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I have some real half life problem for you

thumbs up if you know the reference 

Yeah that does help!

How foolish of me not to think of it in that way. 

However I do find it suprising to see the $$\begin{pmatrix}
0\\
0\\
\end{pmatrix}$$ vector as an eigenvector since that eigenvector is basically applicable to any matrix. Nevertheless I wouldn't know of any other way to solve this.

Thanks Alan.

@@ End of Day Wrap - Wednesday 4/6/14   Sydney, Australia   Time 9:20 pm

Hi everyone,

Please scroll up fo a moment.  zegroes had a question which I answered in my last post.  My welcoming procedure is very hit and miss. I hope that we will eventually have a better system but the member section needs to be improved first.

Today our great answers were given by alan, Rosala, CPhill, Zegroes, GoldenLeaf, NinjaDevo, Feitan, Kitty<3, Kingkuya and Rom.  Thank you all.

NinjaDevo and Kingkaya have just joined in the last day or so.  Welcome to web2.0calc forum.  We hope you learn lots and enjoy yourselves here.

-------------------------------------------------------------

Here are some of the more interesting posts of the day.

#It appears that the curse of the unicorns is real!  We are working towards rectifying this problem.

Does this help?

What figure 2?

Is there even a question here?

Perhaps this site might help you

Thanks Chris. 

A neat little demonstration.

why do you think that A and a are the same pronumeral?

Yes perhaps you are right zegroes.  How rude of me.  

$${\sqrt{{\mathtt{3}}}}$$  is an irrational number.  

This means that it cannot be expressed as a fraction or as a terminating or recurring decimal.

Any decimal value is only an approximation!

You need to use brackets with questions like these otherwese we are not sure what you are asking.

I think that CPhill out did both of us this time anon!  Nothing like a bit of musical banter in a maths forum.

That's what i say!

Hey Rosala,

I'm not, the question is to give a 'proof' that zn = 0 is an asymptotically stable steady state of the system for all n given that abs[r] < 1

Even though it seems obvious that $$z_{n+1} = Az_n \Rightarrow 0 = A 0$$. I don't know the conditions which must be checked before I can formally prove it to be an asymptotically stable steady state of the system

It's not an equation (you haven't set it equal to anything) and it isn't quadratic (for which the x has to be raised to the power 2).  It does however have a quadratic factor, as it can be written as x³(3x² - 5).

I am sorry but that is not correct kingkuya

It can not be simplified.  it just means

 $$-3x^2=-3\times x\times x$$

A good answer zegroes.

Melody wrote: Is that a fact Alan? You definitely should know this

Actually, it's more of a hypothesis based on years of observation (I think someone from the automotive industry did tell me that once as well - a long time ago!) 

I guess your comment, that I should definitely know this, is based on my having spent my working life in Rolls-Royce.  However, R-R hasn't made cars since 1971, which is before I worked there!  I think the only part of a Rolls-Royce car actually owned by R-R these days is the doubleR logo, which is licensed out by R-R.

$$x^8\div x^2=x^{(8-2)}=x^6$$

Is that what you mean?

Hi Chris,

I have not done these questions thoroughly but your answers look alright to me.  

These are sin, cos, tan, cosec, sec and cot.

Deleted - See Bertie's answer below.

(1) -8x - 12y = 36  ->   8x + 12y = -36

(2)  5y -   6x = 41  ->  -6x +   5y =  41

$$\boxed{\begin{array}{rcrcr}
8x & + & 12y &=& -36 \\
-6x & + & 5y &=& 41
\end{array}}$$

\boxed{\begin{array}{rcrcr}
 8x & + & 12y &=& -36 \\
-6x & + & 5y &=&  41 
\end{array}}

 $$\\x=
\frac{\begin{vmatrix}
-36 & 12 \\
41 & 5
\end{vmatrix}}{\begin{vmatrix}
8& 12 \\
-6 & 5
\end{vmatrix}}
=\frac{-36*5-41*12}{8*5-(-6)*12}
=\frac{-180-492}{40+72}
=\frac{-672}{112}=-6\\
\boxed{x=-6}
\\y=
\frac{\begin{vmatrix}
8 & -36 \\
-6 & 41
\end{vmatrix}}{\begin{vmatrix}
8& 12 \\
-6 & 5
\end{vmatrix}}
=\frac{8*41-(-6)(-36)}{8*5-(-6)*12}
=\frac{328-216}{40+72}
=\frac{112}{112}=1\\
\boxed{y=1}$$

Re: 3 times -5 times -2 to the power of 3

Where did you get that x from Rosala?

$$3\times-5\times -2^3\\
=3\times-5\times -8\\
=120\\$$