P $4\mathrm{.}3-14$ The voltage source in the circuit shown in Figure P $4\mathrm{.}3-14$ supplies $83\mathrm{.}802$ W $.$ The current source supplies $17\mathrm{.}572$ W$.$ Determine the values of the node voltages $v_1$ and $v_2.$

Figure P $4\mathrm{.}3-14$

P$4\mathrm{.}4-1$ The voltages $v_a,v_b,$ and $v_c$ in Figure $P4\mathrm{.}4-1$ are the node voltages corresponding to nodes $a,b,$ and c $.$ The values of these voltages are:

$v_a=8\mathrm{.}667V,v_b=2V,$ and $v_c=10V$

Determine the value of $A,$ the gain of the dependent source.