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# Symmetry of algebraic models

CCSS.Math:

## Video transcript

Sid is experimenting with a piece of sandpaper and some would he try scraping the piece of sandpaper over the wood in different ways to see how much is scraped off the thickness of wood scraped off in millimeters as a function of the speed of the sandpaper in meters per second T of V so this is the thickness scraped off so that's how much those sorts of thickness or how much is scraped off and it is a function of speed and actually since they're 1 they're using V and also they're getting negative value so we care about the direction I'll even call that it's actually the velocity so this is the how much is scraped off as a function of velocity it's shown below and so if the velocity is greater than zero that means that the sandpaper is moving to the right that makes sense the standard convention and if the velocity is less than 0 means the sandpaper is moving to the left fair enough the function is even what is the func what is the significance of the evenness of this function well the fact that it's even means that T of V is equal to T of negative V so that tells us that if we if our velocity is 8 is if our velocity is 8 meters per second to the left we're going to get as much scraped off as if we go 8 millimeters per second to the right and we see that right over here so that is equal to that if we go at 6 meters per second to the left we're going to get just as much scraped off as we go 6 millimeters 6 meters per second these are in meters per second to the right so these two are going to be the same so it's really telling us and we could say do it for 4 meters per second and negative 4 is it doesn't matter if we go to the left or the right what really matters is is e is the magnitude of the velocity or the the absolute value of it but doesn't matter if we're going to the left or the right whether we're going to the left or the right for a given for given magnitude of velocity we are going to get the same amount scraped off now let's see which of these choices are consistent with what I just said moving the sandpaper faster scrapes off more wood well that's true we see as the speed increases where the magnitude of the speed increases we scrape off more wood as the magnitude of the speed this negative eight you might say hey that's lower than negative two but the magnitude is larger we're going eight meters per second to the left and we're scraping off more so this is this is this is a true statement but it's not the significant that it's not the significance of the evenness of the function this could have been true even if this was a seven but then this function would no longer be even the piece of wood is six millimeters thick well this doesn't really we actually don't get any of that from the function moving the sandpaper to the right has the same effect as moving it to the left well that seems pretty close to what I had said earlier that for a given speed to the right or to the left we get the same amount that is taken off of the piece of sandpaper or the piece of wood so this looks like our answer keeping the sandpaper still doesn't scrape off any wood well that is true but once again is not the significance of the evenness of this function