## Propriety of an ellipse...

In the plane, an ABC triangle is considered for the vertices B and C are fixed, A being variable so that b +c remains constant and equal to a given length l. (b=distance(A,C), (c=distance(A,B)
How to show that the product tan(B/2=*tan(C/2) remains constant ?

## How can I extract a best-fit function for a list o...

Good day to all.

I have a data set consisting of 12 points in the x-y plane. These points form a periodic pattern and I was wondering if it is possible to obtain a curve that is a best-fit for these points. I have reason to expect that this pattern will repeat for successive points (i.e. points 13, 14, ..., 30).

Does anyone know of a way to obtain a function that can represent this behavior?

MaplePrimes_Best_Fit.mw

## How to insert a section where I want in my documen...

Whoever designed Maple's user-interface thinks very differently from me. How can I insert a 2nd section into Chapter 1? There's no space between the end of Section 1 and the end of Chapter 1 for me to put the cursor, so where should I put the cursor, and what should I do?

## How can I fix this broken Document?...

What do I need to do to the "2 + 3" in the attached Document in order to make it evaluate? I know about F5 to switch between Text and Math modes, but that's not enough to get me where I want to be. The "2 + 3" is already in Math mode, but that's not enough to get it to evaluate.

The Document: t.mw

## ODE System Solve...

R2,R3,R4,R5 have been given,I try to solve the following ode equation: The initial value:r2(0)=r3(0)=r4(0)=r5#(0);system={diff(r2(theta),theta)=R2;diff(r3(theta),theta)=2*R2*U2+R3;diff(r4(theta),theta)=R2*(U2^2+2*U3)+3*R3*U2+R4;diff(r5(theta),theta)=2*R2*(U2*U3+U4)+3*R3*(U2^2+U3)+4*R4*U2+R5}.I want to get the exact solution of subs(theta=2*Pi,U5),But it just gives the form include _Z1,_Z_2,_Z3.How can I get exact value?

restart:

#interface(echo = 2)

 > c10:=-26/9:c01:=-9.330480048:c11:=-199/33:c02:=-7.162134941:c12:=-93/11:c03:=-.756797589:d10:=11/9:d01:=26/9:d11:=19/3:d02:=25/3:d12:=8:d03:=1:
 >
 >
A1 := c03*y^3+c12*x*y^2+c02*y^2+c11*x*y+c01*y+c10*x:B1:=d03*y^3+d12*x*y^2+d02*y^2+d11*x*y+d01*y+d10*x:
 > aa1:=diff(arctan(v/u),u):bb1:=diff(arctan(v/u),v):

A11:= subs({x = -u, y = (v+c10*u/sqrt(w))*sqrt(w)/c01}, -A1):B11:= subs({x = -u, y = (v+c10*u/sqrt(w))*sqrt(w)/c01}, B1):

 > w :=-c01*d10+c10*d01:
 > f11 := subs({x = -u, y = (v+c10*u/sqrt(w))*sqrt(w)/c01}, -A1): collect(%, v):f2 := subs({x = -u, y = (v+c10*u/sqrt(w))*sqrt(w)/c01}, B1): collect(%, v):g := simplify(-c10*f11/sqrt(w)+c01*f2/sqrt(w)): collect(%, v):
 > f111:=collect(1/sqrt(w)*f11,v):f222:=collect(1/sqrt(w)*g,v):
 > F1:=u*f111+v*f222:F11:=subs({u=r*cos(theta),v=r*sin(theta)},F1):F11:=F11/r:F2:=aa1*f111+bb1*f222:F22:=subs({u=r*cos(theta),v=r*sin(theta)},F2):
 > M:=F11/F22:M:=taylor(M,r,6):r1:=coeff(M,r,1):simplify(%):subs(c10=-d01,r1):simplify(%):
 >
 > c10:=-d01:R2:=coeff(M,r,2):R3:=coeff(M,r,3):R4:=coeff(M,r,4):R5:=coeff(M,r,5):
 >
 > #R2,R3,R4,R5 have been given,I try to solve the following ode equation: The initial value:r2(0)=r3(0)=r4(0)=r5#(0);system={diff(r2(theta),theta)=R2;diff(r3(theta),theta)=2*R2*U2+R3;diff(r4(theta),theta)=R2*(U2^2+2*U3)+3*R3*U2+R4;diff(r5(theta),theta)=2*R2*(U2*U3+U4)+3*R3*(U2^2+U3)+4*R4*U2+R5}.I want to get the exact solution of subs(theta=2*Pi,U5),But it just gives the form include _Z1,_Z_2,_Z3.How can I get exact value?
 >
 > U2:=rhs(dsolve({diff(r2(theta),theta)=R2,r2(0)=0})):
 > U3:=rhs(dsolve({diff(r3(theta),theta)=2*R2*U2+R3,r3(0)=0})):
 > U4:=rhs(dsolve({diff(r4(theta),theta)=R2*(U2^2+2*U3)+3*R3*U2+R4,r4(0)=0})):
 > U5:=rhs(dsolve({diff(r5(theta),theta)=2*R2*(U2*U3+U4)+3*R3*(U2^2+U3)+4*R4*U2+R5,r5(0)=0})):
 > U6:=subs(theta=2*Pi,U5):save U6, output5:

## drawing and calculation of an angle...

how to draw and calculate the angle of a dihedral of a regular tetrahedron ? Thank you.

## dimensionless dynamical system...

Hi everyone...

How can anyone help me in the attached file? I want to know how the equation of the system turned into a dimensionless

dynamical system?

## Problem with `remove` command...

Dear friends, please I would like to ask for your help with an odd problem I have using the remove command.

I have an array

A:=Array([1,4,1,7]);

and I need to remove its first element A[1].

A:= remove[flatten](x -> x = A[1], A);

Instead of getting the result  A:= [4 1 7] I get  A:=[4 7], and I can't understand why.

## SCI MODEL help with Equilibrium state and basic r...

Dear house

I am new to maple and will really appreciate some assistance in calculating the disease free , endemic equilibrium states and basic reproduction number for my model.

I have been trying for weeks. any asistance will be much appreciated

SCI_HELP.mw

## How do I find my unknown variable within a vector ...

So I have an equation that basically takes the component of vectors to be used as an equation. The variables that I after are FB1z, FB2x, and FB3y For example here is my equation:

EOM1:=(AFB1[1]+AFB2[1]+AFB3[1])=TEOM[1]

EOM2:=(AFB1[2]+AFB2[2]+AFB3[2])=TEOM[2]

EOM3:=(AFB1[3]+AFB2[3]+AFB3[3])-TEOM[3]:

FBBp1:=FBPP1=(EulP1[1]+EulP2[1]+EulP3[1]):
FBBp2:=FBPP2=(EulP1[2]+EulP2[2]+EulP3[2]):
FBBp3:=FBPP3=(EulP1[3]+EulP2[3]+EulP3[3]):

However there are unknown variable in AFB2[1] named FB2x and AFB3[1] named FB3y. Then AFB1[2] has unknown equation named FB1z and AFB3[2] has FB3y and so on. While in my FBBp1,FBBp2,and FBBp3 holds all of the variable of FB1z, FB2x, and FB3x
I have tried to use 'solve' command to find the variable but my computer won't stop processing it:
sls:=solve({EOM1,EOM2,EOM3,FBBp1,FBBp2,FBBp3},{FB1z,FB2x,FB3y}):

I tried to use the Gauss-Elimination by forming a matrix but it doesn't work as well since I am really confused how to take out the variables out of the vector component.

zzz:=Matrix([0,AFB2[1],AFB3[1],jjj[1]],[AFB1[2],0,AFB3[2],jjj[2]],[AFB1[3],AFB2[3],0,jjj[3]],[FBP1[1],FBP2[1],FBP3[1],EulP[1]],[FBP1[2],FBP2[2],FBP3[2],EulP[2]],[FBP1[3],FBP2[3],FBP3[3],EulP[3]]):
GaussElimination:=(zzz)

I would be very grateful If someone could help me. Thankyou

Edit: here are the .txt files and .mpl files that required to run the program

inersia_platfrom.txt

There is an .mpl file that I couldn't upload so I will upload it in the comments

## Remember tables and forget command...

I have a remember table generated by a recursive procedure

x:= proc(n)
option remember;
....
end proc:

It helps compute x(1), x(2), x(3), x(4).

After several additional steps I have a new x(2), say

x(2):= 3;

With this new x(2) I need to recompute x(3), x(4). I've tried

forget( x, [ x(3), x(4) ], subfunctions = false );

x(3);

x(4);

However, I do not get the new values of x(3) and x(4) but the old ones. What could it be wrong?

## Select element of rtable...

Dear friends,

I have to select the last element of a remember table T from a recursive procedure. I've tried

with(ListTools):

SelectLast(T);

as this command works with rtables, as it is stated in Maple's online help page. However I receive no result.

Can you please tell me how to obtain a correct result?

Many thanks for the help.

## How can I plot the solution curves for varying con...

Good day.

I have a simple function that I would like to plot, but am finding this awkward to do. My objective is to plot the function for varying k-values and I tried doing this using implicitplot and sequencing values of k.

The function in question is:
y := k*x*sqrt(z*(1-z));

The constant, k, takes the values: 5, 10, 15, ..., 100
The variables lie in the range: 0 ≤ x < 1 and 0 ≤ z < 1

So, if someone can tell me how to construct a plot of multiple solution curves for varying k, I would be most grateful.