Which of the following point is the farthest point on the sphere z? + y² + z² = 4 from the point (3,1,-1)? Oa. Ob. d. O e.

Q: Does the sphere x + y + ? = 25 have symmetry with %3D respect to a) the xy-plane? b) the line e: (x,…

A: we have the sphere x2+y2+z2=25  here the radius is 5

Q: Assume that the Earth is a sphere. Howmany points are there on the Earth's surfacethat are…

A: In case of sphere, two points are equidistant from many points. Therefore their are infinite points…

Q: If a bug walks on the sphere x + y? + z² + 2x – 4y – 2z – 30 = 0 how close and how far can it get…

A: Sphere

Q: Let q (1) = . a. Where does q) intersect with the sphere x + y² +z? = 5? b. Find q'(t) and q'(n). c.…

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Q: Consider the sphere r? + y? + 22 = 9. Please find the equation of the plane tangent to this sphere…

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Q: Find the center and radius of the sphere x? – 6x – 8 + y? + 4y +z? – 20z = 0 OA C(3,-2,10), r = 11…

A: Recall: Equation of the sphere :         x-a2+(y-b)2+(z-c)2=r2; where a,b,c is the center and 'r' is…

Q: Find the extreme values of ƒ(x, y, z) = x - y + z on the unit sphere x2 + y2 + z2 = 1.

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Q: %3D at

A: We need to substitute  x=au ,y = bv ,z= cw

Q: Which of the following is not a parametrization of the parabola y = ² ? O x = vt, y =t O x = t, y…

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

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Q: Find the area of the part of the sphere x² + y? + 2? = 12z that lies inside the paraboloid 2 % = x²…

A: Topic = Application of integration

Q: Determine whether the statement is true or false. If D is the disk given by x2 + y2 s 49, then 49 x2…

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Q: Answer the following neatly and completely. 1. Find the point P such that =r, where A(4,3, –2),…

A: Given : z = x2 + 4y2.   To identify the quadric surface and to sketch the graph of z = x2 + 4y2.

Q: Find the center C and the radius r of the sphere S :x2 +y? + z2 - 2x 4y + 4z = 16 O C (2, 4, -4) and…

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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: Which one of the following surfaces is the aph of f(z, y) = y -2 ? 3..

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Q: Evaluate fff(r +y²+y dV, "AP where 2 is the solid hemisphere (half of the sphere) enclosed by x +y…

A: Converting into spherical  coordinates

Q: Find the radius of the sphere x2 + y? + z? – 2x – 8 = 0. %3D 4 O 2 O 3 9,

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Q: Given the sphere S: x2 + y² + z² - 2x + 2y =7. and the planes 1 :x +y +z 0 2: x+y+z 1 let us denote…

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Q: re 2" dr + (x* + 2a²y?)dy where C is the boundary of the region between the circles a² + y? = 1 and…

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Q: Let B be the ball with center at the origin and radius 1 3(x² + y + z?)dV = %3D B

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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: Given a sphere with center (6, 4, – 3) and radius 5. Find an equation of the intersection of this…

A: First write the equation of sphere then satisfy the condition for xz-plane.

Q: 6. Consider the sphere a2 + y? + (z-3)2 = 1. Find the point P (a, b, c) on the sphere such that the…

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Q: Answer the following questions about the sphere whose equation is given by 2² + y? + 2? – 6z + 4y =…

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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: Given a sphere with center (7,3, – 4) and radius 5. Find an equation of the intersection of this…

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Q: Let S be the sphere 2 + y² +2²=9 oriented outwards, an F = (5x, 7z, -3y) Evaluate: (6₂ F. ds. The…

A: let S be the sphere x2+y2+z2=9 oriented outwards and F=5x,7z,-3y evaluate ∫∫SF·dS

Q: Which one of the following accurately describes the set {(r, 0, 2) |r = 5 } %3D in cylindrical…

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Q: 4 Assuming that the curve ris thex + y +z = 0 intersection of the plane and the sphere , then the…

A: As per the question we are given a closed curve Γ , defined as the intersection of the plane x+y+z =…

Q: Let B be the ball with center at the origin and radius 1 I//3(x² + y + z?)dV =

A:

Q: Given a sphere with center (10, 3, – 1) and radius 5. Find an equation of the intersection of this…

A: Given. The ceter of sphere is located at  (10,3,-1) Radius is 5. Equation of XZ plane is Y = 0.

Q: Find the area of the part of the sphere r? + y + z² = 4 that lies within the first octant and inside…

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Q: Evaluate fff(x +y +:' dV, where a is the solid hemisphere (half of the sphere) enclosed by x +y+ =1…

A: Here in the given question, find the integration of the given function:∭Dx2+y2+z232dVWhere Ω is the…

Q: Which of the following is a non-orientable surface? O a. all the other choices are orientable O b.…

A: orientable surface -  The surface for which we can define clockwise consistently.

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: 47. Find the distance between the spheres x? + y² + z² = 4 and x? + y? + z? = 4x + 4y + 4z – 11.

A: The equation of the spheres are given:

Q: )الكــره the Sphere OThe Portion of planes z=l x +y+Z² = \6 between the %3D and z=2.

A: Volume of the sphere x2+y2+z2=16 or x2+y2=16-z2 is: V=∫z=12∬x2+y2≤16-z2dxdydz   =∫z=12π16-z2dz…

Q: Evaluate [[[ =*dxcydz over the sphere x +y² +=² =1.

A: to find:- to evaluate the given integral.

Q: Consider the sphere x + y² +z? = 8. (rsin@ cos )° +(rsin @ sin ø)° +(r cos 0)° = 8 p2 sin? O cos?…

A: We have to explain the identity

Q: Find the points on the cone z? = x² + y² that are closest to the point (4,2,0).

A: Given :       z2 = x2 + y2  at (4 , 2 , 0)   Minimize the distance function is   f(x ,y ,z) =  (x -…

Q: Evaluate J CurlF nds F(x,y,z) = yi – xj - zk, and S is part of the sphere z =V9-x2 - v? and n is…

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Q: . Let F(x, y, z) = (x³, y³, z³). Use Gauss's theorem to find ffsF dS if S is the sphere x? + y? + 22…

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Q: Which of the following is a solid of revolution? (a) Sphere (b) Pyramid (c) Cylinder (d) Cube

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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: Find the center and radius of the sphere x? – 6x – 10+y? + 10y +z? – 20z = 0 OA C(-3,5,10), r = 10…

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Q: Find the area of the part of Sphere x? + y? + z? = 16 that is outside the paraboloid z=16 – x² – y?.…

A: The part of the object outside another object can be obtained by first calculating the intersection…

Q: Let B be the ball with center at the origin and radius 1 SS $3(x² +y? + z²)dV = 16 12m 24m :5

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Q: Use Gauss's D.T. to evaluate SSA.ds where Ã=x'i+y°§+7f qud S is the , surdace of the sphere x+j+z²=…

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Statements and Logic

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