Find a parametric representation of the cone z = /3x + 3y² in terms of parameters p and 0, where (p, 0, p) are spherical coordinates of a point on the surface. X = Edit

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: find a parametrization of the surface. 1.The surface cut from the parabolic cylinder y = x2 by the…

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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: Find the angle between the two planes x − 2y + z = 0 and 2x + 3y − 2z = 0. Then find parametric…

A: The equation of two planes are x-2y+z = 0       ...... (1) 2x+3y-2z = 0   ...... (2) Angle between…

Q: find a parametrization of the surface. The cap cut from the sphere x2 + y2 + z2 = 9 by the cone z =…

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Q: Find a parametric curve r(t) that represents the curve of intersections of the semi ellipsoid…

A: We will find the curve r(t) that represents the curve of intersections of two surfaces.Below find…

Q: A circular helix in xyz-space has the following parametric equations, where θ ∈ R. x(θ) = 4 cos θ…

A: Arc length in 3d We want to determine the  arc length of a  curve given by parametric equation ,…

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: Describe the set in cylindrical coordinates. y^2 + z^2 ≤ 9, x ≥ y

A: Let x=rcosθ, y=rsinθ  and z=z. And the given equation is x ≥ y ⇒ cosθ ≥ sinθ

Q: Find an equation of the form r = f(0, z) in cylindrical coordinates for the surface 5x2 - 5y2 = 5.…

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

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Q: The four corners of a thin homogeneous and square plate with side 2a are folded up so that they…

A: It is given that the side length is 2a.Let the total mass of the system is M.

Q: 3. Let W be the part of the unit sphere centered at origin such that rectangular coordinates of each…

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Q: . Determine the parametric equations of the curve of intersection of the ellipsoid 4x² + y² + 4z² =…

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Q: Find a parametric equation for the curve of intersection of the cone x²+y² = z² and the plane x+2z =…

A: We have to find a parametric equation for the curve of intersection of the cone x2+y2=z2 and the…

Q: Let D be the region enclosed by the surfaces z =-/4-x² - y and x² +y* . Determine JI| zdv by using…

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Q: 4. Consider the surface defined by the portion of the cone z = -Vx2 + y? that lies below the…

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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: Describe the set in cylindrical coordinates. x^2 + y^2 + z^2 ≤ 1

A: To convert into cylindrical co-ordinates let x = r cosθ, y = r sinθ, z=z   For x^2 + y^2 + z^2 ≤ 1…

Q: Identify the surface whose equation in spherical coordinates is given by P=6 cos o O Paraboloid O…

A: We will identify the given surface.

Q: The parametrization G(0, 6) = (a sin 0 cos o, b sin 0 sin ø, c cos 0), 0 < 0 < 7,0 < ¢ < 2n of the…

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Q: A thin plate of constant density is to occupy the triangular region in the first quadrant of the…

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Q: Use spherical coordinates. Evaluate z dv, where E lies between the spheres x2 + y2 + z² = 1 and x2 +…

A: Using spherical  coordinate we can solve it very easily.

Q: Please make sure its right. calc 3 Find a parametric representation for the part of the plane z = x…

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Q: Describe the set of all points P = (x, y,z) satisfying x^2 + y^2 ≤ 4 in both cylindrical and…

A: Given,        x2+y2≤4

Q: Find a parametrization of the curve. The intersection of the surfaces z = x^2 − y^2 and z = x^2 + xy…

A: Given : The surfaces z = x2 - y2 and z = x2 + xy - 1.   To find the parameterization of the curve.

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: Consider the surface S consisting of the part of the paraboloid z=5 - x2 - y2 in the first octant.…

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Q: A. Calculate the centroid coordinates of quarter circle (x + y² a) in the first quadrant, use double…

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Q: Use spherical coordinates. Evaluate z dv, where E lies between the spheres x2 + y2 + z2 = 9 and x2 +…

A: Given equations of spheres: x2+y2+z2=9 x2+y2+z2=36 For spherical coordinates: x=ρ cosθ sinϕy=p sinθ…

Q: Of the curve lying in the plane XZ-, (x - a) ^ 2 + z ^ 2 = r ^ 2 in R ^ 3 The region created by…

A: Given that the region is being created by rotating x-a2+z2=r2 in ℝ3 around the z-axis.  To find the…

Q: Identify the surface whose equation in." spherical coordinates is given by p = 8 cos ø Cone O…

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Q: 2. Use parametric equations to derive the formula for the lateral surface area of a right circular…

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Q: 2. Let W be the portion below the plane z = centered at the origin in R3. Give a domain for…

A: We will use relation between cartesian and spherical co ordinate to find domain of W

Q: Identify the surface whose equation in spherical coordinates is given by p= 2 cos o O Cone O Sphere…

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Q: By using the cylindrical coordinates to evaluate {{[3dV where Q bounded by paraboloid 2=2- x2 - y2…

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Q: A hole is drilled through the center of a sphere x2 + y? +z? = R², leaving a ring-shape solid. If…

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Q: Find parametric equations for the tangent line to the curve of intersection of the paraboloid z = x2…

A: Tangent line to ellipse will be perpendicular to normal's of both the surfaces.  Therefore tangent…

Q: use spherical coordinates to find the moment of inertia about the z-axis of the solid of uniform…

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Q: The motion of a fluid particle is defined parametrically as follows, x(t) = sinh(t), and y(t) =…

A: Given - The motion of a fluid particle is defined parametrically as follows xt = sinht , yt = cosht…

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

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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: Find parametrizations The portion of the paraboloid y = 2(x2 + z2 ), y&lt;=2, that lies above the…

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Q: Identify the surface whose equation in spherical coordinates is given by p= 2 cos o %3D O Sphere…

A: Converting spherical coordinate into rectangular coordinate.

Q: Find a point on the ellipsoid x² + 4y² + z² = 30 where the tangent plane is perpendicular to the…

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Q: verify Stokes § = (a%-y)i - yz'i over the uppea hazf SOD Face Of the sphere =1 bounded by the

A: Given that,  F→=(2x-y)i→-yz2j→-y2zk→ To verify Stoke's theorem: ∫CF→·dr→=∬Scurl F→·n^dS Here C is…

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

A: given sphere x2+y2+z2=R2s and a drill of cylinderical shape x2+y2=R2d use polar coordinate to…