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# Constructing and interpreting absolute value

Video transcript

A riparian buffer is
an area around a stream that's covered in vegetation. The buffer protects
the water in the stream from activity happening
near its location. So let's imagine
this a little bit. So let's say that I have
a stream right over here. So this right over
here is my stream, and the riparian
buffer is an area around the stream that's
covered in vegetation. So this could be the riparian
buffer right over here on this side of the
stream, and maybe there's another one on this side of
the stream right over here. Suppose you run a farm
near a riparian buffer. The buffer begins S feet
from the edge of your farm and ends B feet from
the edge of your farm. How wide is the riparian buffer? So this right over here
could be maybe my farm. So I've got my farm here, those
are my crops, just like that. And they're saying
the buffer begins S feet from the
edge of your farm. So, actually, let's say
that this right over here is the edge of my farm. And it says it begins S feet
from the edge of your farm. So it depends which
side you consider to be the beginning of
the riparian buffer. Maybe we'll take this
side to be the beginning. And so they're saying this
distance right over here is S feet, and it ends B feet
from the edge of your farm. So they're saying that this
distance right over here all the way to the other side of
the riparian buffer is B feet. How wide is the riparian buffer? So the way I made my assumptions
about where the riparian buffer starts and ends,
it looks like it's going to be B minus
S. It looks like it's going to be B minus s,
which would be this distance right over there. So that is B minus
S. But I just assumed the buffer starts
here and ends here. I could have viewed it
the other way around. I could have said, hey,
look, the buffer starts here. The buffer starts on
this side, and this would be my S. And
I could have said, maybe it ends on
this side, and then this would be the B. We
really don't know which one is the start or the
end of the buffer. And in this world
right over here, we would say that
the difference, or how wide the riparian
buffer is, would be S minus B. But one way that we
make sure that we're going to get a positive answer
either way-- because we want our distance to
be positive-- is, well, we could
say, look, we don't know if it's S minus
B or B minus S, so let's just take the
absolute value of these. So absolute value of B minus
S, even in this situation right over here, is going to
give the same exact answer as the absolute value
of S minus B. It's just going to find the absolute
difference between these two values regardless of
which one is larger. So let me make that clear. The absolute value of B
minus S is the same thing as the absolute
value of S minus B. And so I would go with
either one of these. Let's do another one. Doctor When is a time-traveling
alien with a PhD. In the year 1999, Doctor When
is sitting in Central Park, New York City and
eating a hot dog. He then realizes that
he's forgotten his hat. To retrieve his hat,
he travels T years, where T is a
negative to represent going backwards in time. What do we know about
the sum 1999 plus T? So we know that T is
a negative number. He's going backwards in time. So let's look at the choices. 1999 plus T is the absolute
value of T greater than 1999. No, that would've been true
if T is a positive number. Then we'd say, hey,
this right over here is going to be the absolute
value of T greater than 1999. This would have been
only in a positive, so that would have been in a
situation if T is positive. So let's read this one. 1999 plus T is the absolute
value of T less than 1999. That's right. Imagine a situation-- we
know that T is negative-- imagine T as being
equal to negative 3. Then 1999 plus T would
be equal to 1996, which is 3 years less than, so
this is 3 years less than 1999. And this 3 right
over here-- or we could write that
1996 is-- instead of saying 3 years
less than-- it's the absolute value of negative
3 years less than 1999. So this one works out. 1999 plus T is going to
be the absolute value, the absolute magnitude
of that negative number T less than 1999. So we could go with
this, right over here. Let's do one more. You're using an auger to
drill a hole for a fence post. The bottom of the hole is at
a position of negative 2.3 relative to ground level. So let's draw the ground. So here is the ground right over
here, that's the ground level. And the bottom of my
hole-- so I drill a hole. And the bottom of the
hole is at a position of negative 2.3 feet. So this position right over here
is negative 2.3 feet relative to ground level. The fence post has a
length of 4.7 feet. How much higher
is the fence post when it stands atop
the ground than when it is sitting in
the hole you dug? So when it is sitting
atop the ground-- so let me draw the fence post. So when it's sitting
atop the ground, the fence post looks
something like this. And so when it's sitting atop
the ground, it's 4.7 feet high. 4.7, so this distance
right over here. So if I were to draw-- so
let me make this clear. So this right over
here is negative 2.3. This right over here is 4.7. That's how tall it is when it's
sitting on top of the ground. How much higher
is the fence post when it stands atop
the ground than when it's sitting in
the hole you dug? So when you put this fence
post in the hole you dug, it's going to go down 2.3 feet. So it's going to
go down 2.3 feet. You could figure out
what this height is, but they're not even asking us
this height above ground level. They're just saying, how
much does the top go down when it's sitting
in the hole you dug? So it's pretty clear that
this distance right over here is going to be 2.3 feet. It's going to go
2.3 feet lower, when you stick it into the hole. So how much higher
is the fence post when it stands atop
the ground than when it's sitting in
the hole you dug? It's 2.3 feet higher when
it's stands atop the ground.