Let F = < xyz, xy, x"YZ > curlF. · dS, where Use Stokes' Theorem to evaluate S consists of the top and the four sides (but not the bottom) of the cube with one corner at (-4,-4,-4) and the diagonal corner at (1,1,1). Hint: Use the fact that if S and S share the same boundary curve C that curlF . // curlF dS dS = dr = S2

Q: Let C be the curve that consists of 4 straight intervals, beginning at (0, 0, 0) , going to (5, 2,…

A: Consider the given: F=8x+6y+3z+yz ,8x+16y+3z+xz,2x+3y+6z+xy and the points:(0,0,0),(5,2,2),(8,5,6)…

Q: Use Stokes' Theorem to find the circulation of F = 6yi + 5zj + 5xk around the triangle obtained by…

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Q: Let F . Use Stokes' Theorem to evaluate / curlF dS, where S consists of the top and the four sides…

A: Consider the provided question, Given that, F→=xyz, xy, x2yz We need to evaluate  ∬ScurlF→·dS  by…

Q: Evaluate the line integral (2 yi + (r- 2)j+ zyzk) · dr where C is the parametric curve r(t) = ti +…

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Q: Use Stokes' Theorem to evaluate  F · dr  where C is oriented counterclockwise as viewed from above.…

A: The given vector field and region C is as follows.

Q: Use Stokes' Theorem to evaluate F. dr where C is oriented counterclockwise as viewed from above.…

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Q: Let F = < rY, 3z, 4y Use Stokes' Theorem to evaluate | F . dī, where C is the curve of intersection…

A: Here we have, F→=xy, 3z, 4y Using the stoke theorem, we have to evaluate the ∫CF→·dr→=? Where C is…

Q: Find the area under the parametric curve x=t(1+t) , y=1/(1+t) ,  between t= [0,1]

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Q: The line integral P F.d7 can be evaluated using Stoke's Theorem where F = (2x, -3, 1) and C is an…

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Q: Let C be the curve that consists of 4 straight intervals, beginning at (0, 0, 0) , going to (3, 2,…

A: Given F→=22x+7y+5z+yz,4x+20y+3z+xz,2x+3y+10z+xy Now,…

Q: c) Verify Stokes's Theorem for F = (x²+y²)i-2xyj takes around the rectangle bounded by the lines x…

A: Stoke's law is given as ∫cF→.dr→=∫s∫∇×F.n→ds F=x2+y2i^-2xyj^ dr→=(dxi^+dyj^) So F.dr=x2+y2dx-2xydy…

Q: Use Stokes' theorem to evaluate      Scurl(F) · dS. F(x, y, z) = exy cos(z) i + x2z j + xy k,    S…

A: This question is related to vectors, We will solve it using stokes' theorem.

Q: Let F : . curlF - dS, where Use Stokes' Theorem to evaluate S consists of the top and the four sides…

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Q: Use Stokes' theorem to evaluate      CF · dr  where C is oriented counterclockwise as viewed from…

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Q: 2. Use Stokes' Theorem to evaluate S:z=√√√9-x² fF.dr F.dr for F(x, y, z)=5yi-zj+3xk and C

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Q: Let F: = . Use Stokes' Theorem to evaluate curlF · dS, where S consists of the top and the four…

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Q: Use Stokes's Theorem to evaluate JeF - dr- . In each case, C is oriented counterclockwise as viewed…

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Q: Compute (VxF). dS, where S is given by x² + y² + (z − 1)² = 2 and z ≥ 0, F(x, y, z) = (-esinzy, x +…

A: The general form of a vector-valued function is given by F1,F2,F3 where F1,F2 and F3 are the scalar…

Q: 10. Use Stokes' Theorem to evaluate ||(V×F)· dS where F= (z,2x, y) and Sis the hemisphere of x' + y?…

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Q: Let F = . Use Stokes' Theorem to evaluate curlF · d5, where S consists of the top and the four…

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Q: Let F = 0, oriented upwards

A: Stokes theorem

Q: STOKES' THEOREM o may be parameterized by r(r, y) = (1, y, f(x, y)) = curl F

A: We shall answer first three subpart only as per answering guidelines. For others, kindly post again…

Q: Let C be the curve parameterized as follows F(t) := (9 cos(t), 9 sin(t), 12t), 0<ts 10 and let f(x,…

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Q: Let F = . Use Stokes' Theorem to evaluate / curlF · d5, where S is the hemisphere x² + y² + z² =…

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Q: Use Stokes' Theorem to calculate rot F dS, where F = ri + yj + rk and S is the surface given by the…

A: This is a problem of vector calculus. By using stokes theorem formula we will evaluate given…

Q: 1. Compute ff,(V × F) - dS, where S is given by r² + y? + (z – 1)? = 2 and z > 0, and F(x, y, z) =…

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Q: :) Use Stokes' theorem to evaluate RF dr where C F = z?i + yj + xk and C is the triangle with…

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Q: Let F(x.y.z)=-y²i+xj+z² k, S is the shaded part in the figure at right and C the boundary curve of S…

A: Stroke's theorem: Let S be an oriented smooth surface that is bounded by a simple, closed, smooth…

Q: Compute the integral of the Gauß curvature over the surface shown in the picture. The three boundary…

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Q: Let F = . Use Stokes' Theorem to evaluate curlF · dS , where S consists of the top and the four…

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Q: Use Stokes' theorem frotF. ds to evaluate F(x, y, z) = (x + tan¯¹yz)i + y²zj + zk, S is the part of…

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Q: Use Stokes's theorem to evaluate F.dr, where F(r, y, z) = ry i + x°yj+yz k, where C is a triangular…

A: Stroke's theorem:  ∫Fdr=∬ (Curl F) n^dS Curl F=ijkxy2x2yyzy2x2y=iz n^=∇s∥s∥=i^+k^2

Q: Let F < ryz, ry, r'yz Use Stokes' Theorem to evaluate curlF dS, where S consists of the top and the…

A: The given surface is a cube, where the bottom face is not considered. The surface in question has 4…

Q: curl F dS, where Use Stokes' Theorem to determine which of the following is equivalent to F(x, y, z)…

A: The given function is F(x, y, z) = 2x2 i^ + xy j^ + ez k^.The surface S is the part of the…

Q: Use Stokes' Theorem to evaluate F. dr where C is oriented counterclockwise as viewed from above.…

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Q: Let F = . [[ curlF d5 ,where Use Stokes' Theorem to evaluate S consists of the top and the four…

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Q: Let F . F. dr, where Use Stokes' Theorem to evaluate C is the curve of intersection of the…

A: The given vector function: F→=&lt;xy,2z,3y&gt; To find ∫CF→.dr by using Stokes theorem. The Formula…

Q: Let F . // curlF d5, where Use Stokes' Theorem to evaluate S consists of the top and the four sides…

A: Given function is F=xyz,xy,x2yz Now calculate the curl F curl…

Q: Let S be a square plate with boundary C, having each side of length 2 units, lying in the plane x =…

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Q: Let S be a square plate with boundary C having length of each side as 2 units, lying in the plane z…

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Q: Let F = . /| curlF - d5, where Use Stokes' Theorem to evaluate S consists of the top and the four…

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Q: Use Stokes' Theorem to evaluate F · dr where C is oriented counterclockwise as viewed from above.…

A: Concept Used: ∫CF·dr=∫∫ScurlF·dS Where C is the boundary of the surface oriented counterclockwise

Q: 5. Use the Stokes theorem to evaluate f. FdT where F (3x³ + 2y – 2) i + (4x + y* + 2z) j + (2x – 3y…

A: To find- Use the Stokes theorem to evaluate ∫CF→ dr→ where F→ = 3x3 + 2y - zi→ + 4x + y4 + 2zj→ + 2x…

Q: Let F(x.y.z)=-y²i +xj+z? k, S is the shaded part in the figure at right and C the boundary curve of…

A: We will find out the required value.

Q: 3(b). FF as defined above, a misguided professor claims that for any losed curve C, F. dr = 0…

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Q: Use Stokes's theorem to evaluate F dr, where F(r, y, z) = ry i+x*yj+yz k, where C is a triangular…

A: Given that, F(x,y,z)=xy2i+x2yj+yzk Using the stoke's theorem, ∮F.dr=∬S(curl f.n)dS Now let's find…

Q: Let F = (5x4 + 16z, 2x³ + 3y? + 16z, x + y+ ev*+1) and C be the curve defined by 7 (t) = (2 cos(t),…

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Q: Let F = ( ) 5x* + 16z, 2x³ + 3y² + 16z, x + y + eVz³+1 and C be the curve defined by 7(t) = (2…

A: Given that,  F=5x4+16z, 2x3+3y2+16z, x+y+ez3+1 And rt=2cost, 2sint, 16cos2t sin2t, o≤t≤π To find…

Q: Find a parametrization of the curve x^(2/3)+y^(2/3)=8^(2/3) and use it to compute the area of the…

A: Finding the parameters:

Q: 'Use Stokes' Theorem to compute | 1 F. dr where C is the curve where the cylinder a? + y? = 1…

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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.