82. Use Theorem 6.10 to prove that a sphere of radius 5 has surface area 1007.

Q: 41. Prove a famous result of Archimedes: The surface area of the portion of the sphere of radius R…

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Q: A sphere in the first octant is tangent to the three coordinate planes. What is the radius of the…

A: Given:- A sphere in the first octant is tangent to the three coordinate planes To find:- Radius of…

Q: 2. Find the contour integral f,zdz for (a) y is the triangle ABC oriented counterclockwise, where A…

A:

Q: 3. Sketch the parallelogram spanned by (2, 1, 0) and (-3, 1, 0) in the xy plane and find its area.

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Q: 6) Find the area of the part of the sphere X² + y² + Z² = 4 that that lies above the plane Z = 1

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Q: The sphere x² + y² +z² = 100 has the center (0,0,0) and a radius of length 50. Select one: True…

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Q: A rectangle is bounded by the x-axis, the y-axis, and the line 1.5- y y = , , as shown in the…

A: Given: y=4-x4

Q: how/demostrate that the surface

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Q: Consider the circle of radius 2 centered at the origin in two-dimensional space. Let P be the point…

A: The distance between two points can be obtained by using the Pythagoras theorem. The expression for…

Q: find alea in bounded and in which Juadiantgon メ-exis lies fist lind Give U-n. where is explession…

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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: What is a flat surface that extends infinitely in all directions?

A: Plane.

Q: Compute the surface area of the cap of the sphere x2+y2+z2=49 with 6 ≤ z ≤ 7.

A: