Find an equation of the largest sphere contained in the cube determined by the planes x = 0, x = 8, y = 4, y = 12, z = -1, and z = 7. %3D %3D

Q: Q6) Find the area of the portion of the cylinder x2 + y2 = 6y that inside the %3D sphere x² + y? +z²…

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Q: Find the standard equation of the sphere with center C and rad C(1, v2, -5); r= 3

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Q: ²+y? + - 2x – 4y + 8z + 17

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Q: The distance between the centers-of the following two spheres: x²-22x+y2-58y+z?=-961,…

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Q: Q2. Find the volume of the sphere x² + y +z = a (In Cartesian coordinate system). %3D

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Q: Find an equation for the sphere with the given center and radius. Center (0,0,10), radius = 2 O A. X…

A: Topic = Geometry

Q: Find the center and radius of each sphere. Sphere: x + y + z? – 10x – 4y + 10z - Center: Radius:…

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Q: y? dV, where T is the solid tetrahedron with vertices (0, 0, 0), (2, 0, 0), (0, 2, 0), and (0, 0, 2)

A: Given function f(x,y,z)=y2 Tetrahedron T is region with vertices (0,0,0), (2,0,0), (0,2,0) and…

Q: 2x2 dv, where T is the solid tetrahedron with verticies (0, 0, 0), (1, 0, 0), (0, 1, 0), and (0, 0,…

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Q: Show that the given equation represents a sphere and find its center and radius x² + y2 + z? + ax +…

A: The given equation is x2+y2+z2+ax+by+cz+d=0. The general equation of a sphere with center h,k,n and…

Q: Find the center C and the radius a for the spheres x2 + y2 + z2 + 4x - 4z = 0

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Q: (d) [[x - y dA where R is the triangular region with vertices (3, 10), (3, 0) and (-2, 0).

A: Use double integral

Q: • Find the area of the portion of the Sphere x² + y² + 2²² = 9 between the planes Z=1 and 2 = 0.…

A: The given equation of  plane is x2+y2+z2=9. The polar coordinates are x=rcosθ & y=rsinθ. The…

Q: Find the center and radius of the following spheres (x – 3)² + (y – 2)² + (z – 1)² = 9

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Q: Complete the square to write the following equation in the standard form for a sphere. x²+y²…

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Q: The distance between the centers of the following two spheres: x²+10x+y²+14y+z²=-73,…

A: Given that: x2+10x+y2+14y+z2=-73      .......(1)2x2-4x+2y2+2z2+8z=-5     ........(2)

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: Find the equations of the sphere through the circle x + y +2 =1, 2x+ 4y+5z= 6 and touches the plane…

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Q: Find the point on the sphere x? + y² + z² = 3 farthest from the point (-6, 6, –6). Farthest point is

A: Given equation of the sphere, Given point is (-6, 6, -6). Distance of the point (-6, 6, -6) from…

Q: Find the center and radius of the following sphere: x2 + 2x + y? + z2 + 4z + 1 = 5

A: The equation of the sphere is x2+2x+y2+z2+4z+1=5 To find its center and radius.

Q: Find an equation of the sphere that passes through the origin and whose center is (-10, 11, – 2).…

A: Given: Origin point : ( 0 , 0 , 0 ) Center : ( -10 , 11 , -2 )

Q: Find the center C and the radius a for the spheres x2 + y2 + z2 - 4x + 6y - 10z = 11

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Q: The portion of the sphere x² + y² + z² = 25 inside the cylinder x2 + y² = 9

A: Given: The portion of the sphere x2+y2+z2=25inside the cylinder x2+y2=9 To find the area of the…

Q: The solid that is the common interior below the sphere x + y + z = 80 and above the paraboloid z =…

A: We need to find the upper limit for the given integral.region is bounded below by the sphere and…

Q: Graph the first-octant portion of the plane. x+y+z=10 Choose the correct graph below. OA. B. C. OD.

A: The given equation of the plane is x+y+z=10. For the x -intercept set y=z=0 to get x+0+0=10 or…

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: Q3) Find the centers and radius of the spheres in x? + y? + z? + 4x - 4z = 0 x? + y? + z? - 6y + 8z…

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Q: Find the center of the sphere x² + y? + z? + 4x – 8z + 19 =

A: To find the center of the equation from the given equation.

Q: Find the center C and the radius a for the spheres x2 + y2 + z2 - 6y + 8z = 0

A: To Determine: Find the center C and the radius a for the spheres  Given: we have an equation…

Q: Find an equation of the sphere that passes through the origin and whose center is (-6, – 4, 12). OA.…

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Q: Find the point lying on the intersection of the plane x + y +z = 0 and the sphere x2 + y? + z? = 25…

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Q: What is the equation (mathematical expression) for a hollow sphere with center at the origin and…

A: According to question,Given,Center of hollow sphere =Origin 0,0,0,Radius = 10

Q: SSx x dA; R is the portion of the disk x +y s 16 in the second quadrart

A: According to the given information, it is required to find the value of the given integral.

Q: Find the area of the surface . The part of the paraboloidy v? + z? = 9. a. 플 (37/37- 1) b.…

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Q: Find the volume of the sphere x? + y² + z² = a² (In Cartesian coordinate system).

A: To calculate the volume of the sphere, use the following formulae.…

Q: Find the largest and smallest distances between the point P(1, 1, 1) and the sphere x² + y? + z? –…

A: Given circle is x2+y2+z2-2y+6z-6=0, and P(1, 1, 1) Let C be the center of the circle.…

Q: The volume of the tetrahedron enclosed by the coordinate planes and the plane 5x +y+Z = 10 is ? O A.…

A: The volume of the tetrahedron enclosed by the coordinate plane 5x+y+z=10   …..(1) is will be given…

Q: Find the radius and center of the sphere. x2 + y² +z² - 6x + 8y – 4z = - 13 r=

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Q: Find c > 0 such that the area of the region enclosed by the parabolas y = a? – c² and y = c – a? is…

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Q: Find the standard equation of a sphere that has diameter with the end points given below. (3, 8,…

A: to find standard equation of sphere that has diameter with end points 3,8,-2,-1,4,10

Q: Find the center and radius of the sphere x2 + 18x + y? + 4y + z2 + 10z = –74 Center: ( || ) Radius:

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Q: Which of the following represents the radius of the sphere whose equation is x² + 8x +y2 – 16y +z² –…

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Q: of the rectangular prism. A=(3,0,0), B=(3,5,0), C= (0,5,0), 0-(0 ₁1 b. Find AB.√ (3-3)2 + (5-0)² +…

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Q: Find the area of the surface. 12. The part of the sphere x2 + y2 + z2 = 4z that lies inside the…

A: Solution:GivenSphere:   x2+y2+z2=4zParaboloid: z=x2+y2To find the area of the…

Q: Find the center and radius of the sphere. 2 4x + 4y + 4z + x + y+z= 25

A: Topic = Sphere

Q: 2. Find the area of the ellipse S on the plane 2x + y + z = 2 cut out by the cylinder x2 + y? = 2x;…

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Q: Find an equation of the sphere that passes through the origin and whose center is (6, – 6, 3). OA.…

A: We will find the equation of sphere as following.

Q: Find the area of the surface. The portion of the sphere x2 + y² + z² = 625 inside the cylinder x2 +…

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Q: Find the points on the sphere x^2 + y^2 + z^2 = 1 that are closest to and farthest from the point…

A: Given sphere, x2+y2+z2=1 Consider gx,y,z=x2+y2+z2-1=0 The square of the distance between the points…

Q: Find the surface area of a quarter of the sphere x? + y2 + z2 = 4.

A: The equation of a sphere centered at x0, y0, z0 is defined using the formula: x-x02+y-y02+z-z02=r2,…