Split (1)

train · 116k rows

role stringclasses 2 values	content stringlengths 0 2.1k	session_id int64 10 21.7k	sequence_id int64 0 2.38k	annotations listlengths 0 8
volunteer	we have here	15,082	424	[]
student	if we do, 1 = a [(x+1) (x+2)] + b, will we get same thing?	15,082	425	[]
volunteer	right there	15,082	426	[]
volunteer	I think we will	15,082	427	[]
volunteer	Um, actually, I think you would need more	15,082	428	[]
volunteer	I mean, I think we will get the same thing just because, you know, we're still talking about, for example, an apple	15,082	429	[]
volunteer	right, we're still talking about the same thing. We're just kind of trying to rewrite it differently.	15,082	430	[]
volunteer	but I think we'd still end up with the same result.	15,082	431	[]
volunteer	Like if you were to	15,082	432	[]
volunteer	divide it all out, you'd still get the same thing.	15,082	433	[]
volunteer	Um	15,082	434	[]
volunteer	one equals A, let me go back.	15,082	435	[]
volunteer	I'm jumping too much	15,082	436	[]
volunteer	Too many hoops. There we go.	15,082	437	[]
volunteer	So you said	15,082	438	[]
volunteer	1 equals	15,082	439	[]
volunteer	A X + 1, X + 2 + B. So you're saying, what if we didn't separate the denominator?	15,082	440	[]
volunteer	Actually, let's do it your way. Do it on the board.	15,082	441	[]
volunteer	Let's see if you can prove that they're the same.	15,082	442	[]
volunteer	When in doubt, do it out	15,082	443	[]
student	okay	15,082	444	[]
volunteer	You have the board	15,082	445	[]
volunteer	You can't see me, but I'm flourishing my hand as a showman.	15,082	446	[]
volunteer	Did you get 2 x + 3?	15,082	447	[]
volunteer	Where did you get it	15,082	448	[]
volunteer	Uh, yes, yes, yes, yes, yes, yes, I see it.	15,082	449	[]
volunteer	Continue, please	15,082	450	[]
volunteer	Wait, wait, wait. Wouldn't it be the other way around? Wouldn't it be 3X?	15,082	451	[]
volunteer	Ah no, you're right. I'm sorry, I'm sorry. I'm way off.	15,082	452	[]
volunteer	No, you can be 01	15,082	453	[]
volunteer	not 0	15,082	454	[]
student	it became problem	15,082	455	[]
volunteer	Right	15,082	456	[]
volunteer	So now you see why they did it the way they did.	15,082	457	[]
volunteer	because really the only way to do it	15,082	458	[]
student	right	15,082	459	[]
volunteer	Or, I mean, you would, you would need	15,082	460	[]
volunteer	more variables if you're doing it your way.	15,082	461	[]
volunteer	But you have too many equations.	15,082	462	[]
volunteer	I'm sorry, too little equations	15,082	463	[]
volunteer	but it is what it is. So, it's good exercise.	15,082	464	[]
student	b needs a equation	15,082	465	[]
student	yeah, understood	15,082	466	[]
volunteer	I mean, technically, you have what, 12,	15,082	467	[]
volunteer	you have 3 equations, technically.	15,082	468	[]
volunteer	cause you have a	15,082	469	[]
volunteer	you have the X square term, you have the X term, and then you have the X to the 0 term. So you have 3 equations technically. So you could, you could have up to 3.	15,082	470	[]
volunteer	um, variables.	15,082	471	[]
volunteer	All right, that was fun	15,082	472	[]
volunteer	Now we can do	15,082	473	[]
volunteer	um	15,082	474	[]
volunteer	an improper fraction.	15,082	475	[]
volunteer	So example 12 is	15,082	476	[]
volunteer	an improper fraction	15,082	477	[]
volunteer	Oh, I'm sorry, can you see the screen?	15,082	478	[]
volunteer	Actually, are you ready to move on? Do you have any more questions?	15,082	479	[]
volunteer	um, about why they're not using the previous chapter's methodology. Actually, let me go back.	15,082	480	[]
volunteer	We we were talking about it so much. Why don't they have DX in there?	15,082	481	[]
volunteer	Um	15,082	482	[]
volunteer	um, so if you go back	15,082	483	[]
volunteer	or if you're looking at the screen, you see in the integral	15,082	484	[]
volunteer	integral DX over AX2 + BX + C, and you see that you have all these coefficients, right?	15,082	485	[]
volunteer	But what's the first thing they do?	15,082	486	[]
student	right	15,082	487	[]
volunteer	is they factor out A	15,082	488	[]
volunteer	and you know, why is this important?	15,082	489	[]
volunteer	Well	15,082	490	[]
volunteer	if they didn't factor out A	15,082	491	[]
volunteer	and you have this um	15,082	492	[]
volunteer	AX	15,082	493	[]
volunteer	you try to rewrite, and you try to rewrite these expressions, you'd have, like, as you have here, um	15,082	494	[]
volunteer	yeah, if you have A piece and you try to	15,082	495	[]
volunteer	uh factor it	15,082	496	[]
volunteer	you would still end up with this kind of A over B and, and sorry B over A and C over A, um.	15,082	497	[]
volunteer	then when you do your substitution for tea.	15,082	498	[]
volunteer	right? And you had this AX term here.	15,082	499	[]
volunteer	then your	15,082	500	[]
volunteer	you, then you'd end up with A times DX equals dT. So you don't have to worry about this 1/8 term again and again.	15,082	501	[]
volunteer	which would, which would result in this	15,082	502	[]
volunteer	but they just find it easier to have	15,082	503	[]
volunteer	um DX equals DT straight up, but you already have this 1/8 term that they factored out. So it, it's, it'd be the same.	15,082	504	[]
volunteer	They just um find it easier to do it.	15,082	505	[]
volunteer	this way	15,082	506	[]
volunteer	or they just prefer, I'm not sorry, not easy, they prefer to do it this way.	15,082	507	[]
volunteer	So they're already accounting for this one over a term.	15,082	508	[]
student	yeah, right	15,082	509	[]
volunteer	Yeah, and the method they used here was completing the squares.	15,082	510	[]
volunteer	not like um	15,082	511	[]
volunteer	the chapter we're on, which they don't use completing the squares, they prefer	15,082	512	[]
volunteer	having two separate terms, two separate expressions.	15,082	513	[]
volunteer	right? X minus A, X minus B.	15,082	514	[]
volunteer	So that's another difference	15,082	515	[]
student	this also kinda easy too	15,082	516	[]
volunteer	I mean	15,082	517	[]
volunteer	don't speak too soon	15,082	518	[]
volunteer	All right. You haven't, we haven't really done many problems.	15,082	519	[]
volunteer	But the methodology, I guess, is simpler. You don't have to carry about the	15,082	520	[]
volunteer	um substitution method	15,082	521	[]
student	yeah,	15,082	522	[]
volunteer	So that is, but that is a little easier, but you do have to do more, um, yeah, I guess you don't have to think as much.	15,082	523	[]

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