Find the Center of Mass of a Thin Plate Covering $y = 64 - x ^ { 2 }$

question 44

Multiple Choice

Find the center of mass of a thin plate covering the given region with the given density function.
-The region bounded by the parabola $y = 64 - x ^ { 2 }$ and the $x$ -axis, with density $\delta ( x ) = 8 x ^ { 2 }$

• A) \(\bar { x } = \frac { 128 } { 5 } , \bar { y } = 0\)
• B) \(\bar { x } = 0 , \bar { y } = \frac { 128 } { 7 }\)
• C) \(\bar { x } = 0 , \bar { y } = \frac { 128 } { 5 }\)
• D) \(\bar { x } = 0 , \bar { y } = \frac { 256 } { 7 }\)

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Definitions:

Fair Value Hedge

A hedge of the exposure to changes in fair value of an asset or liability or an identified portion of an asset or liability that is attributable to a particular risk.

Cash Flow Hedge

A form of hedge that aims to manage exposure to fluctuations in cash flows related to a particular risk, such as interest rates or foreign exchange rates.

Cash Flow Hedge

A type of hedge that protects against the exposure to variability in cash flows due to a particular risk such as interest rate changes.

Forward Rate

The predetermined price for a transaction that will occur at a specific future date, commonly used in foreign exchange and interest rate markets.