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	H instead of	8,595	1,061	[]
volunteer	So if you could write that out, that would be great.	8,595	1,062	[]
student	Mhm.	8,595	1,063	[]
volunteer	just below my stuff or whatever.	8,595	1,064	[]
student	So	8,595	1,065	[]
student	I	8,595	1,066	[]
student	I	8,595	1,067	[]
student	I	8,595	1,068	[]
student	We was the age over 2.	8,595	1,069	[]
volunteer	OK, let's get back to the side view of the cone.	8,595	1,070	[]
volunteer	So,	8,595	1,071	[]
student	I thought it would be 1/4.	8,595	1,072	[]
student	with R	8,595	1,073	[]
volunteer	well, it will, you put an, OK.	8,595	1,074	[]
volunteer	if you put	8,595	1,075	[]
volunteer	we saw, we saw that there are similar triangles	8,595	1,076	[]
student	Mhm	8,595	1,077	[]
volunteer	The radius to the height will always be 1/2.	8,595	1,078	[]
volunteer	right?	8,595	1,079	[]
student	Yeah	8,595	1,080	[]
volunteer	Therefore	8,595	1,081	[]
volunteer	the radius is always half of the height.	8,595	1,082	[]
student	Mhm	8,595	1,083	[]
volunteer	So just plug in H/2 for R	8,595	1,084	[]
volunteer	So instead of 1/3 pie, you got 1/3 pie	8,595	1,085	[]
volunteer	Now, x will be	8,595	1,086	[]
volunteer	R^2 over 4.	8,595	1,087	[]
volunteer	So the next thing after your pie, put in parentheses 82/4.	8,595	1,088	[]
volunteer	Yeah, but we	8,595	1,089	[]
student	So we don't wanna plug for HA? Is that what you're saying? Cause we already know what H is. We're trying to find age at 15.	8,595	1,090	[]
volunteer	yes, I understand, but we need to get the right, we need to get volume as a function of height so that we can differentiate	8,595	1,091	[]
volunteer	If we don't plug in for R right now.	8,595	1,092	[]
volunteer	So r over 2 square.	8,595	1,093	[]
volunteer	right? Just put a little square good, and now put	8,595	1,094	[]
volunteer	H again	8,595	1,095	[]
volunteer	after that	8,595	1,096	[]
volunteer	Now, stop right there because that's beautiful.	8,595	1,097	[]
volunteer	We're saying that the volume	8,595	1,098	[]
volunteer	in this particular instance is as a function of height, and we can simplify this a little bit, but it's 1/3 pie, R2H.	8,595	1,099	[]
volunteer	But we now have everything in terms of age rather than R If we try to differentiate before we do this,	8,595	1,100	[]
volunteer	we won't, we'll have a much more complicated problem.	8,595	1,101	[]
volunteer	because we'll have several variables. We're only interested in volume as a function of height, not as a function of the radius.	8,595	1,102	[]
volunteer	Am I making sense there	8,595	1,103	[]
student	Yeah.	8,595	1,104	[]
volunteer	So let's simplify that. Why don't you go ahead and write it as B equals 1/3.	8,595	1,105	[]
volunteer	high	8,595	1,106	[]
volunteer	below there, just write V equals 1/3 pi.	8,595	1,107	[]
student	Mhm	8,595	1,108	[]
volunteer	and we'll have H cubed	8,595	1,109	[]
volunteer	over 4	8,595	1,110	[]
volunteer	and we can really say that and just put another set of equal signs.	8,595	1,111	[]
volunteer	equals	8,595	1,112	[]
volunteer	high over 12	8,595	1,113	[]
volunteer	H cubed	8,595	1,114	[]
volunteer	So	8,595	1,115	[]
student	Pytol	8,595	1,116	[]
volunteer	by over 12	8,595	1,117	[]
volunteer	HQ	8,595	1,118	[]
volunteer	OK	8,595	1,119	[]
volunteer	Now	8,595	1,120	[]
volunteer	I, I know that was a lot to go through, but if you followed it,	8,595	1,121	[]
volunteer	you now have V as a function of H only, as opposed to RNH, OK?	8,595	1,122	[]
student	Mm	8,595	1,123	[]
volunteer	If we try, if we try to do it with the R in there	8,595	1,124	[]
volunteer	we would be	8,595	1,125	[]
volunteer	unable to solve the problem	8,595	1,126	[]
volunteer	All right.	8,595	1,127	[]
volunteer	So getting back to the	8,595	1,128	[]
volunteer	now we can go ahead and start differentiating	8,595	1,129	[]
volunteer	We can take DVDT, right?	8,595	1,130	[]
student	OK	8,595	1,131	[]
volunteer	I'm glad I've got somebody who can	8,595	1,132	[]
volunteer	use the board.	8,595	1,133	[]
volunteer	So	8,595	1,134	[]
student	Mhm	8,595	1,135	[]
volunteer	what will we get when we differentiate H with respect to T.	8,595	1,136	[]
student	OK	8,595	1,137	[]
student	Um	8,595	1,138	[]
student	3 pie H^2.	8,595	1,139	[]
volunteer	Good.	8,595	1,140	[]
student	DHDT.	8,595	1,141	[]
volunteer	DHDT	8,595	1,142	[]
student	8	8,595	1,143	[]
volunteer	Does that make sense to you	8,595	1,144	[]
student	Yup	8,595	1,145	[]
volunteer	OK	8,595	1,146	[]
volunteer	Now	8,595	1,147	[]
volunteer	we know that we were given DVDT.	8,595	1,148	[]
volunteer	I forgot what it is, what was it?	8,595	1,149	[]
volunteer	Point	8,595	1,150	[]
student	Uh 0.03 ft.	8,595	1,151	[]
volunteer	Yeah, let's, let's right below that -0.03	8,595	1,152	[]
volunteer	for DVVT	8,595	1,153	[]
volunteer	equals 1	8,595	1,154	[]
volunteer	we can say 1/4 pie.	8,595	1,155	[]
volunteer	312 would be 14 5.	8,595	1,156	[]
volunteer	before, whichever way one.	8,595	1,157	[]
volunteer	Good.	8,595	1,158	[]
volunteer	H^2 DHDT	8,595	1,159	[]
student	But can we just not substitute already.	8,595	1,160	[]

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