The equation z? = 10 – x² – y? defines a/an %3D a) ellipsoid c) paraboloid b) cone d) hyperboloid

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 the center C and the radius a for the spheres in Exercises 51–52. 51. (x + 2)2 + y2 + (z - 2)2…

A: To determine the centre and radius of the sphere.

Q: What is an equation for the largest ball centred at (0,0, 1) that can fit in the paraboloid z = 3 -…

A: To find the equation for the largest ball centered at (0, 0, 1) that can fit in the below equation…

Q: Find the surface area of the paraboloid z= 1 - (x2 + y?) that lies between the sphere x? + y? + z² =…

A: Given the region

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: Compote the volume of a reoion inside the Sphere x" +Y? +z² =4 ond between two sheets of the…

A: We have to find V0, V0 = Volume of sphere - V1-V2And from Symmetry we know that V1 = V2⇒V0 = Volume…

Q: A tank full of cooking oil has the shape of a paraboloid obtained by rotating a parabola about the…

A: We have given a paraboloid tank full of cooking oil. Height of tank = 4m. Radius at its top = 4m. We…

Q: 39. Find the surface area of the portion of the hyperbolic paraboloid r(u, v) = (u+ v) i + (u – v)…

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Q: Use the parametric equations of an ellipse, x = 3 cos (0), y = 4 sin(0), 0≤ 0 ≤ 2T, to find the area…

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Q: Find the area of the surface. The part of the sphere x2 + y2 + z² = 4z that lies inside the…

A: Given sphere is x2+y2+z2=4z that lies inside the paraboloid  z=x2+y2. We have to find the area f the…

Q: B- Find the area of the ellipse resulting from the intersection of the plane x+y+z=6 with the…

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Q: Which of the following is not a parametrization of the parabola y = r² ? Oz= Vt, y=t Oz-t, y-t Oz- ,…

A: We will check which parametrisation is correct.

Q: Which quadric surface is represented by the equation below? 22 = 1 16 y? 4 Ellipsoid Cone Elliptic…

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Q: and the plane - 3 X + Z Intersect along a line. Find Parametnic desenetion of this la

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Q: The solid that is the common interior below the sphere x² + y2 + z2 = 80 and above the paraboloid z…

A: Given sphere is x2+y2+z2=80and the paraboloid z=12x2+y2set up a triple integral for the volume of…

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

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Q: Find the approximate area of ​​the part of the plane x=z that is between the planes y = 0 and y = 6…

A: As per the question we have to calculate the area of the plane surface x = z bounded by the planes y…

Q: The volume of the tetrahedron enclosed by the coordinate planes and the plane 9x +y +Z = 18 is ?

A: We want to find the volume of the tetrahedron enclosed by the co-ordinate planes, i.e. x=0, y=0, z=0…

Q: (b) Find a parameterization, in spherical coordiantes, for the ellipsoid 4x2 + 9y2 + 2²/4 = 1 that…

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Q: Use the parametric equations of an ellipse, x = 5 cos(0), y = 4 sin(0), 0 < 0< 2n, to find the area…

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Q: 8. Find the surface area of the part of the sphere x2 + y? + 22 : = 4z that lies inside the…

A: The solution is given as

Q: Find the isogonal trojecdories of x*+y² =r² at 45",

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Q: Find the area of the part of the sphere x2+y2+z23D 9z that lies inside the paraboloid z =r+y?. a.…

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Q: PICTURE

A: We are given that the cone ax2+by2+z2 = 0 and the ellipsoid 2x2+4y2+z2 = 42 intersect and are…

Q: For the surface x? + y? = 2z? a) Find an equation in cylindrical coordinates

A: In this question, the concept of conversion of the coordinate system is applied. Cartesian…

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 surface area of the part of the circular paraboloid z = x + y that lies inside the cylinder…

A: Solve the given

Q: 5 + 2? + y, the cylinder Evaluate e dV where E is enclosed by the paraboloid z = E 2 + y? = 1, and…

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Q: Use the parametric equations of an ellipse, x = a cos(0), y = b sin(0), o sos 2r, to find the area…

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Q: 1 Find the surface area of the part of the hyperbolic paraboloid z = (x² - y²) that lies inside the…

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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: Find the area of the surface. The part of the paraboloid z = 1 – x2 - y? that lies above the plane z…

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Q: Find the surface area of the part of the hyperbolic paraboloid z = y? –x² that lies between the…

A: Given The hyperboloid z=y2-x2 that lies between the cylinders x2+y2=1 and x2+y2=4.

Q: The equation of a sphere of radius 3. centered at the origin in cylindrical coordinates is + = 9.…

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Q: 16. classify the surface: * 1- y? = 5x2 + 6z? Sphere Elliptic paraboloid Cone Plane Ellipsoid

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Q: Use the change of variables formula to prove that the volume of the ellipsoid given by ()* + (#)* +…

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

Q: Use spheri\cal coordinatcs Evaluate y'zdV, where E lies above the cone 4 = /3 and below the Sphere…

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Q: The object shown in the figure is axially symmetric and its curved surface is described in…

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Q: Which of the following is that orientation of the ellipsoid 3x + y? + 2z2 =1 %3D where the outside…

A: The given problem is to find the positive orientation of the given ellipsoid. Given ellipsoid…

Q: Use the parametric equations of an ellipse, x = 2 cos(8), y = 3 sin(8), 0 < 0 < 27, to find the area…

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Q: Find the area of the ellipse cut from the plane z = 6x by the cylinder x + y = 9. .... Surface area…

A: Substitute the equation of plane in the cylinder equation

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: 8. Draw the figure and Find the area of the part of the sphere x? + y? + z? = 3z that lies inside…

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Q: A tangent plane to the ellipsoid x². y? a b2 meets the axes in A, B, C. Show that the envelope of…

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Q: Evaluated the counter integral 9,+z² - z-1 dz ,where C 1. The circle z| = 0.5 2. The circle |z+1-i=…

A: Given contour integral is  ∮Cezz3+z2-z-1dz We can write it as ∮Cez(z+1)2(z-1)dz Poles of…

Q: The surface area of the part of z = 2+ /4 – x² – y? that lies inside the paraboloid z = x² + y? is

A: Given is the equation of a surface and a paraboloid. The objective is to find the surface area. The…

Q: Which of them are true? I) y? 1 6. Ellipsoid 6. II) y? = 4x? + 16z2 Hyperboloid %3D III) Paraboloid…

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Q: Parametrize the intersection of the surfaces using t = z as the parameter. (If there are multiple…

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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…

Q: The solid that is common to the interior below the hemisphere z = /80 – x² – y2 and above - the…

A: Set up a triple integral.