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A Thin Wire in the Shape of a Quarter-Circle r(t)=6costi+6sintj,0tπ2\mathbf { r } ( t ) = 6 \cos t \mathbf { i } + 6 \sin t \mathbf { j } , 0 \leq t \leq \frac { \pi } { 2 }

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A thin wire in the shape of a quarter-circle r(t)=6costi+6sintj,0tπ2\mathbf { r } ( t ) = 6 \cos t \mathbf { i } + 6 \sin t \mathbf { j } , 0 \leq t \leq \frac { \pi } { 2 } , has a linear mass density π(x,y)=2x+4y\pi ( x , y ) = 2 x + 4 y . Find the mass and the location of the center of mass of the wire.


Definitions:

Chromium Vanadium

Chromium Vanadium is an alloy of chromium and vanadium, commonly used in the production of high strength steel tools due to its durability and resistance to corrosion.

AISI

The American Iron and Steel Institute, an association focused on steel production and its standardization across industries.

Irreversible Chemical Change

A chemical reaction that results in products that cannot easily revert back to the reactants without significant energy input.

Atmospheric Corrosion Resistance

The ability of a material to withstand degradation caused by reactions with atmospheric conditions without additional protection.

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