A door is supported by hinges at A and B$,$ and by cord CE$,$ as shown, and a $46$ lb force is exerted on it at D$.($This force is purely in the $-$x direction.$)$ Hinge A is able to prevent translation in the y direction, but Hinge B is not able to do that. Find

A$)$ the reactions at A and B

B$)$ the tension in the cord $($magnitude$)$

Hint: Since there are two hinges, neither one needs to prevent rotation about axes parallel to the x or z axes.