one man

Alexey Ivanov

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8 years, 301 days
Russian Federation

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These are answers submitted by one man

  solve(r2,{ksi});  or  fsolve(r2); 

And if just combine "transparency" and "thickness"?
For example

restart: with(plots):
f1:=x->0.95*x; 
f2:=x->0.99*x;
f3:=x->0.991*x; 
p1:=plot(f1(x),x=0..2,color=red,legend = f1(x)): 
p2:=plot(f2(x),x=0..2,color=blue,legend = f2(x)): 
p3:=plot(f3(x),x=0..2,color=green,thickness = 10, transparency = .7, legend = f3(x)): 
display(p1,p2,p3);


 

Just in case, search for "Draghilev method" (or Dragilev here:
https://www.maplesoft.com/applications/view.aspx?SID=149514 )
The method, in particular, finds continuous solutions of systems with free variables (underdetermined systems of equations).

You can do this:
 

 restart:
 a := plot({seq((6*x-2*t)/x^2, t = 1 .. 3)}, x = -1 .. 5, y = -1 .. 6):
 b := plot(3/x, x = 0 .. 5, y = -1 .. 6, color = black, thickness = 3):
 plots[display](a, b)

 

Since childhood, I try to avoid strict zeros in coordinates (and generally avoid strictly identical values) due to formulas, because expressions may be nullified after substitution. It is better to shift the point o or d along the oX axis, for example:
 

restart:
with(geometry):
point(o, 0.1e-11, 0.); 
point(A, 0., 1.); 
point(d, 0., 2.);
point(F, .8944271920, 1.4472135960); 
line(lOD, [o, d]); 
line(lAF, [A, F]); 
alpha := FindAngle(lOD, lAF);

alpha = 1.107148718

CompleteSquare(x^2+y^2-2*x-y-2 = 10, x);

 

restart:
EQ1:=-1958143.922*k*wr+2468.8339*k^3*wr-0.9481118254e16*k^2-114000.8376*k^4:
EQ2 :=-1186578.220*R*k^2*wr-312683.0293*k^5-288960.9621*k^3*R:
 allvalues(solve([EQ1, EQ2], [k, wr]));

 

Looks like he's alive and well. Those who have lost hope of communicating with this person can find him, for example, here and here.

 

allvalues(solve({eq1, eq2}, {A, B}));

For calculating the kinematics of the manipulator, Maple of almost any version is quite suitable directly. If a system of nonlinear equations is used to describe the model of a manipulator, then it is very easy mathematically to fix any desired degree of freedom.
Perhaps you can be useful the messages, which can be found at this link:
https://www.mapleprimes.com/posts/210003-Manipulator-With-Variable-Length-Of

 

Is this way acceptable?
Lotka_Volterra_EVENT.mw
 

restart;
f := d+(c*x^3+b*x^2)*(x-1)+(b*x^2+d)^3*(a+x);
expand(f);
sort(collect(expand(f), x), x, ascending);
sort(collect(expand(f), x), x, descending);

There is a universal approach in plots[implicitplot3d]. It can be used also for other equations.
(In the text, any combination of multiplication of two equations.)
composite_surfaces_MP.mw

 implicitplot(x^2*y^2-2*x*y^3+y^4-y^3+x^2 = 1, x = 100 .. 1000, y = 0 .. 1000, numpoints = 100000);

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