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	and we should be able to	8,595	461	[]
volunteer	we need to really	8,595	462	[]
volunteer	get that as a function of time so that we can finish the problem, right?	8,595	463	[]
student	Yeah.	8,595	464	[]
volunteer	So if we look at that angle, the cosine has always got an adjacent side 5000.	8,595	465	[]
volunteer	Um	8,595	466	[]
volunteer	so that, and then it would be over the hypotenuse, which is	8,595	467	[]
volunteer	changing according to Pythagorean's theorem, right?	8,595	468	[]
student	Mhm	8,595	469	[]
volunteer	And that would be	8,595	470	[]
volunteer	the hypotenuse of that would be the square root.	8,595	471	[]
volunteer	I'm just thinking out loud here now.	8,595	472	[]
volunteer	of 5000, I 5000 square.	8,595	473	[]
volunteer	plus the same old number we had 1000 + 600T	8,595	474	[]
volunteer	times	8,595	475	[]
volunteer	T	8,595	476	[]
volunteer	So I'm gonna write this in here for cosine squared.	8,595	477	[]
volunteer	cosine	8,595	478	[]
volunteer	beta	8,595	479	[]
volunteer	and then I'm gonna write it for cosine square data.	8,595	480	[]
volunteer	So just bear with me for a minute here.	8,595	481	[]
student	Yeah, no problem	8,595	482	[]
volunteer	So I'm gonna write cosine theta	8,595	483	[]
volunteer	5000	8,595	484	[]
volunteer	over	8,595	485	[]
volunteer	the square root of 5000	8,595	486	[]
volunteer	square	8,595	487	[]
volunteer	plus	8,595	488	[]
volunteer	1000	8,595	489	[]
volunteer	squared	8,595	490	[]
volunteer	Do you see that	8,595	491	[]
student	OK	8,595	492	[]
volunteer	If you can read my writing	8,595	493	[]
student	I can see.	8,595	494	[]
volunteer	I'm gonna fix this part here, it's too messy.	8,595	495	[]
student	Mhm	8,595	496	[]
volunteer	We're almost done	8,595	497	[]
student	Yeah	8,595	498	[]
student	All right	8,595	499	[]
volunteer	as good as I can do. So do you see that the cosine theta	8,595	500	[]
volunteer	is always gonna be 5000, which is the adjacent side over the hypotenuse.	8,595	501	[]
volunteer	which will be using the Pythagorean theorem.	8,595	502	[]
volunteer	5000 square plus, that should be (1000 + 600T)^2, that should be (1000 + 600T)^2, shouldn't it, not a 1000 tea.	8,595	503	[]
volunteer	I'm sorry	8,595	504	[]
student	Yeah	8,595	505	[]
volunteer	That should be	8,595	506	[]
volunteer	that I've, I've got, I haven't completely written the expression properly. I got we race here.	8,595	507	[]
volunteer	I've got a	8,595	508	[]
student	Well, would that be (1000 + 600T)^2	8,595	509	[]
student	or would it just be	8,595	510	[]
volunteer	it would be the same thing that we used before, 6	8,595	511	[]
student	1000 + 600 tea.	8,595	512	[]
volunteer	1000 + 6600	8,595	513	[]
volunteer	Yeah.	8,595	514	[]
volunteer	So let me just kind of write that	8,595	515	[]
volunteer	up.	8,595	516	[]
volunteer	Yeah, I need to erase.	8,595	517	[]
volunteer	I do apologize. I, I have a problem writing.	8,595	518	[]
volunteer	and	8,595	519	[]
student	No product. It's not a problem.	8,595	520	[]
volunteer	but I think, I think the reasoning is all solid that we've, we've got here.	8,595	521	[]
volunteer	All right	8,595	522	[]
volunteer	I don't really have room, so I'm gonna need to.	8,595	523	[]
volunteer	waste a little bit more	8,595	524	[]
student	Yeah	8,595	525	[]
volunteer	It's it kinda looks complicated, but it's really not something that we're gonna have to simplify it all.	8,595	526	[]
volunteer	cause we'll just plug this right in after we square it.	8,595	527	[]
volunteer	So this is gonna be	8,595	528	[]
volunteer	this is gonna be 5000	8,595	529	[]
volunteer	/	8,595	530	[]
volunteer	No, it's a 1000 + 600T, right?	8,595	531	[]
student	Mm	8,595	532	[]
volunteer	Um	8,595	533	[]
volunteer	600	8,595	534	[]
volunteer	+ 1000	8,595	535	[]
volunteer	tea.	8,595	536	[]
volunteer	square	8,595	537	[]
volunteer	It's 1000 + 600T, isn't it?	8,595	538	[]
student	Yup, it is	8,595	539	[]
volunteer	I can't turn to write that properly. Let me try one more time.	8,595	540	[]
student	Do you want me to write it for you?	8,595	541	[]
volunteer	If you can	8,595	542	[]
volunteer	it would be helpful	8,595	543	[]
student	OK, I'll write.	8,595	544	[]
student	I	8,595	545	[]
student	I	8,595	546	[]
volunteer	Since I've done it wrong about 3 times now.	8,595	547	[]
student	It's OK	8,595	548	[]
volunteer	Yeah, that's much better	8,595	549	[]
volunteer	Great.	8,595	550	[]
volunteer	So we now have an expression for cosine of theta.	8,595	551	[]
student	Mhm	8,595	552	[]
volunteer	and it's based on the same logic that we were using for how tall the	8,595	553	[]
volunteer	you know, the rock, how high up the rocket is at any time. It's the same thing.	8,595	554	[]
volunteer	But we now have an expression for cosine theta and thus we have an expression for cosine squared of theta.	8,595	555	[]
student	Mhm	8,595	556	[]
volunteer	which we could just square the numerator and denominator.	8,595	557	[]
volunteer	we would get	8,595	558	[]
volunteer	5000 squared on the numerator and we would remove the radical sign from the denominator.	8,595	559	[]
volunteer	and we would be done	8,595	560	[]

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