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18-01-2020
Mathematics

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Write an inequality to describe the region. The solid upper hemisphere of the sphere of radius 9 centered at the origin

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sqdancefan sqdancefan

18-01-2020

Answer:

z ≤ √(81 -x² -y²)

Step-by-step explanation:

If the sphere is described in 3-D coordinates as ...

x² +y² +z² = r²

Then the upper surface is ...

z = √(r² -x² -y²)

With r=9, the solid volume below that surface and above the x-y plane is ...

z ≤ √(81 -x² -y²)

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