Suppose we have part of a hyperboloid of two sheets -4x? -4y? + z? = 9 where z 20 (so the upper half) and also zs 15 a) parametrize this surface b) set up (but do not evaluate) an integral that would provide the flux thru the surface for the vector field 10z²k

Q: Parameterize the intersection of z = - Vx² + 7y² _and x² + y? + z? = 200

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Q: What is the flux through the described surface?

A: The surface is described by The vector field is F=<1, 3x, 2y>To evaluate the Flux for the…

Q: Find all points (a, b, c) on the sphere x2 + y2 + z2 = R2 where the vector field F = yz2i + xz2j +…

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Q: :::.. V : 5+j wi +4j Find the specific Scalar .(.. )

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Q: Q3. Find out values of a, b, c for which curl of vector V is zero, where V = (2xy+ 3 yz) i +(x² +…

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Q: he vector v = , is tangent to the surface x2 + 2y3 - 3z2 = 3 at the point (2, 1, 1).  Find a.

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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: 3) Let S be a portion of the surface 3z = 12 – 6x – 3y in the first octant. Suppose that S is…

A: 3z=12-6x-3y divide by 3 z=4-2x-y ⇒2x+y+z=4 clearly it's plane The plane cuts the x-axis at (2,0,0),…

Q: 13. For the vector fields: A = x + 2y ŷ + 3z 2; B = 3y - 2x ŷ. Check both product rule given in…

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Q: Find a vector parametric equation for the ellipse that lies on the plane 4x - 4y + z = -7 and is…

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Q: Find the flux of the vector field V(x, y, z) = 2xy²i+ 5x²yj + 3z³k out of the unit sphere. Flux =

A: Denote the unit sphere by S If the sphere is closed,  then the flux of v(x, y, z) out of S is given…

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: Calculate | F.dr, where F(x, y) = (x²–3y)i+(ye")j and the curve and curve C is the parabola æ = y² +…

A: We have to calculate ∫CF.dr, where Fx,y=x2-3yi+yeyj and the curve C is the parabola x=y2+1 from A1,0…

Q: [1 |A = [a1, a2, a3, a4] 2 11 5 0 3 -1 4 0

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Q: Calculate |E F.dr, where F(aа, у) — (2? —Зу)і+(ye®)j and the сurve and curve ' is the parabola х %3D…

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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…

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

Q: You are given the scalar field = -7y. a) b) c) d) Calculate Vo. Vo =( Calculate V at the point p =…

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