gulliet

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These are answers submitted by gulliet

Write x1(t) explicitly if x1 is a function of t.
dsolve(diff(x1(t), t) = -2*a*x1(t)*(x1(t)-1)+(1-b)*x0);

            /       a (2 x1(t) - 1)       \                             (1/2)   
_C1 + arctan|-----------------------------| + t (a (-2 x0 + 2 x0 b - a))      = 
            |                        (1/2)|                                     
            \(a (-2 x0 + 2 x0 b - a))     /                                     

                 /       /                           (1/2)
              1  |       |  /                      2\     
  0, x1(t) = --- \a - tan\t \-2 a x0 + 2 a x0 b - a /     
             2 a                                          

                                  (1/2)\                          (1/2)\
         /                      2\     | /                      2\     |
   + _C1 \-2 a x0 + 2 a x0 b - a /     / \-2 a x0 + 2 a x0 b - a /     /
Regards, --Jean-Marc
It is not clear what you actually tried, but if the function is complex valued on chosen interval, the plot will be empty. 97_plotemptybecausecomplex.jpg Regards, --Jean-Marc
Here is what I get on my system: 97_sinsinplify.jpg Regards, --Jean-Marc
I know plot3d(equation, range, range) gives you graph, but is there a way to plot a graph in only places where data sets are given instead of one smooth graph?
I believe what you are looking for is the function pointplot3d. See help("pointplot3d") for more info. HTH, --Jean-Marc
The variable t5 is declared twice in the second argument of solve. replace it by t3, so the last line reads:
q := solve(eqns, {t0, t1, t2, t3, t4, t5, t6, t7});
Regards, --Jean-Marc
Could you provide some values/definitions for a5, n1, n2, n3? 

Moreover,

> restart; with(plots); 
> spacecurve({[x, y, z]}, t = 0 .. Pi, scaling = constrained, 
color = blue, thickness = 3)

returns a blank 3d-plot on my system (Maple 12.02, Mac OS X).

Also, I cannot see the pictures you posted for I get the 
following error message:

"Safari can’t open the page
“http://c:/Users/sarper/AppData/Local/Temp/moz-screenshot-1.jpg”
because it can’t find the server “c”." 

Apparently the links you posted do not point to any Maplesolft's servers.

Regards,
--Jean-Marc
The symbol :- is a shortcut for the use statement. See help("use") for more info (or also in MaplePrimes). With Maple 12.02, if I enter :- in the search text box, I arrive to the help page for use. 97_mapleusestatement.jpg Regards, --Jean-Marc
Write plots:-setoptions as in
proc () plots:-setoptions(title = `My Plot`) end proc
97_plotwithprocandtitle.jpg Regards, --Jean-Marc
The correct Maple syntax for your equations is as follows (eq1 and eq2 are just symbolic names for easy reference to each equation):
eq1:=(Psi(1, b)-Psi(1, a+b))/(Psi(0, b)-Psi(0, a+b))^2 = s2/s1^2; 
eq2:=(Psi(2, b)-Psi(2, a+b))/(Psi(0, b)-Psi(0, a+b))^3 = s3/s1^3;
97_eqswithpolylog.jpg Regards, --Jean-Marc
I cannot see the images. If I try to force the display, I get the following error message, "Safari can’t open the page “http://c:/Users/Zach/AppData/Local/Temp/moz-screenshot-2.jpg” because it can’t find the server “c”." which seems to indicate that you have not uploaded the image on the MaplePrimes's server or pasted the wrong url. You should use the file manager, titled My files, located on the left hand side of the page to upload images and get the corresponding url on MaplePrimes. 97_mapleprimesmyfilesmenu.jpg Regards, --Jean-Marc
It looks like you really have only one equation of two variables: eq2 is a symbolic expression for q that can be replaced into eq1.
restart; 
eq1 := (q/a)^2+2*q1*f*cosh(-3*p*q2/(2*a))-1-q1^2*f^2 = 0; 
eq2 := q = a*q1*f*sinh((3/2)*p*q2/a)*q2; 
algsubs(eq2, eq1); 
subs({a = 0.150e9, f = .25, p = 0.174e9, q = 0.199e9}, %); 
solve(%, [q1, q2]);

                      2                                       
                     q               /3 p q2\         2  2    
              eq1 := -- + 2 q1 f cosh|------| - 1 - q1  f  = 0
                      2              \ 2 a  /                 
                     a                                        
                                            /3 p q2\   
                      eq2 := q = a q1 f sinh|------| q2
                                            \ 2 a  /   
                                   2                                  
         2  2     2  2     /3 p q2\    2                  /3 p q2\    
      -q1  f  + q1  f  sinh|------|  q2  - 1 + 2 q1 f cosh|------| = 0
                           \ 2 a  /                       \ 2 a  /    
                     2            2                     2   2    
           -0.0625 q1  + 0.0625 q1  sinh(1.740000000 q2)  q2  - 1

              + 0.50 q1 cosh(1.740000000 q2) = 0
[[              /         /  2           /      /        2          2
[[q1 = q1, q2 = \2. RootOf\_Z  + 4 q1 exp\RootOf\-7569 q1  (exp(_Z)) 

                       3                                      2
   + 30276 q1 (exp(_Z))  + 30276 q1 exp(_Z) - 121104 (exp(_Z)) 

           2   2          4          2   2          2         2   2\\        
   + 625 _Z  q1  (exp(_Z))  - 1250 _Z  q1  (exp(_Z))  + 625 _Z  q1 // + 4 q1 

  /   /      /        2          2                     3                   
  \exp\RootOf\-7569 q1  (exp(_Z))  + 30276 q1 (exp(_Z))  + 30276 q1 exp(_Z)

                     2         2   2          4          2   2          2
   - 121104 (exp(_Z))  + 625 _Z  q1  (exp(_Z))  - 1250 _Z  q1  (exp(_Z)) 

           2   2\\\     /   2     \ /   /      /        2          2
   + 625 _Z  q1 ///^3 + \-q1  - 16/ \exp\RootOf\-7569 q1  (exp(_Z)) 

                       3                                      2
   + 30276 q1 (exp(_Z))  + 30276 q1 exp(_Z) - 121104 (exp(_Z)) 

           2   2          4          2   2          2         2   2\\\    
   + 625 _Z  q1  (exp(_Z))  - 1250 _Z  q1  (exp(_Z))  + 625 _Z  q1 ///^2, 

             \\//   /   /      /        2          2                     3
  label = _L4// \q1 \exp\RootOf\-7569 q1  (exp(_Z))  + 30276 q1 (exp(_Z)) 

                                        2         2   2          4
   + 30276 q1 exp(_Z) - 121104 (exp(_Z))  + 625 _Z  q1  (exp(_Z)) 

            2   2          2         2   2\\\          \]                      
   - 1250 _Z  q1  (exp(_Z))  + 625 _Z  q1 ///^2 - 1. q1/], [q1 = 4., q2 = 0.], 

                                ]
  [q1 = -4., q2 = 1.805513019 I]]
Regards, --Jean-Marc
Assuming I have correctly understood your question, I think Alexander Bogomolny's web site should help you to answer it: "Inscribed and Central Angles in a Circle: What is this about? A Mathematical Droodle". (Note that the website contains a nice interactive JAVA applet and a link to some explanations about what's going on.) HTH, --Jean-Marc
You should search this web site for "premature evaluation" for similar questions to your arise quite often. One possible way to get the plot is as follows:
> restart;
> t := proc (x) if 1 < x then x else x+1 end if end proc;
> plot(t, -1 .. 4);
97_prematureevalutionplot.jpeg Regards, --Jean-Marc
97_limitexp1.jpg Regards, --Jean-Marc
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