Two resistors $$\,{R_1}$$ and $$\,{R_2}$$ (in ohms) at temperatures $${T_1}{}^ \circ K$$ and $${T_2}{}^ \circ K$$ respectively, are connected in series. Their equivalent noise temperature is.

A linear second order single input continuous-time system is described by the following set of differential equations $$$\eqalign{ & \mathop {{x_1}}\limits^ \bullet \left( t \right) = - 2{x_1}\left( t \right) + 4{x_2}\left( t \right) \cr & \mathop {{x_1}}\limits^ \bullet \left( t \right) = 2{x_1}\left( t \right) - {x_2}\left( t \right) + u\left( t \right) \cr} $$$
Where x₁(t) and x₂(t) are the state variables and u (t) is the control variable. The system is

The open-loop transfer function of a feedback control system is G(s)=$${1 \over {{{\left( {s + 1} \right)}^3}}}$$
The gain margin of the system is

The characteristic equation of a feedback control system is given by
s³ +5s² +(K + 6)s + K =0
Where K > 0 is a scalar variable parameter. In the root loci diagram of the system the asymptotes of the root locus for large values of K meet at a point in the s-plane whose coordinates are