FriarFritz Posted October 20, 2020 Report Share Posted October 20, 2020 A few days ago I solved a math problem posted by @Zelly, and that actually was the most fun I've had in quite a while. And I realized that it's also the only active learning I've done in a long time. So give me all your math problems. If you need help on an assignment or something pressing, make sure to say so, and I'll try to get to those ones first. 0 Quote Link to comment Share on other sites More sharing options...
Chasmgoat Posted October 20, 2020 Report Share Posted October 20, 2020 so, are you offering to do my homework? 0 Quote Link to comment Share on other sites More sharing options...
Jozomby Posted October 20, 2020 Report Share Posted October 20, 2020 I definitely read this at first as "Give me your pain" but with a certain character swapped out for an evil Math Overlord instead 3 Quote Link to comment Share on other sites More sharing options...
Shard of Reading Posted October 20, 2020 Report Share Posted October 20, 2020 22 minutes ago, Chasmgoat said: so, are you offering to do my homework? I hope he is. 11 minutes ago, Jozomby said: I definitely read this at first as "Give me your pain" but with a certain character swapped out for an evil Math Overlord instead Giving math problems is the same as giving pain. 1 Quote Link to comment Share on other sites More sharing options...
Condensation Posted October 20, 2020 Report Share Posted October 20, 2020 What's the explicit equation for this sequence: 1, 3, 6, 10, 15, 21... 0 Quote Link to comment Share on other sites More sharing options...
FriarFritz Posted October 20, 2020 Author Report Share Posted October 20, 2020 3 hours ago, Chasmgoat said: so, are you offering to do my homework? Depending on the type of homework. If it's textbook exercises or something similar, where the point is to help you learn the material, then I will try to do any problems that confound or confuse you, and I'll make sure to explain as much of my thinking as possible. If it's a project or whatnot, where you're supposed to show that you've learned the material, please don't ask me to do that for you. It's dishonest and it could get you into difficult situations. 2 hours ago, Condensation said: What's the explicit equation for this sequence: 1, 3, 6, 10, 15, 21... So, the most basic equation for triangle numbers is T_n = T_(n - 1) + n. However, the sequence of perfect squares can be expressed as the sum of two adjacent triangle numbers: n^2 = T_n + T_(n - 1), meaning that we can switch this around to get another equation for triangle numbers: T_n = n^2 - T_(n - 1). Using substitution, we get T_(n - 1) + n = n^2 - T_(n - 1) So: 2(T_(n - 1)) = n^2 - n T_(n - 1) = (n^2 - n) / 2 T_n = ((n + 1)^2 - (n + 1)) / 2 T_n = (n^2 + n) / 2 There you go. 3 Quote Link to comment Share on other sites More sharing options...
revelryintheart Posted October 20, 2020 Report Share Posted October 20, 2020 aw dang you don't do statistics that's the math im in right now hehe 0 Quote Link to comment Share on other sites More sharing options...
Karger Posted October 20, 2020 Report Share Posted October 20, 2020 What is the integral of cos(x) over sin(x)^2 - sin(x) + 12? 0 Quote Link to comment Share on other sites More sharing options...
FriarFritz Posted October 20, 2020 Author Report Share Posted October 20, 2020 7 minutes ago, Karger said: What is the integral of cos(x) over sin(x)^2 - sin(x) + 12? This looks like it's going to involve complex numbers, and I have not yet learned to do complex calculus. I'm also a bit rusty on integrals 0 Quote Link to comment Share on other sites More sharing options...
Karger Posted October 20, 2020 Report Share Posted October 20, 2020 Just now, FriarFritz said: This looks like it's going to involve complex numbers, and I have not yet learned to do complex calculus. I'm also a bit rusty on integrals I think it is doable with just U substitution. 0 Quote Link to comment Share on other sites More sharing options...
FriarFritz Posted October 20, 2020 Author Report Share Posted October 20, 2020 5 minutes ago, Karger said: I think it is doable with just U substitution. Is this how it should look on paper? I don't think there's a u-substitution opportunity there. But the main problem is that the quadratic on the bottom has complex roots, so any attempt to simplify is going to end up complifying the situation 0 Quote Link to comment Share on other sites More sharing options...
Karger Posted October 20, 2020 Report Share Posted October 20, 2020 Just now, FriarFritz said: Is this how it should look on paper? Yes but I meant - 12. 1 minute ago, FriarFritz said: I don't think there's a u-substitution opportunity there. But the main problem is that the quadratic on the bottom has complex roots, so any attempt to simplify is going to end up complifying the situation I think it also has to do with inverse trig functions. 0 Quote Link to comment Share on other sites More sharing options...
Condensation Posted October 21, 2020 Report Share Posted October 21, 2020 1 hour ago, FriarFritz said: Depending on the type of homework. If it's textbook exercises or something similar, where the point is to help you learn the material, then I will try to do any problems that confound or confuse you, and I'll make sure to explain as much of my thinking as possible. If it's a project or whatnot, where you're supposed to show that you've learned the material, please don't ask me to do that for you. It's dishonest and it could get you into difficult situations. So, the most basic equation for triangle numbers is T_n = T_(n - 1) + n. However, the sequence of perfect squares can be expressed as the sum of two adjacent triangle numbers: n^2 = T_n + T_(n - 1), meaning that we can switch this around to get another equation for triangle numbers: T_n = n^2 - T_(n - 1). Using substitution, we get T_(n - 1) + n = n^2 - T_(n - 1) So: 2(T_(n - 1)) = n^2 - n T_(n - 1) = (n^2 - n) / 2 T_n = ((n + 1)^2 - (n + 1)) / 2 T_n = (n^2 + n) / 2 There you go. *clap clap clap*! 0 Quote Link to comment Share on other sites More sharing options...
Mat Posted October 21, 2020 Report Share Posted October 21, 2020 (edited) two plus two Edited October 21, 2020 by Matrim's Dice Ok but seriously this thread is being inserted in my memory for future needs 0 Quote Link to comment Share on other sites More sharing options...
Lunamor Posted October 21, 2020 Report Share Posted October 21, 2020 Prove that everyone is five steps away from Kevin Bacon. 0 Quote Link to comment Share on other sites More sharing options...
danex Posted October 21, 2020 Report Share Posted October 21, 2020 Lim x->1 ((1/x) - 1)/(x-1) its -1, but I had to do the thing where you plug in 0.999 and 1.001. You should be able to do this algebraically with direct substitution and just moving stuff around, but for some reason I couldn’t get it. (the entire problem is just finding the derivative of f(x)=1/x at (1,1)) 0 Quote Link to comment Share on other sites More sharing options...
Lunamor Posted October 21, 2020 Report Share Posted October 21, 2020 (edited) 22 minutes ago, Danex said: Lim x->1 ((1/x) - 1)/(x-1) its -1, but I had to do the thing where you plug in 0.999 and 1.001. You should be able to do this algebraically with direct substitution and just moving stuff around, but for some reason I couldn’t get it. (the entire problem is just finding the derivative of f(x)=1/x at (1,1)) I think that this is correct, though it could be wrong cause I literally learned what limits are two weeks ago Edit: Hmm, got the wrong sign... I should probably let Fritz solve it anyways. Edited October 21, 2020 by Lunamor 0 Quote Link to comment Share on other sites More sharing options...
Shard of Reading Posted October 21, 2020 Report Share Posted October 21, 2020 9 hours ago, Matrim's Dice said: two plus two Pickle. 2 Quote Link to comment Share on other sites More sharing options...
FriarFritz Posted October 21, 2020 Author Report Share Posted October 21, 2020 16 hours ago, Karger said: Yes but I meant - 12. I think it also has to do with inverse trig functions. I think I figured it out: 8 hours ago, Danex said: Lim x->1 ((1/x) - 1)/(x-1) its -1, but I had to do the thing where you plug in 0.999 and 1.001. You should be able to do this algebraically with direct substitution and just moving stuff around, but for some reason I couldn’t get it. (the entire problem is just finding the derivative of f(x)=1/x at (1,1)) So here it's best to solve using theorems about derivatives, rather than trying to find the limit. For example: 8 hours ago, Lunamor said: I think that this is correct, though it could be wrong cause I literally learned what limits are two weeks ago Edit: Hmm, got the wrong sign... I should probably let Fritz solve it anyways. The problem here is in your simplification of the fraction. Adding to or subtracting from the numerator and denominator does not create an equivalent fraction (e.g. (2+1)/(3+1) = 3/4 != 2/3 12 hours ago, Lunamor said: Prove that everyone is five steps away from Kevin Bacon. Unfortunately, that requires data and other statistics stuff. 1 Quote Link to comment Share on other sites More sharing options...
Lunamor Posted October 21, 2020 Report Share Posted October 21, 2020 1 hour ago, FriarFritz said: I think I figured it out: So here it's best to solve using theorems about derivatives, rather than trying to find the limit. For example: The problem here is in your simplification of the fraction. Adding to or subtracting from the numerator and denominator does not create an equivalent fraction (e.g. (2+1)/(3+1) = 3/4 != 2/3 Unfortunately, that requires data and other statistics stuff. Thank you! My algebra skills are pretty lacking 0 Quote Link to comment Share on other sites More sharing options...
Condensation Posted October 21, 2020 Report Share Posted October 21, 2020 Prove that 2+2=4 with an entire ream of paper. 0 Quote Link to comment Share on other sites More sharing options...
Shard of Reading Posted October 22, 2020 Report Share Posted October 22, 2020 18 hours ago, Condensation said: Prove that 2+2=4 with an entire ream of paper. No. 2+2=Pickle. Because Wayne. 0 Quote Link to comment Share on other sites More sharing options...
Condensation Posted October 22, 2020 Report Share Posted October 22, 2020 13 minutes ago, Shard of Reading said: No. 2+2=Pickle. Because Wayne. Oh, I'm sorry. 0 Quote Link to comment Share on other sites More sharing options...
Zelly Posted October 26, 2020 Report Share Posted October 26, 2020 (edited) Welp, I'm fresh out of math problems, but here's some links to a few of my favorite math channels. Do you like numberphile? Numberphile - Monty Hall Or vsauce? How to count past infinity Or vsauce2? The Secret of Snakes and Ladders Or this series of Ted-Ed animated riddles (some are more mathy than others)? https://www.youtube.com/watch?v=z-ZEfxAL9SI Edited October 26, 2020 by Zelly 0 Quote Link to comment Share on other sites More sharing options...
Condensation Posted October 27, 2020 Report Share Posted October 27, 2020 Ooh, I like Ted-Ed. Their videos are cool, especially the animated riddles. 0 Quote Link to comment Share on other sites More sharing options...
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