Ronan

772 Reputation

14 Badges

10 years, 334 days
East Grinstead, United Kingdom

MaplePrimes Activity


These are answers submitted by Ronan

If you have any questions just ask.

Edit:- Corrected my answer as I missed the 1/(x^4+1)
 

restart

NULL

f := proc (x) options operator, arrow; (x^3+9*x^2-9*x-1)/(x^4+1) end proc

proc (x) options operator, arrow; (x^3+9*x^2-9*x-1)/(x^4+1) end proc

(1)

fsolve(f(x), x)

-.1010205144

(2)

slopef := unapply(diff(f(x), x), x)

proc (x) options operator, arrow; (3*x^2+18*x-9)/(x^4+1)-4*(x^3+9*x^2-9*x-1)*x^3/(x^4+1)^2 end proc

(3)

sol1 := [solve(slopef(x) = .5, x)]

[.4396034712, 1.545359967, 1.135924545+3.219224078*I, 0.7028667536e-1+.8729569266*I, -.8928416048, -3.504544275, 0.7028667536e-1-.8729569266*I, 1.135924545-3.219224078*I]

(4)

NULL

graphs := plot([f(x), slopef(x)], x = -10 .. 4, colour = [red, blue])

 

Eqline := proc (x, y, m, c) options operator, arrow; m*x+c = y end proc

proc (x, y, m, c) options operator, arrow; m*x+c = y end proc

(5)

P1y := f(sol1[1])

-3.019451886

(6)

m := .5

.5

(7)

line1 := Eqline(sol1[1], P1y, m, c1)

.2198017356+c1 = -3.019451886

(8)

c1 := solve(line1, c1)

-3.239253622

(9)

line1 := Eqline(x, y, m, c1)

.5*x-3.239253622 = y

(10)

NULL

P2y := f(sol1[2])

1.532928834

(11)

``

line2 := Eqline(sol1[2], P2y, m, c2)

.7726799835+c2 = 1.532928834

(12)

c2 := solve(line2, c2)

.7602488505

(13)

line2 := Eqline(x, y, m, c2)

.5*x+.7602488505 = y

(14)

NULL

P3y := f(sol1[5])

8.253465266

(15)

``

line3 := Eqline(sol1[5], P3y, m, c3)

-.4464208024+c3 = 8.253465266

(16)

c3 := solve(line3, c3)

8.699886068

(17)

line3 := Eqline(x, y, m, c3)

.5*x+8.699886068 = y

(18)

NULL

P4y := f(sol1[6])

.6456334552

(19)

``

line4 := Eqline(sol1[6], P4y, m, c4)

-1.752272138+c4 = .6456334552

(20)

c4 := solve(line4, c4)

2.397905593

(21)

line4 := Eqline(x, y, m, c4)

.5*x+2.397905593 = y

(22)

NULL

graphslines := plot([lhs(line1), lhs(line2), lhs(line3), lhs(line4)], x = -10 .. 4)

plots:-display(graphs, graphslines)

 

NULL


Download equations_of_4_lines.mw

solve(x^4-x^3-3x^2-x+12,x)

This will give you the vlues of x

if you just want numerical answers.

fsolve(x^4-x^3-3x^2-x+12,x)

Hope this helps

Here are two possible ways. Solve the equation before the variables are assigned. e.g. xb:=1000

You can then assign the variables.

or

Use eval and locally give the variables values.

Note your equation has "ab" eb=ab*yb*db*x but "ab" was not assigned you used "xb" so I changed the equation to that.


 

restart

Eq := eb = xb*yb*db*x

eb = xb*yb*db*x

(1)

sol := solve(Eq, x)

eb/(xb*yb*db)

(2)

xb := 1000

1000

(3)

yb := 2500

2500

(4)

db := 5231

5231

(5)

eb := 521

521

(6)

sol

521/13077500000

(7)

restart

NULL

Eq := eb = xb*yb*db*x

eb = xb*yb*db*x

(8)

sol := solve(Eq, x)

eb/(xb*yb*db)

(9)

eval(sol, [xb = 1000, yb = 2500, db = 5231, eb = 521])

521/13077500000

(10)

NULL


 

Download Maple_prine_solve_ans.mw

 This is a way to add elements to a list. 

op[L] removes the brackets from the list. so you get 3,5,7,-6,4,2 to start with. Then ,i^2, i^3 tags on 1,1. The the [   ] reforms a  list. So after 1st loop you now have L as [3,5,7,-6,4,2,1,1]. and it continues

restart

NULL

NULL

L := [3, 5, 7, -6, 4, 2]

[3, 5, 7, -6, 4, 2]

(1)

for i while i^2 < 100 do L := [op(L), i^2, i^3] end do

[3, 5, 7, -6, 4, 2, 1, 1, 4, 8, 9, 27, 16, 64, 25, 125, 36, 216, 49, 343, 64, 512, 81, 729]

(2)

NULL

``


 

Download Loop_List_Add_to.mw

eq := 2*exp(-2*t) + 4*t = 127:

I am not at Maple PC  at the moment.

But looking at the equation,

we see that this your equation isequivalent to exp(-2t) +2t=63.5

as a first approximation 2t=63.5

so t =31.75

exp(-2x31.75) is going to be very small. i.e 5.9000905*10^-29 (from my TI-68 calculator)

Hope that helps.

 

Look up the " is " command. Using it with the  " if " command works to evasluate you conditions. Plus a few corection to you code as @tomleslie did.

potfeld := (x, y) -> 1/sqrt(y^2 + x^2);
for i to 5 do
    for j to 3 do 
       if is(sqrt(i^2 + j^2) <> 0 and sqrt((i - 2)^2 + j^2) <> 0 and potfeld(i, j) < 3) 
        then 
           P[i, j] := plots:-arrow(<i, j>, <D[1](potfeld)(i, j), D[2](potfeld)(i, j)>); 
            else P[i, j] := plots:-arrow(<i, j>, <0.1, 0.1>); 
      end if; 
    end do;
end do;
Pseq := seq(seq([P[k, l]], k = 1 .. 5), l = 1 .. 3);
plots:-display(Pseq, view = [1 .. 5, 1 .. 3], scaling = constrained);

 

The question you have asked requires a decent bit of study. 

I googled "Transformations to hyperbolic plane in Maple"

There are probably many more. 

Hyperbolic Patterns index page (umn.edu)

Hayter_Hyperbolic_report.pdf (dur.ac.uk)

Geometry of Curves and Surfaces with MAPLE - Vladimir Rovenski - Google Books

This one I did actually do several years ago.

Esher’s Limit Circle IV rendered on the complex upper half-plane | Open System - Ark's blog (arkadiusz-jadczyk.eu)

 

Maple doesn't seem to have that formatting at present. You could try and use a single cell table scaled to the correct width.

Not really a plesent solution I admit.

 

Table_Approx_A4.mw

You need a space or a multiplication * between the R and bracket. Then it solves.

solve(R*(sigma + mu)/nu = (N*b + R*sigma)/(nu + mu), R)

R(...) is a function.

Hope this helps

Would this be acceptable as the sum converges
My internet is faulty at present so I can't get the document to display.

restart;


fd := j -> 256/3*j^5*(j - 1)^(2*j - 4)/(j + 1)^(2*j + 4);
S := x -> sum(fd(n)*ln(1 - 1/n^2), n = 2 .. x);
plot(S(x), x = 2 .. 20);
fd(10);
                             "(->)"
evalf(S(10));
for x from 2 by 5 to 200 do
    x, evalf(S(x));
end do;

 

Download MP_sum.mw

 

 

Use solve

T has 4 different value.

solve(T[1], Q); gives  -q*sigma^3/3

You get the same answer for T_2, T_3, T_4


                            

 

 

Might be worth checking this setting.

1 2 3 4 5 Page 3 of 5