Question

solve the system of equations for c1, c2, d1, and d2. none of the variables are zero.

(i) o.o2 3903: С, 119.058)-0, +12(19 1S8)-4×(o 9747) (1) 0.023208- C.( 19.8%)o, + Ct(19.855)-h (3) 0.022 543 C, 20 05320.053 ) 0.021 873 C, 20.2520.2540.9740 -D

Answer 1

Since this is nonlinear system of equations solving for c1, c2, d1, d2 can be very tough. So to find the solutions I wrote the following Python code
------------------------------------------------------------------------------
from scipy.optimize import fsolve
import warnings
warnings.filterwarnings('ignore', 'The iteration is not making good progress')

def equations(p):
        c1,c2,d1,d2=p
        return(c1*(19.658)**(-d1)+c2*0.9747*(19.658)**(-d2)-0.023903,
                    c1*(19.855)**(-d1)+c2*0.9745*(19.855)**(-d2)-0.023208,
                    c1*(20.053)**(-d1)+c2*0.9742*(20.053)**(-d2)-0.022543,
                    c1*(20.254)**(-d1)+c2*0.9740*(20.254)**(-d2)-0.021893)

c1,c2,d1,d2=fsolve(equations,(100,11,0.001,0.001))
------------------------------------------------------------------------------
I run it with an initial value (100,11,0.001,0.001) and got
c1 = 90.9231135727193
c2 = -18.68314402298009
d1 = 2.3964983439790157
d2 = 1.992088713327671

These are not actual solutions but if you put these values in the equations they will be pretty close with tolerance about 10^(-4).