Let P(x)=ax^3+bx^2+cx+d from R[X] with a<>0.If the coeficients of this polinomial are in arithmecical progression, and all of its roots are real then the...
6204
clooneman
Jun 3, 2003 12:17 pm
I didn't!!!!!!! I was just joking. Sorry. I was about to head off home for the weekend and I thought I'd give the silliest answer I could find. At any rate,...
6205
clooneman
Jun 3, 2003 12:38 pm
To paraphrase Homer J Simpson, "a magical, fairy calculator". ... small ... & ... click...
6206
clooneman
Jun 3, 2003 1:00 pm
Couldn't even get the quote right, could I! For those of you whose appetites have been whetted, here goes... Homer: Lisa honey, are you saying you're never...
6207
Silk
silk_roc
Jun 3, 2003 3:19 pm
LOL! ... do ... Magical...
6209
clooneman
Jun 3, 2003 4:53 pm
And I am Irish. Hurrah!!!...
6210
clooneman
Jun 3, 2003 4:55 pm
Out of curiosity, how do you raise integers, etc to the power of i? (I think I asked that before)...
6211
fabian
fabianseoane
Jun 3, 2003 5:18 pm
On Tue, 2003-06-03 at 18:55, clooneman wrote: Out of curiosity, how do you raise integers, etc to the power of i? (I think I asked that before) There is no...
6212
Carlos Assale
c_assalebr
Jun 3, 2003 5:50 pm
As e^i = cos(1) + i*sin(1) and e = a^(1/ln(a)) then a^i = (cos(1) + i*sin(1))^ln(a) Is there a way to go from there....???? Carlos...
6213
clooneman
Jun 3, 2003 6:08 pm
Cos(1)? And sin(1)? In radians? ... of i? ... base=e, ... Then we ... at ... if know ... world' ... degree ... think that ... solution ... connection ... ...
6214
Carlos Assale
c_assalebr
Jun 3, 2003 6:22 pm
Yep!! Carlos...
6215
Lagrangia Louis
lagrangia_louis
Jun 3, 2003 7:11 pm
Well the relation is actually: arctan(1/x1)+arctan(1/x2)+arctan(1/x3)=-pi/4 cause other wise it is impossible. try to write it: ...
6216
Lalit Jain
lalitkumarj
Jun 3, 2003 9:39 pm
Where did e = a^(1/ln(a)) come from? Lalit Jain ... From: Carlos Assale To: mathforfun@yahoogroups.com Sent: Tuesday, June 03, 2003 1:46 PM Subject: Re: [MATH...
6217
Carlos Assale
c_assalebr
Jun 3, 2003 10:15 pm
e^ln(a) = a so e = a^(1/ln(a)) Carlos...
6218
Ricardo Filho
lhradiohead
Jun 3, 2003 11:47 pm
P(x)=ax^2+bx^2+cx+d. (a,b,c,d) is a arithmetical progression, so P(x)=ax^3+(a+r)x^2+(a+2r)^x+(a+3r) let arctan(1/x1)=m arctan(1/x2)=n arctan(1/x3)=p so...
6219
Carlos Assale
c_assalebr
Jun 4, 2003 12:02 am
Dá-lhe patrício!!!! Carlos...
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Lalit Jain
lalitkumarj
Jun 4, 2003 1:57 am
DuHHHHHH!!!! Thanks Carlos for refreshing my brain. Lalit ... From: Carlos Assale To: mathforfun@yahoogroups.com Sent: Tuesday, June 03, 2003 6:10 PM Subject:...
6221
fundoomops
Jun 4, 2003 10:11 am
I can always assume a+ib=p^i where p is a positive number. take logarithms on both sides log(a+ib)=i log p suppose a+ib in polar form is=r*e^i(theta) r=square...
6222
fundoomops
Jun 4, 2003 10:17 am
also consider the case when p is negative then q=p*i*i log(a+ib)=ilog p=i (log q+ 2 log i) log i=i(pi/2) e^(pi/2)=i then proceed similarly. I think for...
6223
fundoomops
Jun 4, 2003 10:19 am
I made a small mistake in assigning this p=q*i*i also consider the case when p is negative then p=q*i*i q>0 log(a+ib)=ilog p=i (log q+ 2 log i) log i=i(pi/2) ...
6224
clooneman
Jun 4, 2003 2:02 pm
Interesting... So are there any rational values of n such n^i is rational? Or can n^i only be rational if n is expressed in terms of pi, to put it broadly? ...
6225
fabian
fabianseoane
Jun 4, 2003 5:34 pm
can n^i only be rational if n is expressed in terms of pi, to put it broadly? One trivial example: 1^i = [cos1 + i*sen1]^ln(1) = [cos1 + i*sen1]^0 = 0. By the...
6226
fabian
fabianseoane
Jun 4, 2003 5:38 pm
Sorri, mistake: of couse [cos1 + i*sen1]^0 = 1 and not 0 as i wrote. On Wed, 2003-06-04 at 19:37, fabian wrote: can n^i only be rational if n is expressed in...
6227
fabian
fabianseoane
Jun 4, 2003 6:05 pm
Sorri, mistake: of couse [cos1 + i*sen1]^0 = 1 and not 0 as i wrote. On Wed, 2003-06-04 at 19:37, fabian wrote: can n^i only be rational if n is expressed in...
6228
clooneman
Jun 4, 2003 6:07 pm
That would have been me. ... e. I ... is ... terms of ... <c.assale@t...> ... the ... normally ... (i*x) in ... and ... =0] ... not ... area, ... an ... but i ...
6229
Carlos Assale
c_assalebr
Jun 4, 2003 6:18 pm
Is there an elegant solution to the following problem? Draw a circinference with center in C(0,0) and radius r. Take a point P(a,b) outside it. Draw a line...
6230
Carlos Assale
c_assalebr
Jun 4, 2003 6:46 pm
Till now what I got is (alpha is the angle between the line and x axis): r = b*cos(alpha) - a*sin(alpha) or r/cos(alpha) = b - a*tan(alpha) How to go forward...
6231
fabian
fabianseoane
Jun 4, 2003 7:07 pm
you make the ecuation of the line, that is, y-b = m(x-a) and the circle, that is y^2 + x^2 = r^2 Then you equal both equations with y: [m(x-a) + b]^2 =...
6232
Carlos Assale
c_assalebr
Jun 4, 2003 9:02 pm
Let me see if I got the rationale of your solution. Plese tell me if I'm right or wrong. The solutions of the equation system lead us to find the abcissas for ...
6233
fundoomops
Jun 4, 2003 9:08 pm
Try this. We know that from a point outside the circle we can draw two tangents to the circle. The radius of the parent circle is=r. Let us find out the length...
