MaplePrimes Questions

​​​​​​use epilson- delta definition of a limit to prove that

Limit as x approaches 5 of 1/x =1/5

There seems to be a bug: in some of the cases, the intersection command works, in others it doesn't.

I'd appreciate any hints as to why this is the case.

 

intersection_of_two_lines.mw

Hello,

I think its a simple question and I hope, someone can help me. For Example:

I have a list of numbers ("M") and I want to write these numbers in a new List but with the restriction

if x<Mthen Mi*2
else Mi 

Can someone explain how to solve this in maple?

Thank you very much.
Maritn

 

I am looking for a pragmatic solution to the question: Can my rolled carpet fit inside a given cardboard box?

It is the (generally unsolvable) problem "straw in a box":

https://www.maa.org/sites/default/files/pdf/upload_library/22/Polya/jerrard93.pdf

...with the restriction that the cylinder is aligned along the spatial diagonal.

 

So the application is this:
Is it possible to put a 120cm long rolled (radius 10cm) carpet inside a cardbord box of (inner) dimensions 118cm x 58cm x 38cm ?

Maple code would be perfect, but I have very little Maple experience so I cannot even provide any attempts/code at this stage.

Thanks!

A Happy New Year, people in mapleprimes,

I have a question, but this might be an inappropriate question to this site.

In Introduction to Maple, there is a calculation with a double square root.
Related to it, I want to calculate the following expression, which has a value of zero.

-3*(sqrt(10+4*sqrt(5)))+sqrt(50+20*sqrt(5))+sqrt(10-4*sqrt(5))+sqrt(50-20*sqrt(5));

Is there any way to use maple  so as to explain how the above expression takes the value of zero?

On earth, I cannot understand why this takes zero.

I hope you will give me a hint.

Thanks in advance.

 

I am trying to assess stability from real roots of Eigenvalues that are returned in the RootOf from. I tried allvalues(), evalf() both return the same RootOf list. If memory serves me correctly any square matrix should have and Eigenvalue solution.

Any suggestions?

Eignevalues.mw
 

NULL

with(LinearAlgebra)

Xd := 1.81
Xq := 1.76; Xpd := .3; Xe := .65; re := 0.3e-2; et := 1.0

M := 7; Tdo := 8; Ke := 200; Te := 0.2e-1

Q := -2.7; k := 0.2e-1; m := 1; FORW := 1

D curve PointsPoints      
             
           Pt__a := 0, .66

Pt__b := .56, .55 
Pt__c := .94, .34; Pt__d := 1.0, 0; Pt__h := 1.0, 0; Pt__g := .95, -.311; Pt__f := .59, -.398; Pt__e := 0, -.428
PSS

KSTAB := 9.6

     
TW := 1.4; T1 := .154

T2 := 0.33e-1

P := 1

Q := -.5

eto := abs(et); Ipo := P/eto; Iqo := Q/eto; Eqo := sqrt((Iqo*Xq+eto)^2+(Ipo*Xq)^2); Eo := sqrt((-Ipo*re-Iqo*Xe+eto)^2+(Ipo*Xe-Iqo*re)^2); `sin&delta;o` := (eto*Ipo*(Xq+Xe)-re*Xq*(Ipo^2+Iqo^2)-eto*Iqo*re)/(Eqo*Eo); `cos&delta;o` := (eto*(eto+Iqo*(Xq-Xe)-Ipo*re)-Xe*Xq*(Ipo^2+Iqo^2))/(Eqo*Eo); iqo := (Ipo*(Iqo*Xq+eto)-Iqo*Ipo*Xq)/Eqo; ido := (Ipo^2*Xq+Iqo*(Iqo*Xq+eto))/Eqo; eqo := eto*(Iqo*Xq+eto)/Eqo; edo := iqo*Xq; A := re^2+(Xe+Xpd)*(Xq+Xe); K1 := Eqo*Eo*(re*`sin&delta;o`+(Xe+Xpd)*`cos&delta;o`)/A+iqo*Eo*((Xq-Xpd)*(Xq+Xe)*`sin&delta;o`-re*(Xq-Xpd)*`cos&delta;o`)/A; K2 := re*Eqo/A+iqo*(1+(Xq+Xe)*(Xq-Xpd)/A); K3 := 1/(1+(Xq+Xe)*(Xd-Xpd)/A); K4 := Eo*(Xd-Xpd)*(Xq+Xe)*`sin&delta;o`/A-re*`cos&delta;o`; K5 := edo*Xq*(re*Eo*`sin&delta;o`+(Xe+Xpd)*Eo*`cos&delta;o`)/(eto*A)+eqo*Xpd*(re*Eo*`cos&delta;o`-(Xq+Xe)*Eo*`sin&delta;o`)/(eto*A); K6 := eqo*(1-Xpd*(Xq+Xe)/A)/eto+edo*Xq*re/(eto*A); A4 := Matrix(6, 6, {(1, 1) = 0, (1, 2) = 377, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (1, 6) = 0, (2, 1) = -K1/M, (2, 2) = 0, (2, 3) = -K2/M, (2, 4) = 0, (2, 5) = 0, (2, 6) = 0, (3, 1) = -K4/Tdo, (3, 2) = 0, (3, 3) = -1/(K3*Tdo), (3, 4) = -1/Tdo, (3, 5) = 0, (3, 6) = 0, (4, 1) = K5*Ke/Te, (4, 2) = 0, (4, 3) = K6*Ke/Te, (4, 4) = -1/Te, (4, 5) = Ke/Te, (4, 6) = 0, (5, 1) = -K1*KSTAB*T1/(T2*M), (5, 2) = 0, (5, 3) = -K2*KSTAB*T1/(T2*M), (5, 4) = 0, (5, 5) = -`#mn("1")`/TW, (5, 6) = -(T1+TW)/(T2*TW), (6, 1) = -K1*KSTAB/M, (6, 2) = 0, (6, 3) = -K2*KSTAB/M, (6, 4) = 0, (6, 5) = 0, (6, 6) = -`#mn("1")`/TW}); Eig := Eigenvalues(A4)

allvalues(Eig)

evalf(Eig[1])

RootOf(10000000000*_Z^6+(14285714290*`#mn("1")`+503236834300)*_Z^5+(5102040817*`#mn("1")`^2+718909763500*`#mn("1")`+1193248786000)*_Z^4+(256753486900*`#mn("1")`^2+1704641123000*`#mn("1")`-94259434520000)*_Z^3+(608800401100*`#mn("1")`^2-52350222800000*`#mn("1")`+1273591282000000)*_Z^2+(10698531930000*`#mn("1")`^2+632925408400000*`#mn("1")`+1000000)*_Z+226044788700000*`#mn("1")`^2-10000000)

(1)

``


 

Download Eignevalues.mw
 

 


 

Download Eignevalues.mw

 

 

Dears,

Consider the problem min{|a+2*i| : i integer}, where a is a number of the form 2k*t for a fixed integer k>1 and t in [0,1]. A simple checking shows that i must belongs to the interval [-(1+a)/2,(1-a)/2] and as the legth of this interval is 1, there is two integers in this interval.

How can I compute this integer i with Maple? The commad "ceil" not seem very suitable. Some idea?
Many thanks in advance for your comments.

At the beginning of my work sheet I used the matrix palette to create several matrix. Now when I try to use the palette this is what I get. 

`Matrix(2, 3, {(1, 1) = Typesetting:-msub(Typesetting:-mi("n"), Typesetting:-mrow(Typesetting:-mn("1"), Typesetting:-mo(","), Typesetting:-mn("1"))), (1, 2) = Typesetting:-msub(Typesetting:-mi("n"), Typesetting:-mrow(Typesetting:-mn("1"), Typesetting:-mo(","), Typesetting:-mn("2"))), (1, 3) = Typesetting:-msub(Typesetting:-mi("n"), Typesetting:-mrow(Typesetting:-mn("1"), Typesetting:-mo(","), Typesetting:-mn("3"))), (2, 1) = Typesetting:-msub(Typesetting:-mi("n"), Typesetting:-mrow(Typesetting:-mn("2"), Typesetting:-mo(","), Typesetting:-mn("1"))), (2, 2) = Typesetting:-msub(Typesetting:-mi("n"), Typesetting:-mrow(Typesetting:-mn("2"), Typesetting:-mo(","), Typesetting:-mn("2"))), (2, 3) = Typesetting:-msub(Typesetting:-mi("n"), Typesetting:-mrow(Typesetting:-mn("2"), Typesetting:-mo(","), Typesetting:-mn("3")))})`

To get a matrix from the palette I have to create it on a new worksheet and cut and past it into the existing work sheet.

What is happening?

Hi, I am a Maple newbie. My problem is I do not know how to generate the result to find the answers of these question: 

  1. a)   Sketch the surface area of the part of paraboloid z = x2 + y2 that lies under the plane z=8.

b)   Compute the surface area.

  1. a)   Sketch the solid that lies above the cone z = (x2 + y2)1/2 and inside the sphere x2 + y2 + z2 = 16.

b)   Compute the volume of the solid.

It is possible to calculate these question? Does anyone has a suggestion? Thank you. 

Hi all,

Please help me to get a solution for all the desired data in the attached file. As you could see through it, just for 4 out of 20 desired Br, there are answers by the command:
Notice that If I write Br= -7.0 there is no solution, but I wrote Br= -6.999999, and the solution was achieved simply; just by applying an approximation value for '7'.
 

I don't know why for other data there are no solution...

Best

System_of_Equations.mw

restart;
with(PDETools);
diff(r(t), t)-(diff(a[3](t), t))*r(t)/a[3](t)+a[1](t)*p[3](t)-3*r(t)*r(t) = 0;
                                        
dsolve(diff(r(t), t)-(diff(a[3](t), t))*r(t)/a[3](t)+a[1](t)*p[3](t)-3*r(t)^2 = 0, r(t));

 it does not give any solution ,please help.

how to see all steps of solution in maple? for eg: any second order differential eq.

how to solve optimal system of vector   fields in lie theory in maple?

Am trying to draw a series of triangles for animation.  I try to construct the triangles in a loop using:

triangle(cat(T1,`a`),[A,B,C]):

  so that the names of the triangles are meant to beT14, T15, T16

I have tried unsuccessfully to use the plots and draw commands ie

draw({seq(tabl[i], i=4..6)}, insequence=true, scaling=constrained);

plots[display({seq(tabl[i], i=4..6)}, insequence=true, scaling=constrained);

  Can the animation be done in either?  

It seems to want a variable in a list/set format - How do I set that up?  Any comments, or help gratefully received.  The program is below.  Part of the output does give triangles - but they all seem identical:-(

 

restart:

# # # # # # # # # # # # # # # # # # # # # # # # # # # #

# Altitude exploration  program

#Trying to draw a sequence of triangles for animation

# # # # # # # # # # # # # # # # # # # # # # # # # # # #

with(plots):

with(geometry):

for a from 4 to 6 do

b:=a+1: c:=a+2:

angA:=arccos((a+5)/2/(a+2));

point(A,0,0),point(B,c*cos(angA),c*sin(angA)),point(C,a+1,0):

tabl[a]:=triangle(cat(T1,`a`),[A,B,C]):

printf("a=%d\n",a);

triangle(cat(T1,`a`),[A,B,C]):

end do:
 

for i from 4 to 6 do

draw({seq(tabl[i], i=4..6)}, scaling=constrained);

printf("a=%d\n",i);

end do;
 

print(`After do`);

draw({seq(tabl[i], i=4..6)}, insequence=true, scaling=constrained);

Warning, the name changecoords has been redefined

 

Warning, the name arrow has been redefined

 

Warning, these names have been redefined: circle, ellipse, homothety, hyperbola, line, point

 

a=4

a=5

a=6

a=4

a=5

a=6

What is a suitable replacement for eliminate?

Here is my code:

 

A := {x[5] = x[2]/x[1], x[6] = x[3]/x[2], x[7] = x[1]/x[4], x[8] = (2*x[2]+x[4])/(2*x[1]+x[3]+x[4])};
B := {x[1], x[2], x[3], x[4], x[8]};

([eliminate])(A, B);
([eliminate])(A, B minus {x[1]});
([solve])(A, B);


In the older versions of Maple the first example of eliminate would return same result as the solve example, but with current version I need to resort to the second example.

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