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8
volunteer
I'm sorry, say again
8,595
1,561
[]
student
The uh 12 cubic centimeters.
8,595
1,562
[]
volunteer
So it is, let me go back up to the top and read it with you.
8,595
1,563
[]
volunteer
So the volume remains constant at 12 pi cubic meters.
8,595
1,564
[]
volunteer
So what does that say about DVDT?
8,595
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[]
student
Uh, that is constant. It's 0.
8,595
1,566
[]
volunteer
Yes, that's the key right there. So that's a little bit of a trick.
8,595
1,567
[]
volunteer
DVDT is 0 because they're telling you that it is a constant.
8,595
1,568
[]
student
No
8,595
1,569
[]
volunteer
And we know that the derivative of a constant is zero, so that first term
8,595
1,570
[]
volunteer
gets blown away, right
8,595
1,571
[]
student
Right
8,595
1,572
[]
volunteer
OK, let's see how we're doing. So you already know you got age. Let's see, what do we have V and DHBT?
8,595
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student
The position is negative, um, 1 m. So just -1.
8,595
1,574
[]
volunteer
Um
8,595
1,575
[]
volunteer
right, shrinking. And what is
8,595
1,576
[]
volunteer
uh B
8,595
1,577
[]
student
And then the V is the 12 pi.
8,595
1,578
[]
volunteer
You got it. So let's plug in and see what you get for t at.
8,595
1,579
[]
volunteer
as the A equals.
8,595
1,580
[]
student
OK
8,595
1,581
[]
student
Mm
8,595
1,582
[]
student
I'll just write it on here
8,595
1,583
[]
student
OK
8,595
1,584
[]
student
over
8,595
1,585
[]
student
So is it basically to for high overnight.
8,595
1,586
[]
volunteer
Mhm.
8,595
1,587
[]
student
You have to fur further, yeah, we can further do it but I really.
8,595
1,588
[]
volunteer
Mhm.
8,595
1,589
[]
student
free and cover.
8,595
1,590
[]
student
and then
8,595
1,591
[]
student
not forgetting the
8,595
1,592
[]
student
so.
8,595
1,593
[]
student
need
8,595
1,594
[]
student
ter s and meters
8,595
1,595
[]
student
That.
8,595
1,596
[]
volunteer
So let's see what you you're talking the BOD things so
8,595
1,597
[]
volunteer
everything's in uh
8,595
1,598
[]
volunteer
square meters, right?
8,595
1,599
[]
student
per hour
8,595
1,600
[]
volunteer
Um
8,595
1,601
[]
student
square meters
8,595
1,602
[]
volunteer
let's see
8,595
1,603
[]
volunteer
We, let's see what they say.
8,595
1,604
[]
volunteer
Yeah, meters and square meters per
8,595
1,605
[]
volunteer
uh
8,595
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[]
student
per hour I mean
8,595
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[]
volunteer
where did they say the time?
8,595
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[]
volunteer
Oh, I'm gonna
8,595
1,609
[]
student
like just below
8,595
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[]
student
where it says um
8,595
1,611
[]
volunteer
call per hour, I see, right.
8,595
1,612
[]
student
yeah, for uh
8,595
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[]
student
OK.
8,595
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[]
volunteer
So the square meters per hour, right?
8,595
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[]
student
And it is square meters because we're finding that DADT, which is the derivative of the uh area, right?
8,595
1,616
[]
volunteer
Correct
8,595
1,617
[]
student
OK.
8,595
1,618
[]
volunteer
So that's kind of what we're just basing it on, yeah.
8,595
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[]
volunteer
So
8,595
1,620
[]
volunteer
let me just step back for a minute and think about what you got here.
8,595
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[]
volunteer
So we know that if the if the height is shrinking
8,595
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[]
student
Mhm
8,595
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[]
volunteer
and the thing is staying constant. I'm just thinking out loud here. The area must be going up and you have a positive area, right?
8,595
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volunteer
Cause
8,595
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[]
volunteer
so what I'm, I'm just thinking intuitively about your answer, which I think it makes sense.
8,595
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[]
volunteer
Um.
8,595
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student
OK
8,595
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[]
volunteer
they're telling you that the volume is constant
8,595
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[]
volunteer
but that the height is shrinking.
8,595
1,630
[]
volunteer
Therefore, it seems logical that the area is increasing or the radius, you know, radius and area are increasing, and that's what you came up with. You came up
8,595
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[]
volunteer
with the fact that
8,595
1,632
[]
volunteer
in order for the volume
8,595
1,633
[]
student
Well sorry you like the little Betty didn't hear what you say.
8,595
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volunteer
you want me to start over
8,595
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[]
volunteer
Oh, OK
8,595
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[]
volunteer
Um
8,595
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volunteer
so I'm just looking at your answer, which I believe is correct.
8,595
1,638
[]
volunteer
Reme I'm just thinking about what the whole problem says, which could be uh
8,595
1,639
[]
volunteer
could be kind of the answer to part E here, but
8,595
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student
OK.
8,595
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[]
volunteer
um
8,595
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[]
volunteer
so they told you the volume was constant.
8,595
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[]
volunteer
in the problem
8,595
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[]
volunteer
But yet they told you the height was shrinking.
8,595
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[]
volunteer
right?
8,595
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[]
volunteer
But
8,595
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student
Mhm. Yeah.
8,595
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[]
volunteer
so that means in order for the volume to be to be constant and the high shrinking that the area, the cross-sectional areas must be getting bigger, right?
8,595
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student
Yeah.
8,595
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volunteer
And that's what your answer your answer says, the areas
8,595
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[]
volunteer
increasing
8,595
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[]
volunteer
even though the, the height is decreasing at 1 m per second
8,595
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volunteer
or per hour
8,595
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[]
volunteer
The area is increasing at 45/3 square meters per hour.
8,595
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volunteer
So.
8,595
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volunteer
So first of all, can you, do you know what the answer to this question is or this one?
8,595
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student
Yeah, there's a, it's I can check it.
8,595
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volunteer
Yeah, let's make sure we're
8,595
1,659
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student
Yeah
8,595
1,660
[]