A beam with simple supports at B and E is loaded as shown. Given that P$1=12$kN$,$ P$2=7$kN$,$ P$3=6$kN$,$ w$1=17$kN$/$m$,$ w$2=24$kN$/$m$,$ a$=$b$=$c$=1$m$,$ d$=$e$=2$m$,$ and f$=0\mathrm{.}4$m$,$ EI$=20{10}^3$ kN$m^2.$

$($a$)$ Calculate reaction force at E$.$

$($b$)$ Calculate slope at x$=2\mathrm{.}59$m$.$

$($c$)$ Calculate deflection at x$=3\mathrm{.}6$m$.$