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solve

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solve

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solve

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solve

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solve-sqrt

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solve

eq1:-0.3*x+0.2*y+0.1*...

eq2:0.1*x-0.2*y+0.3*z=0;

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solve

eq1: x1=b*tp*2/3;

eq2: x2=b*tp*2/3+a*tp...

eq3: x3=b*tp*2/3+a*(t...

Calculate

solve

Run Example
(%i1)eq1:R3/(R3+R2)*24=15;
                                  24 R3
(%o1)                            ------- = 15
                                 R3 + R2
(%i2) eq2:(R3+R2)/(R1+R2+R3)*24=24-15;
                               24 (R3 + R2)
(%o2)                          ------------ = 9
                               R3 + R2 + R1
(%i3) eq3:R1+R2+R3=24/0.02;
(%o3)                        R3 + R2 + R1 = 1200.0
(%i4) solution:solve([eq1,eq2,eq3],[R1,R2,R3]);

rat: replaced -1200.0 by -1200/1 = -1200.0
                                        675       1125
(%o4)                  [[R1 = 750, R2 = ---, R3 = ----]]
                                         4         4
(%i5) eR1:solution[1][1];
(%o5)                              R1 = 750
(%i6) eR2:solution[1][2];
                                        675
(%o6)                              R2 = ---
                                         4
(%i7) eR3:solution[1][3];
                                        1125
(%o7)                              R3 = ----
                                         4
(%i8) float(eR3/(eR1+eR2+eR3)*24);
                               24.0 R3
(%o8)                        ------------ = 5.625
                             R3 + R2 + R1
(%i9) 
Run Example
kill(all);
(%o0)                                done
(%i1) Ik:16;
(%o1)                                 16
(%i2) U0:92;
(%o2)                                 92
(%i3) a:I/Ik=1-(U/U0)^2;
                                            2
                                 I         U
(%o3)                            -- = 1 - ----
                                 16       8464
(%i4) l:solve(a,U);
(%o4)            [U = - 23 sqrt(16 - I), U = 23 sqrt(16 - I)]
(%i5) m:solve(a,I);
                                       2
                                      U  - 8464
(%o5)                          [I = - ---------]
                                         529
(%i6) define(I(U),rhs(m[1]));
                                         2
                                        U  - 8464
(%o6)                         I(U) := - ---------
                                           529
(%i7) define(U(I),rhs(l[2]));
(%o7)                       U(I) := 23 sqrt(16 - I)
(%i8) P(I,U):=I*U;
(%o8)                           P(I, U) := I U
(%i9) plot2d(I(U),[U,0,92], [xlabel, "U[V]"], [ylabel, "I[A]"]);
plotplot2d(I(U),[U,0,92], [xlabel, "U[V]"], [ylabel, "I[A]"]);plot2d(U(I),[I,0,16], [ylabel, "U[V]"], [xlabel, "I[A]"]);
plotplot2d(U(I),[I,0,16], [ylabel, "U[V]"], [xlabel, "I[A]"]);plot2d([P(I(U),U)],[U,0,92], [xlabel, "U[V]"], [ylabel, "P[W]"]);
plotplot2d([P(I(U),U)],[U,0,92], [xlabel, "U[V]"], [ylabel, "P[W]"]);plot2d([P(I,U(I))],[I,0,16], [xlabel, "I[A]"], [ylabel, "P[W]"], [grid, 10, 10]);
plotplot2d([P(I,U(I))],[I,0,16], [xlabel, "I[A]"], [ylabel, "P[W]"], [grid, 10, 10]);define(Iabgeleitet(U),diff(P(I(U),U),U));
                                            2    2
                                         2 U    U  - 8464
(%o13)               Iabgeleitet(U) := - ---- - ---------
                                         529       529
(%i14) define(Uabgeleitet(I),diff(P(U(I),I),I));
                                                       23 I
(%o14)        Uabgeleitet(I) := 23 sqrt(16 - I) - --------------
                                                  2 sqrt(16 - I)
(%i15) Umax:solve(Iabgeleitet(U),U);
                                  92           92
(%o15)                   [U = - -------, U = -------]
                                sqrt(3)      sqrt(3)
(%i16) Imax:solve(Uabgeleitet(I),I);
                                        32
(%o16)                             [I = --]
                                        3
(%i17) P[max]=float(Imax[1]*Umax[2]);
(%o17)                 P    = (I U = 566.5730641647529)
                        max
(%i18) R[L]=float(Umax[2]/Imax[1]);
                               U
(%o18)                   R  = (- = 4.979646071760522)
                          L    I
(%i19) 
Run Example
float(solve((50*48=55*16+(50*x)+(50*(48-16-x)),x)));
(%o1)                              [x = 0.0]
(%i2) 

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