Find the equation of the sphere of radius 3 centered at (2, 3, 9). Ox? + y? + z? = 9 Ox² + y? +z? = 94 O (x – 2)? + (y – 3)² + (z – 9)² = 9 O (x – 2)? + (y – 3)² + (z – 9)² = 3 O (x + 2)? + (y + 3)2 + (z + 9)2 = 9

Q: Solve fff. 3x² + 3y²dV by using cylindrical coordinates, where G is a solid in the first octant that…

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Q: 42. Whatever the value of p > 0 in the equation y = x²/(4p), the y-coordinate of the centroid of the…

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Q: What is the equation of the plane to the surface z = e3y sin(3x) +2 at the point P ,0, 3 %3D O x- y…

A: The solution is given in the next step.

Q: 4. The terminal point of v=3i-2j is (4, -4) if the initial point is (1,-2). 5. The standard equation…

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Q: Find the maximum value of f(x,y,z)=2x+5y+13z on the sphere x²+y²+z²=36

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Q: Find the center C and the radius a for the spheres in Exercises 51–52. 51. x2 + y2 + z2 - 6y + 8z =…

A: We’ll answer the 51th question since we answer only one question at a time. Please submit a new…

Q: Let C be the boundaries of the ellipse 49x2 + 9y? = 49 taken in the counterclockwise direction. A…

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Q: Find the point on the sphere (x - 1)² +y² + (z + 9)² = 9 nearest to a. the xy-plane. b. the point…

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Q: Find the center and radius of the sphere X² + y² + z² −2x−4y + 8z + 17 = 0

A: Given: Equation of a sphere is x2+y2+z2-2x-4y+8z+17=0. To find the center and radius of the sphere.…

Q: Find a parametrization of the cylinder x2 + ( y - 3)2 = 9, 0 ≤z ≤ 5.

A: Given, the cylinder                         We have to find a parameterization of this given…

Q: Match the ellipsoids shown in the figure above with t 1) x2 + 4y + 4z? = 16 2) 4x2 + y +4z? = 16 3)…

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

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Q: F = [y3,n3] 4 c is the Parrabola y - sa2 from A (0,0) +0 Bl2,20) SF.di = Syoda tao dy y=5a2 Since y…

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

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Q: 6. What is an equation for the largest ball centred at (0,0, 1) that can fit in the paraboloid z…

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Q: (b) f(x, y) dA where D lies below the paraboloid z = x2 + y?, above the ry-plane, and inside the %3D…

A: Let's find.

Q: 323 + 4z2-5z+1 dz (z-2i)(23-2) 1. Compute: where C = {|z| = 3} is the circle of radius 3 centred at…

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Q: Find a parameterization for the quarter sphere x² + y² + z² = a² where z > 0 and x > 0.

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Q: Q2 (a) Solve , 3x? + 3y²dV by using cylindrical coordinates, where G is a solid in the first octant…

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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: Find the equation of the sphere with center c= (0, -1, 2) and radius r= 5. O x2 + y + 1)2 + (z + 2)2…

A: Biref answer is given below.

Q: The part of the cylinder y? + z2 = 81 that lies between the planes x = 0 and x = 5. (Enter your…

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Q: Find the point on the ellipsoid x2 + y2/4 + z2/9 = 1 for which x + y + z is largest.

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Q: et T(x, y, z)= 100+ x² + y² represent the temperature at each point on the sphere x² + y² + z² = 80.…

A: Given: Tx,y,z=100+x2+y2sphere g= x2+y2+z2=80plane h =x-z=0

Q: 1. The part of the sphere x? + y² + z² = a² that lies within the cylinder x² + y² : = ax and above…

A: To Determine :-  The part of the sphere x2 + y2 + z2 = a2 that lies within the cylinder x2 + y2 = ax…

Q: 4-22-y2 Compute y? Vx2 +y? + z² dz dx dy by converting to spherical 4-x2- coordinates.

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Q: 29. A tank full of water has the shape of a paraboloid of revolu. tion as shown in the figure; that…

A: Height is 4 feet and radius at the top is 4 feet So the parabola passes through the point (4,4) The…

Q: The upper half of the unit sphere x2+y2+z2=1 is z=Square root of 1-x2-y2. Find its centroid

A: Solution Given The intersection gives z2=1-x2+y2we need to find the centroid

Q: The exact solution of the 2q(z - px - qy) = 1 + q^2 equation and by using this solution, Find the…

A: The given equation can be written in the form of the Clairaut's equation as below: z=px+qy+121+q2q…

Q: Find the value of ∫∫s(x^2y^2z^2)dS correct to four decimal places, where S is the part of the…

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Q: Obtain the Solution x, y > 0, xy > 1 of 1 the PDE Ury Such that x+y 2у и 3 0, их on the hyperbola…

A: 1st we set up the initial value condition and draw the figure than set up PDE and solve it

Q: 3. Find the maximum and minimum values of the function f(x, y,z) = x + y+z on the ellipsoid x? +4y²…

A: Given the function is fx,y,z=x+y+z              ...1 and let hx,y,z=x2+4y2+9z2-1764=0…

Q: Find the center C and the radius r of the sphere S: x2 + y2 + z2 + 4x + 8y – 8z =-11

A: A geometrical object which is in the shape of ball is called sphere. Outer surface of sphere is…

Q: 4. You want to find the point (s) on the ellipsoid of equation 4x2 +9y? + z? = 1 That are closer to…

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Q: Find the maximum and minimum values of f(x, y, z) = x - z on the ellipsoid x² + 2y? + 22 = 1.

A: maximum=? minimum=?

Q: Find the center C and the radius a for the spheres (x - 1)2 + (y - 2)2 + (z + 1)2 = 103 + 2x + 4y -…

A: Standard equation of sphere is given as x-x12+y-y12+z-z12=r2, where x1,y1,z1 is center of sphere and…

Q: Find the maximum value of  f(x,y,z)=27x+7y+3z on the sphere x2+y2+z2=81

A: For this question we will use Lagrange multipliers where f(x,y,z)=given function and…

Q: Find the maximum value of f(x,y,z)=25x+3y+17z on the sphere x2+y2+z²=100

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Q: 1. Classify the equations below according to the type : * i) Uxx- 2uxy – 2uy = 0 O hyperbolic O…

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Q: 4) The solid lies between planes perpendicular to the x-axis at x = 0 and x = 6. The cross sections…

A: Given: y=-5x  to the parabola y=5xAs we can see in the diagram is given below.

Q: 11. Evaluate ([(y² +z? )dS where S is the part of the paraboloid x=4-y -? that lies in front of the…

A: We will evaluate the given integral.

Q: 6. The part of the surface z = 1 + 3x + 2y² that lies above the triangle with vertices (0, 0), (0,…

A: Given: A surface z=1+3x+2y2 and vertices of triangle (0, 0), (0, 1) and (2, 1). To find: Area of…

Q: Find the absolute maximum and absolute minimum of the function f (x, y, z) = x³ + 2y along the curve…

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Q: Find the maximum value of f(x,y,z)=9x+14y+29z on the sphere x2+y2+z²=25

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Q: The equation of the sphere with radius r = V75 and center C(2,1, – 1) is (a) x² + y² + z² + 4x + 2y…

A: The general equation of a sphere with radius r and center a,b,c is x-a2 + y-b2 + z-c2 = r2

Q: 35. Above the cone z = a² + j? and below the sphere x² + y² + z² = 1

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Q: Identify the surfaces of equations in the Cartesian form. Show your complete solutions. (a) 2² = 4 +…

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Q: Evaluate +y² 1 Ez² + y² JJJ₁² dV, where E lies between the spheres z² + y² + 2² +2² 16 in the first…

A: Given that,