Let F = (z,0. y) and let S be the oriented surface parametrized by (u, v) = (u² – v, u, v²) for 0 < u < 4. -1

Q: Let F(x, y, z) = (xz, yz, z²). (a) Let S be the cylinder a2 + y² = 4, 1 < z < 3, oriented by the…

A: Hello. Since your question has multiple questions, we will solve first question for you. If you want…

Q: Find the coordinates of the centroid of the curve given belov x = cos t+tsin t, y =t cos t- sin t,…

A: Given data: The x-coordinate of the curve is x=cos t+tsin t. The y-coordinate of the curve is y=tcos…

Q: Let S be the surface given by a piece of the plane y = 0, with 0 < x <1 and 0 < z< 2. the unit…

A: Given: To find the flux of F through S by considering F = 3j + k. Let's take unit normal n =j.

Q: Find the area and centroid bounded by the curve 5y? = 16x and the curve y2 = 8x – 24.

A: Since you have asked multiple question, we will solve the one question for you. If you want any…

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: Calculate F· dS where F = (3xy', ze", 2°) and S is the surface of the solid bounded by the cylinder…

A: We need to calculate ∬SF→.dS which is the flux. Now, we can use the divergence theorem to find…

Q: Consider the solid Q bounded by the surfaces: S1 : y = 4 – x², S2: z = 4 – r, S3 : S4 : y = 0 %3D…

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Q: Q3// A surface S is defined by 2x2 + z = 1 and the bounded by the planes y = 0,y 2, x 0,z = 0 in the…

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Q: 1. Evaluate the surface integral fs (r + y + z)dS, S is the parallelogram with parametric equations…

A: We are entitled to solve only one question at a time. As the question number is not mentioned, So we…

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: 4. Let S be the open surface, x² + y² + z² = 4; z > 0. Evaluate the following surface integral,…

A: Given that S is the open surface x2+y2+z2=4, z≥0 To evaluate ∬SF·ndS Here, F=x,0,0 Let us…

Q: . Evaluate (x² + y) dv G if G is the solid bounded by the parabolic cylinder z = y², xy-plane and…

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Q: Calculate the surface integralff, ds, where S is the hemisphere x² + y² + z² = 1, z ≥ 0. The…

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Q: Find the circulation of F(x, y, z) = (-y sin 2, x sin z, xy cosz +12) around the circle cut from the…

A: Given that,F(x, y, z)=(-ysinz, xsinz, xycosz+12) around the circle cut from the sphere x2+y2+z2=5 by…

Q: The solid in the first octant bounded by the coordinate planes and the plane z = 8 – x – y dz dy dx

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Q: (5) Use Stokes' Theorem to find the line integral |(* + 2y°)i + (y + z°) +(= + 2r*)k) • dř where C…

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Q: Use Gauss' Divergent Theorem to calculate F. dS, where F = (2x + sen (e+1)) i+ 3yj+ cos(z?)k and S…

A: Given

Q: b) Given F(x, Y, z) = (x³ + cosh z) i+ (2y³ – 3x²y)j – (x² + 4y²z) k. Use Gauss's theorem to…

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Q: The volume of the solid generated by the curve y = e, between z = 2 and z = 6 about the z- azis is

A: Given: The curve is y=e-x   To determine: The volume of the solid generated by the curve y=e-x…

Q: Find the polar moment of inertia about the origin of a thin triangular plate of constant density d =…

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Q: Find the value of the integral fs (V x A). da if the vector A = yi + zj + xk and Sis the surface…

A: Given the vector A=yi+zj+xk and S is the surface defined by the paraboloid z=1-x2-y2

Q: 13. Calculate the flux of F across S.F = (3x, xz, z2) and S is the surface bounded by the paraboloid…

A: Given vector field is  F=3x,xz,z2 we have to find the flux through F where S is the surface bounded…

Q: Let F(x, y, z) = 2xi – 2yj + z²k. Evaluate Is where S is the cylinder x2 + y2 = 9 with z E [0, 1].…

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Q: Calculate F - dS where F = (e² sin y, e² cos y, yz²) S is the surface of the box bounded by the…

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Q: 2. Evaluate f, z³ /x² + y² + z² dV where E is the solid hemisphere that lies above the xy-plane and…

A: Solution:- equation of sphere having centre origin (0,0) and radius=1 x2+y2+z2=1…

Q: b) Use Gauss theorem to evaluate F.ndS, where F(r, y, 2) = (2x²y² + In z) i – xy³ j – tanh(a² + y³)…

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Q: 2. Let S be the surface x² + y² = (2-2)², y Evaluate Jl F = (2x+y-xz, -x, -(2 — z)²), choosing a…

A: Using parametrization of the surface S

Q: Use Stokes's theorem to evaluate o F· dr, where F(x, y, 2) = xy² i+x²yj+yz k, where C is a…

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Q: Calculate F. dS where F = (e* sin y, e² cos y, yz²) S is the surface of the box bounded by the…

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Q: Calculate F- dS where F = (e" sin y, e* cos y, yz²) S is the surface of the box bounded by the…

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Q: Integrate G(x, y, z) = x - y - z over the portion of the plane x + y = 1 in the first octant between…

A: Given G(x,y,z)=x-y-z

Q: Let F(x, y,z) = (-xe² +3x, -ye² + arctan(x? + z), 2e²) and S the portion of the sphere acoording to…

A: Given that Fx,y,z=-xez+3x, -yez+arctanx2+z2, 2ez. Also, S=x,y,z| x2+y2+z2=1, z≥0. To determine the…

Q: Find a unit normal vector to the surface f(x, y, z) = 0 at the point P(4, – 5, – 5) for the fur 5x…

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Q: Let F (x, y, z): = (x + 2y2, y + z2, z + 2x2), and let C be the curve that results from the…

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Q: | 5y? dx +xy dy

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Q: Use spherical coordinates to evaluate the triple integral ∫∫∫ √(x^2 + y^2 + z^2) dv where G is the…

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Q: Use Green's Theorem to calculate the work done by the force F on a particle that is moving…

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Q: Find the flux integral ∫∫scurl(F).dS, where F(x,y,z) = [-y + 2cos(πy)e2x + z2, x2cos(zπ/2) -…

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Q: The solid in the first octant bounded by the coordinate planes and the plane z = 3 – x –y dz dy dx

A: Answer is:∫03∫03-x∫03-x-ydzdydx Proof is attached below.

Q: S is the surface with parametric equations x = Зи+ v, у — Зи— v, z = uv for (u, v) in the region D…

A: The integral of a scalar valued function can be calculated as follows, using the parametrization:…

Q: Use Green's theorem to calculate the work done by force F on a particle that is moving…

A: GivenF(x,y)=x32-8yi+5x+8yj,C: Boundary of a triangle with vertices (0,0), (5,0) and (0,5)To…

Q: Use Stokes' theorem to calculate , F.ds, where F = (z, x, y) and C is the boundary %3D of a triangle…

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Q: - S is the surface with parametric equations x = 3u+v, y = 3u-v, z = uv for (u, v) in the region D…

A: We will find out the required value.

Q: Evaluate (x² + y) dv G if G is the solid bounded by the parabolic cylinder z = the planes x = 0, x =…

A: Here I am using simple tripple integration to solve this question.

Q: Use the polar coordinates to evaluate volumes : 2) Below z = V1- x2 – y2 inside x² + y2 = above the…

A: Using the polar coordinates we have to evaluate the volumebelow z=1-x2-y2 inside x2+y2=14 above xy…

Q: Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise. e5x + 2y dx +…

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Q: Compute the line integral (yze"y= + y² + z – 2x) dx + (xze"v² + 2xy) dy + (xye"y= +x+ 3z²) dz C…

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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: The area of the surface obtained by rotating the curve y = et +e asxsb, about the x-axis is 1/2 e2 +…

A: Find the surface area rotating the curve about x axis

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.