derive the equations for slope and deflection separately for segment $AB$ and segment

BC$.$ EI is a constant.

Hint: This problem needs some critical thinking $-$ Due to the loading at the overhang,

two $x$ coordinates must be considered as illustrated in the figure $(x_{\text{I}}$ for segment $AB,$ and

$x_2$ is for segment $BC).$

The four constants of integration $($two for each segment$)$ can be determined using three

boundary conditions, namely, and one continuity condition: For segment $AB,$ deflections

at A and $B$ are zero; for segment $BC,$ deflection at $B$ is zero; and deflection equation for

$AB$ equals the deflection equation for $BC$ since the deflection at $B$ only has one value.

If $E=29,000$ksi,$I=1070i{n}^4,P=10$kips,$a=10ft,$ calculate the deflection at point $C$

using the derived formula.