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- = 1/ 40 -8 12 - -4 -4 20 0 5) :

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xr:=gama/delta;

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x0:=3: y0:=10:

sys:= { diff(x(t),t) = alfa*x(t)-beta*x(t)*y(t), diff(y(t),t) = -gama*y(t)+delta*x(t)*y(t), x(0)=x0, y(0)=y0};

dsol := dsolve(sys, numeric);

dsol(0);

with(plots): odeplot(dsol, [t,x(t)],0..200, col or=orange,numpoints=50);

odeplot(dsol, [x(t),y(t)],0..100, color=orange,numpoints=200);

T:=evalf(2*Pi/(alfa*gama)^(1/2));

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a:=(Pi/4):v0:=10: g:=10: m:=1:

NLPSolve(sqrt(x^2+y^2),{y-(x*tan(a) (g*x^2)*(1+tan(a)^2)/(2*v0^2))=0}, assume = nonnega tive,maximize);

S:=v0^2/g;

[ 9.9999999999999982 [ x = 9.9999999999999982 y = 0. ] ],, S := a:=(Pi/4):v0:=10: g:=10: m:=1: NLPSolve(m*g*y,{y (x*tan(a)-(g*x^2)*(1+tan(a)^2)/(2*v0^2))=0}, assume = nonnegative,maximize);

S:=(v0)^2/g;

h:=(v0*sin(a))^2/(2*g);

U:=m*g*h;

[ 25.0000000000003020, [ x = 4.99999998997172402, y = 2.50000000000003020] ] S :=.. :..-.:.., 2008.

h := U := Maple.

:

2 x1 + 3x 2 4 x1 + 2 x 2 2 x2 x1 0, x 2 Z = 4.6 x1 + 4.1x 2 max.

, : 1=3, 2=3.

with(Optimization):

c := Vector([4.6,4.1], datatype = float);

A := Matrix([[2,3],[4,2],[0,2]], datatype = float);

b := Vector([15,18,8], datatype = float):

result:=LPSolve(c, [A, b],assume=nonnegative,maximize);

4. c := 4. 2. 3.

A := 4. 2.

0. 2.

3.

result := 26., 2. restart:with(Optimization):

Maximize(2*x1-2*x2, {4*x1-5*x2=0, 5*x1+4*x2=0,x1=0});

[ 0., [ x1 = 0., x2 = 0. ] ] Maximize(2*x^2+y+2*y^2, {y^2-x=2, 2*x+y=6});

[ 18.0000000000000072, [ x = 2.00000000000000044, y = 2.00000000000000044] ] LPSolve(2*x1-2*x2, {4*x1-5*x2=0, 5*x1+4*x2=0,x1=3, x1=0, x2=0});

[ 1.2000000000000, [ x1 = 3., x2 = 2.40000000000000034] ]..,.

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0.5x1+0.5x2 0.5x3+0.5x4 0.125x1+0.125x4 2x1+x2+x3+x4. / /. 7-..: , 2007. 903.


9. - Maple 2.12

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sin sin dT ( x) = = 0. 1. v1 v dx, sin = const.

sin. Maple.

restart:n1:=1: n2:=1.3:

a:=1: b:=3: c:=5: with(Optimization):

NLPSolve(n1*sqrt(a^2+x^2)+n2*sqrt(b^2+(c-x)^2),{x=c}, assume = nonnegative);

x:=2.103: sinf1:=x/sqrt(a^2+x^2): sinf2:=(c-x)/sqrt((c x)^2+b^2): n:=sinf1/sinf2;

n:=n2/n1;

[ 7.75022771342699368, [ x = 2.10277825025574616 ] ] n := 1. n := 1.,, (n=1.3) (n=1.4);

.

, n( y ) = n(1 + a y ), ( n n )..

n0 a y ( x) = ch( x), a n n n a= y ( x) = a x2,, h hn.

y(x) b:

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bc.

(bc).,, (. 33).

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restart:n[1]:=1: n[2]:=1.3: n[3]:=1.4:

a:=1: b:=3: c:=5: x[3]:=c: with(Optimization):

L:=n[1]*sqrt(a^2+x[1]^2)+n[2]*sqrt(b^2+(x[2] x[1])^2)+n[3]*sqrt(b^2+(x[3]-x[2])^2);

NLPSolve(n[1]*sqrt(a^2+x[1]^2)+n[2]*sqrt(b^2+(x[2] x[1])^2)+n[3]*sqrt(b^2+(x[3]-x[2])^2),{x[1]=c,x[2]=c}, assume = nonnegative);

2 2 2 1 + x1 + 1.3 9 + x2 2 x2 x1 + x1 + 1.4 34 10 x2 + x L := [ 11.1445271598127462, [ x1 = 1.08667590242779766, x2 = 3.14652338726764702 ] ] restart:with(Optimization):

L:= n[1]*sqrt(a^2+x[1]^2)+sum(n[k+1]*sqrt(b^2+(x[k+1] x[k])^2),k=1..N-1);

a:=0.5: b:=0.01: c:=10:

N:=7: n[1]:=1;

n[2]:=1.3;

dn:=0.02:

for i from 2 to N-1 do n[i+1]:=n[i]+dn od;

x[N]:=c:

NLPSolve(n[1]*sqrt(a^2+x[1]^2)+sum(n[k+1]*sqrt(b^2+(x[k+ ]-x[k])^2),k=1..N-1),{seq(x[k]=c,k=1..N-1)}, assume = nonnegative);

N 2 2 a 2 + x1 + b2 + xk + 1 2 xk + 1 xk + xk L := n1 nk + k= n1 := n2 := 1. n3 := 1. n4 := 1. n5 := 1. n6 := 1. n7 := 1. [ 26.1566660517168188, [ x1 = 0.357812300371984248, x2 = 1.16276262439100074, x3 = 1.95465999942869040, x4 = 2.73393402938907793, x5 = 3.50099294300603248, x6 = 4.25622509466887512 ] ] (. 33).

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