Find a parametrization, using cos(t) and sin(t), of the following curve: The intersection of the plane y 2 with the sphere x² + y? + z? = 104 r(t) = (O0:0)

Q: Suppose r(t) = ⟨t, 0⟩, for a ≤ t ≤ b, is a parametric description of C; note that C is the interval…

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Q: If E is the solid that lies under the plane z = 3 which its base on the xy-plane is between the two…

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Q: Find an equation for the plane tangent to the given surface at the specified point. z = v², y = u? +…

A: Given that

Q: Find a parametrization, using cos(t) and sin(t), of the following curve: The intersection of the…

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Q: Select the correct parametrization of the following curve: The intersection of the plane y = 2 with…

A: Find the relation between x and z from the equation of the plane y = 2 and the equation of the…

Q: (c) The cone r² = 4(y² + z?) for (0 <x < 4

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Q: Let D be the unit disk: x + y² < 1. Evaluate I| 7exp(x² + y²) dx dy by making a change of variables…

A: Given:The integral

Q: Consider the ellipsoid 4x? + y?+ 222 = 25. Find all the points where the tangent plane to this…

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Q: Find the coordinates of the centroid of the curvex = et cos t, y = et sin t, 0 ≤ t ≤ p.

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Q: Consider the following. C: counterclockwise around the circle x2 + y2 = 49 from (7, 0) to (0, 7) (a)…

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Q: Find the parametrization of the tangent line to the space curve r(t) = (e" , sin(t), (t + 1)-³) at t…

A: Given that  r(t)=(e^(4t),sin(t),(t+1)^(-3)) at t=0 We have to find out the parameterization of the…

Q: Use cos(t) and sin(t), with positive coefficients, to parametrize the intersection of the surfaces…

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Q: (a) The moment of inertia of a surface about the z axis is given by the formula I (le x2 + y? dS.…

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Q: 1. Find by integration the area of the surface of revolution generated by revolving the loop about…

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Q: Find the curvature of the plane curve with equation y (x, f (x)) on the curve, by using the…

A: We will find out the required value of curvature .

Q: Find the length of the parametric x = e*, y = e=t, z = /2t, where 0 <t<1. ||

A: Given: x=et, y=e-t, z=2t  where 0≤t≤1

Q: Use a scalar line integral to find the length of the curve r(t) = (20 sin , 20 cos ,5), for 0 < t <…

A: Given

Q: Use cos(t) and sin(t), with positive coefficients, to parametrize the intersection of the surfaces…

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Q: Find the parametrization r(t) = [x(t), y(t), z(t)] of the curve obtained by intersecting the…

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Q: Give the integral representing the length of the parametric curve x=t^3, y=t^4, 0≤t≤1.

A: Given: A parametric curve:   Now the length of the parametric curve is given by the formula:

Q: 2. Use Stokes theorem to evaluate fs da. a) a = x2 sin z da + y? dy + ry dz, S is the part of the…

A: As per our guidelines, we are supposed to answer only one question and rest can be reposted Given:…

Q: use a parametrization to find the flux ∬S F . n dδacross the surface in the specified direction. F =…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: use a parametrization to find the flux ∬S F . n dδacross the surface in the specified direction. F =…

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Q: Determine the surface area of the solid obtained by rotating the following parametric curve about…

A: Given parametric curve is x=9+t2 and y=2t, 0≤t≤2. We have to determine the surface area of the solid…

Q: Consider the plane curve C ∶ r(t)=(1/3t^3, 1/2t^2) (a)Make a table of values and sketch the curve…

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Q: Consider the parametrization y: [0,47] → R, (t) = (t cos t, t sin t), of a counter-clockwise spiral…

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Q: H=pz coup ap te'sing a4 tp'ar At point (1, ,0)

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Q: The parametric form of the solutions of the PDES -y zz +x zy = 0, :(s, s²) = s³ (s, s*) %3D %3D z…

A: Option (c) is correct

Q: Find a parametrization, using cos(t) and sin(t), of the following curve: The intersection of the…

A: Given problem is :

Q: Find the line integral with respect to arc length ∫C(6x+4y)ds, where C is the line segment in the…

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Q: . Show that the tangent plane to the surface 2yyo cz at the point P(xo,Y0, zo) is given by the 2rro…

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Q: Find a parametrization for the curve y = Vx with terminal point (0, 0) using the angle 0 in the…

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Q: Use the Stokes' theorem to evaluate p Fdr where F = 3yi + yj+ :k and C is the circle r2 + y? = 3 at…

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Q: The parametric form of the solutions of the PDES -y žz + x zy = 0 , z (s, s²) is z(s, 1) = s cost…

A: Second option is correct

Q: Find the circulation of F= (xy)i+(yz')j-(2xyz)k around the curve C in the counterclockwise direction…

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Q: Find a parametrization for the curve that matches the lower side of the parabola x-1=y2. A. x =…

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Q: 2. Let a(t) = (3t-t, 3t2, 3t + t), for te R. %3D (i) Calculate the equation of the osculating plane…

A: Introduction: The formula of curvature of and torsion is given by, κ(t)=α"(t)…

Q: 2. Let R(t) = }sin 4t î – bcos“(21) j + 2t Ř. Find the moving %3D trihedral of the curve of R(t) at…

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Q: In each of the following cases, define a parametrised curve y : [a, b] → C whose image * is: (a) The…

A: When we deal with contours ,we think about function of two and three variables. Contours in two…

Q: find the Jolume of the salid genereted by revaling- the curve 4t'qy=36 between y = 0. and g=2 Gbout…

A: The objective is to find the volume of the solid about y-axis.

Q: Find the work done by the force field F(x,y)=5x2i−2xyj on a particle that moves once around the…

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Q: Select the correct parametrization of the following curve: The intersection of the plane y = 2 with…

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Q: Compute the surface area of the surface generated by revolving the astroid with the parametrization…

A: In this question, we find the surface of revolution by rotating the given parametric curve around…

Q: Evaluate the unoriented line integral +y² + z²) ds along the parametric curve a : [0, 1] → R³ with…

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Q: C is the intersection curve between the paraboloid z = x² + y? and the plane 6x + 8y – z = 21,…

A: Strokes theorem:

Q: For the parametric surface r(u, v) = (u cos v, u sin v, 0) where 0 ≤ ≤2 and 0 ≤ ≤ 27 and which is…

A: Given r(u,v)=u cosv, u sinv, 0 where 0≤u≤2,  0≤v≤2π r→u=cosv, sinv, 0 r→v=-u sinv, u cosv, 0…

Q: Let F = (x'e* +2.xy - 2y)i+(cos y+x² +3x)j and let C be the ellipse with equation (2x - 2y) +(x+ y)°…

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