MATHCAD PRACTICE EXAM $-$ PROBLEM $1$: Beam AB is supported by a pin connection at point A and by a cable CD $.$ A load $W=250lb.$ is attached to the beam at point B $.$ The tension in the cable CD depends on the distance between points A and D $,$ since this distance affects the angle of the cable with the horizontal.

The following equation can be used to determine the tension in the cable, being $L$ the length of the beam $AB,Lc$ the length of the cable CD $,$ and $d$ the distance between points A and D :

$T=\frac{WL{L}_c}{d\sqrt[\phantom{2}]{L_c^2-d^2}}$

a$)$ Knowing that the length of the beam $L=100$ in and the length of the cable $Lc=60$ in$,$ start by making a plot of $T$ as a function of the distance $d.$ Suggested range for $d=5$ to $60$ in $.$

b$)$ Find the value of the distance $d$ that makes the tension in the cable equal to $3000$ lb $.$ May use the function root or a solve block for this question.

c$)$ Call the function minimize to determine the distance $d$ that produces the smallest tension in the cable. May use a solve block if constrains are required.

PLEASE HELP ME SOLVE IT IN MATHCAD!!