Suppose the vector field v(x, y, z) = (4xy2, -4xz², 5x) represents the velocity field of a fluid. Find the circulation where C is the intersection of paraboloid z = 4 - 2x2 - 2y2 with cylinder x² + y² = 4. Enter an exact answer. Provide your answer below: Sev-dr = v. dr,

Q: A force F = -3i +j+6k acts through the point (5,-2,-1). Find its moment about the point (3,0,2).

A: Moment of force about the point is given by cross product of position vector r about a point and…

Q: Your friends correctly calculate the gradient vector for f(x, y)=x²+y at the point (2,-3) as…

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Q: H=pz Csup ap te'sin dg tpan 2 At point (1, ,6)

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Q: Find a vector function that represents the curve of intersection of the paraboloid z = 5x² + 2y² and…

A: The paraboloid z=5x2+2y2 and the cylinder y=3x2. We have to find a vector function that represents…

Q: 2. Find the gradient of the following scalar functions: a) T = 8/(x+y+2:²) b) V=3x²y³z c) U =…

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Q: 2 x = 8 - y, x =y - 8

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Q: Determine the acceleration (vector and magnitude) of the fluid particle occupying the point (-2, 1,…

A: Accleration is given by  a→ =DV→Dt= ∂V→∂t+(V.→∇)V→Here, V→ =2xy i^+xz j^+yz k^Hence, ∂V→∂t= ∂2xy…

Q: When body is an equilibrium ,the net force is not vanish

A: False. The given statement is false. We know that: There are two conditions that must be met for an…

Q: Determine the parametric equations of the flow lines for the velocity vector field, v, where v =…

A: The given velocity vector is v=yi+xj. To Find: parametric equations for flow lines of the above…

Q: 3. Find a vector function that represents the curve of intersection of the paraboloid z =. and the…

A: To find the vector function that represents the curve of intersection of the paraboloid z=x2+y2, and…

Q: Find the increase rate of the scalar V at point P from origin to the point P(2,6; 9,8 ; 9,5) where…

A: According to question given that The origin to the point P(2,6 ;9,8 ; 9,5) where V=3, 3xy+ 2, 6xyz

Q: nd the flux of the vector v=⟨x,y,z⟩ along the surface of the right tetrahedron below.

A: Flux of the vector

Q: Let the temperature T in degrees at the point (x,y,z), with distances measured in cm, be T(x,y,z)=3x…

A: Here I am attaching image so that you understand each and every step.

Q: 6) Let f(xxx)=3xy²-x² be a potential function of a fluid velocity field. a) Find the magnitude of…

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Q: Evaluate 1+ x° + y°dS, where S is the helicoid with vector equation т(и, и) — 0 <u < 3, 0 < v< T

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Q: Find the gradient vector field of f(r,y, z) = x*y* +y³z³ + æz°.

A: The gradient vector field of f(x,y,z) is given by ∇f=∂∂xf(x,y,z) i^+∂∂yf(x,y,z) j^+∂∂zf(x,y,z) k^…

Q: The acceleration of a particle at any time >=0 is given by: dr a = == (25cos2t)i + (16sen2t)j +…

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Q: Let the temperature / in degrees at the point X,y,z), with distances measured in cm, be T(X,y,z)=5x…

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Q: A particle is acted upon by constant forces 4i+j-3k and 3i+j-k and is displaced from the point…

A: Introduction: When a force is acting upon a particle and there is a displacement, the force works on…

Q: Find the centroid

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Q: Find the outward flux of F = (4x +25y*,0,) 10z through the surface 25 4 9

A: Solution:-

Q: The force exerted by an electric charge at the origin on a charged particle at the point (x,y,z)…

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Q: Find a Vector ū: non zero Vector perpendicular to the

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Q: The separation vector can be written as R = (x – x')ê+ (y – y')ŷ + (z - z')2, Find

A: Given,             R→=(x-x')x^+(y-y')y^+(z-z')z^

Q: 5. For f(x, y) 2x +y v 3i-4j find the rate of change of fat (1,2,6) in the direction of the vector =…

A: rate of change of the function at the given point along the given direction

Q: Utilize Green's Theorem to figure out the work done by the force: F(x, y) = x(x + 3y)i + 3xy²j in…

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