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

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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 $\underset{1}{\overset{x}{\int }}\frac{dt}{t}=\ln x$ 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: $Lety=x$
$\frac{dy}{dt}=-0.0004286y$
$\frac{dy}{y}=-0.0004286dt$
$\int \frac{1}{y}dy=\int -0.0004286dt$
$\ln |y|=-0.0004286t$
$e^{-0.0004286t}=y$
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 $\left[\begin{array}{cc}1& 0\\ 0& -1\end{array}\right]$ into some product of the matrices $\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]$ and $\left[\begin{array}{cc}1& 1\\ 0& 1\end{array}\right]$, 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)