Give me your math problems

[FriarFritz]

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.

 

[Chasmgoat he/him]

so, are you offering to do my homework?

[Jozomby he/him]

I definitely read this at first as "Give me your pain" but with a certain character swapped out for an evil Math Overlord instead 

[Shard of Reading he/him]

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.

[Condensation she/her]

What's the explicit equation for this sequence: 1, 3, 6, 10, 15, 21...

[FriarFritz]

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.

[revelryintheart she/her]

aw dang you don't do statistics

that's the math im in right now hehe

[Karger he/him]

What is the integral of cos(x) over sin(x)^2 - sin(x) + 12?

[FriarFritz]

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 

[Karger he/him]

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.

[FriarFritz]

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

[Karger he/him]

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.

[Condensation she/her]

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*!

[Mat he/him]

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

[Lunamor she/her]

Prove that everyone is five steps away from Kevin Bacon.

[danex he/him]

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))

[Lunamor she/her]

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

[Shard of Reading he/him]

9 hours ago, Matrim's Dice said:

two plus two

Pickle.

[FriarFritz]

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.

[Lunamor she/her]

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 

[Condensation she/her]

Prove that 2+2=4 with an entire ream of paper.

[Shard of Reading he/him]

18 hours ago, Condensation said:

Prove that 2+2=4 with an entire ream of paper.

No. 2+2=Pickle. Because Wayne.

[Condensation she/her]

13 minutes ago, Shard of Reading said:

No. 2+2=Pickle. Because Wayne.

Oh, I'm sorry.

[Zelly]

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

[Condensation she/her]

Ooh, I like Ted-Ed. Their videos are cool, especially the animated riddles.