Find the flux of the vector field F = (z, y°, through the helicoid with parameterization r(u, v) = (u cos v, v, u sin v) 0 < u < 1, 0 < v

Q: Find the flux of the vector field F(x, y, z) = 3xi+3yj+6zk across the portion of the surface z = 25…

A: The flux F across the surface is given by ϕ=∫σF·nds=∬RF·∇GdA

Q: Find the flux of the vector field F = (y, – z, x) across the part of the plane z = 4 + x + 2y above…

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Q: Evaluate the surface integral ∬SF⋅dS for the given vector field F and the oriented surface S. In…

A: Compare the given equation with general equation and find the value of P, Q and R.

Q: Use the divergence theorem to calculate the flux of the vector field F(x, y, z) = −1xyi – 2yzj —…

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Q: Find the outward flux of the vector field F = (x³, y³, z²) across the surface of the region that is…

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Q: Find the surface integral F. dS of the vector field F(x, y, z) = (-x, -4, yz®) along the part of the…

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Q: Find the outward flux of the field F = (x + y)î + yĵ + zk across the closed surface: S: z = 16x² -…

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Q: Let v = (x*z, 2 – 4xyz, xz) be the velocity field of a fluid. Compute the flux of v across the…

A: Given, v→=x2z,2-4xyz,xz225x2+16z2=y-202 Then, calculating div v→ div…

Q: Find the flux of the vector field F (x, y, z) = (e-y, -y, x sin z) across the positively oriented…

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Q: ompute the flux of the vector field F = ri + yj+ zk through the surface S, which is a closed…

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Q: Find the flux of the field F = xy i - z k outward (normal away from the z-axis) through the cone z =…

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Q: Use the divergence theorem to calculate the flux of the vector field F(x, y, z)=-3ry-ly:j-Szak…

A: To find- Use the divergence theorem to calculate the flux of the vector field F→x, y, z = -3xyi^ -…

Q: Let = (xz, 2 4xyz, rz) be the velocity field of a fluid. Compute the flux of i across the surface…

A: Flux of velocity about a surface is the measure of amount of velocity of fluid hitting the surface.…

Q: Compute the flux of the vector field F(x, y, z) = 2xj+ 4yk through the surface S, where S is the…

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Q: Find the flux of the vector field F = (y, – z, x) across the part of the plane z above the rectangle…

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Q: Find the net flux of the vector field F(x, y, z) = (2x, - 2y, z) over the closed surface enclosed by…

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Q: Let S be a simple closed surface in R' that encloses a solid region with volume equal to 5. Find the…

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Q: Use the divergence theorem to calculate the flux of the vector field F(x, y, a) + (2y-3')] + 7k…

A: Solution :

Q: Find the flux of the field F = x2 j - xz k outward (normal away from the yz-plane) through the…

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Q: b) Find the flux of the vector field F(x,y,z) = 3xi – yj + 2zk; across o where o is the portion of…

A: The given question belonging to the vector calculus  in which we have to find the value flux of the…

Q: Find the flux of the vector field F(x, y, z) = (y z, y, æz) across the surface S, where S is the…

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Q: |Compute the flux (just another name for the surface integral) of the vector field F = zk through…

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Q: Find the work done by the force field F(x,y) = x²i – xy²j around the circle (Clockwise direction)…

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Q: Find the outward flux of the vector field F = (x°, y°, z²) across the surface of the region that is…

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Q: Find the work done by the force field F(x, y, z) = (x – y², y – z?, z – x2) on a particle that moves…

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Q: Find the work done by the force field F(x,y) = (-y,x) in moving an object along the path y = V4 – x2…

A: Given force field Fx,y=−y,x and object moving along the path y=4−x2  from 2,0 to -2,0. We have to…

Q: Find the work done by the force field F(x, y) = (x^2-lny)i + (e^x^2+y^2)j on a particle that travels…

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Q: Q1 Use Stokes theorem to compute the flux of the curl of a vector field F = (2x – y)ĩ – yz? j- y²zk…

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Q: Find the flux of the field F =-x i - y j + z2 k outward (normal away from the z-axis) through the…

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Q: Find the flux of the vector field F = (y, - a, z) through the helicoid with parameterization r(u, v)…

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Q: Find the work done by the force field F(x, y) = x* +y? on a particle that moves along the quarter…

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Q: Calculate the net outward flux of the vector field F = xy i + (sin xz + y2)j + (exy2 + x)k over the…

A: Given surface 'S' is surrounding region D bounded by the planes y=0, z=0, z=2-y and z=1-x2

Q: Find the upward flux of the vector field F(x,y,z)= (-y, x, 9) across the part of the hemisphere…

A: Consider the provided question,

Q: Integrate the vector field h(x,y) = y^2i + (2xy-e^2y)j over the circular arc C parametrized by r(t)…

A: The answer is given by using the formula of line integral

Q: Compute the flux of the vector field F = xi + yj through the surface S, which is the part of the…

A: Given: F→=xi→+yj→ z=36-x2+y2 ds=1+∂z∂x2+∂z∂y2dxdy       =1+4x2+4y2dxdy   and…

Q: disk

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Q: Find the flux of the vector field F = (y, – z, x) across the part of the plane z = 3+ 4x + 2y above

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Q: Find the counterclockwise circulation and the outward flux of the field F = (-sin y)i + (x cos y)j…

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Q: Find the outward flux of the field F = 3xz2 i + y j - z3 k across the surface of the solid in the…

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Q: Find the work done by the gradient vector field F(x, y, z) = V (e² + y² + z²) in %3| mov ing a…

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Q: Integrate the vector field h(x,y) = (y^2)i + (2xy-e^(2y))j over the circular arc C parametrized by…

A: Given that h(x,y)=y2i+2xy-e2yj  The parametric equation of the circular arc is  r(t)=cos(t) i+sin(t)…

Q: Find the gradient vector field (F(r, y, z)) of f(x, y, z) = z sin(ry). F(2, y, z) = (

A: Given function is  f(x,y,z) = z^2 sin(xy)

Q: The outward flux of the vector field F=(x,0, z) across the cylinder x + y = 1, for 0<z<1, is %3D…

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Q: Without using a potential function, find the total work performed by the force field F(x, y) =…

A: Work done by vector field while moving a particle along a curve = Line integral of that vector field…

Q: Find the surface integral F. dS of the vector field F(x, y, 2) = (-æ, -y, yz®) along the part of the…

A: The complete solutions are given below

Q: Compute the flux of the vector field F = 2xzi + 5yk through the surface S, which is the hemisphere…

A: In this question, we find the flux for the given vector field across the surface of the hemisphere.

Q: Find the flux of the vector field F = [x,y,z] through the oriented surface S: z= x^2 + y^2, z <= 1…

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Q: Compute the flux of the vector field F = zi + 8xj through the parameterized surface S oriented…

A: We have find the flux of the given vector field through the parameterized surface S oriented upward.

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.