First Problem: It is based on problem R$5-8$ of Hibbeler.

$*$R$5-8.$ The tapered shaft is made from $2014-$T$6$ aluminum alloy, and has a radius which can be described by the equation $r=a(1+b{x}^{\frac{3}{2}})m,$ where $x$ is in meters. Determine the angle of twist of its end $A$ if it is subjected to a torque of $TN*m.$ Problem R$5-8$

$\backslash$table$[[a=\frac{ln(+{10}^5)}{400},b=log(+10),c=log(+),T=,$Twist angle$],[,,,,]]$