Maple 2016 Questions and Posts

These are Posts and Questions associated with the product, Maple 2016

When I launch Maple, I have to activate my license, so I type my purchase code and then I fill the form, but I receive the message "not enough activations left on this account". I used and installed Maple on an old computer and sold it because it was really old, now with my new computer I would like to re-install Maple, is there a way I can use my old activation key, instead of buying Maple again ? 

Hi, there.

I have a program, and I want to make an interface where I can text in the figures and show the results. But I have no idea about this. Anyone can give me some instructions? Thanks!

I am trying to solve a vector calculus problem, find r(t) given:

a(t) = < 4t, sin t, cos(2t) > ,  v(0) = <1,0,0>  , r(0) = <0, 1, 0 >

My approach below seems kind of complicated for such a straightforward problem.  I am trying to do this without copying pasting previous results. Also there might be a recursion issue when i defined v in terms of v(t).

 

 

Question on the ditto operator, labels, and unapply, using three examples.

 

Example 1:

The ditto operator produces no output. Why is that? I presumed that the ditto operator is equivalent to copying pasting the last output.

 

Example 2:

Here the label approach seems to work, but in example three, both the ditto and label approach fails.

 

Example 3:

Someone earlier said that I should use unapply.

Why isn't    " v := x->% " equivalent to "v:=unapply(%,x)"

And why does the label approach fail in the vector calculus example.

The object in the above display consists of a thin red disk and attached thin blue disk. They have radii 1.0 and 0.2 and masses 1.0 and 0.2 respectively.

Starting from rest at the above position they are given an initial angular velocity of Omega radians/second which starts the object rolling along the positive x axis.

If Omega is great enough that, at some time during the roll, the vertical component of the centrifugal force on the blue disk exceeds the downward force of gravity on the object, will the object begin a spinning projectile motion above the x axis?

Assuming both disks have negligible thickness, what Physics laws will govern the rolling and (possible) spinning projectile motions and what mathematics describes these motions? 

Why do I get different answers for the same command?

 different_answers.mw


 

``

restart

x := proc (n) options operator, arrow; cos(n*Pi) end proc;

proc (n) options operator, arrow; cos(n*Pi) end proc

(1)

"f:=k->"sum(k*x(n), n = 2 .. 3);f(1);

0

 

f(1)

(2)

f := proc (k) options operator, arrow; sum(k*x(n), n = 2 .. 3) end proc;

proc (k) options operator, arrow; sum(k*x(n), n = 2 .. 3) end proc

 

0

(3)

``


 

Download different_answers.mw

I have written a Maple code which extracts terms in a matrix into two new matrices dependent on certain markers. I am running into problems with this particular code as it requires enormous amounts of RAM when going to large matrix sizes (32GB+); and will take 4-5 days to complete for larger matrix sizes, or simply crashes.

Each matrix element is an algebraic expression containing A and B and the markers hh and ss. The example in the attached Maple file (3 x 3 matrix) is a minimal working example and the actual expressions are much longer and the matrices much larger (5000 x 5000 or larger). I utilise the symmetry of the matrix to ease the process, and use the tril command of MTM to extract only the lower triangular matrix; as this is all that is needed for the next stage (I have yet to test how efficient this command is, but use it for now).

The two markers hh and ss are targeted and if found in an expression that term will be extracted accordingly. The matrix elements are expanded and a procedure run over the matrix and will extract terms with hh into one matrix and terms with ss into another matrix. I think the map(expand,...) part is what causes the memory issue; but I believe this needs to be done to correctly extract terms.

Any help or tips are greatly appreciated on how to increase efficiency and improve this method.
 

Sub_matrix_extraction.mw

-Yeti

 

 



I did dummy indices implication using add command as below. is it OK or there are mistakes?

Is there another way to imply dummy index summation in maple instead of using add command?

any suggestion???

restart

II := 9:

JJ := 9:

with(LinearAlgebra):

 

 

F := add(add(add(add(R[i, m]*R[k, m]*(U[i, j]*U[k, j]+U[i, j]*V[k, j]+V[i, j]*V[k, j]+W[i, j]*W[k, j])/((2*m+1)*(2*j+1)), i = 0 .. II), k = 0 .. II), m = 0 .. II), j = 0 .. JJ):

EqU := seq(seq(diff(F, U[i, j]), j = 0 .. JJ), i = 0 .. II):

EqV := seq(seq(diff(F, V[i, j]), j = 0 .. JJ), i = 0 .. II):

EqW := seq(seq(diff(F, W[i, j]), j = 0 .. JJ), i = 0 .. II):

var := [seq(seq(U[i, j], j = 0 .. JJ), i = 0 .. II), seq(seq(V[i, j], j = 0 .. JJ), i = 0 .. II), seq(seq(W[i, j], j = 0 .. JJ), i = 0 .. II)]:

NULL

sys := [EqU, EqV, EqW]:

Aa, bb := GenerateMatrix(sys, var):

Aa

RTABLE(18446744074191847422, anything, Matrix, rectangular, Fortran_order, [], 2, 1 .. 300, 1 .. 300)

(1.1)

``


 

Download Mesal.mw

 

 

 

 ODE:= -2 sin(1/2 theta(t)) cos(1/2 theta(t)) (diff(theta(t),t)^2-9.8000 sin(theta(t))-(150+4 sin(1/2 theta(t))^2) (diff(theta(t),t,t)=0:

 ICS:=  theta(0) = Pi/6, D(theta)(0) = DthetaZero:

Hi, i wonder if there is a way to solve this 20×20 equations system for maple. Im trying fsolve but it doesn't work. aceitoso
 

nu := 6.1795*10^(-5)

0.6179500000e-4

(1)

varepsilon := 0.46e-1

0.46e-1

(2)

L__1 := 10.

10.

(3)

L__2 := 15.

15.

(4)

L__3 := 10.

10.

(5)

L__4 := 5*sqrt(2.)

7.071067810

(6)

L__5 := 6.

6.

(7)

L__6 := 6.

6.

(8)

L__7 := 20*sqrt(3.)*(1/3)

11.54700539

(9)

L__8 := 15.

15.

(10)

L__9 := 15.

15.

(11)

L__10 := 20.

20.

(12)

Re1 := 4*Q__1/(Pi*D__1*nu)

20604.24864*Q__1/D__1

(13)

Re2 := 4*Q__2/(Pi*D__2*nu)

20604.24864*Q__2/D__2

(14)

Re3 := 4*Q__3/(Pi*D__3*nu)

20604.24864*Q__3/D__3

(15)

Re4 := 4*Q__4/(Pi*D__4*nu)

20604.24864*Q__4/D__4

(16)

Re5 := 4*Q__5/(Pi*D__5*nu)

20604.24864*Q__5/D__5

(17)

Re6 := 4*Q__6/(Pi*D__6*nu)

20604.24864*Q__6/D__6

(18)

Re7 := 4*Q__7/(Pi*D__7*nu)

20604.24864*Q__7/D__7

(19)

Re8 := 4*Q__8/(Pi*D__8*nu)

20604.24864*Q__8/D__8

(20)

Re9 := 4*Q__9/(Pi*D__9*nu)

20604.24864*Q__9/D__9

(21)

Re10 := 4*Q__10/(Pi*D__10*nu)

20604.24864*Q__10/D__10

(22)

A__1 := (2.457*ln(1/((7/Re1)^.9+.27*varepsilon/D__1)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__1/Q__1)^.9+0.1242e-1/D__1))^16

(23)

A__2 := (2.457*ln(1/((7/Re2)^.9+.27*varepsilon/D__2)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__2/Q__2)^.9+0.1242e-1/D__2))^16

(24)

A__3 := (2.457*ln(1/((7/Re3)^.9+.27*varepsilon/D__3)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__3/Q__3)^.9+0.1242e-1/D__3))^16

(25)

A__4 := (2.457*ln(1/((7/Re4)^.9+.27*varepsilon/D__4)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__4/Q__4)^.9+0.1242e-1/D__4))^16

(26)

A__5 := (2.457*ln(1/((7/Re5)^.9+.27*varepsilon/D__5)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__5/Q__5)^.9+0.1242e-1/D__5))^16

(27)

A__6 := (2.457*ln(1/((7/Re6)^.9+.27*varepsilon/D__6)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__6/Q__6)^.9+0.1242e-1/D__6))^16

(28)

A__7 := (2.457*ln(1/((7/Re7)^.9+.27*varepsilon/D__7)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__7/Q__7)^.9+0.1242e-1/D__7))^16

(29)

A__8 := (2.457*ln(1/((7/Re8)^.9+.27*varepsilon/D__8)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__8/Q__8)^.9+0.1242e-1/D__8))^16

(30)

A__9 := (2.457*ln(1/((7/Re9)^.9+.27*varepsilon/D__9)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__9/Q__9)^.9+0.1242e-1/D__9))^16

(31)

A__10 := (2.457*ln(1/((7/Re10)^.9+.27*varepsilon/D__10)))^16

1763934.700*ln(1/(0.7551394026e-3*(D__10/Q__10)^.9+0.1242e-1/D__10))^16

(32)

B__1 := (37530/Re1)^16

14680.75929*D__1^16/Q__1^16

(33)

B__2 := (37530/Re2)^16

14680.75929*D__2^16/Q__2^16

(34)

B__3 := (37530/Re3)^16

14680.75929*D__3^16/Q__3^16

(35)

B__4 := (37530/Re4)^16

14680.75929*D__4^16/Q__4^16

(36)

B__5 := (37530/Re5)^16

14680.75929*D__5^16/Q__5^16

(37)

B__6 := (37530/Re6)^16

14680.75929*D__6^16/Q__6^16

(38)

B__7 := (37530/Re7)^16

14680.75929*D__7^16/Q__7^16

(39)

B__8 := (37530/Re8)^16

14680.75929*D__8^16/Q__8^16

(40)

B__9 := (37530/Re9)^16

14680.75929*D__9^16/Q__9^16

(41)

B__10 := (37530/Re10)^16

14680.75929*D__10^16/Q__10^16

(42)

f__1 := 8*((8/Re1)^12+1/(A__1+B__1)^1.5)^(1/12)

8*(0.1173811769e-40*D__1^12/Q__1^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__1/Q__1)^.9+0.1242e-1/D__1))^16+14680.75929*D__1^16/Q__1^16)^1.5)^(1/12)

(43)

f__2 := 8*((8/Re2)^12+1/(A__2+B__2)^1.5)^(1/12)

8*(0.1173811769e-40*D__2^12/Q__2^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__2/Q__2)^.9+0.1242e-1/D__2))^16+14680.75929*D__2^16/Q__2^16)^1.5)^(1/12)

(44)

f__3 := 8*((8/Re3)^12+1/(A__3+B__3)^1.5)^(1/12)

8*(0.1173811769e-40*D__3^12/Q__3^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__3/Q__3)^.9+0.1242e-1/D__3))^16+14680.75929*D__3^16/Q__3^16)^1.5)^(1/12)

(45)

f__4 := 8*((8/Re4)^12+1/(A__4+B__4)^1.5)^(1/12)

8*(0.1173811769e-40*D__4^12/Q__4^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__4/Q__4)^.9+0.1242e-1/D__4))^16+14680.75929*D__4^16/Q__4^16)^1.5)^(1/12)

(46)

f__5 := 8*((8/Re5)^12+1/(A__5+B__5)^1.5)^(1/12)

8*(0.1173811769e-40*D__5^12/Q__5^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__5/Q__5)^.9+0.1242e-1/D__5))^16+14680.75929*D__5^16/Q__5^16)^1.5)^(1/12)

(47)

f__6 := 8*((8/Re6)^12+1/(A__6+B__6)^1.5)^(1/12)

8*(0.1173811769e-40*D__6^12/Q__6^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__6/Q__6)^.9+0.1242e-1/D__6))^16+14680.75929*D__6^16/Q__6^16)^1.5)^(1/12)

(48)

f__7 := 8*((8/Re7)^12+1/(A__7+B__7)^1.5)^(1/12)

8*(0.1173811769e-40*D__7^12/Q__7^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__7/Q__7)^.9+0.1242e-1/D__7))^16+14680.75929*D__7^16/Q__7^16)^1.5)^(1/12)

(49)

f__8 := 8*((8/Re8)^12+1/(A__8+B__8)^1.5)^(1/12)

8*(0.1173811769e-40*D__8^12/Q__8^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__8/Q__8)^.9+0.1242e-1/D__8))^16+14680.75929*D__8^16/Q__8^16)^1.5)^(1/12)

(50)

f__9 := 8*((8/Re9)^12+1/(A__9+B__9)^1.5)^(1/12)

8*(0.1173811769e-40*D__9^12/Q__9^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__9/Q__9)^.9+0.1242e-1/D__9))^16+14680.75929*D__9^16/Q__9^16)^1.5)^(1/12)

(51)

f__10 := 8*((8/Re10)^12+1/(A__10+B__10)^1.5)^(1/12)

8*(0.1173811769e-40*D__10^12/Q__10^12+1/(1763934.700*ln(1/(0.7551394026e-3*(D__10/Q__10)^.9+0.1242e-1/D__10))^16+14680.75929*D__10^16/Q__10^16)^1.5)^(1/12)

(52)

H__1 := piecewise(Q__1 > 0, 8000*10^6*f__1*L__1*Q__1^2/((9.8*(Pi^2))*D__1^5), -8000*10^6*f__1*L__1*Q__1^2/((9.8*(Pi^2))*D__1^5))

piecewise(0 < `#msub(mi("Q"),mi("1"))`, 6.616893624*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^12/`#msub(mi("Q"),mi("1"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("1"))`/`#msub(mi("Q"),mi("1"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("1"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^16/`#msub(mi("Q"),mi("1"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("1"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("1"))`^5, -6.616893624*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^12/`#msub(mi("Q"),mi("1"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("1"))`/`#msub(mi("Q"),mi("1"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("1"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^16/`#msub(mi("Q"),mi("1"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("1"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("1"))`^5)

(53)

H__2 := piecewise(Q__2 > 0, 8000*10^6*f__2*L__2*Q__2^2/((9.8*(Pi^2))*D__2^5), -8000*10^6*f__2*L__2*Q__2^2/((9.8*(Pi^2))*D__2^5))

piecewise(0 < `#msub(mi("Q"),mi("2"))`, 9.925340436*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("2"))`^12/`#msub(mi("Q"),mi("2"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("2"))`/`#msub(mi("Q"),mi("2"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("2"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("2"))`^16/`#msub(mi("Q"),mi("2"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("2"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("2"))`^5, -9.925340436*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("2"))`^12/`#msub(mi("Q"),mi("2"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("2"))`/`#msub(mi("Q"),mi("2"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("2"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("2"))`^16/`#msub(mi("Q"),mi("2"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("2"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("2"))`^5)

(54)

H__3 := piecewise(Q__3 > 0, 8000*10^6*f__3*L__3*Q__3^2/((9.8*(Pi^2))*D__3^5), -8000*10^6*f__3*L__3*Q__3^2/((9.8*(Pi^2))*D__3^5))

piecewise(0 < `#msub(mi("Q"),mi("3"))`, 6.616893624*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^12/`#msub(mi("Q"),mi("3"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("3"))`/`#msub(mi("Q"),mi("3"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("3"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^16/`#msub(mi("Q"),mi("3"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("3"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("3"))`^5, -6.616893624*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^12/`#msub(mi("Q"),mi("3"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("3"))`/`#msub(mi("Q"),mi("3"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("3"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^16/`#msub(mi("Q"),mi("3"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("3"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("3"))`^5)

(55)

H__4 := piecewise(Q__4 > 0, 8000*10^6*f__4*L__4*Q__4^2/((9.8*(Pi^2))*D__4^5), -8000*10^6*f__4*L__4*Q__4^2/((9.8*(Pi^2))*D__4^5))

piecewise(0 < `#msub(mi("Q"),mi("4"))`, 4.678850351*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^12/`#msub(mi("Q"),mi("4"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("4"))`/`#msub(mi("Q"),mi("4"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("4"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^16/`#msub(mi("Q"),mi("4"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("4"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("4"))`^5, -4.678850351*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^12/`#msub(mi("Q"),mi("4"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("4"))`/`#msub(mi("Q"),mi("4"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("4"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^16/`#msub(mi("Q"),mi("4"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("4"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("4"))`^5)

(56)

H__5 := piecewise(Q__5 > 0, 8000*10^6*f__5*L__5*Q__5^2/((9.8*(Pi^2))*D__5^5), -8000*10^6*f__5*L__5*Q__5^2/((9.8*(Pi^2))*D__5^5))

piecewise(0 < `#msub(mi("Q"),mi("5"))`, 3.970136174*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^12/`#msub(mi("Q"),mi("5"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("5"))`/`#msub(mi("Q"),mi("5"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("5"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^16/`#msub(mi("Q"),mi("5"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("5"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("5"))`^5, -3.970136174*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^12/`#msub(mi("Q"),mi("5"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("5"))`/`#msub(mi("Q"),mi("5"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("5"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^16/`#msub(mi("Q"),mi("5"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("5"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("5"))`^5)

(57)

H__6 := piecewise(Q__6 > 0, 8000*10^6*f__6*L__6*Q__6^2/((9.8*(Pi^2))*D__6^5), -8000*10^6*f__6*L__6*Q__6^2/((9.8*(Pi^2))*D__6^5))

piecewise(0 < `#msub(mi("Q"),mi("6"))`, 3.970136174*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^12/`#msub(mi("Q"),mi("6"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("6"))`/`#msub(mi("Q"),mi("6"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("6"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^16/`#msub(mi("Q"),mi("6"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("6"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("6"))`^5, -3.970136174*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^12/`#msub(mi("Q"),mi("6"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("6"))`/`#msub(mi("Q"),mi("6"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("6"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^16/`#msub(mi("Q"),mi("6"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("6"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("6"))`^5)

(58)

H__7 := piecewise(Q__7 > 0, 8000*10^6*f__7*L__7*Q__7^2/((9.8*(Pi^2))*D__7^5), -8000*10^6*f__7*L__7*Q__7^2/((9.8*(Pi^2))*D__7^5))

piecewise(0 < `#msub(mi("Q"),mi("7"))`, 7.640530634*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^12/`#msub(mi("Q"),mi("7"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("7"))`/`#msub(mi("Q"),mi("7"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("7"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^16/`#msub(mi("Q"),mi("7"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("7"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("7"))`^5, -7.640530634*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^12/`#msub(mi("Q"),mi("7"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("7"))`/`#msub(mi("Q"),mi("7"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("7"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^16/`#msub(mi("Q"),mi("7"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("7"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("7"))`^5)

(59)

H__8 := piecewise(Q__8 > 0, 8000*10^6*f__8*L__8*Q__8^2/((9.8*(Pi^2))*D__8^5), -8000*10^6*f__8*L__8*Q__8^2/((9.8*(Pi^2))*D__8^5))

piecewise(0 < `#msub(mi("Q"),mi("8"))`, 9.925340436*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^12/`#msub(mi("Q"),mi("8"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("8"))`/`#msub(mi("Q"),mi("8"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("8"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^16/`#msub(mi("Q"),mi("8"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("8"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("8"))`^5, -9.925340436*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^12/`#msub(mi("Q"),mi("8"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("8"))`/`#msub(mi("Q"),mi("8"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("8"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^16/`#msub(mi("Q"),mi("8"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("8"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("8"))`^5)

(60)

H__9 := piecewise(Q__9 > 0, 8000*10^6*f__9*L__9*Q__9^2/((9.8*(Pi^2))*D__9^5), -8000*10^6*f__9*L__9*Q__9^2/((9.8*(Pi^2))*D__9^5))

piecewise(0 < `#msub(mi("Q"),mi("9"))`, 9.925340436*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("9"))`^12/`#msub(mi("Q"),mi("9"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("9"))`/`#msub(mi("Q"),mi("9"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("9"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("9"))`^16/`#msub(mi("Q"),mi("9"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("9"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("9"))`^5, -9.925340436*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("9"))`^12/`#msub(mi("Q"),mi("9"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("9"))`/`#msub(mi("Q"),mi("9"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("9"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("9"))`^16/`#msub(mi("Q"),mi("9"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("9"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("9"))`^5)

(61)

H__10 := piecewise(Q__10 > 0, 8000*10^6*f__10*L__10*Q__10^2/((9.8*(Pi^2))*D__10^5), -8000*10^6*f__10*L__10*Q__10^2/((9.8*(Pi^2))*D__10^5))

piecewise(0 < `#msub(mi("Q"),mi("10"))`, 1.323378725*10^10*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^12/`#msub(mi("Q"),mi("10"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("10"))`/`#msub(mi("Q"),mi("10"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("10"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^16/`#msub(mi("Q"),mi("10"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("10"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("10"))`^5, -1.323378725*10^10*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^12/`#msub(mi("Q"),mi("10"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("10"))`/`#msub(mi("Q"),mi("10"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("10"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^16/`#msub(mi("Q"),mi("10"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("10"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("10"))`^5)

(62)

NULL

fsolve({Q__1 = Q__4, Q__3 = Q__7, 4*Q__1/(Pi*D__1^2) = 3.5, 4*Q__10/(Pi*D__10^2) = 3.5, 4*Q__2/(Pi*D__2^2) = 3.5, 4*Q__3/(Pi*D__3^2) = 3.5, 4*Q__4/(Pi*D__4^2) = 3.5, 4*Q__5/(Pi*D__5^2) = 3.5, 4*Q__6/(Pi*D__6^2) = 3.5, 4*Q__7/(Pi*D__7^2) = 3.5, 4*Q__8/(Pi*D__8^2) = 3.5, 4*Q__9/(Pi*D__9^2) = 3.5, H__1+H__4 = H__5+H__8, H__3+H__7 = H__6+H__10, Q__1+Q__5 = Q__2, Q__4+Q__8 = 980*(1/60), Q__5+Q__9 = Q__8+17, Q__7+Q__10 = 950*(1/60), Q__2+Q__3+Q__6 = 4000*(1/60), Q__9+Q__10+17.5 = Q__6}, {D__1 = 30, D__10 = 30, D__2 = 30, D__3 = 30, D__4 = 30, D__5 = 30, D__6 = 30, D__7 = 30, D__8 = 30, D__9 = 30, Q__1 = 20, Q__10 = 5, Q__2 = 40, Q__3 = 20, Q__4 = 20, Q__5 = 20, Q__6 = 20, Q__7 = 20, Q__8 = 5, Q__9 = 5})

fsolve({`#msub(mi("Q"),mi("1"))` = `#msub(mi("Q"),mi("4"))`, `#msub(mi("Q"),mi("3"))` = `#msub(mi("Q"),mi("7"))`, 4*`#msub(mi("Q"),mi("1"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("10"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("2"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("2"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("3"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("4"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("5"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("6"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("7"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("8"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^2) = 3.5, 4*`#msub(mi("Q"),mi("9"))`/(Pi*`#msub(mi("D",fontstyle = "normal"),mi("9"))`^2) = 3.5, `#msub(mi("Q"),mi("1"))`+`#msub(mi("Q"),mi("5"))` = `#msub(mi("Q"),mi("2"))`, `#msub(mi("Q"),mi("4"))`+`#msub(mi("Q"),mi("8"))` = 49/3, `#msub(mi("Q"),mi("5"))`+`#msub(mi("Q"),mi("9"))` = `#msub(mi("Q"),mi("8"))`+17, `#msub(mi("Q"),mi("7"))`+`#msub(mi("Q"),mi("10"))` = 95/6, piecewise(0 < `#msub(mi("Q"),mi("1"))`, 6.616893624*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^12/`#msub(mi("Q"),mi("1"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("1"))`/`#msub(mi("Q"),mi("1"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("1"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^16/`#msub(mi("Q"),mi("1"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("1"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("1"))`^5, -6.616893624*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^12/`#msub(mi("Q"),mi("1"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("1"))`/`#msub(mi("Q"),mi("1"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("1"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("1"))`^16/`#msub(mi("Q"),mi("1"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("1"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("1"))`^5)+piecewise(0 < `#msub(mi("Q"),mi("4"))`, 4.678850351*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^12/`#msub(mi("Q"),mi("4"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("4"))`/`#msub(mi("Q"),mi("4"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("4"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^16/`#msub(mi("Q"),mi("4"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("4"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("4"))`^5, -4.678850351*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^12/`#msub(mi("Q"),mi("4"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("4"))`/`#msub(mi("Q"),mi("4"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("4"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("4"))`^16/`#msub(mi("Q"),mi("4"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("4"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("4"))`^5) = piecewise(0 < `#msub(mi("Q"),mi("5"))`, 3.970136174*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^12/`#msub(mi("Q"),mi("5"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("5"))`/`#msub(mi("Q"),mi("5"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("5"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^16/`#msub(mi("Q"),mi("5"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("5"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("5"))`^5, -3.970136174*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^12/`#msub(mi("Q"),mi("5"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("5"))`/`#msub(mi("Q"),mi("5"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("5"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("5"))`^16/`#msub(mi("Q"),mi("5"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("5"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("5"))`^5)+piecewise(0 < `#msub(mi("Q"),mi("8"))`, 9.925340436*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^12/`#msub(mi("Q"),mi("8"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("8"))`/`#msub(mi("Q"),mi("8"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("8"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^16/`#msub(mi("Q"),mi("8"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("8"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("8"))`^5, -9.925340436*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^12/`#msub(mi("Q"),mi("8"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("8"))`/`#msub(mi("Q"),mi("8"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("8"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("8"))`^16/`#msub(mi("Q"),mi("8"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("8"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("8"))`^5), piecewise(0 < `#msub(mi("Q"),mi("3"))`, 6.616893624*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^12/`#msub(mi("Q"),mi("3"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("3"))`/`#msub(mi("Q"),mi("3"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("3"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^16/`#msub(mi("Q"),mi("3"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("3"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("3"))`^5, -6.616893624*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^12/`#msub(mi("Q"),mi("3"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("3"))`/`#msub(mi("Q"),mi("3"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("3"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("3"))`^16/`#msub(mi("Q"),mi("3"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("3"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("3"))`^5)+piecewise(0 < `#msub(mi("Q"),mi("7"))`, 7.640530634*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^12/`#msub(mi("Q"),mi("7"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("7"))`/`#msub(mi("Q"),mi("7"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("7"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^16/`#msub(mi("Q"),mi("7"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("7"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("7"))`^5, -7.640530634*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^12/`#msub(mi("Q"),mi("7"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("7"))`/`#msub(mi("Q"),mi("7"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("7"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("7"))`^16/`#msub(mi("Q"),mi("7"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("7"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("7"))`^5) = piecewise(0 < `#msub(mi("Q"),mi("6"))`, 3.970136174*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^12/`#msub(mi("Q"),mi("6"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("6"))`/`#msub(mi("Q"),mi("6"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("6"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^16/`#msub(mi("Q"),mi("6"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("6"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("6"))`^5, -3.970136174*10^9*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^12/`#msub(mi("Q"),mi("6"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("6"))`/`#msub(mi("Q"),mi("6"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("6"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("6"))`^16/`#msub(mi("Q"),mi("6"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("6"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("6"))`^5)+piecewise(0 < `#msub(mi("Q"),mi("10"))`, 1.323378725*10^10*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^12/`#msub(mi("Q"),mi("10"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("10"))`/`#msub(mi("Q"),mi("10"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("10"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^16/`#msub(mi("Q"),mi("10"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("10"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("10"))`^5, -1.323378725*10^10*(1.173811769*10^(-41)*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^12/`#msub(mi("Q"),mi("10"))`^12+1/(1.763934700*10^6*ln(1/(0.7551394026e-3*(`#msub(mi("D",fontstyle = "normal"),mi("10"))`/`#msub(mi("Q"),mi("10"))`)^.9+0.1242e-1/`#msub(mi("D",fontstyle = "normal"),mi("10"))`))^16+14680.75929*`#msub(mi("D",fontstyle = "normal"),mi("10"))`^16/`#msub(mi("Q"),mi("10"))`^16)^1.5)^(1/12)*`#msub(mi("Q"),mi("10"))`^2/`#msub(mi("D",fontstyle = "normal"),mi("10"))`^5), `#msub(mi("Q"),mi("2"))`+`#msub(mi("Q"),mi("3"))`+`#msub(mi("Q"),mi("6"))` = 200/3, `#msub(mi("Q"),mi("9"))`+`#msub(mi("Q"),mi("10"))`+17.5 = `#msub(mi("Q"),mi("6"))`}, {`#msub(mi("Q"),mi("1"))` = 20, `#msub(mi("Q"),mi("10"))` = 5, `#msub(mi("Q"),mi("2"))` = 40, `#msub(mi("Q"),mi("3"))` = 20, `#msub(mi("Q"),mi("4"))` = 20, `#msub(mi("Q"),mi("5"))` = 20, `#msub(mi("Q"),mi("6"))` = 20, `#msub(mi("Q"),mi("7"))` = 20, `#msub(mi("Q"),mi("8"))` = 5, `#msub(mi("Q"),mi("9"))` = 5, `#msub(mi("D",fontstyle = "normal"),mi("1"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("10"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("2"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("3"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("4"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("5"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("6"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("7"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("8"))` = 30, `#msub(mi("D",fontstyle = "normal"),mi("9"))` = 30})

(63)

NULL


 

Download aceitoso.mw

 

Is any package or algorithm which enable me to compute constraint structure of a singular Lagrangian in physical phenomena?

i would be very thankfull if someone help me in thisway please :)

I recently changed to a very high resolution monitor. The worksheet material is fine, since I can control the  zoom level, but the material at the top panel, the menus and information in the help page panels is much too small,  How can it be controlled?

 

Thank you,                        --Micha Hofri

Comment:   The responder tomleslie indeed identified the problem --- fixed pixel-count programming  Some software products, such as the FireFox browser provide access to hundreds of configuration parameters.  Surely the Maple tools have such a file, but I have seen no access.

The monitor I use is indeed of high resolution, the manufacturer says it is 3840x2160, (24'' -- I use 2 of them in a T configuration).  It is a delight, except when trying to read minute characters.

I suppose I need a pointer from the people in the know........Micha Hofri

 

Responding to a comment by Mac Dude that the issue may have to do with Windows.  I assume he refers to the MIcroSoft OS.

My computers run the Mint distribution of linux (window manager is Mate).  These matters are important, yet my needs would likely be addressed by the Maple user interface mechanisms.

My difficulty is finding a way to interact with these mechanisms, I suppose.   --Micha Hofri

 

 

The worksheet below shows a river whose velocity is a function of the distance from its mid point to either bank.

In this worksheet, as an example, a boat of fixed speed crosses the river heading at all times towards its destination which is directly across the river from its starting point. The boat's path is animated.

I presume an experienced boat captain could constantly vary his heading so as to cross in a minimum time.

Can a function for this minimum crossing time heading be found and the worksheet altered to show the minimum time path?

  Rivercrossing.mw

 

There seems to be a bug with improper integration:

integrate(cos(t)*exp(-x*t),t=-infinity..infinity)

gives

0

Substituting any number for x, or assuming x >= 0  (or x<=0) does give the correct result,

The problem also persists when assuming x>-1 (or x>-Maple_floats(MIN_FLOAT))

Please can someone help with maple comand to obtain Jacobian elliptic functions particularly in code editing region?

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