Find the orthogonal trajectories of the conicoid (x + y)z = 1 of the conics in which it is cut by the system of the plane x − y + z = K where K is a parameters

Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 4x + 8y + 12z on the elipse…

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Q: A fluid has density 1200 kg/m3 and flows with velocity ī measured in meters, and the components of ū…

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Q: Find the centroid of the “triangular” region bounded by the lines x = 2, y = 2 and the hyperbola xy…

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Q: Compute the flux of F = 3(x + z)i +j+ 3zk through the surface S given by y = x2 + z2, with 0 0, z 2…

A: flux is determined as shown below

Q: Let L denote the intersection line between the planes 2x-y-3z=4 and 2x+y-z=2 A) Determine a…

A: Solution of the system of equation will give the equation of the line of intersection.

Q: Find the flow of F=xzi-yk through the upper part of plane z-1 in the x +y² +z = 4sphere. %3D

A: The general form of a vector-valued function in three dimensions is given by F=F1i+F2j+F3k, where…

Q: Determine the centroid bounded by the parabolas x=y^2 and x^2=-8y

A: Consider the given curves. x2=-8yx=y2

Q: Let G be the wedge in the first octant that is cut from the cylindrical solid y2 + z2 ≤ 4 by the…

A: In the first octant, all the coordinates are positive, i.e. x≥0, y≥0, z≥0. So we will take all the…

Q: A fluid has density 1000 kg/m³ and flows with velocity = ci +yj + zk, where x, y, and z are measured…

A: We have to find the rate flow outward through the part of paraboloid . We can to use the methods of…

Q: Determine the x-component (m) of the centroid of the given figure if the cut portion is a semicircle…

A: Given, a=39 m, b=16 m and c=2 m To find the x-component of the centroid of the given figure.

Q: 2. Calculate the centroid of the thin plate R which bounded by a = 1, y = 0 and, x² + y² = 4.

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Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 6x + 12y + 18z on the elipse…

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Q: Find the average height of the hemispherical surface z = sqrt(a2 - x2 - y2 )above the disk x2 + y2…

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Q: Given the curve y = x´ and the line y =2- x Find the ordinate of the centroid of the region bounded…

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Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 4x+ 8y + 12z on the elipse…

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Q: Find a parametrization of the cylinder x2 + ( y - 3)2 = 9, 0 ≤z ≤ 5.

A: Given, the cylinder                         We have to find a parameterization of this given…

Q: 5.Consider the ellipsoid V(x,y,z)=rx2+σy2+σ(z−2r)2=c>0.Vx,y,z=rx2+σy2+σz−2r2=c>0.…

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Q: IntegrateF(x, y, z) = z, over the portion of the plane x + y + z = 4 that lies above the square…

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Q: A solid cube, 2 units on a side, is bounded by the planes x = +-1, z = +-1, y = 3, and y = 5. Find…

A: Given:

Q: Find the centroid of the region in the plane enclosed by the curves y = +-(1 - x2)^(-1/2) and the…

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Q: A: Determine the mass and center of mass of the solid that bounded by the paraboloid = 9y? + 9x2 and…

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Q: Find a parametrization of the hyper-boloid of two sheets (z2/c2)-(x2/a2)-(y2/b2)=1

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Q: Find the centroid (δ = 1) of the solid enclosed by the cylinder x2 + y2 = 4, bounded above by the…

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Q: Find the maximum volume of a box that is resting on the xy-plane with one vertex at the origin and…

A: Given the plane is 3x+4y+2z=12

Q: A fluid has density 800 kg/m³ and flows with velocity i = ri + yj+ zk, where x, y, and z are…

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Q: Determine the centroid, C(X,9.2). of the solid formed in the first octant bounded by z+y- 16 = 0 and…

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Q: Find all point on the plane x+ yt z= 5 in the first octant at which f(x, y,z) xy'z' has a maximum…

A: We have to find all points on the plane x+y+z=5 in the first octant at which fx,y,z=xy2z2 has a…

Q: (a) 'Find the orthogonal trajectories on the surface of the sphere x' + y? + z = 0 with the…

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Q: Use Divergence theorem to find the outward flux of F = 2xz i - 2xy j – z2 k across the boundary of…

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Q: 4. (Section 17.8) Use the Divergence Theorem to calculate [[F F-dS, where F = y + ryj – zk and S is…

A: To use the divergence theorem to calculate ∫∫SF⋅dS.

Q: Find the centroid (, j) of the region that is contained in the right-half plane {(x,y) | x > 0}, and…

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Q: Find the centroid of the solid generated if the region bounded by the y-axis, the lines y=1 and y =…

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Q: The solid in the first octant bounded by the coordinate planes, y+ z = 4, and x = y.

A: The objective is to find the volume for y+z=4,x=y The volume of the integral formula is,…

Q: The solid bounded by y = 4, z = x², z = 2y, and z = 4.

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Q: Integrate G(x, y, z) = x - y - z over the portion of the plane x + y = 1 in the first octant between…

A: Given G(x,y,z)=x-y-z

Q: y 1 X 1 2.

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Q: to find the use lagrange Multiplier Point p (x1s,Z) Closest to the origion on the Plane 2x +y - 2=5…

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Q: Find the average height of the hemispherical surface z = √(a2 - x2 - y2) above the disk x2 + y2 ≤ a2…

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Q: (b) Integrate (x, y,z)=(y+z)+1 the paraboloid 4x - y-z -0 by the plane x 1. over the surface cut…

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Q: Find the area of the portion of the paraboloid x = 4 - y2 - z2 that lies above the ring 1<=y2 +…

A: Given surface is  The required surface area is given by where

Q: Find the centroid of the polyhedron with four triangular faces in the first octant that is bounded…

A: The region is bounded by the three coordinate planes and the plane x+y+z=1. Thus, the region can be…

Q: find the flux of f=zk across the portion of the sphere x2+y2+z2=a2 in the first octant in the…

A: Given the field, F=zk The surface S is the portion of the sphere x2+y2+z2=a2 in the first octant in…

Q: Find the centroid of the homogeneous lamina enclosed by the graphs of the given equations. y = x2,…

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Q: Find the centroid of a thin, flat plate covering the “triangular” region in the first quadrant…

A: Consider the given curve.

Q: find ⌠⌠F*dS if F(x,y,z)=2xi+2yj+2zk and S is the paraboloid z=8-x^2-y^2 lying above the rectangle…

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Q: Use the Lagrange multiplier technique to compute the minimum and maximum val- ues of f(x, y, z) =…

A: Given function is fx,y,z=x+y+z Compute the minimum and maximum of the function fx,y,z on the…

Q: Find the centroid of a thin, flat plate covering the region enclosed by the x-axis, the lines x = 2…

A: Given information:

Q: Find the average height of the (single) 34. Average height of a cone cone z = Vx² + y² above the…

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Q: Verify Green's Theorem in the plane for F = (x² + y²)î + (x² – y²)f in the anti-clockwise direction…

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