• Mathematician Chat v. 3.999...
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Anyone want to help me out with calc? [t]http://i.imgur.com/9f2Lh4H.png[/t] I can get v'(t)=<4/sqrt(t),1/t,8> and when I put the magnitude under the integral it gives me a really funky problem that I don't know how to do. integral(sqrt(16/t+1/t^2+64)), which is the point where I'm stuck. It should be simple since it's calc 3 but I placed out of calc 1 and 2 with my AP credit and I haven't taken calc for about a year and I probably forgot a lot of the integration techniques.
Try factoring the the argument of your square root.
[QUOTE=Falubii;48749287]Try factoring the the argument of your square root.[/QUOTE] I had to use wolfram alpha to factor it, but how do you factor them when the variables are in the denominator? I only remember how to do it to polynomials when they're in the numerator. Other than that I got an easier integral I was able to solve. Thanks.
Rewrite 1/t as some other variable? It's the same principle.
[QUOTE=Falubii;48749646]Rewrite 1/t as some other variable? It's the same principle.[/QUOTE] wow holy crap i never knew you could do that
[QUOTE=titopei;48748300]Anyone want to help me out with calc? [t]http://i.imgur.com/9f2Lh4H.png[/t] I can get v'(t)=<4/sqrt(t),1/t,8> and when I put the magnitude under the integral it gives me a really funky problem that I don't know how to do. integral(sqrt(16/t+1/t^2+64)), which is the point where I'm stuck. It should be simple since it's calc 3 but I placed out of calc 1 and 2 with my AP credit and I haven't taken calc for about a year and I probably forgot a lot of the integration techniques.[/QUOTE] Do a u substitution. Although in this case 'u' might be a poor choice of variable because you might confuse yourself with the already existing 'u'. So in this case we'll say, let: w = 1/t Note you have to integrate over 'dw' now, so bear in mind that: dw/dt = -1/t^2 or, dt = - dw * t^2 or, using the definition of w, dt = -1/w^2 * dw. Using the definition of w the sqrt argument can be simplified: 1/t^2 + 16/t + 64 = w^2 + 16w + 64 Which is a perfect square, (w+8)^2 The sqrt and the square cancel out and you're left with the integral over: -(w+8)/w^2 dw Which can be simplified to: (-1/w - 8/w^2) dw And then integrate over the appropriate limits (remember you need to integrate from w(a) to w(t) now, not from a to t).
Of course you don't even have to do a u substitution there: the radical factors directly, but it helps put it into a more familiar form.
Wow, learning that the product topology is the categorical product in [B]Top[/B] makes it suddenly obvious why it's the more well-behaved product and we rarely use the box topology. Also, I've been fearing learning tikz for a while but goddamn tikz-cd is really natural and the diagrams look so nice.
[QUOTE=NixNax123;48642833]differential equations so far is going pretty well, i really like how the problems make you think, and how you can even see how useful they would be (even though I know most real world applications are PDEs, this is still cool). it's quite challenging to actually derive a DE from a word problem, but I guess that will just come with practice. would've loved to major instead of minor in math if i had the time for a double major[/QUOTE] Don't worry, as a chemical engineering major my process controls class expects us to look at a simple diagram and create a differential equations using mass and energy balances, pure math courses don't have to deal with units. Differential equations isn't a hard class, the one I took got into numerical approximation methods which are a blast to do
[QUOTE=JohnnyMo1;48776649] Also, I've been fearing learning tikz for a while but goddamn tikz-cd is really natural and the diagrams look so nice.[/QUOTE] I tried using tikz but I found it really unintuitive. I can see the power behind it as it allows for loops and conditionals, but I've never needed that level of complexity in my diagrams. I prefer WYSIWYG editors like Inkscape with the LaTeX plugin.
[QUOTE=Wunce;48778551]I tried using tikz but I found it really unintuitive. I can see the power behind it as it allows for loops and conditionals, but I've never needed that level of complexity in my diagrams. I prefer WYSIWYG editors like Inkscape with the LaTeX plugin.[/QUOTE] There are several ways to do commutative diagrams in tikz and some of them I've seen before are a little weird which probably scared me off, but the matrix way is pretty nice. Just make a matrix with columns separated by & and new rows marked by \\, put some objects in some of the entries like A, B, C or what have you, and then tell the arrows where to point with simple relative directions (like uur for the entry two rows up and one column over). Plus all the fiddly options like making arrows bend or moving the label to the opposite side of an arrow is simple.
Hey, I don't know if it's okay to ask for help in here, but can anyone help me understand why: 4csc^2(2x) + (4csc^2(2x) * cot^2(2x)) is equal to: 4csc^2(2x) * (1+cot^2(2x)) ? I apologise if regular text is a bit dense, I can upload a screenshot of some mathematica if that's better. I just can't think why these two are congruent. Tia!
[QUOTE=Cabbage;48780183]Hey, I don't know if it's okay to ask for help in here, but can anyone help me understand why: 4csc^2(2x) + (4csc^2(2x) * cot^2(2x)) is equal to: 4csc^2(2x) * (1+cot^2(2x)) ? I apologise if regular text is a bit dense, I can upload a screenshot of some mathematica if that's better. I just can't think why these two are congruent. Tia![/QUOTE] For the future: [URL]https://www.codecogs.com/latex/eqneditor.php[/URL] [IMG]https://latex.codecogs.com/gif.latex?4csc^2(2x) &plus; 4csc^2(2x)cot^2(2x)[/IMG] Anyways, this can be factored out into multiples of [IMG]https://latex.codecogs.com/gif.latex?4csc^2(2x)[/IMG] Since each term is multiplying itself by it (in this case, 1 for the left side, and cot^2(2x) for the right side). So, you can simply take that out, and voila: [IMG]https://latex.codecogs.com/gif.latex?4csc^2(2x)(1&plus;cot^2(2x))[/IMG]
[QUOTE=NixNax123;48780237]For the future: [URL]https://www.codecogs.com/latex/eqneditor.php[/URL] [IMG]https://latex.codecogs.com/gif.latex?4csc^2(2x) + 4csc^2(2x)cot^2(2x)[/IMG] Anyways, this can be factored out into multiples of [IMG]https://latex.codecogs.com/gif.latex?4csc^2(2x)[/IMG] Since each term is multiplying itself by it (in this case, 1 for the left side, and cot^2(2x) for the right side). So, you can simply take that out, and voila: [IMG]https://latex.codecogs.com/gif.latex?4csc^2(2x)(1+cot^2(2x))[/IMG][/QUOTE] Aaah, yeah I thought it was simple, I just didn't see it. Thanks for your help! And yeah LaTeX is much easier on the eyes.
Can anyone give me any tips on how to conceptualize volumes of solids a little better? For instance we learned disk and washer method and volume by cylinders. I find it hard to really "see" whats going on, as opposed to all of the other things we have learned. I mean eventually I can work through most problems but it just takes me longer than if I was doing like a trig substitution problem or integration by parts. I can "see" how those work and I can really understand it quite well, but I could never really do that for volumes. Can anyone give any advice on understanding how to do volumes in my sleep and really understand it?
[QUOTE=shadowdude14;48792000]Can anyone give me any tips on how to conceptualize volumes of solids a little better? For instance we learned disk and washer method and volume by cylinders. I find it hard to really "see" whats going on, as opposed to all of the other things we have learned. I mean eventually I can work through most problems but it just takes me longer than if I was doing like a trig substitution problem or integration by parts. I can "see" how those work and I can really understand it quite well, but I could never really do that for volumes. Can anyone give any advice on understanding how to do volumes in my sleep and really understand it?[/QUOTE] I'm sure Khan Academy or PatrickJMT has a video on those topics. They are usually good resources for solidifying concepts. Or you could check out Paul's online notes if your textbook is confusing you.
Every time I do stuff with LaTeX I get reminded how long it takes to produce a good result. The only way to be productive with it has to be with finished templates or close to no stylizing, right?
[QUOTE=JohanGS;48805357]Every time I do stuff with LaTeX I get reminded how long it takes to produce a good result. The only way to be productive with it has to be with finished templates or close to no stylizing, right?[/QUOTE] I've slowly been building my own template over time. I used to load the previous document and just get rid of all of the text when I was new to it, but now I've created my own style file that contains all of the packages I use with the formatting I tend to use, and then I just write a separate document for different chapters/sections whatever and load it in. Doesn't take too long anymore. The better you get at it, the quicker the whole process is.
[QUOTE=sltungle;48805410]I've slowly been building my own template over time. I used to load the previous document and just get rid of all of the text when I was new to it, but now I've created my own style file that contains all of the packages I use with the formatting I tend to use, and then I just write a separate document for different chapters/sections whatever and load it in. Doesn't take too long anymore. The better you get at it, the quicker the whole process is.[/QUOTE] Any tips along the way?
[QUOTE=JohanGS;48805437]Any tips along the way?[/QUOTE] Organise your preamble as logically as you can and have it as neat as possible so it's easy to make changes if you have to. Like any piece of coding, comment the fuck out of it so you know what packages do what if you forget.
hey is there any good free formula text tools? i have to either write out all my calculations for this lab or type them up into a table, and word's formula tools are OK but not great, and my next lab will be about heat-exchanger modeling so lots of formulas
[QUOTE=Sableye;48818535]hey is there any good free formula text tools? i have to either write out all my calculations for this lab or type them up into a table, and word's formula tools are OK but not great, and my next lab will be about heat-exchanger modeling so lots of formulas[/QUOTE] [url]http://overleaf.com[/url]
[QUOTE=NixNax123;48818590][url]http://overleaf.com[/url][/QUOTE] Overleaf is not bad but I prefer [url]http://www.sharelatex.com[/url] (their pdf renderer is still in beta and rendering as an image is ugly) [editline]3rd October 2015[/editline] Also I think sharelatex's help section is much nicer. Lots of nice clear tutorials on using certain packages. Really helping me learn to use feynmf.
They also have this thing: [url]https://www.getdatajoy.com/[/url]
[QUOTE=JohanGS;48818732]They also have this thing: [url]https://www.getdatajoy.com/[/url][/QUOTE] I've been really hoping to use this, but I've been having trouble on my computer for some reason. Loads a project slightly less than half way, then doesn't load any more. Happens in IE, Chrome, and Firefox, completely baffles me. Works on my work computers.
[QUOTE=JohnnyMo1;48818605]Overleaf is not bad but I prefer [url]http://www.sharelatex.com[/url] (their pdf renderer is still in beta and rendering as an image is ugly) [editline]3rd October 2015[/editline] Also I think sharelatex's help section is much nicer. Lots of nice clear tutorials on using certain packages. Really helping me learn to use feynmf.[/QUOTE] I tried that before I found overleaf, but I guess I just preferred Overleaf's UI more. However, that was before I even knew how to use LaTeX, and I found overleaf a year later when a friend suggested it to me. Maybe once I actually start using LaTeX for serious projects (as opposed to just making my CS lab reports look nicer), I'll check out ShareLaTeX. Thanks for reminding me about that!
[QUOTE=NixNax123;48819086]I tried that before I found overleaf, but I guess I just preferred Overleaf's UI more. However, that was before I even knew how to use LaTeX, and I found overleaf a year later when a friend suggested it to me. Maybe once I actually start using LaTeX for serious projects (as opposed to just making my CS lab reports look nicer), I'll check out ShareLaTeX. Thanks for reminding me about that![/QUOTE] You're welcome. I could have sworn this wasn't the case but when I was testing out overleaf again just now I couldn't zoom in on the pdf preview at all. That was quite annoying because it's pretty important for detailed formatting.
Anyone interested in discussing the Monty Hall problem? I've been doing some reading on it recently and I think I found the trip up on it. The problem is that you randomly pick a door, and then the presenter opens the door you haven't picked [I]that contains a goat[/I] (or one of them if you've picked the car). People make the mistake in thinking the presenter randomly chooses a door. I can't prove it mathematically (though I could probably make a model that proves it experimentally in Excel) but I suspect that if the presenter chooses the goat door then it's statistically a better option to switch while if the presenter just randomly chooses a door there is no statistical advantage to switching.
[QUOTE=download;48877170]Anyone interested in discussing the Monty Hall problem? I've been doing some reading on it recently and I think I found the trip up on it. The problem is that you randomly pick a door, and then the presenter opens the door you haven't picked [I]that contains a goat[/I] (or one of them if you've picked the car). People make the mistake in thinking the presenter randomly chooses a door. I can't prove it mathematically (though I could probably make a model that proves it experimentally in Excel) but I suspect that if the presenter chooses the goat door then it's statistically a better option to switch while if the presenter just randomly chooses a door there is no statistical advantage to switching.[/QUOTE] ANY door the presenter picks is a goat door. If you've picked the car, the presenter can only pick goats, and if you've picked a goat, the presenter makes sure to only reveal the remaining goat. It doesn't matter as to whether or not his choice is random, because [I]your[/I] choice is random. The logic as to why it's advantageous to switch becomes more apparent as you take the number of doors you have to pick from to become large (say 10, 100, a million, or infinity), while only allowing one to contain a car still. If you were given the choice to randomly pick 1 door out of 1,000,000 doors, then 999,998 of the doors were opened to reveal goats you'd switch, because it's almost a certainty that you picked wrong the first time around. As the number of doors approaches infinity, there's absolutely no reason for you to stick with your initial choice.
[QUOTE=sltungle;48877881]ANY door the presenter picks is a goat door. If you've picked the car, the presenter can only pick goats, and if you've picked a goat, the presenter makes sure to only reveal the remaining goat. It doesn't matter as to whether or not his choice is random, because [I]your[/I] choice is random. [/QUOTE] I'm aware. I thought I made that clear. I was asking that if the presenter's choice is random then there's no advantage to switching.
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