Wikipedia:Reference desk/Archives/Mathematics/2012 April 21

= April 21 =

Integration - Calculus
As part of an assignment, I've derived this expression (dx/dt=-0.0004286x) by following my course notes. Now I'm meant to rearrange and integrate to show that it takes 1.49hours for x to go from 0.2 to 0.02. The coefficient -0.0004286 was arrived at using time in units of seconds. The notes said to remember that ʃdx/d=ln x. I haven't done calc for years, so I'd appreciate a little bit more help than that just to get me started. 203.27.72.5 (talk) 07:58, 21 April 2012 (UTC)
 * See separation of variables. Widener (talk) 10:07, 21 April 2012 (UTC)
 * I think the notes would have said $$\int \frac{dx}{x} = \ln x + C$$ Widener (talk) 10:09, 21 April 2012 (UTC)
 * No, they definitely leave out the "+ C". Maybe my lecturer is no better at calc than I am :P. 203.27.72.5 (talk) 20:37, 21 April 2012 (UTC)
 * Maybe they said $$\int_1^x \frac{dt}{t} = \ln x$$ then. Widener (talk) 06:34, 22 April 2012 (UTC)

Ok, I read the article on separation of variables. I followed it as best I could and I think I'm still wrong. Here's what I did: $$Let y = x$$ $$\frac{dy}{dt} = -0.0004286 y$$ $$\frac{dy}{y} = -0.0004286 dt$$ $$\int \frac{1}{y} dy = \int -0.0004286 dt$$ $$\ln |y| = -0.0004286 t$$ $$e^{-0.0004286t} = y$$ If that's wrong, what am I doing wrong? If it's right, how do I use that to show that it takes 1.49 hours for x to go from 0.2 to 0.02? 203.27.72.5 (talk) 21:33, 21 April 2012 (UTC)
 * Oh, wait...it is right and I worked the rest out for myself! Thanks so much for your pointers! 203.27.72.5 (talk) 21:38, 21 April 2012 (UTC)

~ Need Solid Judgement On Mathematical Tools ~ [NOT SOLVED]
Which of these is the best in this category of Mathematical Tools? The best would have
 * comprehensive range of tools
 * good usability of website, and UI of tools that anyone are able to use them

Calculators 
 * stattrek.com/online-calculator/
 * easycalculation.com/
 * wessa.net/
 * vassarstats.net/
 * alcula.com/calculators
 * danielsoper.com/statcalc3/default.aspx

Feel free to suggest the best single math tools site if you already know from experience.

Test example:

If c = a/b

but you do not know a

The calculator will output a. Does this with c and b being unknown also. Same formula.

Thingstofollow (talk) 11:08, 21 April 2012 (UTC)
 * There is likely to be no "best single math tools site"- it'll depend on what exactly you want to do. I use http://www.wolframalpha.com. Try it on your example: http://www.wolframalpha.com/input/?i=c%3Da%2Fb and I think it does what you want. (a=bc) Staecker (talk) 12:54, 21 April 2012 (UTC)
 * -.001 our of 5 star answer. There's not even a tool on there to easily do correlation. It's like you didn't even read. Thingstofollow (talk) 20:35, 27 April 2012 (UTC)

Matrix Decompsotion
I wish to decompose the matrix $$ \begin{bmatrix} 1 & 0\\0 & -1 \end{bmatrix}\, $$ into some product of the matrices $$ \begin{bmatrix} 0 & -1\\1 & 0 \end{bmatrix}\, $$ and $$ \begin{bmatrix} 1 & 1\\0 & 1 \end{bmatrix}\, $$, as well as their respective inverses. How might I go about this? Hints preferable to answers. Thanks. meromorphic  [talk to me]  16:53, 21 April 2012 (UTC)


 * On second thoughts, I think we need -I in there as well, else the negative determinant cannot be achieved. meromorphic   [talk to me]  19:34, 21 April 2012 (UTC)
 * I don't think this question has an affirmative answer given that the determinant of my matrix is negative and the determinant of the other two is positive. Thanks anyway. meromorphic   [talk to me]  19:58, 21 April 2012 (UTC)

Most popular math (grades 1-9) materials?
What math textbooks/ebooks/instructional tools, for grades 1-9, are the most popular or common being used in classrooms today? --Agentundertables (talk) 18:33, 21 April 2012 (UTC)
 * The ones in China or India I'd guess ;-) Dmcq (talk) 10:51, 22 April 2012 (UTC)