The stresses shown in the Figure act at a point on the free surface of a machine component.

a$)$ Determine the normal stresses ${}_x$ and ${}_y$ and the shear stress ${}_{xy}$ at the point.

b$)$ Determine the principal stresses and the maximum in$-$plane shear stress acting at the point

c$)$ Show those stresses on an appropriate sketch

d$)$ Compute the absolute maximum shear stress at the point

e$)$ Draw Mohr's Circle for this problem and use it as an alternative to determine $($i$)$ the missing stresses in the figure $($ii$)$ the principal stresses and maximum in$-$plane shear stress acting in the plane.