1) Consider the closed surface: z = h – x^2 – y^2, h>0, and z=0. Let F=(x^2,y^2,z^2). Find the flux due to F through the surface.
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: Let S be the portion of the cylinder y = ln x in the first octant whose projection parallel to the…
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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: Determine the solid bounded by the surfaces 9x2+4y2=30 and the plane 9x+4y−6z=0 in the first octant.
A: Given surface is 9x2+4y2=30 and plane is 9x+4y-6z=0 Bounded region in first octane ⇒x≥0, y≥0, z≥0…
Q: Integrate G(x, y, z) = xyz over the surface of the cube cut from the first octant by the planes x =…
A: Here, the surface is in the first octant. Therefore, the integration is
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: (a) Integrate g(x,y,z) = Inx+y over the surface of the region cut from the plane 4x+3y+2z=1 by the…
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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: Integrate ƒ(x, y) = sqrt(4 - x2) over the smaller sector cut from the disk x2 + y2 <=4 by the…
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Q: A fluid has density 1000 kg/m3 and flows with velocity ū = xi + yj + zk, where x, y, and z are…
A: A fluid density 1000 kg/m3 andflows with velocity v→=xi→+yj→+zk→where x,y and z are measured…
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 >…
A: From given data we see that the surface is oriented towards xz plane, Hence, d→s=dxdzj→
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: Consider the surfaces z = x^2 +y^2 and z+ 2x+ 2y = 0 Find the projection of the curve on…
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Q: Let F(x, y, z) =7x2+8y2+13z2. Find the equation to the tangent plane to the level of surface F(x,…
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Q: Find the area of the portion of the cylindrical surface y = 4 - x2 in the first octant that is…
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Q: d) An open surface F is given by F = {(x,y, z) |z = 4 – x² – y² , z > 0} . Compute the flux of V…
A: V(x,y,z) = <2x+3y,2y+3x,-4z>F={ (x,y,z) : z=4-x2-y2 , z≥0}Consider, g(x,y,z) = z+x2+y2-4…
Q: Integrate G(x, y, z) = x over the surface given by z = x2 + y for 0 ≤ x ≤ 1, -1 ≤ y ≤ 1.
A: The function is fx,y,z=x2+y-z=0 ......1 Gx,y,z=x…
Q: Compute the flux of F = (5(z + 2), 5, 52) through the surface S given by y = ² + 2, with 0 0, z 2 0,…
A: We have to find flux.
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: An equation of the tangent plane to the surface z = In(x - 2y) at (3, 1,0) is given by z = x + 2y- 1…
A: This question is related to three dimensions geometry.
Q: Let S be the surface of z = 6 –- x² – 4y² with z > 2 Find the flux of F = [1 – 4y, 1 + x, 2z]on S
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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 <y<9, x…
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Q: Compute the flux of F = (r, y, z*) across the cone z = x2 + y?, %3D 0<<1, in the downward direction.
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Q: 7. Find the flux of F(x, y, z) = x î+ y ĵ+ z² k across the sphere of radius 1 centered at the origin…
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Q: = xyz exists over a surface S c ed by the plane x-0,y%3D0,z%3D0, z=y V dS over the curve surface.
A: Given: V= xyz x2+y2=9 To find: ∫s V ds For solving the convergence x2+y2=9 (mod 1s) we use Chinese…
Q: 18. z = 4 – x2 – y², 0<z< 3; f (x, y, z) = x² / (4 – 2) - -
A: Use polar coordinates to solve the integral
Q: Find a vector normal to the surface x2 + yz = 5 at (2, 1, 1).
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Q: In Exercises 25–26, find the areas of the surfaces generated by revolv-ing the curves about the…
A: Given:
Q: use divergence theorem to find the outward flux of f =2xzi-3xyj-z^2k across the boundary of the…
A: By divergence theorem
Q: Sketch the section of the surface at z = 0 on y = sinx in xy-plane on [0,27). y = sinx 4 56 1 3. 6…
A: The given equation of the curve is: y=sinx To draw the given equation on the x-y plane we need to…
Q: 2. Calculate the centroid of the thin plate R which bounded by r = 1, y = 0 and, 2² + y² = 4.
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Q: 4. Obtain the equation of the tangent plane to the surface with parametric representation r(u, v) =…
A: Note: We'll answer the first question since the exact one wasn't specified. Please submit a new…
Q: 6. Compute the flux of F = [0, 0, z²] through the spherical surface S given as the upper hemisphere…
A: To find- Compute the flux of F→ = 0, 0, z2 through the spherical surface S given as the upper…
Q: The level curves of the surface z = x2 + y2 are circles in the xy-plane centered at the origin.…
A: Consider , Equation of the surface given: z = x2 + y2 The level plot is as shown below:
Q: Let C be a curve given by the intersection of the surfaces z = x2 +y2;z = 3−2x . The value of the…
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Q: Find the flux of F(x, y, 2) = (r, y, 2) across the surface o which is the surface of the solid…
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Q: 5. Compute the flux of F(r, y.2) =zi- 2yj+ 2ak across the surface of the cylinder bounded by a+y =9…
A: Solve the problem as shown below.
Q: Find a parametrisation of the curve of intersection of the surfaces: x^2 + 2y^2 + z^2 = 5 and x^2 +…
A: This is parameterisation of curve problem
Q: Sketch the section of the surface at z = 0 on y = sinx in xy-plane on [0,2x]. y = sinx 1 3 4 5 1 1 2…
A: Let's find.
Q: Calculate the flux of F across G. F(x, y, z) = 2xi + 2yj + 2zk; G is the surface of the sphere x2 +…
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Q: verify Stokes § = (a%-y)i - yz'i over the uppea hazf SOD Face Of the sphere =1 bounded by the
A: Given that, F→=(2x-y)i→-yz2j→-y2zk→ To verify Stoke's theorem: ∫CF→·dr→=∬Scurl F→·n^dS Here C is…
Q: (2) Let S be the surface of the sphere of radius 4 centered at the origin oriented away from the…
A: We can apply divergence theorem to find this
Q: Let σ be the surface denoted by z = x² + y² + 2xy bounded by x² + y² = 2. Knowing that the density…
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Q: A fluid has density 1200 kg/m³ and flows with velocity v = xi + yj + zk, where x, y, and z are…
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Q: 2)Use Stokes' Theorem to evaluate | F.dr where F =2xyi- yj+2xzk and S is the first octant surface of…
A: The given problem is to evaluate the line integral in the surface of first octant with upward…
Q: Find the polar moment of inertia about the origin of a thin triangular plate of constant density δ =…
A: Given: y=2x and y=4 Thus the region bounded by the y-axis and the line y=2x and y=4 is shown as…
Q: Find the surface area of z =1-(x^2)-(y^2) that is above the xy plane
A: Given equation of plane is z=f(x,y)=1-x2-y2 we have to find the surface area above xy plane.
Q: A line intersects the xy plane at an x– intercept of N and a y intercept of F. Determine the volum…
A: Given:- A line intersects the xy plane at an x intercept of N and a y intercept of F. To find :-…
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- Find the vector equation that represents the curve of intersection of the paraboloid z=3x^2+y^2 and the surface y=x^3. Write the equation so that one of the functions is simply t.Find the upward flux of F = (14e*, -7e, -6) through the first-octant part of the triangle x+2y+3z = 6. Answer: EUse Green's Theorem to evaluate∮tan^-1(y)dx-(xy^)/(1+y^2) dy where C is the square with vertices (0, 0), (1, 0), (1, 1) and (0, 1) and oriented counterclockwise. A. -1 B. 2 C. 1 D. -2
- Sketch the surface x = 2y2 +3z2Suppose div(F(5,3,2)) = 240. Estimate the flux of F out of a small, outward-oriented box of side length 0.2 centered at the point (5, 3, 2) with edges parallel to the coordinate axes. Flux 2Find a vector equation for the curve of intersection between the surfaces y^2-x^2=9 and 2x-3y-z=12.
- For a given surface z-x^2-y^2=10 Find the parametric representation of the straight line which passes through the point (1,1,12) and perpendicular to the given surfaceConsider the line perpendicular to the surface z=x^2+y^2 at the point where x=3 and y=2. Find a vector parametric equation for this line in terms of the parameter t.Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The paraboloid z = 3x2 + y2 and the parabolic cylinder y = 2x2 r(t) = (1,322 + 9^) * Need Help? Read It