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Studying for a test? Prepare with this lesson on Números negativos y valor absoluto.
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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.