(February 13, 2022 at 11:07 am)FlatAssembler Wrote: Hey, guys!
So, in my Introduction to Robotics class, we are supposed to solve, as a part of solving an example, this equation (page 12):
1/s+1/(s+2)+1/(s+6-2i)+1/(s+6+2i)=1/(s+1)
Now, the very next step we are given goes like this:
3s^4+32s^3+106s^2+128s+80=0
I do not understand how they got from the first equation to the second one. Can somebody here explain me that?

Isolate your variable, multiply by the complex conjugate (where necessary), then find a common denominator. The rest should be self-evident. If the answer is horrifyingly wrong then I blame you for taking math advice from a geologist.

Type it in Matlab.

(February 15, 2022 at 11:41 pm)Paleophyte Wrote:

(February 13, 2022 at 11:07 am)FlatAssembler Wrote: Hey, guys!
So, in my Introduction to Robotics class, we are supposed to solve, as a part of solving an example, this equation (page 12):
1/s+1/(s+2)+1/(s+6-2i)+1/(s+6+2i)=1/(s+1)
Now, the very next step we are given goes like this:
3s^4+32s^3+106s^2+128s+80=0
I do not understand how they got from the first equation to the second one. Can somebody here explain me that?

Isolate your variable, multiply by the complex conjugate (where necessary), then find a common denominator. The rest should be self-evident. If the answer is horrifyingly wrong then I blame you for taking math advice from a geologist.

Geologists study math?

(P.S. This is a math joke.)

(February 15, 2022 at 3:04 am)FlatAssembler Wrote:

(February 13, 2022 at 11:50 am)GrandizerII Wrote: https://pasteboard.co/OpS78RwMHcd4.png

https://pasteboard.co/TG8gsyJuDdwy.png

Easy algebra, as long as you know what to do with the i's.

In case this is new to you, i^2 = -1

Thanks, I think I understand it now.

---

(February 13, 2022 at 6:57 pm)The Valkyrie Wrote: If 1r=15, then 2r squared is the sum of 3n cubed multiplied by 7c subtracted from the square root of 11cr plus banana.

Sorry, I don't get the joke.

It's not a joke.

(February 13, 2022 at 11:07 am)FlatAssembler Wrote: Hey, guys!
So, in my Introduction to Robotics class, we are supposed to solve, as a part of solving an example, this equation (page 12):
1/s+1/(s+2)+1/(s+6-2i)+1/(s+6+2i)=1/(s+1)
Now, the very next step we are given goes like this:
3s^4+32s^3+106s^2+128s+80=0
I do not understand how they got from the first equation to the second one. Can somebody here explain me that?

By the way, it looks like this equation has two negative real roots and two complex roots. One of the real roots is approximately -5.471 and the other is approximately -3.678. I haven't searched for the complex roots.

(February 16, 2022 at 10:28 am)polymath257 Wrote:

(February 13, 2022 at 11:07 am)FlatAssembler Wrote: Hey, guys!
So, in my Introduction to Robotics class, we are supposed to solve, as a part of solving an example, this equation (page 12):
1/s+1/(s+2)+1/(s+6-2i)+1/(s+6+2i)=1/(s+1)
Now, the very next step we are given goes like this:
3s^4+32s^3+106s^2+128s+80=0
I do not understand how they got from the first equation to the second one. Can somebody here explain me that?

By the way, it looks like this equation has two negative real roots and two complex roots. One of the real roots is approximately -5.471 and the other is approximately -3.678. I haven't searched for the complex roots.

That would take some digging.

When I’m doing algebra, I generally just add 6 to everything (it worked once, I’m hopeful it’ll do so again).


Boru

(February 16, 2022 at 10:28 am)polymath257 Wrote:

(February 13, 2022 at 11:07 am)FlatAssembler Wrote: Hey, guys!
So, in my Introduction to Robotics class, we are supposed to solve, as a part of solving an example, this equation (page 12):
1/s+1/(s+2)+1/(s+6-2i)+1/(s+6+2i)=1/(s+1)
Now, the very next step we are given goes like this:
3s^4+32s^3+106s^2+128s+80=0
I do not understand how they got from the first equation to the second one. Can somebody here explain me that?

By the way, it looks like this equation has two negative real roots and two complex roots. One of the real roots is approximately -5.471 and the other is approximately -3.678. I haven't searched for the complex roots.

How did you figure it out?

(February 18, 2022 at 3:57 am)FlatAssembler Wrote:

(February 16, 2022 at 10:28 am)polymath257 Wrote: By the way, it looks like this equation has two negative real roots and two complex roots. One of the real roots is approximately -5.471 and the other is approximately -3.678. I haven't searched for the complex roots.

How did you figure it out?

Graphing the function and seeing where it crosses the axis. You can tell from the coefficients that all real roots are negative. The roots are irrational, so the best approach, unless you are doing algebraic number theory, is to use approximations.

(February 14, 2022 at 10:04 am)polymath257 Wrote:

(February 13, 2022 at 9:30 pm)Jehanne Wrote: How about modern algebra?  Don't talk about that to most Trump supporters.

Hey, they don't even want arabic numbers to be taught in our school system......

A subject dealing group homo-morphisms would definitely be something they would dislike.

Math humor:

1. What's purple and commutes? An abelian grape.

2. What's yellow and equivalent to the axiom of choice? Zorn's lemon.

I think I have a by orders of magnitude funnier math joke (actually an anecdote from my student life), which I posted on Reddit:

https://www.reddit.com/r/latin/comments/...&context=3 Wrote:Today, at the university (I study Computer Science), we were taught about the set theory. The professor (who is, by the way, called Radoslav Galić) was explaining to us why the cardinal number of a union of sets is not always equal to the sum of the cardinal number of sets in that union: "If that were true, a dog should have eight legs. A dog, namely, has two front legs, two hind legs, two left legs and two right legs. The sum of the cardinal numbers of those sets is eight (four times two), but the cardinal number of the union of those sets is, of course, four."

My joke is at least understandable to a broader audience, your jokes are not.