Evaluate the triple integral. JUr ryz dV where Tis the solid tetrahedron with vertices (0,0,0), (1,0,0), (1,1,0), and (1,0,3).

Q: The center of the sphere whose one of its diameters has end points P1(1,-3,-1) and P2(2,0, 1) is…

A: Sphere Definition: A sphere is a three-dimensional counterpart of a circle, with all its points…

Q: Parameterize (in 2 variables u, v) the paraboloid 4x2 +y2 -z=0

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Q: 7) A building is 300 feet tall. It casts a 165 foot long shadow. A statue near the building is 40…

A: Given: A building is 300 feet tall. It casts a 165 foot long shadow. A statue near the building is…

Q: Find the equations r = g (0, z) (cylindrical) and p = f (0, 4) (spherical) for the hyperboloid x² =2…

A: To find-  Find the equation r = gθ, z (cylindrical) and ρ = fθ, ϕ (spherical) for the hyperboloid…

Q: Find the volume of a parallelepiped spanned by 2i - 5j - 7k, i-k and 9i – 3k.

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Q: 6. Show that (an)neN C R is bounded if and only if lim supn→∞ an < +∞o.

A: To Prove:  ann is bounded sequence if and only if limsupan&lt;+∞.

Q: Consider a triangle ABC, on each of whose sides equilateral triangles are dra

A:

Q: Transform (0, 5, 2) from rectangular into spherical form (here z is any negative number).

A: given rectangular coordinates is of the form (x, y, z) are (0,5,z) Now we are going to find…

Q: The distance between the centers of the following two spheres: is x²-58x+y2+36y+z²=-1164,…

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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 point on the sphere x²+y²+z²=961 that is farthest from the point (19,1,–9).

A: We have to find the farthest point from the given point.

Q: 2. Find the volume of the parallelepiped the following 3 vectors describe the edges: i.q=i-2j-3k, b=…

A: The given problem is to find the volume of the parallelepiped from the given following 3 vectors…

Q: (2, 3.5)

A: Here, the given function is,

Q: Solve the initial value problem below using the method of Laplace transforms. y" - 4y' - 12y = 0,…

A: Given equation is: y"-4y'-12y=0 ,y(0)=1,y'(0)=38 We have to find the value of y(x)

Q: A plane P passes through the points (0, 0, 17), (5, 0, 11) and (0, 9, 13). A rectangle R has…

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Q: The sphere of radius 2 centered at (0,0,1) is pictured below. Select the equation which best…

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Q: If the coordinates of the ends of a focal chord of the parabola y²=4ax and (x,,y,) and (x,.y;) then…

A: Consider the given parabola y2=4ax Suppose Ax1 , y1  and  Bx2 , y2 be the ends of the focal chord of…

Q: Derive a cubic spline with natural boundary condition using the following points: (−2, 1), (0,0),…

A: Sol:-] To derive a cubic spline with natural boundary condition, we need to find the cubic…

Q: Find the center and the radius of the sphere that has the given x2 + y2 + z2 + 10x – 7y + 2z + 26 =…

A: Given a equation of the sphere , x2+y2+z2+10x-7y+2z+26=0 To fin the center and the radius of the…

Q: Find an equation for the sphere centered at (2, 2, –2) and passing through (2, 2, 3). 1. x² + y + z²…

A: Given center is (2,2,-2) and the point is (2,2,3)We know the equation of sphere is…

Q: Find the area of the surface of the part of the cylinder ? + 2² = 4 that lies above the square in…

A: For the given part of the cylinder  x2+z2 =4  which lies above the x-y plane at the vertices…

Q: The center of the sphere x² –2x+y² +z² +2z=6 is Select one: O a. None O b. (-1,0,1) O c. (2,0,-2) O…

A: