Solve the Problem $z = \sqrt { 36 - x ^ { 2 } - y ^ { 2 } }$

question 9

Multiple Choice

Solve the problem.
-Find the center of mass of the hemisphere of constant density bounded $z = \sqrt { 36 - x ^ { 2 } - y ^ { 2 } }$ and the $x y - p l a n e$ .

• A) \(\bar { x } = 0 , \bar { y } = 0 , \bar { z } = \frac { 9 } { 4 }\)
• B) \(\bar { x } = 0 , \bar { y } = 0 , \bar { z } = 4\)
• C) \(\bar { x } = 0 , \bar { y } = 0 , \bar { z } = \frac { 3 } { 2 }\)
• D) \(\bar { x } = 0 , \bar { y } = 0 , \bar { z } = 2\)

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Definitions:

Normally Distributed Curve

A mathematical depiction illustrating a bell-shaped distribution where the data exhibits a symmetrical spread around the mean value.

Median

The median is the central number in a series of data after it has been organized in either increasing or decreasing sequence.

Median

The middle value in a list of numbers, which divides the data set into two halves.

Standard Deviations

A numerical metric that calculates the extent of spread or deviation of a dataset values from its average.