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

question 24

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:

JButtons

Components in Java's Swing framework, used for creating clickable buttons in graphical user interfaces (GUIs).

JLabels

Components in Java Swing used to display a short string or an image icon.

Bounding Box

A rectangle that is used to describe the outer boundary of a geometric shape or object in 2D or 3D space.

Repaint

The method in graphical user interfaces that triggers a component to be redrawn.