(10) Given that the vector field F= 2z i- 3 x j + 4 y k Evaluate f F. dr where S is the portion of the paraboloid z = 16 - x² - y? for z 2 0 in the first octant

Q: x-y, z + y + 3,z²) and the net is decribed by the equation y = 1- x² - z on

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Q: Let C be the curve of intersection of the paraboloid x² + y² = z and the cylinder + (y − 1)² = 1 (a)…

A: We will use the basic knowledge of vector calculus and differential calculus to answer all three…

Q: Compute feF. dr where C is the curve of intersection of the paraboloid z=9-x² - y² and the plane z =…

A: To compute the line integral ∫CF⋅dr. We have F=2x2+3zi+4ey+8xj+6z2+7yk and  C is the curve of…

Q: The surface H is defined by (x² + y²)² + z = 1; z ≥ 0. The vector field A(r) is given by A = (x, y,…

A: The surface H  is defined by    .The vector field  is given by   .We have to sketch the surface H.

Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

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Q: Find the flux of the vector field F(x, y, z) = ri across the outward oriented sphere %3D

A: In this question, we find the flux of the vector field f(x,y,z)=xi The surface is a sphere of radius…

Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

A: Given that v=<x-y, z+y+9, z2> and the given curve is y=1-x2-z2,y≥0 To find: The value of ∬S…

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: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

A: Adding the plane surface y=0 to close the surface and apply the gauss divergence theorem.

Q: Find the curl of the vector field F. F = (x-y+z)i+ (6x-y+7z)j+ (9x +6y + z)k curl F = i+

A: We have to find the curl F

Q: y X Consider the vector field u(x) = x²+²x² + y²j+6k. i Calculate y dr, where C is the straight line…

A: Introduction:  A line integral is an integral where the function to be integrated is evaluated along…

Q: Consider the vector field v(x) = 2+y22-2²y2j+2k. Calculate y dr, where C is the straight line from…

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Q: Is the vector field F = y? – 2x², 2xy + 3| conserva Yes No yz Is the vector field F y? – x2 con Vy?…

A: According to the guidelines issued by the company we are supposed to answer only first question.…

Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

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Q: Consider the vector field given by F(x, y) = (6xy – 152 y)i + (3a? + 3y – 10a°y)j find a function…

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Q: Evaluate the 1-form φ = x2yz dx − z dy on the vector field V (x, y, z) = xU1(x, y, z) − yzU2(x, y,…

A: We need to evaluate the 1-form of  ϕ=x2yz dx - z dy.....(1) in the vector field  V(x,y,z) = x…

Q: Let C₁ be the line segment from the point (-4, 8) to the point (2, -4), C₂ be the arc on the…

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Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

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Q: 3. Let f: R2 → R be the function which satisfies for all (x, y) E R² that f(x, y) = 100 – x² – 2y?…

A: A scalar function f(x,y) is a rule that is used to associate a number, or quantity with a particular…

Q: a|bc = a|c_if a and b are relatively prime. ylgn ihi

A: True

Q: Sketch the vector field of F = (-y,0) in the xy-plane. %3D

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Q: Sketch the vector field in the xy-plane. 7(7) = -7/11711³ O O y y X X O O y y X X

A: F→r→=-r→r→3