Math Is Fun Forum
You are not logged in.
- Topics: Active | Unanswered
#26 Re: Help Me ! » I don't understand the question! » 2011-12-17 04:31:47
Did you get the answers?
Hi, I've worked out the answer for part(A), but doesn't have a clue about part(B), still trying to figure out how to make a start 
(I haven't been given the answers by the way)
#27 Re: Help Me ! » I don't understand the question! » 2011-12-17 04:20:51
Thank you Bob! Now it makes more sense. However, I'm still not sure what the question is asking though. Is it asking to find values of S where it's impossible like S=47? If so, how am I supposed to do this? (I can do part A because the value of S is given, but part(B) seems different and I'm not confident with it).
#28 Help Me ! » I don't understand the question! » 2011-12-16 23:15:56
- bubokribuck
- Replies: 23
Here is the question. I don't get part(B) at all. Doesn't make any sense to me. Can someone explains it a little bit please. Where did 83 and 357 come from (or 44 and 396)? I don't understand what I'm asked to do. Please help!
#29 Help Me ! » gradient operator of a function » 2011-12-11 05:56:45
- bubokribuck
- Replies: 0
(1) Let
, Find grad(f)..(2) Identify the points at which grad(f) is
a) orthogonal to the z-axis
b) parallel to the x-axis
c) zero.
I have managed to solve for (1), but don't have a clue how to solve the second part. I have not come across about the theory of "orthogonal to z-axis" and "parallel to x-axis", tried to look up on the internet but still quite confused.
However, for (c) I have come up with something like
, so the points at which grad(f)=0 are (0,0,0). Is that right?#30 Help Me ! » How to prove "strictly diagonally dominant matrix is convergent"? » 2011-11-26 08:47:52
- bubokribuck
- Replies: 0
Question:
Ax=b
Let the coefficient matrix A be written in the form A=D-L-U, where D is the diagonal matrix whose diagonal is the same as that of A, -L is the strictly lower triangular part of A and -U is the strictly upper part of A. Furthermore, let T[sub]j[/sub] = D[sup]-1[/sup](L+U) be the iteration matrix for Jacobi's method. Prove that Jacobi's method is convergent if the coefficient matrix is diagonally dominant.
If A and b are given, I know how to use the Jacobi's method to find out whether or not A is convergent. But how should I prove that "Jacobi's method is convergent if A is diagonally dominant" using just those given letters and symbols?
#31 Re: Help Me ! » Mathematical modelling » 2011-11-21 09:21:02
I've always thought that f(x) = y = 3x-5
so x(t) needs to be represented by another letter, but looks like it's not necessary.
Thank you very much, now I get it! 
#32 Re: Help Me ! » Mathematical modelling » 2011-11-21 04:51:13
Hi Bob, sorry that I still have one small problem.
Can you show me how you got dx/dt=-rx/w from r.x(t)/w please.
Thank you!
#33 Re: Help Me ! » Mathematical modelling » 2011-11-20 08:15:27
Thank you so much Bob! You've saved my life! I've managed to solve the problem eventually. Thank you again! (just can't thank you enough )
#34 Re: Help Me ! » Mathematical modelling » 2011-11-20 06:47:28
Thank you very much Bob! At first I didn't remember what "Separation of variables" was, but your working out has reminded me. If I haven't done it incorrectly, the final equation should be something like
, for some constant C.I hope this is right.
#35 Re: Help Me ! » Mathematical modelling » 2011-11-20 02:30:41
so dx/dt = -rx/w
use separation of variables and the initial condition to complete the problem.
If I'm not wrong, dx/dt = -rx/w can be written as x'(t) = -rx/w, right? If this is true, then what x(t) equals to? Can I write something like x(t) = ??? to start with?
#36 Re: Help Me ! » Mathematical modelling » 2011-11-20 02:06:07
Ah, I think I'm getting it now. So here's what I thought:
x(t) is the amount of substance at time t. When t=0, x(t) is the initial amount of the substance. When t=1, it is as the substance has been drained off for 1 minute at rate r. (suppose t is in minutes)
Is the above statement correct?
#37 Re: Help Me ! » Mathematical modelling » 2011-11-20 01:55:32
Thank you very much for your help Bob!
But I'm still quite confused. If x(t) is the amount of the substance, then what x and t each stands for? And if the substance will never be drained off completely, what does t=0 mean then? (I need to include x[sub]0[/sub] somewhere in the formula but don't know where to put it).
#38 Re: Help Me ! » Mathematical modelling » 2011-11-20 00:51:37
Thanks, that helps a lot
So dx/dt is the time for the substance to be drained off completely, right?
#39 Help Me ! » Mathematical modelling » 2011-11-19 17:32:33
- bubokribuck
- Replies: 14
I've been given this question to solve:
x(t) is something dissolved in water of w liters. The water with the substance is drained off at rate r.
It asks me to construct a formulation of a continuous time model (which will be a differential equation) and to come up with a general solution to this continuous time model, which I don't even know where to start. Any suggestions please?
#40 Re: Help Me ! » Prove k^4+2k^3+2k+k is divisible by 6. » 2011-11-02 10:24:09
Thanks for TheDude correcting my error, and thank you both for helping me solve the problem, I have successfully solved it. Thanks
#41 Help Me ! » Prove k^4+2k^3+2k+k is divisible by 6. » 2011-11-01 15:27:30
- bubokribuck
- Replies: 5
The question is to prove by induction that
is divisible by 30 (n is any positive integer). I've done up to the stage where I haveAs I've already assumed that k^5-k is true (i.e, it's divisible by 30), so I now just need to prove that
is divisible by 6 so that would be divisible by 30 too, and then I'll have solved the problem.However, I am struggled to prove that
is divisible by 6. Can someone help me please.