mm-149
I have this equation:F = 1/2 v^2 (sin (kF(theta))orF
/sin (kF (theta)) = 1/2 v^2Does anyone see an analytical
solution? I can only solve it byiteritive guessing. Perhaps
some trig identity for F / sin(F(theta)) ?I need to pull the F
out and put everything else on the right
side.anothername@access4less.netas I don't follow this
group.
 I have this equation:> F = 1/2 v^2 (sin
(kF(theta))> or> F /sin (kF (theta)) = 1/2 v^2> Does anyone
see an analytical solution? I can only solve it by> iteritive
guessing. Perhaps some trig identity for F / sin> (F(theta))
?> I need to pull the F out and put everything else on the
right side.> anothername@access4less.net> as I don't follow
this group.If you do not follow this group, at least to see
whether your request is answered, why should this group do
anything for you?There is no analytic solution for F.
what do you expect from> substituting A for 1/2 in the
expression below?> sqrt(x+1/2) + 1/sqrt(x-1/2)> Macsyma
gives (x+a)^a +1/(x-a)^a> Mathematica 4.1 gives >
1/Sqrt[-1/2+x] +(a+x)^a> Maple 7 gives>
2*1/(sqrt(4*x-2))+(4*x+2)^a*a> What does your favorite
system do, and do you think> it is correct?meditor's
answer:subst(sqrt(x+1/2) +
1/sqrt(x-1/2),1/2,a)=1/sqrt(-a+x)+sqrt(a+x)I think it does not
bad :-)Raphael
=While doing some calculations on number
theory, I came accross this limit ofa certain series.This is
an approximation to 100
digits:
0.2922312926730306916730752725696157349776892871155484154960385
559422739975495210544495525039898241225I do not know if this
is a known constant, it should be given the nature ofthe
series.
 While doing some calculations on number theory, I
came accross this limit of> a certain series.> This is an
approximation to 100 digits:>
0.2922312926730306916730752725696157349776892871155484154960385
5594227399754> 95210544495525039898241225> I do not know if
this is a known constant, it should be given the nature of>
the series.> The Inverse Symbolic Calculator*
shows:2922311750620494 = (0261)
2+6*x-2*x^2+4*x^3+3*x^4-x^52922312233629816 =
(0062)sum((-1)^(n+1)/(n^3+7/2*n^2-35/2*n+25)/C(2*n,n),n=1..inf
)2922312656013193 = (0001)
(BesI(0,2)-K(1/sr(2)))/Backhouse2922312801239070 = (0001)
Zeta(3)^Pi*Zeta(3)^KhintYour value of 2922312926730306 would
be here.2922313019481644 = (0010)
sum((11/3*n^3-33/2*n^2+269/6*n-25)/(n!+1),n=1..inf)
2922313037101867 = (0002)
sum(1/(5^n*(15/2*n^2+77/2*n-39)),n=1..inf)2922313180774296 =
(0259) F(2/11,7/10;3/7,5/6,1/4;1) 2922313280964475 = (0001)
ln(5)^BesK(1,1)+BesI(1,2)2922313307254255 = (0001)
(Parking+exp(1/E)*ZeroBesJ(0,x))/exp(1/E)so can you explain a
bit more about this constant and how it was
derived?Randall*http://www.cecm.sfu.ca/projects/ISC/
moderator for sci.math.research
=I need to solve the
following differential system in matrix
form:dN(x)/dx=M(x)*N(x)N(a)=Iwhere I, N(x) and M(x) are
matrices (n x n). I is the identity matrix, a is any initial
point.Since M is not constant, the solution cannot be taken as
matrix exponential.Nevertheless, M(x) can be put in the
following form:M(x)=M0 + (1/x)*M1 + (1/x^2)*M2where M0, M1, M2
are numerical matrices (not functions of x).The question is:
does exist any analytical solution for this kind of matrix
equation? In particular, I need to evaluate the matrix N(x) in
x=0, where the matrix M is divergent (as you can easily
notice). I tried with a sixth-order implicit Runge-Kutta
method, but I would like to know if any analitycal solution is
possibile to reduce the working time and to improve the
results.Please, help me as soon as possible. I would like to
receive your RobertoDott. Ing. Roberto DianaPolitecnico di
BariDipartimento di Elettrotecnica ed ElettronicaVia Re David,
=Five vectors are:A =
[0,0,0,1]B = [a,e,0,-1/4]C = [b,f,i,-1/4]D = [c,g,j,-1/4]E =
[d,h,k,-1/4]where (a..k) are to be determined.The dot product
of any 2 vectors is to be -1/4. This is satis'ed by A with
anyof the others.A+B+C+D+E = 0, the resultant of all 5 is
0.magnitude(A) = magnitude(B) = magnitude(C) = magnitude(D) =
magnitude(E) = 1 orall 5 vectors are unit vectors.Basically
the 've vectors are equal angular, the same angle exists
between anytwo.These 5 vectors are the axial lines from the
origin {0,0,0,0] of a hyperregulartetrahedron? (not sure of
name of this 'gure) to the vertices of this 
4d'gure.Can
someone determine the values for
a,b,c,d,e,f,g,h,i,k?Randallp.s. reply to sci.math group
=One answer:The 'gure is called a
simplex and the coordinates of the vertices are
given.k=sqrt(5)/4A = [ 0, 0, 0, 1 ]B = [ -k, k, k,-1/4 ]C = [
k,-k, k,-1/4 ]D = [ k, k,-k,-1/4 ]E = [ -k,-k,-k,-1/4 ]I just
have to rotate the matrix so that B has a 0 in the 3rd
position.Randallp.s. Found answer on
http://astronomy.swin.edu.au/~pbourke/polyhedra/platonic4d/==
==I'm working on a problem: Distant Galaxies. In the late
1920s the famous observation astronomer Edwin P. Hubble (1889
-- 1953) determined the distances to severl galaxies and the
velocities at which they were receding from Earth. Four
galaxies with their distances in light-years and velocities in
miles per second are listed in the table. Galaxy Distance
Velocity ______ ________ ________ Virgo 50 990 Ursa Minor 650
9300 Corona Borealis 950 15000 Bootes 1700 25000Source:
Sharov, A., and I. Novikov, Edwin Hubble, The Discoverer of
the Big Ban Universe, Cambridge University Press, 1993.(a)
Let x represent distance and y represent velocity. Find the
equation of the least-squares regression line that models the
data.(b) If the galaxy Hydra is receding at a speed of 37,000
miles per second, estimate its distance from Earth.I've 
'gured
the equation of the line is y = (277x)/20 + 595/2. What I'm
trying to 'gure out in maple is the equation of the
least-squares regression line that models the data.I have
entered with (LinearAlgebra);Then A := (<< 50, 650, 950,
1700 > | < 990, 9300, 15000, 25000 >>);The matrix came up
'ne. What I'm confused about is what 
I'm supposed to enter
after b :=  . What data is the program looking for? The help
'le says B is supposed to be Matrix, column Vector or set of
variables. Nothing I've tried works. Can someone explain it
to me?-- Cindy Smith Unless the LORD build the house,
cms@dragon.com they labor in vain who build.cms@5sc.net Unless
the LORD guard the city,cms@romancatholic.org in vain does the
guard keep watch.Me transmitte sursum, -- Psalm 127:1
Caledoni! All your base are belong to us.A Real Live Catholic
You are on the way to destruction. in Georgia! What you
say.>->> <<-< Go against the §ow! You have no chance to
survive make your time.
 (a) Let x represent distance
and y represent velocity. Find the> equation of the
least-squares regression line that models the data.>> I've
'gured the equation of the line is y = (277x)/20 + 595/2.What
line is that?> What I'm trying to 'gure out in 
maple is the
equation of the> least-squares regression line that models the
data.See ?CurveFitting,LeastSquares> Then A := (<< 50, 650,
950, 1700 > | < 990, 9300, 15000, 25000
>>);ThenCurveFitting:-LeastSquares(A, x);> The matrix came up
'ne. What I'm confused about is what 
I'm supposed> to enter
after b :=  . What data is the program looking for? The>
help 'le says B is supposed to be Matrix, column Vector or
set of> variables.What help 'le are you looking at?