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	Ok.	17,825	145	[]
volunteer	what are the length of the major and minor axes for the ellipse?	17,825	146	[]
student	not too sure	17,825	147	[]
volunteer	Ok.	17,825	148	[]
volunteer	So the ellipse in standard form is x^2/2^2 + y^2/5^2 = 1	17,825	149	[]
volunteer	So. the ellipse runs from -2 to 2 on the x axis. And -5 to 5 on the y-axis.	17,825	150	[]
volunteer	Does that make sense?	17,825	151	[]
student	how did you get there	17,825	152	[]
student	to the standard form	17,825	153	[]
student	divide 100 on both sides	17,825	154	[]
volunteer	Right. Give me a couple more minutes please.	17,825	155	[]
student	ok	17,825	156	[]
volunteer	All right. This is going to be similar to the last problem. Put on your thinking cap!	17,825	157	[]
volunteer	So. We can picture triangles just like the squares we had last time.	17,825	158	[]
volunteer	And you are right that area is (1/2)bh.	17,825	159	[]
volunteer	We actually know that each base of the triangles is exactly 2y.	17,825	160	[]
volunteer	Do you see that?	17,825	161	[]
volunteer	Think of the largest triangle at the center if that helps.	17,825	162	[]
volunteer	Jamie, are you there?	17,825	163	[ { "pii_type": "PERSON", "surrogate": "Jamie", "start": 0, "end": 5 } ]
student	yea	17,825	164	[]
student	sorry i went to the bathroom	17,825	165	[]
volunteer	Let me take a break also for a couple of minutes, ok?	17,825	166	[]
student	sure	17,825	167	[]
volunteer	I'm back	17,825	168	[]
student	ok	17,825	169	[]
volunteer	So. We've got all these isocelles right triangles that have a base of 2y, does that make sense?	17,825	170	[]
student	yes	17,825	171	[]
volunteer	Good. So we want to get the area of a representative triangle and then integrate over each thin slice, dx.	17,825	172	[]
volunteer	Now. We need to formulate the area of a representative triangle.	17,825	173	[]
volunteer	Let's call the each leg length b.	17,825	174	[]
volunteer	Then, by the Pythagorean Theorem b^2 + b^2 = (2y)^2	17,825	175	[]
student	wait isnt b the base ie the hypotenuse	17,825	176	[]
volunteer	Think of these triangles coming to a point at the top wthe base being the hypotenuse.	17,825	177	[]
volunteer	We can use another variable if that confuses you.	17,825	178	[]
student	yes please	17,825	179	[]
volunteer	Ok. Remember that each triangle has a base (which is the hypotenuse) and two congruent legs, let's call them s for sides.	17,825	180	[]
student	ok	17,825	181	[]
volunteer	Then for each triangle, (2y)^2 = s^2 + s^2	17,825	182	[]
volunteer	By the Pythagorean Theorem.	17,825	183	[]
volunteer	Tell me if that makes sense.	17,825	184	[]
student	ok	17,825	185	[]
student	makes sense	17,825	186	[]
volunteer	Good.	17,825	187	[]
volunteer	So 4y^2 = 2s^2	17,825	188	[]
volunteer	and s^2 = 2y^2	17,825	189	[]
volunteer	Right?	17,825	190	[]
student	yea	17,825	191	[]
volunteer	But the area of a triangle is (1/2)(s)(s) = (1/2)s^2 = y^2	17,825	192	[]
volunteer	Ask questions if it is not clear.	17,825	193	[]
student	that last part didnt make sense	17,825	194	[]
volunteer	glad you stopped me	17,825	195	[]
volunteer	So. We are visualizing all these very thin triangles with bases lying on the floor which is shaped like an ellipse.	17,825	196	[]
student	ok	17,825	197	[]
volunteer	We know that the hypotenuse of each of these triangles can be represented as 2y.	17,825	198	[]
student	ok	17,825	199	[]
volunteer	Good.	17,825	200	[]
volunteer	Now each of these triangles happens to be isoceles right	17,825	201	[]
volunteer	So. We want know what the side are.	17,825	202	[]
volunteer	The Pythagorean Theorem says that (2y)^2 = s^2 + s^2 for each of these triangles.	17,825	203	[]
student	ok	17,825	204	[]
volunteer	They have congruent sides	17,825	205	[]
volunteer	4y^2 = 2s^2 simplifiying.	17,825	206	[]
student	ok	17,825	207	[]
volunteer	s^2 = 2y^2 further simplifying.	17,825	208	[]
student	ok	17,825	209	[]
volunteer	But notice that if we multiply each side of this equatio by 1/2, we have the area of a representative triangle	17,825	210	[]
volunteer	Do you see this? It's okay if you don't	17,825	211	[]
student	no i don't	17,825	212	[]
volunteer	Glad you stopped me	17,825	213	[]
volunteer	I think you followed to the point where we said s^2 = 2y^2. Correct?	17,825	214	[]
student	yes	17,825	215	[]
volunteer	But the area of a representative triangle is (1/2)(bh) = (1/2)(s)(s) = (1/2)s^2 = y^2.	17,825	216	[]
student	oh so the height isnt like what i had in the drawing	17,825	217	[]
student	on the board	17,825	218	[]
student	its s?	17,825	219	[]
volunteer	s is the leg of the triangle.	17,825	220	[]
volunteer	h is not involved in the calculation.	17,825	221	[]
volunteer	You have the two congruent sides - each is s	17,825	222	[]
student	is bh=ss?	17,825	223	[]
volunteer	(1/2)(bh) = (1/2)(s)(s) = (1/2)s^2	17,825	224	[]
volunteer	We are not using the h you have marked on your triangle.	17,825	225	[]
volunteer	We are using the legs of a isosoles triange.	17,825	226	[]
volunteer	We are kind of going around in circles	17,825	227	[]
student	ok	17,825	228	[]
volunteer	Please ask me some question.	17,825	229	[]
volunteer	s	17,825	230	[]
student	why the legs for b and h	17,825	231	[]
student	and not the general height	17,825	232	[]
volunteer	Please draw me an isoceles right triangle on the board.	17,825	233	[]
student	this?	17,825	234	[]
volunteer	Yup!	17,825	235	[]
volunteer	Now label each side s	17,825	236	[]
volunteer	Great!	17,825	237	[]
volunteer	Now calculate the area of that triangle, please	17,825	238	[]
volunteer	The base is s and the height is s	17,825	239	[]
volunteer	So what is the area?	17,825	240	[]
student	ohh ok	17,825	241	[]
volunteer	What is the area if the base is s and the height is s?	17,825	242	[]
volunteer	Right. (1/2)s^2	17,825	243	[]
volunteer	But since s^2 = 2y^2, (1/2)s^2 = y^2, the area of our representative triangle.	17,825	244	[]

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