A$.$ Derive q$($x$),$ Vy$($x$),$ Mz$($x$),\backslash$theta $($x$),$ and y$($x$)$ for this beam. Keep the known quantities in their variable form for simplicity. Define any constants as well.

B$.$ Plug the knowns into Vy$($x$),$ Mz$($x$),\backslash$theta $($x$),$ and y$($x$).$ The bar is Mg $($E $=44\mathrm{.}8$ GPa$)$ and Iz $=5$ x $10-8$ m$4.$ Evaluate the four functions at x $=0\mathrm{.}5$ using MATLAB. As always, watch for off$-$by$-$one errors. Include your code and print all answers to the command window.

$$ w $=-10$ kN$/$m

$$ Fay $=2\mathrm{.}5$ kN$,$ Fby $=3\mathrm{.}0$ kN$,$ Fc $=-1\mathrm{.}5$ kN

$$ Mb $=0\mathrm{.}5$ kN$$m

$$ a $=0\mathrm{.}4$ m$,$ L $=0\mathrm{.}6$ m

C$.$ Plot the four functions $($with MATLAB$).$When you publish your code the graphs should be displayed.