The $2-$D cross section of a wind vane is given below.

a$)$ If the height of the vane is $h=14cm$ and the width of the vane is $b=6cm,$ determine the equation of the line $y(x).(5$ points$)$

b$)$ Determine the area of the vane by integration with respect to $x.$ Show all work. $(5$ points$)$c$)$ Determine the $x-$coordinate of the centroid by integration with respect to $x.$ Show all work. $(5$ points$)$

d$)$ Determine the $y-$coordinate of the centroid by integration with respect to $y.$ Show all work.

Recall: $(y)bar$

$=\frac{1}{A}{\displaystyle \underset{0}{\overset{h}{}}}yx(y)dy$

$(10$ Points$)$