Ronan

1371 Reputation

16 Badges

13 years, 227 days
East Grinstead, United Kingdom

MaplePrimes Activity


These are answers submitted by Ronan

This is not as efficient as the other solutions. It just shows more of the steps involved.
 

restart

with(plots)

NULL

P := [6, -3]

[6, -3]

(1)

line := x+2*y-1

x+2*y-1

(2)

lineperp := 2*x-y+c

2*x-y+c

(3)

NULL

c := solve(eval(lineperp, [x = 6, y = -3]), c)

-15

(4)

lineperp

2*x-y-15

(5)

display(implicitplot([line, lineperp], x = -5 .. 8, y = -8 .. 5), pointplot(P, colour = red), scaling = constrained)

 

Pint := eval([x, y], solve({line, lineperp}))

[31/5, -13/5]

(6)

Focus := P+(P-Pint)

[29/5, -17/5]

(7)

display(implicitplot([line, lineperp], x = 0 .. 10, y = -5 .. 5), pointplot([P, Pint, Focus], colour = [red, green, blue]), scaling = constrained)

 

``

distptl := proc (a, b, c) options operator, arrow; (a*x+b*y+c)/sqrt(a^2+b^2) end proc

proc (a, b, c) options operator, arrow; (a*x+b*y+c)/sqrt(b^2+a^2) end proc

(8)

Parb := (x-Focus[1])^2+(y-Focus[2])^2 = distptl(1, 2, -1)^2

(x-29/5)^2+(y+17/5)^2 = (1/5)*(x+2*y-1)^2

(9)

"(->)"

4*x^2+(-4*y-56)*x+y^2+38*y+225 = 0

(10)

``````

display(implicitplot([Parb, line, lineperp], x = 3 .. 10, y = -6 .. 1, colour = [pink, yellow, purple]), pointplot([P, Pint, Focus], colour = [red, green, blue]), scaling = constrained)

 

NULL


 

Download Parabola_from_vertex_and_line.mw

I deleted my original answer to correct my solution. This is not as efficient as @Rouben Rostamian . It just expands out the steps involved.


 

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

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


                            

 

4 5 6 7 8 Page 6 of 8