Compute ,F · dS for F = (xy, 5y,0), S being the cone z² = x + y²,x² + y? < 4, z > 0, with the normal %3D pointing downward.

Q: Given the curve y = x´ and the lines y = 0 and y=2 – x Find the moment of R with respect to the…

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Q: Calculate F · dS where F = (e* sin cos y, yz?) y, et and S is the surface of the box bounded by the…

A: By using the divergence theorem, we can make equality between the surface integral of a function and…

Q: valuate the line integral, where C is the given curve. z2 dx + x2 dy + y2 dz, C is the line segment…

A: Follow next step

Q: Calculate the integral of f(z,y, 2) = 6z2 + 6y² + 2³ over the curve c(t) = (cost, sin t,t) for 0<t<…

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Q: Show that at any point (x,y) on the curve y=bex/a ,the length of the subtangent is constant and the…

A: The given curve is y=bexa.

Q: Evaluate the line integral, where C is the given curve. xyeVZ dy, C: x = 4t, y = 3t2, z = 4t³, 0sts…

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Q: Evaluate fpxV47x² + 47y² dA, where D is the shaded region enclosed by the lemniscate curve r? =…

A: To find the value of the double integral         ∫∫Dx47x2+47y2dA where D is the region enclosed by…

Q: Calculate the integral of f(x, y, z) = 7x² + 7y² + z³ over the curve c(t) = (cost, sin t, t) for 0…

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Q: Find the lateral surface of the cone generated by revolving the line y = mx from x = 0 to x = 1…

A: The given line equation is y=mx from x=0 to x=1 about the axis. Find the lateral surface of the…

Q: Find the average value of f(, y) = 2ry over the rectangle with vertices (0, 0), (5, 0), (5, 3), (0,…

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Q: Find the normal line for the level surface f(x,y,z) = 5x3 + cos (5y) + In (6z) = c at the point…

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Q: Find the normal line for the level surface f(x,y,z) = 3x5 + cos (5y) + %3D In (5z) = c at the point…

A: Question is solved.

Q: Find the normal line for the level surface f(x,y,z) = 7x³ + cos (4y) + In (4z) = c at the point…

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Q: Use a parameterization to find the flux | F.n do of F = 5xy i- 4z k outward (normal away from the…

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Q: The joint pdf of a two-dimensional RV (X, Y) is given by f(x, y) = xy² + 0Sx 1), P (Y < –),

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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: Locate the centroid y of the cross section and determine the moment of inertia of the section about…

A: Given - A 3-d object with it's measurements To find the centroid  y and  the moment of inertia of…

Q: (2) Use the transformaiton u = xy, v = x² – y? to find JJ (æ* – y*)e*³ dA where R is the region in…

A: Given: The region bounded by the hyperbola xy=1 &amp;3, x2-y2=3 &amp;4 Where u=xy and v=x2-y2

Q: Evaluate the line integral (xy dx + y dy), where C is the curve y = sin(x), 0 ≤ x ≤ π/2

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Q: Calculate the integral of f(x,y,z)=3x2 +3y2 +z4 over the curve c(t)=(cost,sint,t) for 0≤t≤π. ∫c…

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Q: Calculate the area under y = x2 over [0, 1] using Eq. (11) with the parametrizations (t3, t6) and…

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Q: Use cylindrical coordinates to evaluate SI vz dv where E is the solid E bounded by the cylinder,…

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Q: Evaluate fff (3x + 2y)dV, where S is the solid bounded above by the plane z=4, below by plane z=0…

A: ∫∫∫(3x + 2y) dV=∫∫∫(3x + 2y) dxdydz = ∫z = 04∫y = -13∫x =-11(3x + 2y) dxdydz = ∫z = 04∫y = -134y…

Q: Find the moment of inertia about the x-axis of a thin plate of density d = 1 gm/cm2 bounded by the…

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Q: Find the moment of inertia of the area bounded by the parabola y^2 = 4x, x-axis, and the line x = 1,…

A: Given

Q: Calculate the moments of inertia (Ix and Iy) of the shaded area given in the figure with respect to…

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Q: Calculate the angle between the normals to the surfaces x²y + z = 3_ and x log z − y² = −4 at the…

A: Angle between two normal vectors a and b is  θ=cos-1±a·b

Q: Compute the flux of F= xi+yj+ z*k across the cone z =Vx2 + y? , 0szs1, in the downward direction.…

A: We have to find the flux in the downward direction.   Let us assume that x=rcosθ, y=rsinθ, z=r Then…

Q: Evaluate the line integral, where C is the given curve. хуеу2 dy, C: х %3D 3t, у%3D 2t?, = 2t3, 0st<…

A: x=3t, y=2t2,z=2t3

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: Evaluate the line integral along the curve C. (y + z)ds, C is the straight-line segment x= 0, y =…

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Q: Let S denote the part of the cone z = Vx2 + y? that lies between the surfaces z = 2 + sin(xy) and z…

A: Given : S denotes the part of the cone z=x2+y2 that liesbetween the surfaces z=2+sinxy and…

Q: Find the average of the function f(r,0)=r sin(0/2) over a disk of radius R centered at the origin.

A: Given function: f(r,θ)=r2*sinθ2Disk description: radius=R0 and center at the origin To find: Average…

Q: Use cylindrical coordinates. JSS x² + y2 dv, where E is the region that lies inside the cylinder x²…

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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…

A: We have to find double integral of F. ds

Q: Given the curve y = x´ and the lines y = 0 and y = 2 – x Find the moment of R with respect to the…

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Q: Find the polar moment of inertia of the region in the xy plane bounded by x² - y? 1,x2- y2=9, xy…

A: Solution is in step 2

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: 1. Compute the average height of the cone z = a> 0. r² + y² above the disk x² + y² ≤ a² for

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Q: E) Sketch the solid bounded by the cylinder ** +y = 4 and the planes y+z = 4 and z = 0

A: Here, we need to sketch the solid bounded by the cylinder x2+y2=4 and the planes y+z=4 and z=0.

Q: Compute the surface area of the cone generated by revolving the curve c(1) = (1, mt) about the…

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Q: Compute the line integral of the scalar function f(x, y, z) = 2x² + 8z ver the curve c(t) = (et, t2…

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Q: . Integrate f(x, y) = cos (x² + y²) (a) over the closed unit disk; (b) over the annular region 1 <…

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

Q: Evaluate the line integral. e ds where C is the curve given by x=2t, y=3t, 0<t<2

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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: 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: Use Stokes' Theorem to calculate fe F-dĩ, where F = zyi+3=j+5zk, and C is the closed path around a…

A: Here given that F→=xy i^+3z j^+5x k^ and curve C in xz-plane. To find: ∫C F→·dr→ by Stokes' theorem.

Q: * Evaluate the sur face in tegral S F · d3, where + y?7 + :? and S is the boundary of the solid…

A: Given data: F→=x2i→+y2j→+z2k→ S is the boundary of the solid half-cylinder  0≤z≤1-y2, 0≤x≤2 Using…

Q: Find the normal line for the level surface f(x,y,z) = 7x5 + cos (5y) + In (9z) = c at the point…

A: The given level surface is: f(x,y,z)=7x5+cos(5y)+ln(9z)Given point is:  (9, 3, 10)

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.