Solve the Problem $x ^ { 2 } + y ^ { 2 } = 2 z$

question 130

Multiple Choice

Solve the problem.
-The shape and density of a thin shell are indicated below. Find the coordinates of the center of mass.
Shell: "nose" of the paraboloid $x ^ { 2 } + y ^ { 2 } = 2 z$ cut by the plane $z = 3$
Density: $\delta = \sqrt { x ^ { 2 } + y ^ { 2 } + 1 }$

• A) \(\left( 0,0 , \frac { 15 } { 8 } \right)\)
• B) \(\left( 0,0 , \frac { 96 } { 11 } \right)\)
• C) \(\left( 0,0 , \frac { 9 } { 11 } \right)\)
• D) \(( 0,0,8 )\)

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Definitions:

Futures Contracts

Futures contracts are standardized legal agreements to buy or sell a particular commodity or financial instrument at a predetermined price at a specified time in the future.

Futures Exchanges

Marketplaces where futures contracts and options on futures contracts are traded, facilitating the buying and selling of commodities or financial instruments at a predetermined future date.

Delivery Date

The specific date on which a financial transaction, especially pertaining to futures or options contracts, is scheduled to be settled or executed.

Futures Contracts

Standardized agreements to buy or sell a particular commodity or financial instrument at a predetermined price at a specified time in the future.