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:

Transmission Electron Microscope

A microscopy technique in which a beam of electrons is transmitted through a specimen to form an image.

Electromagnets

A type of magnet in which the magnetic field is produced by an electric current.

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The biological process through which organisms produce offspring, either sexually or asexually.

Metabolism

The complex of life-sustaining chemical reactions in organisms that allow for the growth, reproduction, and maintenance of their structures as well as response to their environments.