A Thin Wire in the Shape of a Quarter-Circle $\mathbf { r } ( t ) = 6 \cos t \mathbf { i } + 6 \sin t \mathbf { j }$

question 28

Short Answer

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

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Definitions:

Gross Profit Ratio

A financial metric indicating the proportion of money left from revenues after accounting for the cost of goods sold, presented as a percentage.

Return on Sales Ratio

A financial metric that measures the efficiency of a company in generating profits from its sales by comparing net income to total sales revenue.

Liquidity

The ease with which assets can be converted into cash without significant loss in value, crucial for meeting immediate and short-term obligations.

Asset Management

The organized method of creating, managing, preserving, and trading assets in an economically efficient way.