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
student	When	8,595	861	[]
student	it is one hat.	8,595	862	[]
volunteer	OK	8,595	863	[]
volunteer	So I think the key to this problem is probably gonna be something that might surprise you like similar triangles.	8,595	864	[]
volunteer	Um	8,595	865	[]
volunteer	so	8,595	866	[]
volunteer	if you think about it	8,595	867	[]
volunteer	um	8,595	868	[]
student	Oh, we're missing something. So what are you gonna not do it. So we have that 0.	8,595	869	[]
student	03 ft.	8,595	870	[]
student	This looks like it could be the volume.	8,595	871	[]
volunteer	the water is draining from the bottom of the cone at a rate of	8,595	872	[]
volunteer	cubic feet per second, right?	8,595	873	[]
student	Is this the volume	8,595	874	[]
volunteer	That's volume, yes	8,595	875	[]
volunteer	So the volume	8,595	876	[]
student	Yeah, cause I thought you.	8,595	877	[]
volunteer	so what, what, let's see, the volume of a cone, you can help me out here, is it uh 1/3	8,595	878	[]
volunteer	1/3 pie	8,595	879	[]
volunteer	R2H, I believe, 13R2 H.	8,595	880	[]
volunteer	Yeah	8,595	881	[]
volunteer	Right	8,595	882	[]
student	Something I need to like remember and learn, or it's definitely the formulas of these like shapes cuz I really have no idea like on any of them. I don't think they're gonna give us a formula sheet, so you have to remember all that.	8,595	883	[]
volunteer	Right	8,595	884	[]
volunteer	Um	8,595	885	[]
volunteer	I'm	8,595	886	[]
volunteer	I'm pretty sure the volume of a cone, I'm gonna check	8,595	887	[]
volunteer	give me a minute to check for the formula. I'll be right back.	8,595	888	[]
student	Mhm	8,595	889	[]
volunteer	Yeah	8,595	890	[]
volunteer	OK	8,595	891	[]
student	Well, so it's, it's, what did you say it was?	8,595	892	[]
volunteer	It's out, I'll write it out there for us.	8,595	893	[]
student	OK	8,595	894	[]
volunteer	try not to mess it up	8,595	895	[]
volunteer	up too fine too fine here. So,	8,595	896	[]
volunteer	volume	8,595	897	[]
volunteer	is 1/3	8,595	898	[]
volunteer	I	8,595	899	[]
volunteer	r^2	8,595	900	[]
volunteer	H.	8,595	901	[]
volunteer	So that's a critical	8,595	902	[]
volunteer	critical formula for us	8,595	903	[]
student	What does it look like H has some feet and it's working.	8,595	904	[]
volunteer	because I'm really terrible.	8,595	905	[]
student	No, it's OK.	8,595	906	[]
volunteer	But thanks for the humor. I, I need it.	8,595	907	[]
student	Yeah.	8,595	908	[]
volunteer	OK, so	8,595	909	[]
volunteer	we can see that um	8,595	910	[]
volunteer	BV	8,595	911	[]
volunteer	so we know that DV	8,595	912	[]
volunteer	DT	8,595	913	[]
volunteer	cause	8,595	914	[]
student	Mhm	8,595	915	[]
volunteer	negative	8,595	916	[]
volunteer	0.03	8,595	917	[]
volunteer	feet per cubic second.	8,595	918	[]
volunteer	DV	8,595	919	[]
volunteer	So that's interesting information. And so	8,595	920	[]
volunteer	um,	8,595	921	[]
volunteer	if we're trying to find the rate, the height of the water is changing when the height is 15. We could solve for	8,595	922	[]
volunteer	H	8,595	923	[]
volunteer	Well, let's think about this	8,595	924	[]
volunteer	If we took the derivative of both sides of the equation with respect to time.	8,595	925	[]
student	Do you want me to take the derivative of it?	8,595	926	[]
volunteer	Well, not quite, but I'm still kind of thinking for a second here.	8,595	927	[]
volunteer	So,	8,595	928	[]
volunteer	um	8,595	929	[]
volunteer	so we have one problem	8,595	930	[]
volunteer	Not only is H changing	8,595	931	[]
volunteer	but R is changing as well.	8,595	932	[]
volunteer	So if you think about it	8,595	933	[]
volunteer	when, when the water starts going down,	8,595	934	[]
student	Mhm	8,595	935	[]
volunteer	the radius is, the radius is 1 ft at the top when it's full, right?	8,595	936	[]
student	Mhm	8,595	937	[]
volunteer	But when it, when it goes down, not only is the height changing	8,595	938	[]
volunteer	but the radius is also changing.	8,595	939	[]
student	Right	8,595	940	[]
volunteer	So what we need is we, we can't just go willy-nilly off into the	8,595	941	[]
volunteer	um	8,595	942	[]
volunteer	we, we need to have, be able to account for that.	8,595	943	[]
volunteer	in our	8,595	944	[]
volunteer	in our calculations.	8,595	945	[]
student	OK	8,595	946	[]
volunteer	Well, one little trick, one little trick here is	8,595	947	[]
volunteer	that if we look at the side view of um	8,595	948	[]
volunteer	give me a minute here to kind of work this out.	8,595	949	[]
volunteer	But if we looked at the side view	8,595	950	[]
volunteer	we know at the top	8,595	951	[]
volunteer	it's got a radius of	8,595	952	[]
volunteer	1 ft	8,595	953	[]
volunteer	When the height is	8,595	954	[]
volunteer	2 ft	8,595	955	[]
volunteer	but when	8,595	956	[]
volunteer	we're at any other time	8,595	957	[]
volunteer	uh	8,595	958	[]
volunteer	or height	8,595	959	[]
volunteer	it's going to be different, and there's a relationship between	8,595	960	[]

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