Evaluate F(x,y,z) = (x3 +y³)i + (y³ + z³)j + (z³ + x³)k, and and S is the sphere with center the origin and radius 2. Upload Choose a File

Q: The intersection of the sphere (x-3)^2 + (x+2)^2 + (z-1)^2 = 49 with each of the coordinate planes…

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Q: b) Use the idea in part (a) to determine an explicit one-to-one correspondence between zt and the…

A: as you asked only the solution for (b) , the solution of the part (b) is given below...

Q: Prove that A 12 is diagonalizable. -.

A: step 2 complete solution

Q: Find the distance from the point P(1, 4, 0) to the plane through A(0, 0, 0), B(2, 0, -1), and C(2,…

A: Given points A0,0,0 , B2,0,-1 & C2,-1,0The direction ratios of AB⇒2-0,0-0,-1-0=2,0,-1Similarly…

Q: Plot the following non-linear data en a scatterplet. Develop the quadratic model and expenental…

A: Given data, x y 0 3 1 7 2 10 3 24 4 50 5 95 Scatter plot:

Q: how that the point (1,0,-1) is the centre of the sphere passing through…

A: Let O=(1,0,-1), A=(1,8,-8) B=(-9,0,5) C=(7,-8,-1) D=(-7,0,7) It is enough to show that…

Q: Determine the surface with the equation 2x2-3y2-4z2-12x-6y-21=0

A: We have to determine the surface with the equation 2x2-3y2-4z2-12x-6y-21=0.

Q: Find 3 different homogeneous coordinate representations for the Cartesian point (1,-2)

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Q: Let y= - Find the intersection of these surfaces, Calculate the GB of wrt lex order x>4>2)

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Q: Find the area of the surface. The part of the cylinder y² + z² = 9 that lies above the rectangle…

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Q: Find the point on the sphere x +y +z = 4 farthest from the point (1, – 1,1). The point is ( ID:…

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Q: Standardize the cone with equation 7x2+4xy+4y2-8x-12y+9=0

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Q: Find the maximum volume of a box that is resting on the xy-plane with one vertex at the origin and…

A: Given the plane is 3x+4y+2z=12

Q: The shortest distance from (−7,6,−8) to the xy-plane is

A: Since the plane is a xy-plane so, the point will be (-7,6,0).

Q: 7. Find the scalar equation of any plane which contains the line = (1,2,1)+ t(3,6,-1)

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Q: If a sphere passes through the points A(0, 1, 2) and B(−1, 2, 2) and its center C lies on the…

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Q: A point moves so that sum of the squares of its distances from the vertices of a triangle is always…

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Q: Find the point on the sphere x+y²+z²=625 that is farthest from the point (-23,14,-13). 23 625 V1200…

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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: definition set and drawan the plane Find the

A: Using elementary properties of logarithmic function and square root function set is obtained then…