x=-cost + 1 (y = - sin t+ t 8- The parametric curve 0

Q: A hole is drilled through the center of a sphere x²+y² +z? = R,², leaving a ring-shape solid. If the…

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Q: 1. Convert the equation of the sphere : x + y +6y+z? = 0 Into. a) Cylindrical coordinates (An…

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Q: A hole is drilled through the center of a sphere x² + y² + z² = R,², leaving a ring-shape solid. If…

A: A per your request , (b) The equation of sphere is given as , x2+y2+z2=Rs2 and Radius of drill=Rd…

Q: A hole is drilled through the center of a sphere x² + y² + z² = R,², leaving a ring-shape solid. If…

A: The radius of the sphere is 'Rs' and radius of cylindrical driller is 'Rd'. When the cylindrical…

Q: A point moves along the intersection of the elliptic paraboloid z = 9x? + 3y² and the plane.x…

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Q: 1: Describe the solid bounded by the sphere ² +y² + z² = 9 and the pla 2 over the xy-plane using %3D…

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Q: (a) The moment of inertia of a surface about Sls x? + y? dS. Find the moment of inertia cylinder x?…

A: (a) Given, the suface z=xy lying inside the cylinder                         x2+y2=3.

Q: Find the parametric equations for the curve of intersection between the cylindrical surface S: x +…

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Q: sketch the solid whose spherical coordi- nates (p, 4, 0) satisfy the given inequalities. 0<p<2/cos…

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Q: 15. Find the radius of curvature at 0 = ÷n of the parametric equations x = 3(0 + cos 0), y = 3(1 —…

A: Given two parametric equations, x=3(θ+cosθ),y=3(1-cosθ) To find the radius of curvature at θ=π3

Q: Find the surface area of the solid that is obtained by rotating the graph of the parametric curve…

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Q: Consider the surface S shown in the gure and whose parameterization is given by: r(u, v) = (sin v,…

A: Consider the surface S shown in the gure and whose parameterization isgiven by: r(u, v) = (sin v, u…

Q: In which part of the (x, y) plane the following equation is elliptic? Uzr + 4ury + (x² + 4y*) uyy =…

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Q: ns are pre uestionnaire). Box Luck!!! Question 46 Which of the following best describes the surface…

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Q: Determine the area of the surface with parametric equat ions x = 2u?, y = v², z = 2uv, %D 0<u< 3, 0<…

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Q: As shown in the picture at right, a solid is bounded below by the xy-plane, above by the sphere x² +…

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Q: Are there any points on the hyperboloid r2 - y? – 22 = 1 where the tangent plane is parallel to the…

A: Given hyperboloid ;    x2-y2-z2=1  and equation of plne which is parallel to tangent plane  x+y-z=0

Q: find a parametrization of the surface. 1.The portion of the cylinder (x - 2)2 + z2 = 4 between the…

A: 1) Given information:

Q: What is the center of gravity of the solid formed when the plane region bounded by y^2 = 4x in the…

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Q: Evaluate the surface integral. (4x + 4y + 4z)dS Where S is the parallelogram with parametric…

A: To evaluate this integral, first change the variables to the parameters given in the surface as.

Q: A hole is drilled through the center of a sphere x +y +z? = R,', leaving a ring-shape solid. If the…

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Q: Q2: A cube of edge 24mm is resting on the top of a frustum of cone of base diameter 60mm and top…

A: We are asked to draw the isometric view of the solid.

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: A hole is drilled through the center of a sphere x?+y² + z² = R,?, leaving a ring-shape solid. If…

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Q: Find the area of the surface that is generated by revolving the portion of the curve y = 2/1-, zE…

A: Use formula of surface area revolved about x axis

Q: Convert into cylindrical coordinates. Tis in the First Octant bounded by Z = 3√x²+4/² Z SS S dy √x²…

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Q: 2. The portion of a cylinder of radius 3 centered along the y-axis that lies between the planes y =…

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Q: 3. Find the exact area of the surface obtained by rotating the curve described by the parametric…

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Q: At what points does the curve r(t) = ti + (3t - t2)k intersect the paraboloid z = x2 + y2? (If an…

A: Given- r(t)=ti^+(3t-t2)k^z=x2+y2 To find the intersection point of the given curve and paraboloid.

Q: The planet is spherical with a radius of 1 unit in length. Suppose that in a coordinate system whose…

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Q: Find a point on the ellipsoid x2 + 4y2 + z2 = 9 where the tangent plane is perpendicular to the line…

A: Given  The equation of ellipsoid is given by fx,y,z=x2+4y2+z2-9 The line is x=2-4t, y=1+8t and…

Q: Write the equation x +z* - (y- 1) = 0 in cylindrical sy stem. W hich surface does it represent? Give…

A: Given :            The equation x2 + z2 - (y - 1)2 = 0   To write the given equation in…

Q: Consider the spherical surface E of center at C= (0,0.2) and radius 3. There are two planes parallel…

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Q: 2. Find the area of the surface generated by revolving the curve r = Vcos 20, 0s0 ST/4. about the y…

A: Surface area generated by revolving the curve 'r' about y-axis = 2π∫αβxr2+(drdθ)2 dθ

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

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Q: 3- Find the surface area of the solid obtained by rotating the curve z= 2/4- y; 0Sysabout the…

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Q: Sketch the curve of intersection of the surfaces. The ellipsoid 2x + 2y² + z? = = 24 and the…

A: We have to write the intersection curve

Q: Quertion: Conidee a dihedral Dy= (agbra" =b'=lab)= 1). Give the detxls of your! work.

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Q: Use cylindrical coordinates to evaluate SIſe* dv, where Gis the solid bounded by paraboloid z = 2+x…

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Q: 1. Let S be the part of the plane 2.x – 2y + z = 1 inside the “cylinder" whose walls are given by…

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Q: 1. Find the area of the surface generated by revolving the parametric curve x =rcos , y = r sin &…

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Q: 30. The equation of the tangent plane to the surface z = x? – 2y² at x = 1, y = 0 is (а) 2 — : 2т —…

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Q: In which of the choices below is a parametrization for the tangent line to the curve of intersection…

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Q: Find the area of the surface obtained by rotating the curve of parametric equations T = 2 cos 0, y =…

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Q: S Find the voleime of the solid generated by revolving the region baunded by the given lines Cnd…

A: Hint: Try Disk Method to find the volume.

Q: (10) Sketch the solid bounded by z = x2 + y? and z 4- x2 - y². Use cylindrical coordinates to find…

A: Given ∫∫∫Dx2+y2dVand solid bounded by z=x2+y2 and z=4-x2-y2

Q: Evaluate the area of the surface generated by revolving the curve y = 2/a, from x = 0 to x = 3. y -…

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Q: 17. Let T be the solid bounded below by the half-cone z = Vr2 + y? and above by the spherical…

A: Consider T be the solid bounded below by the half cone z=x2+y2 and above by the sphere x2+y2+z2=1.…

Q: Find an equation for the paraboloid z = 2 – – (x² + y²) in cylindrical coordinates. (Type theta for…

A: Given: - The equation is, z=2-(x2+y2) To find: -The equation for the paraboloid in the cylindrical…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.