Q$2(7$ Points$)$ Compound beam ABC is made of two segments $AB$ and $BC$ that are linked at point $B$ with a pin. The beam is loaded with $P=1\mathrm{.}5$ kips at distance $2\frac{a}{3}$ from point A and a triangularly distributed load on segment $BC$ with peak intensity $q_0=0\mathrm{.}5$kip$\frac{s}{f}t.(a)$ Derive the elastic curve equation for the segment $BC$; $($b$)$ Find the deflection and slope at $B.$ Assume that $E=29{10}^6$ and $I=53\mathrm{.}8i{n}^4.$