Solve the Problem $z = \frac { 7 } { 8 } \sqrt { x ^ { 2 } + y ^ { 2 } }$

question 273

Multiple Choice

Solve the problem.
-Find the center of mass of the solid enclosed between the cone with equation $z = \frac { 7 } { 8 } \sqrt { x ^ { 2 } + y ^ { 2 } }$ and the plane with equation $z = 7$ if the density at any point is proportional to the distance from that point to the plane $z = 7$ .

• A) \(( \bar { x } , \bar { y } , \bar { z } ) = \left( 0,0 , \frac { 21 } { 5 } \right)\)
• B) \(( \overline { \mathrm { x } } , \overline { \mathrm { y } } , \overline { \mathrm { z } } ) = \left( 0,0 , \frac { 14 } { 3 } \right)\)
• C) \(( \bar { x } , \bar { y } , \bar { z } ) = \left( 0,0 , \frac { 49 } { 12 } \right)\)
• D) \(( \bar { x } , \bar { y } , \bar { z } ) = \left( 0,0 , \frac { 35 } { 8 } \right)\)

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Definitions:

pH

A scale used to specify the acidity or basicity of an aqueous solution, with values less than 7 indicating acidity and values greater than 7 indicating basicity.

Disulfide Bridges

Covalent bonds between sulfur atoms of two cysteine residues within or between protein molecules, crucial for protein structure.

Cysteic Acid

An oxidized sulfur-containing amino acid, derived from cysteine, notable for its role in certain biological processes and protein structure.

Fischer Projection

A two-dimensional representation of a three-dimensional organic molecule by projection, often used to describe carbohydrates.