Hello Bill. I have one more question. As you can see the problem has a solution. However I want to find solutions to a limited range of them such as, for example 0<theta<1 ,0.4<dam<2, dbm>0 and ofcourse reals (not complex numbers) .You have any idea?
ClearAll["Global`*"]
rc = 47;
IntensityA = 12808;
IntensityB = 30852;
IntensityC = 82858;
KBC = 1.07;
KAB = 4.36;
BAB = (IntensityA/IntensityB)*KAB;
BBC = (IntensityB/IntensityC)*KBC;
lba = 4.13;
lbb = 2.05;
lcc = 1.83;
lcb = 1.49;
lca = 2.96;
laa = 3.45;
lac = 2.12;
lab = 1.73;
lbc = 2.53;
At100 = 0.014;
Pc = 3.85;
Pb = 7.18;
MwB = 231.85;
MwC = 79.88;
rb = rc + dbm;
ra = rc + dbm + dam;
dc = 2rcCos[i];
db = Sqrt[rb^2 - (rcSin[i])^2] - rcCos[i];
da = Sqrt[ra^2 - (rcSin[i])^2] - Sqrt[rb^2 - (rcSin[i])^2];
f1 = 0.25 + 28.49461Exp[-3.63(rb/rc)];
f2 = -0.05 + 39.79446Exp[-3.63(rb/rc)];
theta = (At100rcPcMwB)/(3dbmPbMwC)
S = Pi(rc^2)((Sin[i + Pi/36])^2 - (Sin[i])^2);
SC = (1 - Exp[-dc/lcc])Exp[-da/lca](1 + thetaExp[-db/lcb] - theta)
S;
SB = theta(1 - Exp[-db/lbb])
Exp[-da/lba](1 + Exp[-dc/lbc]Exp[-db/lbb])Sf1;
SA = (1 - Exp[-da/laa])(1 +
Exp[-dc/lac]Exp[-da/laa](1 + thetaExp[-2db/lab] - theta))S;
SCb = (1 - Exp[-dc/lcc])*
Exp[-da/lca](1 + thetaExp[-db/lcb] - theta)*S;
SBb = theta(1 - Exp[-db/lbb])
Exp[-da/lba](1 + Exp[-dc/lbc]Exp[-db/lbb])Sf2;
SAb = (1 - Exp[-da/laa])(1 +
Exp[-dc/lac]Exp[-da/laa](1 + thetaExp[-2db/lab] - theta))S;
Ic = Sum[SC, {i, 0, Pi/2, Pi/36}];
Ia = Sum[SA, {i, 0, Pi/2, Pi/36}];
Ib = Sum[SB, {i, 0, Pi/2, Pi/36}];
Icp = Sum[SC, {i, 0, Pi/2, Pi/36}];
Iap = Sum[SA, {i, 0, Pi/2, Pi/36}];
Ibp = Sum[SB, {i, 0, Pi/2, Pi/36}];
R1 = (0.785(Ia/Ib) + 0.215(Iap/Ibp)) - BAB;
R2 = (0.785(Ib/Ic) + 0.215(Ibp/Icp)) - BBC;
Assuming[Reals, FindRoot[{R2 == 0, R1 == 0}, {{dbm, 1}, {dam, 0.8}}]]
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