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NationalTutoringObservatory
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MathEd-PII

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volunteer
I think you just, yeah
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volunteer
So you're right
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volunteer
I apologize
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volunteer
I'm, I'm, I bow to your expertise.
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volunteer
Sorry, you're returning your work in.
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student
its ok haha
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volunteer
Um, but did, did that make sense kind of why we're doing this kind of why they use the word approximation when they talk about this
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volunteer
because there is um
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student
yeah i get it
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volunteer
there is an error value.
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volunteer
that is entirely dependent on what your step size is.
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volunteer
And the bigger your step size, you're kind of delta X or DeltaT, whatever your delta input is.
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volunteer
the less accurate
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volunteer
your method becomes.
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volunteer
And all this stems from physics.
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volunteer
like kind of observing the world and just saying that like, hey, if I know
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volunteer
if I know an object either position
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volunteer
Is there any way I can relate that to its philosophy or the opposite. If I knew an object's velocity,
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volunteer
what is the relationship with its position.
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volunteer
assuming you don't, assuming you only know one and not the other.
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volunteer
And the derivatives and antiderivatives
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volunteer
um were the solutions to that.
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volunteer
Because knowing, like in this example, you know its velocity at any point in time.
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volunteer
and now you are approximating
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volunteer
its position at any point in time.
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volunteer
And the smaller the step size,
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volunteer
um, the more accurate you can get to what its actual position is for any point next. Right now we have a step size of like 1.5. So for every 90 seconds, you know where this object is, a hot air balloon.
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volunteer
the elevation
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volunteer
But in between those 90 seconds, you don't know.
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volunteer
right? That's where the approximation comes in. That's the kind of gray area where we don't know what's happening
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volunteer
Um, we have an idea of what's happening
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volunteer
right? Based on what we can see the what the changes to the velocity.
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volunteer
but we don't know what the actual values are.
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student
Hello
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volunteer
hello
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student
I want to learn geometry
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volunteer
I am not sure what you mean?
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student
nvm I meant that I want to deepen my understanding of tenth grade geometry since I'm in tenth grade and geometry is currently a struggle for me
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[ { "pii_type": "GRADE_LEVEL", "surrogate": "tenth grade", "start": 54, "end": 65 }, { "pii_type": "GRADE_LEVEL", "surrogate": "tenth grade", "start": 88, "end": 99 } ]
volunteer
do you have a problem that you are working on?
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student
no
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volunteer
Is there a particular topic that you wanted to go over?
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student
yeahh
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volunteer
what topic is that?
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student
idk how to explain the topic but I put a question on the board and that question is like the topic I sturggle
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student
I think the topic is just called lines
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volunteer
Parallel lines
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volunteer
You need to know what kinds of angles of equal and what kind are supplementary. Do you know what supplementary means?
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student
I think supplementary is when two angles equal 180 degrees
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volunteer
yes. Also, they can form a straight angle.
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student
okayy
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volunteer
In the diagram, angles and b together form a straight angle and they add 180°
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student
gotcha
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volunteer
angles that have the same relationship to the parallel lines and the transversal are called corresponding angles
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volunteer
So, for example, the two red angles are both formed in the same way by the transversal and one of the parallel lines
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volunteer
the same goes for the black angles and the green angles.
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volunteer
do you see that?
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student
yes
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volunteer
when you have parallel lines and a transversal, corresponding angles are equal
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volunteer
Angles C and F are both inside the parallel lines but on opposite sides of the transversal, right?
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volunteer
C and F are called alternate interior angles.
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student
I understand
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volunteer
the interior means they are inside the parallel lines and the "alternate" means they are on opposite sides of the transversal.
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student
ok
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volunteer
with parallel lines, alternate interior angles are equal
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volunteer
angles A and H are also on "alternate" sides of the transversal, but they are outside (exterior) to the parallel lines.
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volunteer
so A and H are alternate exterior angles
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volunteer
when you have parallel lines. alternate exterior angles are allso equal.
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student
ok
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volunteer
How about angles E and F. What do you think we can say about them?
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student
u want me to say the relationship between angles e and f?
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volunteer
yes
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volunteer
aren't they like the angles a and b in the diagram that I drew above?
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student
yeah
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student
both angles are on a straight line
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volunteer
so what do you think angles E and F add up to ?
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student
180
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student
degrees
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volunteer
In the diagram for your problem, I drew in a new angle "e". Do you see it?
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student
yes
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volunteer
What can you say about angles "a" and "e", do you think?
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volunteer
not sure?
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student
im confused
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student
but I think they are on the same line
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volunteer
they are actually just like angles A and E in the big diagram below
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volunteer
they are corresponding angles
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student
OHH I'm so dumb how didn't I notice that\
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volunteer
therefore, the measure of a equals the measure of e
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student
bruh I should have kneww
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volunteer
Well, you need to spend some time looking at a good diagram of parallel lines with alt interior and exterior and corresponding angles until you get used to visualizing
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volunteer
them
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student
ok
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volunteer
now, we said that e and b add up 180 degrees, right?
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student
oh yeah
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volunteer
because they are supplementary angles
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volunteer
they tell us that b = 2x +13, right
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volunteer
so we can replace b with the expression 2x +13
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volunteer
does that make sense?
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student
yes
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volunteer
they also tell us that a =3x +12
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volunteer
but now we know that e is the same measure as a, right?
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