Use the surface integral in Stokes' Theorem to calculate the circulation of the field F =xi+ 5xj +zk around the curve C: the ellipse 4x + 9y = 2 in the xy-plane, counterclockwise when viewed from above. • dr =

Q: use the surface integral in Stokes’ Theorem tocalculate the circulation of the field F around the…

A: Use the surface integral in Stokes’ Theorem to calculate the circulation of the field F around the…

Q: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F around the…

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Q: 14. Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field: F =…

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Q: In Exercises 39 and 40, use the surface integral in Stokes' Theorem to find the circulation of the…

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Q: Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F =x…

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Q: 3. Use Stokes' theorem to evaluate the line integral F· dr where A = -yi + xj and C is the boundary…

A: Stoke's theorem given by ∫CF.dr=∫∫Scurl A×n^ds According to the question, A=-y i+x j…

Q: Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F = zi +…

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Q: use the surface integral in Stokes’ Theorem to calculate the circulation of the field F around the…

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Q: use the surface integral in Stokes’ Theorem tocalculate the flux of the curl of the field F across…

A: Given  F=(y-z)i+(z-x)j+(x+z)k S:r(r,θ)=(rcosθ)i+(rsinθ)j+(9-r2)k 0≤r≤3, o≤θ≤2π

Q: Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F = 4zi +…

A: The given question can be solved as shown in step2

Q: Verify Stokes Theorem for the vector field F(x, y, z) = (y-z)i + 3xy j + 5zk by evaluating the line…

A: note :  As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F = (y² +z²)i…

A: To calculate the circulation of the field F=y2+z2i+x2+y2j+x2+y2k around the curve C: The square…

Q: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F=xi+ 4xj +z*k…

A: Find the explanation below

Q: 3. Use the surface integral is Stokes' Theorem to calculate the flux of the curl of the field F…

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Q: #5. Use Stokes' Theorem to evaluate curl F· dS, where F(x,y,z)= x (sin z)i+ y²j+xyk and S is the…

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Q: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F around the…

A: Given The given vector field is F=yi+xzj+x2k and the surface is 8x+y+z=8. Apply formula…

Q: Use a CAS and Stokes' theorem to evaluate curl(F) · dS, where F(x, y, z) = 2yi + ej - arctan(x)k…

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Q: Evaluate the flux integral F-ds where Pis the part of the paraboloid -= 4-x -y above the xy plane…

A: Any integral which is to be evaluated at the surface is called the surface integral. Divergence…

Q: Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F= 2zi +…

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Q: Use Stokes' Theorem to evaluate || curl F. dS. F(x, y, z) = x² sin(z)i + y²j + xyk, S is the part of…

A: Here use the stokes theorem to find the integral of the function and given that the function…

Q: 4. Verify Stokes's Theorem for the vector field F(x, y, z) = ( yz, – xz, z) over the cone z² = x² +…

A: a) Given that the vector field Fx,y,z=yz,-xz,z over the cone  z2=x2+y2 with 0≤z≤2 oriented downward.…

Q: Use Stokes' theorem to evaluate curl F. dS, where F(x, y, z) = e*Y cos(z)i + x²zj + xyk, and S is…

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Q: 14. Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field: (r…

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Q: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F around the…

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Q: Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F = 4zi +…

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Q: Use Stokes' Theorem to find the work done by the force field F= on a particle that traverses counter…

A: Given data: The force field is F→=z3,12x,y The equation of circle is C:x2+y2=9 in the plane z=5.

Q: Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated…

A: Let F be a vector field and C be the boundary of the surface S. The Stoke's theorem states that…

Q: Use Stokes' Theorem to evaluate ∫∫ s  curl F. dS  F(x,y,z) = x2 sin zi +y2 j +xyK, S is the part of…

A: Given: F(x,y,z)=x2 sin z i + y2 j +xy k and S is the surface of paraboloid z=1-x2-y2, which is above…

Q: 3. Use the surface integral is Stokes' Theorem to calculate the flux of the curl of the field F…

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Q: Use Stokes' Theorem to find the circulation of the vector fieldF = (a2 – y, 4z, r2) around the curve…

A: We will be using little bit of geometry and Stokes theorem to solve the problem

Q: Use Stokes' Theorem to evaluate curl F. dS. F(x, y, z) = x2y3zi + sin(xyz)j + xyzk, S is the part of…

A: Stokes theorem: ∫∫ScurlF.dS=∫CF.dr

Q: Use Stokes' Theorem to evaluate |/ curl F. dS. F(x, y, z) = tan-(x²yz²)i + x²yj + x²z?k, S is the…

A: Stokes' Theorem:                                 ∮C F .dr =∬S curl F. dS Where C is the boundary of…

Q: 9) Use Stokes' Theorem to evaluate || curl (F)· dS where F(x, y, z) = (x sin z)i+(x)j+(xy)k and S is…

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Q: Use Stokes' Theorem to evaluate curl F · dS. F(x, y, z) = x2y3zi + sin(xyz)j + xyzk, S is the part…

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Q: use the surface integral in Stokes’ Theorem tocalculate the flux of the curl of the field F across…

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Q: Use Stokes' Theorem to find the value of the line integral of the vector field F around the curve C…

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Q: Use Stokes theorem to evaluate ff.curl F.nds. where F = (xyz, x, e* cos z), while S is surface x² +…

A: Solution :

Q: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F around the…

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Q: Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F= 3yi +…

A: Given, F→=3yi^+5-3xj^+z2-2k^r→=3sinφcosθi^+3sinφsinθj^+3cosφk^ So, the flux of curl F is, Flux of…

Q: Use Stokes' Theorem to evaluate curl F· dS. F(x, y, z) = x² sin(z)i + y²j + xyk, S is the part of…

A: Given problem is :

Q: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F around the…

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Q: find the surface integral of the field F over the portion of the given surface in the specified…

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Q: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F = x²i+…

A: Given : F=x2i+4xj+z2k

Q: (4) Use Stokes' Theorem to calculate the work-done by the force field F(r, y, z) = (x² + z²)î + (y²…

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Q: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F = (y +z)i+…

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Q: Evaluate the flux integral , curl (z cos x î + y j+ x sin y k) dS where S is the part of the outward…

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Q: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F = by the…

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Q: use the curl integral in Stokes’ Theorem to find the circulation of the field F around the curve C…

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Q: 3. Use the surface integral is Stokes' Theorem to calculate the flux of the curl of the field F…

A: Given field : F=x2yi+2y3zj+3zk    surface S is r(r,θ)=(r cosθ)i+(r sinθ)j+rk    0≤r≤1,     0≤θ≤2π

Q: 03 Verify Stokes theorem for the vector field F= 2(-+x)i-zyi-zy'k over the upper hlf surface of…

A: To find- Verify Stokes theorem for the vector field F→ = 2-y2 + xi→ + z2yj→ - zy2k→ over the upper…

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!