Marla is running clockwise around a circular track. She runs at a constant speed of $3$ meters per second. She takes $46$ seconds to complete one lap of the track. From her starting point, it takes her $12$ seconds to reach the northernmost point of the track.

Impose a coordinate system with units in meters, the center of the track at the origin, and the northernmost point on the positive $\backslash ($ y $\backslash )-$axis. $($Round your answers to two decimal places.$)$

$($a$)$ Give Marla's coordinates at her starting point.

$\backslash [$

$($x$,$ y$)=\backslash$left$(\backslash$begin$\{$array$\}\{$l$\}$

$\backslash$quad

$\backslash$end$\{$array$\}\backslash$right$)$

$\backslash ]$

$($b$)$ Give Marla's coordinates when she has been running for $10$ seconds.

$\backslash [$

$($x$,$ y$)=(\backslash$quad x$)$

$\backslash ]$

$($c$)$ Give Marla's coordinates when she has been running for $905\mathrm{.}3$ seconds.

$\backslash [$

$($x$,$ y$)=(\backslash$quad$)$

$\backslash ]$