Meeting in General-20250619_131700-Meeting

Recording
June 19, 2025, 5:17PM
3h 5m 17s

Mandana Ettehad 0:24

So now we start.
At first, what's the rate of change?
The rate of change measured how much one quantity or.
Dependent variable changed in relation to another quality or independent
very well.
So what means that changing this distance overtime example speak and
change in temperature overtime rate of temperature change?
We have two types for rate of change.
The first one.
Average rate of change.
Change that shirt over a specific interval of time and the other one
changed the Osher at the specific moment in time.
OK, so we have two types.
For the first one over specific interval of time.
I'll give you how are you?
Hello.
What time is it?
Huh.
Why you said that you you join online?
Huh.
OK.
So we said we have two types of you understand yesterday or no, huh.
OK so.
Hmm.
Yeah, I send it.
I send it to the teams.
That's rate of change.
I want to see what's the rate of change.
OK.
We said we have two types of.
Rate of change for the first one or shirt over a specific interval, but for the
second one specific moment in time, bye.
For example, moving car a car leaves Ottawa at 12:00 PM.
And arrive in Toronto at 4:00 PM, having travel 400 kilometers to calculate
the average.
Well, how we can find it?
For average.
Change in distance.
Divided 2 changing time.
So what means that for example?
For this question.
What time?
The car arrive 4:00 PM.
When the car start 12:00 PM.
OK.
And go 400 kilometers so.
400 kilometers.
In four hours.
Yes.
You find it or no.
OK.
So we want to see what's the rate of change.
OK.
For example, at Carl leaves Ottawa at 12:00 PM and arrive internal at 4:00
PM.
So how many hours?
Four hours, right?
Four hours he go 400 kilometers.
So we want to.
Fine.
Average velocity.
So what should we do?
Goes 400 kilometers.
Divided.
In four hours, right, 400 divided.
Four that.
100 OK.
So we can say the average velocity is 100 kilometers.
For each hour, OK.
Hmm.
Understanding average rate of change and slope.
For example, imagine an underwater.
Earthquake on the OSHA floor.
It's great.
A bait.
That's spread out.
In the circle or pattern across the column surface of the ocean, the radius
of the wave increases at time passes at table.
Give us the radius at different times from zero to.
10 second.
So.
So for this question.
What's the independent variable?
Time, right?
Why?
Because it flows on its own.
But what's the dependent dependent variable?
That's radius because it depends on how much time has passed.
OK, so the formula of that.
Is average rate of change.
That means change in radius.
Change.
In.
Ready Divided 2 change.
In time, OK, so.
In general, we can say.
Dependent.
Variable.
Divided 2.
Independent.
Why?
OK.
So average rate of change this change in readiness divided 2 independent
change in time change your radius is.
Dependent and change in time is independent.
For example.
See here at times 0 radius is 0.
After nine second, the reading is 85 and that 10 second, the radiant is 95.
So now we want to find the average rate of change in 10 seconds.
OK, what should we do?
We say change in radius or dependent very well.
How we can find it for example for here in 10 second?
Ready 2 minus.
Ready at 1 divided time 2 minus time one.
OK, so for example for 10 second this one and this that means ready 295
mine is ready IF10.
The time to 10 -, 0.
9.5.
OK.
So we can say the average rate of change from zero to 10 second is 9.5
OK.
9.5m in one second, OK.
So.
Michael, can you tell me the average rate of change?
Uh, in?
Second night between 2nd 9:00 and 10:00.
Hmm, why?
OK.
See, we want to find the average rate of change, OK.
We say.
Here.
We said we have two types of rate A of change one of them.
The average is all share in over a specific interval of time, OK and the
other one or sure at this specific moment.
Now we want to talk about average rate of change.
That means occurred over at specific interval of time. OK.
OK.
So how we can find it?
I give you example or can.
So.
We have two viral independent variable for example.
For this example, we want to see what's the average rate of change 4.
A this question, OK, we want to see that.
Average rate of change.
OK, so at first.
We said we have independent and dependent variable.
So what's the difference between independent and dependent the
independent variable for this question is time.
Why?
Because it follows on its own. OK.
But it depends variable is radius.
Why?
Because it depends on how much time has passed.
OK, so we have dependent and and OK.
It dependent and in now we want to find the average rate of change.
So for general formal, we can say.
Average rate we want to find the average rate of change.
We can say the general formula of that is.
Dependent.
Libel.
Divided 2.
Independent then?
Right. OK.
So that's the general form to find average rate of change, OK, dependent
right?
Well, do I added two independent Bible.
So for this question, which one is dependent variable?
The readiness right.
Why?
Because it depends on how much time has passed.
Without time, we can say.
The change of the radius, right?
So the radius is.
Depend right?
So we can say the general formula that depend variable divided 2
independent variable.
For example, we want to see.
I want to find the average rate of change from zero from 2nd 02/10.
OK, we want to find the average rate of change about the.
Right.
Yes.
OK, So what should we do?
What's the formula of that?
Which one is the?
Which one is the dependent variable?
Hmm. Alright.
Yes.
OK, so see here at times 0 radius is 0 OK.
At time 9, radius is 85 and at a time 10:10 seconds the radius is.
95 right.
OK, so now we want to find the average rate of change in from zero to 10.
What should we do?
At first we should say the.
R2, that's means radius.
In 2nd 10.
The second minus R1, what's the R1?
Huh.
R1 radius.
In second.
OK.
See, we want to find the average rate of change.
OK, from second zero to 10 in second zero.
See here.
For example, at time 0.
Others line fine.
OK.
So we won't want to find the average rate of change, OK and this?
When we start, the redness is zero.
OK, after that's time.
That's right.
For example.
That's time. Let's.
Also.
This.
That's readies, and that's time.
OK, we want to find the average rate.
Between second zero and 2nd 10 OK.
When we start, the redness is.
Huh.
After 5 seconds, the radius is.
100 after 10 minutes, Reddit is.
150 for example, if here is time and here is radius.
When we start, that's here after 10.
After 5 minutes, the READIEST is.
100.
Here after 10 minutes radius is.
150 OK, so now what?
We want to find the rate of change for that between second.
Zero and 10.
We want to see after 10 minutes, what's the rate of rain.
Average of the rate change.
OK, So what should we do?
The second readies minus first radius.
Divided.
To second time minus first.
OK after 10 minutes.
Our radius is.
1:50 but when we start our audiences.
Zero, so 150 -, 0 the divided.
We say we want to see the rate.
Average rate of change between 2nd and 0 and 10.
OK, so 10 -, 0.
That means 150 divided to 10:00.
That's 50.
OK, so for each second goes 15.
Met.
OK, you got it or no?
So now can you tell me what's the average rate of change between 2nd
5:00 and 10:00 Michael?
Hmm.
Hmm.
Yes or no.
Average rate of change.
What should we do?
Huh.
OK, so between second.
5 and 10 what's our R2?
OK.
-100.
10 -, 5.
15.
5.
10.
Handmade for each second, OK?
1st is that it?
You sure?
OK.
OK.
Park, can you tell me what's that?
Average rate of change between second one and 15 or 0 and 50.
OK.
So can you tell me again?
OK, so which number?
96.
Between.
Zero and 15.
OK.
We said R2.
I want time 2 minus time one.
See here we sit between time zero and time 50.
Your art, too, is here are one is here one and 215 -.
Zero.
Their rate of change averages have changed between.
2nd 0 and 50 OK.
OK. Uh.
See here.
Understanding average rate of change and it's handling.
So the average rate of change.
And Jenna?
Now there.
The average rate of change between two points on a graph?
OK, it should be like this one.
For example, what that means the average rate of change?
Tell us how much one quantity like why change in relation to another like
eggs over a certain?
Interval OK so.
Parth, what's the meaning of?
Average rate of change.
Hmm.
OK.
So we said if we want to see.
Between two points are sorry.
The average rate of change tell us how much one quantity, like why
change in relation to another?
OK.
Like eggs or a certain interval.
So what means that for example we have?
Two points here.
P1 and P2P1 is one point and P2 is the other point.
So we want to see what's the.
Average rate of change between .1 and .2.
OK.
How we can find it?
We should use.
The general formula of that is change.
And why?
Divided to change.
In eggs.
OK, so I say it again.
We have two points.
OK, this one this P1NP2 we want to see what's there.
Average rate of change between two points.
What should we do, Michael?
The difference between why?
Divided 2 difference between it's.
OK.
What you don't?
Yeah.
Younger.
Yeah.
Sure.
OK, so we say how we can find it strange rate of change.
We have two points here, .1 and .2.
Each point has eight and Y.
For example P1 that means .1, but it's one and Y1HE too.
Has it still and white?
OK, so now we want to see the average average rate of change
between .1 and .2.
How we can find it?
The average rate of change equal to Y 2 -, y one.
Divided 2X2 minus.
Where is my.
That's.
OK.
You got it.
So watching video for average rate of change, white minus Y one, do you
write it too?
It's still minus X, so for example and I want to show you my graph.
For example, P1 is four and six and P 2.2 is a six and 10 so.
At first we want to find.
The average rate of change, what should we do?
Why 2 -, Y one?
Which one is Y2?
Are you sorry?
10 -, 6, So that's X1 Y1X 2Y2.
Divided 2.
Thank you.
10 -, 6.
4 -, 6, -, 4.
OK.
That's true.
So that I the average rate of change between .1 and .2 is 2.
How we can draw it in a graph so P1?
You can't just stop eggs is 4, Y is 6, and for P2 X equal to six.
And why equal to?
Hmm.
Ten.
It's your.
Why?
And it's your ex.
If your ex is 4, you're Y is.
Why is?
Six if.
Eggs 6Y is 10.
OK, so.
This one.
Is the average.
Right.
Ah, between .1 and .2.
OK so.
This one.
Is Delta X, you know delta the difference between 2nd and 1st and this
one is delta.
Why?
OK, so for fun.
This one we say delta Y divided 2D X you got it.
No.
Yes.
OK.
See, we want to find average rate between .1 and .2.
Each point has 8X and Y OK for example 4.1.
You don't have one and Y one is 4 Y one is.
64.2.
We have each two and white.
If we want to find that average rate between uh, .1 and .2, we should use
this formal delta Y divided to delta X delta Y.
That means difference between second Y and 1st.
Why?
For example, for here delta Y equal to Y 2 -, Y one right and delta axis X 2
-, X one.
OK, so we should use this one.
See here.
This one I use other.
This point is .1 right?
This is .1.
The ex is 4 and the Y is 6 OK and this one is.
The .2 right.
The is C and.
Why is that so?
This, this one this the average rate between .1 and .2.
How we can find it delta?
It's is here right see and this one the different.
Delta why the difference between Y2 and Y1?
OK.
So this one, the white delta white divided to delta X.
Equal to.
Average right, OK.
OK, so now they give you another example.
P.
P1.
OK.
So average rate between P.
Pete, 3, and P1P3 and P2P3N PY.
So 5 the average rate between P3 and P1 poetry and point 2.3 and .1 right
in your notebooks and.
488161632 it's.
OHS.
Sorry, sorry, sorry.
You do it. Hi.
No.
What's this graph?
Sure.
Leave it using this.
Why?
Yeah.
No.
OK.
OK.
What's the average average?
Right up, change between .3 and .1.
My online Students, do you have any question?
Do you have any question?
OK, perfect.
So now.
What's that?
Um average rate of change between PP, .3 and .1.
Two, between .3 and .2.
Between .3 and .1.
Two.
So you see, for all of them is to.
OK.
And for all of them is the same.
So when you draw the graph, because all of the average are the same and
it's two.
So the when you want to drag graph you should drop line 1 means that.
See here.
That's X that's Y4.
4816.
8/16.
32.
The first one is four and eight.
That's point 1.2.
And point treat OK.
So the average the average rate of change for all of them are the same
and equal to two.
So when you want to draw the graph, you should dry.
You should try it as a line.
OK.
But for example at this one, if the average rate between P1 and P2 is 2P2
and three is 4 P for example 4:00 and 3:16, it's not saying and for the
second time.
Be the same.
You should draw.
Like this OK.
Yeah.
OK, for example here.
Uh.
We have two points, P1 and P2P1.
What's the leap for the .1?
What's the X?
P 1.1 here.
For that point, uh two was the eggs.
And the why one.
Why two?
OK.
So can you tell me how we can find a average rate of change?
Huh.
Huh.
So do you know?
I explained to now we want to find the average rate of change between PY
one and P2.
We said we have a general formal.
What's that?
OK, so we should write 5 -, 2, up or down.
Ohm.
You sure?
So we said we should write delta Y divided to delta X so.
5 -, 2, It should be up or down down 5 -, 2 OK for up.
What should we?
10 -.
Four, thank you.
So 10 time is 466 minus 2-3 and the average really tough change for
between .1 and .2 is 2.
Yeah, 6 divided to threes to right.
OK, So what means that?
For this question P1 and P2, the average rate of change is to the.
This means that on average, for every one unit increase in XY increase by
two OK.
So no.
The average rate of change between two points.
2.
That.
The average.
Rate of change between two points is the same as the slope of there
second line connecting connecting them if the graph.
Represent a function.
This tell us how to function changes over and interval to find how a
function change at a single point.
You can see it here.
OK.
See, we said the average rate of change.
See the average rate of change between.
.1 and .2 is delta Y divided to Delta X Delta Y.
That means the second Y.
Minus first and they'll type the second X minus.
First, OK.
So now you can go for your break after that.
Explain this OK.
But as much as you everything.
I optional.
The.
No.
OK.
OK, so now.
I give you another example.
Find one.
Come.
Thank you.
Give them to him.
Thank you.
Tell.
OK, so now.
P1.
P2.
He one.
So now do this.
And draw the graph.
Where are you?
Do it.
Nothing.
Probably.
So you did.
I told you say 1 minus.
OK.
So I give you another example, for example amount of money at the start
and end of the year to find the amount of money at the beginning and the
end of the year.
We look at the first and last point on the graph, OK, so.
Uh, for example, for this question, we don't have points, just we have a
graph, OK and.
And Y axis is amount of dollar and X axis is time.
OK so.
Amount of that is dependent or undependable.
Why you laughing?
Listen.
Amount of dollar is dependent or undependable.
Depends dependent.
Yeah.
And the time is independent.
We said dependent divided to independent or independent divided 2
dependent.
Which one, huh part.
Dependent.
It should be.
Why in graph and independent it should be X?
In the graph, OK, time is independent, right?
So it should be easy and amount of dollar is dependent, so it should be Y
and we say the general form of that is delta Y divided to delta X.
So for this question, we don't have any points, just we have a graph and
we want to find the average.
Average.
Average.
Ratoff change OK so.
For this one, Parth, can you tell me what's the average rate of change
between month of month?
Four and.
Zero.
Between month four and month 0.
Value average rate of change.
Huh.
You should write it up or down.
OK.
That's right, it should be here, right 900 minus.
Or.
Supposed to be.
As an answer.
Final answer.
Two doing.
225.
So amount of the average.
Right up, chain between month and zero and four is 225.
Dollar.
Yeah, down there.
See here.
Dollar.
OK, honey, can you tell me what's the average?
Average.
A rate of change between Month 9 and I'm sorry, eight and five month a.
And month 5.
Huh.
Huh.
You know.
So what should we do?
OK, so which one is Y2?
We said between mom, eight and five is here, right? So.
How much?
1000, right.
So we should write this one up or down.
So, but first we should write for month 8, right?
Because White 2 minus what?
How much for month 8?
1000 minus for five years.
1000 So for Delta X we should write.
Minus.
0 divided 230 OK, so average rate of change between month eight and
five is 0.
Few baby.
Pretty your name is hard for me.
Steven.
Can you?
I tell me.
What's the rate of average?
Sorry, average rate of change between month 10 and six.
10:00 AM six.
Hmm.
You can't tell me again.
10.
Where are you?
OK, so we should.
I'm instead of delta.
Why we should write?
Minus.
That alright.
And.
And so that delta ice, we should write.
Mine has.
Divided 4.
Negative $100.
OK, Peniel.
Can you tell me?
I average rate of.
Change between month 10.
And.
Floor.
Exactly.
Alright.
What are you doing?
Huh.
Nothing.
You sure?
Peniel.
So how you find it?
Huh.
OK.
So on up, what should we right?
900.
How you find 900 per month 10?
Sorry, that's 900.
If you're not, don't know what's the number that I said from one to 3/4.
600 minus.
Mump 4 is 900, but we say we should write white too minus Y 1:00.
So at first we should write 600.
After that we should write 900.
So for Delta is what should we write?
10 -, 4.
My -306 that's -50, OK.
Lee.
Can you tell me the average?
Rate of change between.
Month 9.
Month 9:00 and 4:00.
100,000.
Minus.
800 you sure?
None 700 -, 900 for Delta X.
700 -, 900.
9 -, 4.
How you find 100?
See here.
One month, nine it should be here, right?
Nine is here like.
So for 9:00, that's.
800.
Oh yeah, that's 800.
It should be 20.
For month nine is 800.
Yeah, see.
The 5th 20 because see for month nine is 800 not 700.
OK, see then 19 is here.
800 minus for month 4.
Lee, see.
Four month four is 900 -, 900.
9 -, 4, So -100 divided 25, it should be -20.
OK, you got it.
Perfect.
Michael, you got it or no?
OK, see to find the amount of money at the beginning and the end of the
year.
We look at the first and last point, but every time.
When we want to find the Delta Y and delta X, we should mine uh.
Always it should be white too.
The second one minus first one and for Delta second X minus first six.
OK, so the first point on the graph is 0 and 100, so it's here.
See for the month is 0.
If the month is 0, the what the YR.
Amount of why is?
That's X.
That's why, which means there was $500 in the account at the beginning
of the year or month, zero.
OK.
And for the last point, the last point is.
Here, Mom 12, right.
It's 200, so the last point on the graph is 12 and 200.
So the 12 is X and the A 200 is.
Why so?
Which means there was $200.00 in the account at the end of your year.
Our mom, 12, OK.
That's the last point.
And that's first.
If you want this, what should we do?
That's delta.
Why?
That's Delta X delta.
Why the wide delta?
OK.
So now.
See here at Carrol leaves Ottawa at 12:00 PM.
And arrive in Toronto at 4:00 PM.
So that's your ex, or that's your wife?
That's time, right?
Time it's dependent or independent.
On dependent right?
So undependable.
It should be.
Why?
Or it should be.
It should be.
It should be eggs or it should be white.
See.
We talk about.
Average rate of change, right?
And say we have eggs and we have white.
The general form is delta Y divided to delta X.
OK, so now for this question.
A car leaves hotel go at 12:00 PM and arrive at 4:00 PM or 16.
That's 16, so this one, it should be our Y or it should be our ex.
Eggs.
That's right.
So this one it should be OK.
So a car leaves Ottawa at 12:00 PM, so that's X1 or X2.
Car start from 12:00 PM and arrive 4:00 PM.
Yes, X1 the path 4:00 PM is X1 or X2 eggs 2 having traveled 400
kilometers.
So that's your why or that's your ex.
Why one or Y2?
That's too right, because I when we start that SEF kilometers right and we
goes 400 kilometers, so 0 kilometers is wide one and 400 kilometers is
wide two.
So now we want to find the average.
So how we can find the average?
How we can find average?
We said we have general formal.
So what's the general formula of that path?
Can you tell me what's the general full moon for the formal?
Yeah, it's not working.
What?
Right.
So can you tell me again?
OK, so the general form is delta Y or delta X.
But Delta X right?
So that's the general formula of that.
OK, so.
Now a can you give me a average lacity?
What should we do?
12 -, 4, It should be an up or down.
You you told me delta Y divided delta so how it can be?
OK, so 12 minus.
12 minus see.
Thank you.
So.
For off watch it.
What saying?
What should we write an app?
400 -, 0 so.
400 divided 8 that's.
50 ohm.
Papa.
I see no.
I understand.
OK, see 4:00 PM or 16.
Right.
And that's your second time.
OK, see here.
Can you show me here 5?
3 equal to 15, right?
OK.
War equals to 16, right?
And we start listen to you write it right.
There's no we start at 12:00 PM, so that's our X1 and we finish or we
arrive at 4:00 PM or six.
We should write 16, right?
Because this one, our second ex, right and it should be X 2 -, X one.
So X2 is 4:00 PM.
Now here we write 12.
So here it should be 16.
OK, so 16 -, 12 it should be.
Four, OK.
So for average delta.
Why divided by Delta X our delta X?
It should be 16, right?
Because the second time is 4:00 PM or 16 -, 12 and on off 400 minus zero
400 divided.
By four it should be 100.
100 metres meter.
Sorry, kilometer for each hour, OK?
Because for the why is flowmeter more time is hour?
Kilometers for each hour.
You got it.
So.
34 o'clock.
Yeah, it's uh, 4:00 PM and 4:00 PM is your second time.
So your second time minus first time, right?
And if you put 4 -, 12, it's negative and we don't have time in negative
time, right?
So you should put and the second time it should be bigger than the first
one, so you can try 4.
You should write 16 OK.
For example, if in 12:00 AM and arrive in Toronto at 4:00 AM, you should
write 0 instead of AM, right 4:00 AM for example, that at 12:00 AM and
arrive in Toronto at 4:00 AM.
You should write 4 -, 0 OK.
You got it?
Yeah. OK.
OK, so now for this question.
Paragus is.
You sure?
OK.
For average rate of change.
Change your Reddit Reddit is dependent or undependable.
Depend time is.
And so red is it should be on top or bottom.
Yeah.
OK, see.
Delta, why delta?
It's what's our delta Y which one is Y in the graph, the time or radius?
Which one it is our eggs here, our white, our white should be time or it
should be radius, right?
And exit should be.
Time, OK, so.
What's the average leak?
Can you tell me what's the average rate of change between a second ten
and 2nd 0?
Between 2nd 10 and 2nd 0.
Please.
This one and this.
So we say the general formula that is delta.
Delta.
And that's so on top we should write.
Which one is our way time already?
Matter.
OK button.
9.5m for each second because for Redis is matter what time is sick, OK.
You got it.
OK.
See, we said independent variable is time.
And dependent variable is radius.
So this one time it should be X or Y.
Randy is it should be.
Why OK.
OK, see.
The average rates have changed from zero to 10 is 9.5m for each second
in the last second.
What's the last second?
What's the last second that means between?
Between.
Parth last second.
OK, see. Hello.
Love you.
They come.
And this one at times 0 radius is 0 at time 9 radius is 85 and at time 10
Redis is 95.
So in the last section, 1 means that last section.
That means last one second, right?
So it should be within nine second nine and 2nd 10.
Last.
But nine.
OK.
OK.
So can you tell me?
What's the average rate of change in the last second?
Huh.
OK, so 95 -, 8510 -, 9 and should be there, right?
OK.
So the average rate of change from zero to 10 for 10 second is 9.5 meters
OK.
But in the last second, the wave Grid 10M, which means it's spent up.
So see here.
So it can be light or no when we want to draw the graph.
It should be line or no.
It should be like this or it should be like this?
In graph.
The first one, the second it should be first one or it should be second one
for this.
Huh.
Pentium it should be like first one or second one.
The graph of this question we say the average rate of change from zero to
10 is 9.5, but in the last second just for one minute, one second it's 10
meters.
So the graph that it should be lined or it should be like.
Why?
So like you said, you did last.
No, I checked with myself.
I'm crazy.
It should be like first one or second one.
How about you?
First one.
For 9 minutes.
49029 Go 9.59 point 5 meters for each.
What in the last second 10?
It should be.
Why is the?
Why do you say that should be like the first one?
So much.
Thank you.
OK, see in if you graph the data, the points might not form a straight line.
They could form it.
Her suggestion and non liner OK because see for 9 minutes.
For each second, not ten meters.
If for each, for example, for each second to readers I.
Or if it's saying it should be light.
But see here for the 9 minutes goes 9 meters.
But for one, the last second goes 10 meters, so it should be like second
one.
OK, you got it.
OK, so and for the final, the average rate of change tell?
You.
How fast the way is radius is increasing overtime.
It's the same as the slope.
Of the second line on the graph, OK.
And with that.
In this process, not.
About.
OK.
2nd.
OK.
So now.
You.
Define uh.
Average rate of change between Second zero second four second one and
2nd for 2nd.
Do it now.
Andre 109 hundred 100.
Yeah.
OHP second zero.
Yeah, the average.
They can 0.
Right all.
No.
No.
Sorry.
Finish.
I don't know.
What's that?
Yeah.
For the first.
No.
What?
Not.
No.
You dumb.
OK, first one.
Your penis.
No.
If you.
Ohio.
Really.
OK, so the.
For the first one.
For the first one, between seconds zero and 2nd 4.
It's a six 1600 -, 0 and as a delta eggs is 1 -, 0 it should be 400 S one and
S4 it should be.
500 right.
S Tran S4.
700.
S1 and S2.
Hmm.
100 OK, see here.
I think you're one and second two in the first, second and OK.
Here is first, second between Second Zero and second one OK and
between Second Tree and 2nd 4 is last second OK.
For the first second between S1 and S2 is 100m for each second, but first
between Second Tree and 2nd 4.
Or last second, it's 700.
OK, so you can see it's not saying right for the first second good, just 100
meters, but for last second go 700 meters.
OK, so it should be like this the graph.
It should be like this.
It's can be like right?
Because for the first, second and last second are not same but for
example if first, second with two seconds zero and one with the same with
second one and two is the same with second two and three is the same
with second three and four, all of them are the same.
So it should be like the line.
OK.
You got it.
My online Students, do you have any question?

Carrol Ijeoma Kanu 2:33:50

Ma'am, these when the graph is is curved, how do you how did you do
this?

Mandana Ettehad 2:33:51

But.
Graph is is cramped.
How do you how do you?

Carrol Ijeoma Kanu 2:34:00

Like radios and time with the curve graph.

Mandana Ettehad 2:34:00

Huh.
Like radio and time looking right?
So we say time is dependent or independent.

Carrol Ijeoma Kanu 2:34:12

Time is independent.

Mandana Ettehad 2:34:13

What time is in London is dependent or undependable.

Carrol Ijeoma Kanu 2:34:18

On dependent.

Mandana Ettehad 2:34:18

On dependent on dependent, right?
So I'm dependent, it should be.
It's OK and.

Carrol Ijeoma Kanu 2:34:27

You know.
Mandana Ettehad 2:34:29
Rabbit is dependent or undependable.
OK, see here.
Just one minute I show you.
Ohm.
OK, see independent variable.
It's time, right?

Carrol Ijeoma Kanu 2:34:49

Yes.

Mandana Ettehad 2:34:50

Time is independent because it's flows on its own.
OK, but radius is dependent so.
Radius is dependent because it's depends on how much time has passed.
OK, so time it should be eggs and radius.
It should be white, always independent.
Is X and dependent is Y and how we understand the graph which should
be like this we say the first second.
What's the average?
Um, what's the average rate of change in first, second?
It's 100, right?

Carrol Ijeoma Kanu 2:35:38

Yes.

Mandana Ettehad 2:35:38

Yes, but for last second is.
707 hundred.

Carrol Ijeoma Kanu 2:35:45

700.

Mandana Ettehad 2:35:47

OK.
So they're not saying here is 700 here is 100, so it's not safe.

Carrol Ijeoma Kanu 2:35:49

No.

Mandana Ettehad 2:35:55

So it should be like this, but if.

Carrol Ijeoma Kanu 2:35:58

Yeah.
Mandana Ettehad 2:36:00
For all of them be the same, it should be lying.

Carrol Ijeoma Kanu 2:36:06

You OK?

Mandana Ettehad 2:36:07

You OK?
OK, so I give an example.

Carrol Ijeoma Kanu 2:36:10

It.

Mandana Ettehad 2:36:11

Another example for line.
For example.
P1 is 24P2.

Carrol Ijeoma Kanu 2:36:25

But it's.
Are you?
And then the.

Mandana Ettehad 2:36:32

Or.

Carrol Ijeoma Kanu 2:36:33

Busy but this wait.

Mandana Ettehad 2:36:36

8P38.
60 OK, so.

Carrol Ijeoma Kanu 2:36:44

Yeah.
Yeah.

Mandana Ettehad 2:36:49

What's the average?
Uh.
Rate of change between .2 and .18 -, 4, four -2 right.

Carrol Ijeoma Kanu 2:36:58

Big I hope.
Yes.
Mandana Ettehad 2:37:03
Four.
Divide that by two.
Is 2.

Carrol Ijeoma Kanu 2:37:07

It's the three.

Mandana Ettehad 2:37:09

What's for a between P3 and P216 minus eight 8 -, 4 OK?

Carrol Ijeoma Kanu 2:37:14

Feelings.
Yeah. Yes.

Mandana Ettehad 2:37:20

Eight as far as OK.
So now see here.

Carrol Ijeoma Kanu 2:37:26

The what?

Mandana Ettehad 2:37:27

Uh, Martha.
First, they can what means first between P1 and P2 right?

Carrol Ijeoma Kanu 2:37:34

The.

Mandana Ettehad 2:37:37

For the first second average rate average rate of.

Carrol Ijeoma Kanu 2:37:37

Yes.
Thank you.
Yes.
Yeah, we kept and I'll just say that's, yeah.

Mandana Ettehad 2:37:44

There is 2.
How about the last?
The last ticket that means which wins second, right?

Carrol Ijeoma Kanu 2:37:50

You're different, the yes.
Mandana Ettehad 2:37:55
Two as well.
So for the first, second and last second are the same, so it should be like a
line.

Carrol Ijeoma Kanu 2:37:57

Then.

Mandana Ettehad 2:38:02

OK, it should be line because for the first second that's the 1st.

Carrol Ijeoma Kanu 2:38:04

Did.
The yeah.

Mandana Ettehad 2:38:13

And this one is lastic, so both of them are the same, so it should be like a
line. OK.

Carrol Ijeoma Kanu 2:38:15

And.
Yes.

Mandana Ettehad 2:38:24

Do you have another question?

Carrol Ijeoma Kanu 2:38:26

No, ma'am.
Thank you.

Mandana Ettehad 2:38:27

Have you're welcome?

Carrol Ijeoma Kanu 2:38:30

How much?

Mandana Ettehad 2:38:32

And other students.
Do you have any question?
No.
OK, see here a rate have changed.
So how quickly 11 quantity the dependent variable OK.
Changed with respect to another quantity.
There.
Independ.
Variable the average rate of change reset represent the rate of change
over specific interval.
That is the speed of change between two points within a certain range.
The average rate of change with represent the rate of change over.
And specific interval that is the speed of change between two points
within a certain range, OK.
Word delta Y.
Is the change in the dependent variable and delta X is independent
variable to find the average rate of change you can use the table of values
for two points or like the two X values into the equation.
To calculate there.
The corresponding why?
Well, you.
OK.
No.
For this one I think.
OK, for this one yesterday, you understand everything or no, no.
OK.
So.
I reviewed this one why equal to a?
OK, so that's that function and we want to see what the robot BK a in this,
OK.
At first.
Fraser.
Here we have y = 2 X power of two and we have Y equal to X 2 + 2.
Why equal to X 2 -, 2 so Parth?
For this one it should be like this, right?
Because the degree of that is 2.
But now we want to see what's the role of see.
For the second one, the sea is.
+2 OK and for the third one see.
Minus negative.
OK, so we want to see what's the rule of that?
What should we do?
We say if you find the simple way is that you give number replace number
instead of X&Y right.
So for example, if your ex is 0 for this one, now I.
Why equal to X2 power of two?
This one is X power of two, right?
If X equal to 0, Y equal to.
Hmm.
Your X equal to 0, your Y equal to.
Hmm, I can't hear you.
Why is?
You sure?
For this one part?
Hmm.
Y equal to X2 power of two.
If you're X equal to 0, Y equal to.
X equal to 1, Y equal 2.
Equal to two Y equal 2.
X equal to -1.
Why are you called to?
Huh.
Hmm.
Parth X equal to -1. Why?
But.
Looking at them.
Parth.
Takes 2 + 2.
Why your ex is -1 what's your why?
Huh.
It's equal to -1.
What's your Y?
What's the degree of that?
Oh.
It's.
OK, your ex is -1 Y is.
Hmm.
-1 music.
You can.
Part.
Can you replace -1 instead of eggs please?
You're right.
OK.
Really for this one you need paper.
OK, your ex is -1 Y is.
Huh.
OK, so what's your why?
Why amount of why -1?
OK, you're the one.
You're white.
Should be.
You should replace -1 negative 1 instead of.
What's faster 2/1?
1 + 2.
But it's a negative.
It's not YouTube, but when you put inside what make one power of two,
the two is even and we say doesn't matter, it's positive or negative every
time if our.
A degree is even the number should be positive, so -1 wait is this.
Yeah, that's why I was asking you just that's it's a realistic.
Just you should request Ohio.
I didn't want it set up.
Please -1 power up two is.
It's with us at the thinking it's us confused because of the event.
Eggs power of 2 + 2 if your -1 what your wife.
So we should replace my food.
That if. Yeah.
Hello.
What find?
So why equals minus one 2 + 2 minus?
One 1 + 2, yeah, but I think.
Getting.
One apple.
+2 apple.
Now, how many apples do you have?
Yeah.
Three, but what about the X key?
And that's just.
OK, see.
We want to understand what's the role of +2 in a graph.
The first one is Y equal to each power of two.
The shake off that like this.
OK, now we want to find a graph of why equal to it's 2 + 2.
This simple way for Andrew stand the shape of that we should.
If you remember, I told you you should put numbers instead of X&Y and
you can draw the graph.
OK, so at work you put 0 instead of 0 power of 2 + 2 two.
Group 4 instead of six, huh? 4.
White.
Six existing.
So that is just.
OK.
See just one minute.
Listen.
6.
Three X -, 2, six.
So we want to draw this.
What should we do every time?
If you have function and you want to draw the graph, you should.
Replace numbers instead of each after one.
Why so now you have your kids and you have your wife.
OK, we and why you can find the points and draw the graph.
OK, so now if your exit 0, you're Y is that's X and that's Y, right?
If X0Y is 2, it should be here.
Your EX1 your why?
Tree here, -1 tree.
Here 2.
Let's see here -2.
6:00 so it should be like this.
OK so.
For white equal to X power of two, it should be like this.
But why equal to each 2 + 2 + 2?
This one is your.
Seat.
What's the C doesn't have any eggs or something?
That's just the number.
OK, for example, if you have this, if you have X4 plus 2X plus 32X2, three
X + 5, what's your see?
As five.
OK, that's your see.
Hmm.
C doesn't have any X or something, just a number real number.
OK, so now for this one, what's our C?
It's true, right?
So we want to see what's the difference between what equals 2 and Y
equals it's 2 + 2.
What's the difference between first one, second one?
Both of them are both of them.
Degree of them is 2 leading coefficient for both of them is one.
But here we have +2.
So now we want to see what's their robot.
Is 2 in the graph.
How we can find it?
We should draw.
We should draw this polynomial.
OK, how we can write it?
Replace the number instead of eight.
So we find it here.
It's zero here, Y2 if your X13 minus 1336 minus one six.
So the shape of the graph like this.
OK, So what happens?
I'm here is ohk.
This one I'm here is 2 right?
So what's the robot?
This four every time we.
Your SIS is positive or negative.
Positive.
But if you have, why equal to X2?
Why equals X 2 -, 2?
What's your see?
-2 OK so if.
So now we want to see the role of C.
Why?
Why equals X2?
Why equal to X 2 + 2?
Why equal to X 2 -, 2?
For first one, why equal to X?
Two, it should be like this.
For each 2 + 2 we say stop from here, right?
Like this?
And for this one.
Start from here.
All of them are the same, but what's the difference between them here?
See if positive or negative.
So when?
Your seat is positive.
You should go up.
Two, OK.
For example, if you have one equal to X 2 + 3.
We should go up the tree, so if it's up to we have tree, it should be start
from here from three and like this.
Eat your sees negative here, right?
See you later.
We should go down.
Start from here.
So for the C4C.
If access is changed or what, why is change or excess change?
See why?
Right.
So what's if you're sick?
Bigger than 01.
Bigger than one. Sorry.
It should go up to 345.
If it's negative, it should go down.
For this one, see that's X 2 + 0, right?
It's true or it's 2 + 0.
Both of them are the same, right?
So that means we start from zero if it's the +2, we should start from 2IN
white.
OK, for this PC, yes the white exist is change for this one.
Why equals 2 minus negative -2?
This negative we should stop promoting -2.
We start from here, so if you're sick, you're not positive.
It should go up if see is negative, if we should go down.
OK, you got it.
OK, so now we want to talk.
About the.
What's the deal?
For example.
Why is it called this power of two?
Why?
It's -2.
OK.
This.
This is see, right that's fixed.
It's too, mother love.
Eggs doesn't have any degree or let's fix.
Let's what's the sign up that?
What's the sign up this?
If it's positive, we should go up.
If it's maybe, then we should go.
Yeah, X exercises.
Change your whitefish, Chang.
Why?
What see here.
This one is.
Inside the bracket and they have degree here.
For example, for this one, for this one is fixed, but this one and we have
the power to here so.
Two power 28.
If it's three, this one is changed last week.
Still this one?
Yeah.
OK.
But inside the brush, that's.
We also see what's the robot.
This. Yeah.
More of this, for example, it's positive to go.
Your sea is positive too.
Your sea is Negan, but for this one is changed.
What means that it's -2.
If you have negative here, you're this pose.
If you have positive here, your Disney, but the number is that very
example here E.
-2 this one positive or negative you have negative right.
So your dad is posit OK, so for this one.
Deep equal to positive?
How about this one?
There is.
What?
I told you.
Here is positive.
The sea is positive.
This seemed the sign is the same here -2 seasoning, but for this week is
not safe right now.
Yeah, this sign should be changed.
For example, if it's negative, you're dead is if it's positive.
Thank you.
Do you like?
Do you like food?
OK, that's enough for today.
Bye bye.
For today's enough.
I see you tomorrow.
Bye bye.

Mandana Ettehad stopped transcription