distance from origin to point x,y is 217.

Q: A point moves along the intersection of the elliptic paraboloid z = 9x + 7y and the planex = 1. At…

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Q: The base of a solid is bounded by y= x² and y= 4. All parallel cross – sections are squares…

A: Please rate

Q: 9-x²-y² is the upper √y half of the disc centered at origin with radius r = 3 The domain of f(x, y):…

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Q: endicular to the plane z + 3y – x = 7 and containing the points (2, 5, 0) and (0, 2, -1)

A: Here we have to find the equation of plane which is perpendicular to the other plane.

Q: The region is bounded by the curves y = x² and y = 4x - x² and is rotated about the line X = 4. %3D…

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

A: Given problem is :

Q: A solid is obtained by rotating the shaded region about the specified line. about the line y = 5 y x…

A: NOTE: Refresh your page if you can't see any equations. . given functions are

Q: Find the points on the cone z = x + y2 that are closest to the point (8, 2, 0). %3D (x, y, z) =…

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Q: Use Lagrange multipliers to find the highest point on the curve of intersection of the surfaces.…

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Q: 2 What Is the equatlon of the clrcle with a radius of 5 and center at (2, 3)? F (x + 2)2 + (y + 3)2…

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Q: Find the average z-coordinate of points in a hemisphere of radius 8 centered at the origin with its…

A: We have to find the average z coordinate of the hemisphere of radius 8 centered at origin with base…

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: The area of the region inside the cirde Y = 6 cose and outside the Cardiaid V= 2(1+ Cose) ayo is + 4…

A: Let us consider the curve r=f(θ) The area under the curve is obtained by bounded region is…

Q: How would I go about solving ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2…

A: We will find out the limits first.

Q: By using the cylindrical coordinates to evaluate {{[3dV where Q bounded by paraboloid 2=2- x2 - y2…

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Q: Show that the area of the plane region bounded by the curves,  x=y^2 -1,  x= 1 - y^2  is 8/3 square…

A: Given equation of cyrves, x=f(y)=y2-1,x=g(y)=1-y2

Q: Region Ris enclosed by the curve y = 2 Vx – 3, the line y = 4, and the line a = 3. y = 2/z – 3 y = 4…

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Q: Find the area of the surface. The part of the plane z = 4 + 3x + 2y that lies above the rectangle…

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Q: Calculate the volume under the elliptic paraboloid z=3x2+7y2 and over the rectangle R=[−2,2]×[−4,4

A: Explanation: We know that,  Volume =∬zdydx By using the double integral concept, the volume of the…

Q: Find the surface area of the part of the plane 3x + 3y+ z = 9 that lies above the triangle formed by…

A: In the question we have to find the surface area of the plane.

Q: Find the area of the surface. The part of the plane z = 7+ 2x + 3y that lies above the rectangle [0,…

A: We have to find the area of the surface of the given problem.

Q: Consider the region in the first quadrant bounded by y=x^2, the y-axis, and y=4. -the y-axis using…

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Q: Use Lagrange multipliers to find the minimum distance from the curve or surface Cone: z = √x2 + y2…

A: The surface of the cone               z=x2+y2 or z2-x2-y2=0                                (1)…

Q: The region in the first octant bounded by the coordinate planes, the plane y + z = 2, and the…

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