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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)[reply]

See separation of variables. Widener (talk) 10:07, 21 April 2012 (UTC)[reply]

I think the notes would have said

\int {\frac {dx}{x}}=\ln x+C

Widener (talk) 10:09, 21 April 2012 (UTC)[reply]

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)[reply]

Maybe they said

\int _{1}^{x}{\frac {dt}{t}}=\ln x

then. Widener (talk) 06:34, 22 April 2012 (UTC)[reply]

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)[reply]

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)[reply]

Resolved

~ 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)[reply]

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)[reply]

-.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)[reply]

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)[reply]

~~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)~~[reply]

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)[reply]

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)[reply]

The ones in China or India I'd guess ;-) Dmcq (talk) 10:51, 22 April 2012 (UTC)[reply]