context
stringlengths 545
71.9k
| questionsrc
stringlengths 16
10.2k
| question
stringlengths 11
563
|
|---|---|---|
in the last video , we started on this problem right here , where we said let omega be a complex cube root of unity , and omega can not be equal to 1 . and so we figured out what all of the complex cube roots of unity were . we figured out -- well , we knew that 1 was one of them , and we used that to factor out this third degree equation right over here . and we figured out the other roots , cube roots , of unity were negative 1 plus or minus the square root of 3i over 2 . and we said , look , the problem said let omega be one of the , or be a complex cube root of unity . so i just picked it to be the negative version . so i said let omega be this thing right over here . now , just to kind of explore the space a little bit , we said , ok , what 's omega squared ? and we figured out that it was actually the conjugate of this . it 's the plus version of this . so we got omega squared right over here . and then i kind of wasted your time a little bit because we know what omega cubed is . we know that omega is a cube root of unity , so omega cubed must be unity . but it was n't harmful , i guess , to go through the process . it shows you sometimes my brain gets into a rut and just does stuff that it does n't have to do . but we figured out -- we multiplied this times omega to show that , hey , it is definitely equal to 1 . so what we were able to do is set up a situation , and we will use this to think about the next part of the problem . so omega is equal to negative 1/2 . or maybe i should say omega to the first power is equal to negative 1/2 minus the square root of 3 over 2i . omega to the second power -- let me write it over here -- omega to the second power is equal to negative 1 plus the square root of 3 over 2i . and then omega to the third power , and that was pretty straightforward , is equal to 1 . and i touched on this in the last video . what is omega to the fourth power ? omega to the fourth power is going to be omega to the third times omega . so it 's going to be omega again . so this is also going to be -- let me scroll to the left a little bit -- this is also going to be omega to the fourth power . omega to the fourth power is the same thing as a omega to the first power , which is this . now , what 's to the fifth power ? well , it 's going to be omega times the fourth power , so it 's omega times this . well , omega times this is the same thing as omega squared , so it 's going to be that . so this is omega to the fifth power . and what 's omega to the sixth power ? well , that 's just the same thing as taking omega cubed and squaring it , so this is also going to be 1 . so this is omega to the sixth . or you could just use , it 's this times omega because it 's to the fifth power , and we saw that that 's also equal to 1 . and the reason why i went up to the sixth power is because , if you 'll remember the old problem , we 're rolling a die . and on that die -- i 'm assuming it 's a normal six-sided die -- we 're going to get values between 1 and 6 . and we 're going to take omega to the different powers , and we 're going to see if it equals to 0 . and we want to find the probability of this being equal to 0 . so let me write this down . we want to find the probability that omega -- and we 're just using the omega that we picked because they said it 's one of the complex roots that is n't 1 -- so we want to find the probability that omega to the first die of the roll plus omega to the second die of the roll plus omega to the third die of the roll , that when you take their sum , that that is equal to 0 . this is what we need to figure out . so to figure this out , let 's just figure out what combinations of powers of omega will even add up to 0 . how can we even add them up to 0 ? i mean , they all have to cancel out some way . and if you look at them , it looks pretty interesting of how they might cancel out . if i take one version of this , the only way that they really can cancel out is if i take one version of this , and add it to this , and then add it to this . let me show you . if i take negative 1/2 minus the square root of 3 over 2i , and i add it to this , and i add it to this , negative 1/2 plus the square root of 3 over 2i , and then i add it to 1 , and then i add it to this , and then i add it to this , what do i get ? well , you 're going to have this guy and this guy are going to cancel out . negative 1/2 plus negative 1/2 are going to be equal to negative 1 . you add negative 1 to 1 , it 's going to be equal to 0 . so essentially , what it was asking us , what 's the probability that i get , for each of these terms , that i get one each of each of these powers of omega ? or another way of thinking about this , what 's the probability -- so if we think of it this way . let 's think of it this way . r1 could be equal to -- we 're going to get omega here , which is the same thing as omega the fourth power . so r1 could be 1 or 4 . and this is in the situation where the first one gives us omega . the second one is omega squared , or the second one gives us this value . and then the third one gives us 1 . so r2 would be 5 or 2 . and then r3 would be equal to 3 or 6 . now , i want to be very clear . we could swap these around . there 's actually six ways that you could -- instead of this being the first roll , this roll could be 1 or 4 , and then this one could be 5 or 2 , and then this one could be 3 or 6 . so there 's actually six ways of doing this , i guess you could say . you could permute these six different ways , or 3 times 2 times 1 . but we 'll think about that in a second . but assuming that we want this way , where this first one is going to evaluate to this , and the second one is going to evaluate to this , and the third one is going to evaluate to this , what 's the probability of that happening ? and then we 're going to multiply that 6 by 6 because there are six ways to arrange these terms right over here . so let 's do that . so what 's the probability of that happening ? well , the probability that r1 is a 1 or a 4 , well , that 's two values out of six , so the probability is 1/3 there . the probability that r2 is a 5 or 2 , well , that 's also going to be 1/3 . there 's two values out of a possible of six . the probability that r3 is a 3 or a 6 , only two possibilities there . so two out of six possible faces of the die , so times 1/3 . so the probability that this first one is going to evaluate to this value right over here , the second one is going to evaluate to this value , and the third one is going to evaluate to 1 , is going to be 1/3 times 1/3 times 1/3 , which is 1/27 . and i touched on this already , there 's six ways . you could rearrange this six ways . you have three terms , and you 're putting them in three places . so in the first place , you could put three of the terms . in the second place , you have two terms left that you could put . and in the last place , you only have one term left . so there 's 3 times 2 times 1 ways to arrange these things . we can arrange this 3 times 2 times 1 different ways , so there 's six different arrangements . the probability of each is 1/27 . so the probability under question , this thing over here , there 's six arrangements . there 's six arrangements of getting these things to be added up in this way , and the probability of each of them is 1/27 . so it 's equal to 6/27 , and if you divide the numerator and the denominator by 3 , it 's equal to 2/9 . and we 're done . it was n't too bad , i think . the probability of getting omega to the r1 plus omega to the r2 plus omega to the r3 , where r1 and r2 and r3 are numbers obtained from rolling a fair die , the probability -- when you add all of these , it 's going to be equal to 0 -- is 2/9 . and i thought that was a pretty neat problem .
|
and then the third one gives us 1 . so r2 would be 5 or 2 . and then r3 would be equal to 3 or 6 .
|
why should w^2 = conjugate of w ?
|
in the last video , we started on this problem right here , where we said let omega be a complex cube root of unity , and omega can not be equal to 1 . and so we figured out what all of the complex cube roots of unity were . we figured out -- well , we knew that 1 was one of them , and we used that to factor out this third degree equation right over here . and we figured out the other roots , cube roots , of unity were negative 1 plus or minus the square root of 3i over 2 . and we said , look , the problem said let omega be one of the , or be a complex cube root of unity . so i just picked it to be the negative version . so i said let omega be this thing right over here . now , just to kind of explore the space a little bit , we said , ok , what 's omega squared ? and we figured out that it was actually the conjugate of this . it 's the plus version of this . so we got omega squared right over here . and then i kind of wasted your time a little bit because we know what omega cubed is . we know that omega is a cube root of unity , so omega cubed must be unity . but it was n't harmful , i guess , to go through the process . it shows you sometimes my brain gets into a rut and just does stuff that it does n't have to do . but we figured out -- we multiplied this times omega to show that , hey , it is definitely equal to 1 . so what we were able to do is set up a situation , and we will use this to think about the next part of the problem . so omega is equal to negative 1/2 . or maybe i should say omega to the first power is equal to negative 1/2 minus the square root of 3 over 2i . omega to the second power -- let me write it over here -- omega to the second power is equal to negative 1 plus the square root of 3 over 2i . and then omega to the third power , and that was pretty straightforward , is equal to 1 . and i touched on this in the last video . what is omega to the fourth power ? omega to the fourth power is going to be omega to the third times omega . so it 's going to be omega again . so this is also going to be -- let me scroll to the left a little bit -- this is also going to be omega to the fourth power . omega to the fourth power is the same thing as a omega to the first power , which is this . now , what 's to the fifth power ? well , it 's going to be omega times the fourth power , so it 's omega times this . well , omega times this is the same thing as omega squared , so it 's going to be that . so this is omega to the fifth power . and what 's omega to the sixth power ? well , that 's just the same thing as taking omega cubed and squaring it , so this is also going to be 1 . so this is omega to the sixth . or you could just use , it 's this times omega because it 's to the fifth power , and we saw that that 's also equal to 1 . and the reason why i went up to the sixth power is because , if you 'll remember the old problem , we 're rolling a die . and on that die -- i 'm assuming it 's a normal six-sided die -- we 're going to get values between 1 and 6 . and we 're going to take omega to the different powers , and we 're going to see if it equals to 0 . and we want to find the probability of this being equal to 0 . so let me write this down . we want to find the probability that omega -- and we 're just using the omega that we picked because they said it 's one of the complex roots that is n't 1 -- so we want to find the probability that omega to the first die of the roll plus omega to the second die of the roll plus omega to the third die of the roll , that when you take their sum , that that is equal to 0 . this is what we need to figure out . so to figure this out , let 's just figure out what combinations of powers of omega will even add up to 0 . how can we even add them up to 0 ? i mean , they all have to cancel out some way . and if you look at them , it looks pretty interesting of how they might cancel out . if i take one version of this , the only way that they really can cancel out is if i take one version of this , and add it to this , and then add it to this . let me show you . if i take negative 1/2 minus the square root of 3 over 2i , and i add it to this , and i add it to this , negative 1/2 plus the square root of 3 over 2i , and then i add it to 1 , and then i add it to this , and then i add it to this , what do i get ? well , you 're going to have this guy and this guy are going to cancel out . negative 1/2 plus negative 1/2 are going to be equal to negative 1 . you add negative 1 to 1 , it 's going to be equal to 0 . so essentially , what it was asking us , what 's the probability that i get , for each of these terms , that i get one each of each of these powers of omega ? or another way of thinking about this , what 's the probability -- so if we think of it this way . let 's think of it this way . r1 could be equal to -- we 're going to get omega here , which is the same thing as omega the fourth power . so r1 could be 1 or 4 . and this is in the situation where the first one gives us omega . the second one is omega squared , or the second one gives us this value . and then the third one gives us 1 . so r2 would be 5 or 2 . and then r3 would be equal to 3 or 6 . now , i want to be very clear . we could swap these around . there 's actually six ways that you could -- instead of this being the first roll , this roll could be 1 or 4 , and then this one could be 5 or 2 , and then this one could be 3 or 6 . so there 's actually six ways of doing this , i guess you could say . you could permute these six different ways , or 3 times 2 times 1 . but we 'll think about that in a second . but assuming that we want this way , where this first one is going to evaluate to this , and the second one is going to evaluate to this , and the third one is going to evaluate to this , what 's the probability of that happening ? and then we 're going to multiply that 6 by 6 because there are six ways to arrange these terms right over here . so let 's do that . so what 's the probability of that happening ? well , the probability that r1 is a 1 or a 4 , well , that 's two values out of six , so the probability is 1/3 there . the probability that r2 is a 5 or 2 , well , that 's also going to be 1/3 . there 's two values out of a possible of six . the probability that r3 is a 3 or a 6 , only two possibilities there . so two out of six possible faces of the die , so times 1/3 . so the probability that this first one is going to evaluate to this value right over here , the second one is going to evaluate to this value , and the third one is going to evaluate to 1 , is going to be 1/3 times 1/3 times 1/3 , which is 1/27 . and i touched on this already , there 's six ways . you could rearrange this six ways . you have three terms , and you 're putting them in three places . so in the first place , you could put three of the terms . in the second place , you have two terms left that you could put . and in the last place , you only have one term left . so there 's 3 times 2 times 1 ways to arrange these things . we can arrange this 3 times 2 times 1 different ways , so there 's six different arrangements . the probability of each is 1/27 . so the probability under question , this thing over here , there 's six arrangements . there 's six arrangements of getting these things to be added up in this way , and the probability of each of them is 1/27 . so it 's equal to 6/27 , and if you divide the numerator and the denominator by 3 , it 's equal to 2/9 . and we 're done . it was n't too bad , i think . the probability of getting omega to the r1 plus omega to the r2 plus omega to the r3 , where r1 and r2 and r3 are numbers obtained from rolling a fair die , the probability -- when you add all of these , it 's going to be equal to 0 -- is 2/9 . and i thought that was a pretty neat problem .
|
you add negative 1 to 1 , it 's going to be equal to 0 . so essentially , what it was asking us , what 's the probability that i get , for each of these terms , that i get one each of each of these powers of omega ? or another way of thinking about this , what 's the probability -- so if we think of it this way .
|
so we should get double the probability of what you got in the end ?
|
in the last video , we started on this problem right here , where we said let omega be a complex cube root of unity , and omega can not be equal to 1 . and so we figured out what all of the complex cube roots of unity were . we figured out -- well , we knew that 1 was one of them , and we used that to factor out this third degree equation right over here . and we figured out the other roots , cube roots , of unity were negative 1 plus or minus the square root of 3i over 2 . and we said , look , the problem said let omega be one of the , or be a complex cube root of unity . so i just picked it to be the negative version . so i said let omega be this thing right over here . now , just to kind of explore the space a little bit , we said , ok , what 's omega squared ? and we figured out that it was actually the conjugate of this . it 's the plus version of this . so we got omega squared right over here . and then i kind of wasted your time a little bit because we know what omega cubed is . we know that omega is a cube root of unity , so omega cubed must be unity . but it was n't harmful , i guess , to go through the process . it shows you sometimes my brain gets into a rut and just does stuff that it does n't have to do . but we figured out -- we multiplied this times omega to show that , hey , it is definitely equal to 1 . so what we were able to do is set up a situation , and we will use this to think about the next part of the problem . so omega is equal to negative 1/2 . or maybe i should say omega to the first power is equal to negative 1/2 minus the square root of 3 over 2i . omega to the second power -- let me write it over here -- omega to the second power is equal to negative 1 plus the square root of 3 over 2i . and then omega to the third power , and that was pretty straightforward , is equal to 1 . and i touched on this in the last video . what is omega to the fourth power ? omega to the fourth power is going to be omega to the third times omega . so it 's going to be omega again . so this is also going to be -- let me scroll to the left a little bit -- this is also going to be omega to the fourth power . omega to the fourth power is the same thing as a omega to the first power , which is this . now , what 's to the fifth power ? well , it 's going to be omega times the fourth power , so it 's omega times this . well , omega times this is the same thing as omega squared , so it 's going to be that . so this is omega to the fifth power . and what 's omega to the sixth power ? well , that 's just the same thing as taking omega cubed and squaring it , so this is also going to be 1 . so this is omega to the sixth . or you could just use , it 's this times omega because it 's to the fifth power , and we saw that that 's also equal to 1 . and the reason why i went up to the sixth power is because , if you 'll remember the old problem , we 're rolling a die . and on that die -- i 'm assuming it 's a normal six-sided die -- we 're going to get values between 1 and 6 . and we 're going to take omega to the different powers , and we 're going to see if it equals to 0 . and we want to find the probability of this being equal to 0 . so let me write this down . we want to find the probability that omega -- and we 're just using the omega that we picked because they said it 's one of the complex roots that is n't 1 -- so we want to find the probability that omega to the first die of the roll plus omega to the second die of the roll plus omega to the third die of the roll , that when you take their sum , that that is equal to 0 . this is what we need to figure out . so to figure this out , let 's just figure out what combinations of powers of omega will even add up to 0 . how can we even add them up to 0 ? i mean , they all have to cancel out some way . and if you look at them , it looks pretty interesting of how they might cancel out . if i take one version of this , the only way that they really can cancel out is if i take one version of this , and add it to this , and then add it to this . let me show you . if i take negative 1/2 minus the square root of 3 over 2i , and i add it to this , and i add it to this , negative 1/2 plus the square root of 3 over 2i , and then i add it to 1 , and then i add it to this , and then i add it to this , what do i get ? well , you 're going to have this guy and this guy are going to cancel out . negative 1/2 plus negative 1/2 are going to be equal to negative 1 . you add negative 1 to 1 , it 's going to be equal to 0 . so essentially , what it was asking us , what 's the probability that i get , for each of these terms , that i get one each of each of these powers of omega ? or another way of thinking about this , what 's the probability -- so if we think of it this way . let 's think of it this way . r1 could be equal to -- we 're going to get omega here , which is the same thing as omega the fourth power . so r1 could be 1 or 4 . and this is in the situation where the first one gives us omega . the second one is omega squared , or the second one gives us this value . and then the third one gives us 1 . so r2 would be 5 or 2 . and then r3 would be equal to 3 or 6 . now , i want to be very clear . we could swap these around . there 's actually six ways that you could -- instead of this being the first roll , this roll could be 1 or 4 , and then this one could be 5 or 2 , and then this one could be 3 or 6 . so there 's actually six ways of doing this , i guess you could say . you could permute these six different ways , or 3 times 2 times 1 . but we 'll think about that in a second . but assuming that we want this way , where this first one is going to evaluate to this , and the second one is going to evaluate to this , and the third one is going to evaluate to this , what 's the probability of that happening ? and then we 're going to multiply that 6 by 6 because there are six ways to arrange these terms right over here . so let 's do that . so what 's the probability of that happening ? well , the probability that r1 is a 1 or a 4 , well , that 's two values out of six , so the probability is 1/3 there . the probability that r2 is a 5 or 2 , well , that 's also going to be 1/3 . there 's two values out of a possible of six . the probability that r3 is a 3 or a 6 , only two possibilities there . so two out of six possible faces of the die , so times 1/3 . so the probability that this first one is going to evaluate to this value right over here , the second one is going to evaluate to this value , and the third one is going to evaluate to 1 , is going to be 1/3 times 1/3 times 1/3 , which is 1/27 . and i touched on this already , there 's six ways . you could rearrange this six ways . you have three terms , and you 're putting them in three places . so in the first place , you could put three of the terms . in the second place , you have two terms left that you could put . and in the last place , you only have one term left . so there 's 3 times 2 times 1 ways to arrange these things . we can arrange this 3 times 2 times 1 different ways , so there 's six different arrangements . the probability of each is 1/27 . so the probability under question , this thing over here , there 's six arrangements . there 's six arrangements of getting these things to be added up in this way , and the probability of each of them is 1/27 . so it 's equal to 6/27 , and if you divide the numerator and the denominator by 3 , it 's equal to 2/9 . and we 're done . it was n't too bad , i think . the probability of getting omega to the r1 plus omega to the r2 plus omega to the r3 , where r1 and r2 and r3 are numbers obtained from rolling a fair die , the probability -- when you add all of these , it 's going to be equal to 0 -- is 2/9 . and i thought that was a pretty neat problem .
|
and we 're done . it was n't too bad , i think . the probability of getting omega to the r1 plus omega to the r2 plus omega to the r3 , where r1 and r2 and r3 are numbers obtained from rolling a fair die , the probability -- when you add all of these , it 's going to be equal to 0 -- is 2/9 . and i thought that was a pretty neat problem .
|
why the probability for r1 , r2 , r3 ca n't be found out by 6c2 ( combination ) ?
|
in the last video , we started on this problem right here , where we said let omega be a complex cube root of unity , and omega can not be equal to 1 . and so we figured out what all of the complex cube roots of unity were . we figured out -- well , we knew that 1 was one of them , and we used that to factor out this third degree equation right over here . and we figured out the other roots , cube roots , of unity were negative 1 plus or minus the square root of 3i over 2 . and we said , look , the problem said let omega be one of the , or be a complex cube root of unity . so i just picked it to be the negative version . so i said let omega be this thing right over here . now , just to kind of explore the space a little bit , we said , ok , what 's omega squared ? and we figured out that it was actually the conjugate of this . it 's the plus version of this . so we got omega squared right over here . and then i kind of wasted your time a little bit because we know what omega cubed is . we know that omega is a cube root of unity , so omega cubed must be unity . but it was n't harmful , i guess , to go through the process . it shows you sometimes my brain gets into a rut and just does stuff that it does n't have to do . but we figured out -- we multiplied this times omega to show that , hey , it is definitely equal to 1 . so what we were able to do is set up a situation , and we will use this to think about the next part of the problem . so omega is equal to negative 1/2 . or maybe i should say omega to the first power is equal to negative 1/2 minus the square root of 3 over 2i . omega to the second power -- let me write it over here -- omega to the second power is equal to negative 1 plus the square root of 3 over 2i . and then omega to the third power , and that was pretty straightforward , is equal to 1 . and i touched on this in the last video . what is omega to the fourth power ? omega to the fourth power is going to be omega to the third times omega . so it 's going to be omega again . so this is also going to be -- let me scroll to the left a little bit -- this is also going to be omega to the fourth power . omega to the fourth power is the same thing as a omega to the first power , which is this . now , what 's to the fifth power ? well , it 's going to be omega times the fourth power , so it 's omega times this . well , omega times this is the same thing as omega squared , so it 's going to be that . so this is omega to the fifth power . and what 's omega to the sixth power ? well , that 's just the same thing as taking omega cubed and squaring it , so this is also going to be 1 . so this is omega to the sixth . or you could just use , it 's this times omega because it 's to the fifth power , and we saw that that 's also equal to 1 . and the reason why i went up to the sixth power is because , if you 'll remember the old problem , we 're rolling a die . and on that die -- i 'm assuming it 's a normal six-sided die -- we 're going to get values between 1 and 6 . and we 're going to take omega to the different powers , and we 're going to see if it equals to 0 . and we want to find the probability of this being equal to 0 . so let me write this down . we want to find the probability that omega -- and we 're just using the omega that we picked because they said it 's one of the complex roots that is n't 1 -- so we want to find the probability that omega to the first die of the roll plus omega to the second die of the roll plus omega to the third die of the roll , that when you take their sum , that that is equal to 0 . this is what we need to figure out . so to figure this out , let 's just figure out what combinations of powers of omega will even add up to 0 . how can we even add them up to 0 ? i mean , they all have to cancel out some way . and if you look at them , it looks pretty interesting of how they might cancel out . if i take one version of this , the only way that they really can cancel out is if i take one version of this , and add it to this , and then add it to this . let me show you . if i take negative 1/2 minus the square root of 3 over 2i , and i add it to this , and i add it to this , negative 1/2 plus the square root of 3 over 2i , and then i add it to 1 , and then i add it to this , and then i add it to this , what do i get ? well , you 're going to have this guy and this guy are going to cancel out . negative 1/2 plus negative 1/2 are going to be equal to negative 1 . you add negative 1 to 1 , it 's going to be equal to 0 . so essentially , what it was asking us , what 's the probability that i get , for each of these terms , that i get one each of each of these powers of omega ? or another way of thinking about this , what 's the probability -- so if we think of it this way . let 's think of it this way . r1 could be equal to -- we 're going to get omega here , which is the same thing as omega the fourth power . so r1 could be 1 or 4 . and this is in the situation where the first one gives us omega . the second one is omega squared , or the second one gives us this value . and then the third one gives us 1 . so r2 would be 5 or 2 . and then r3 would be equal to 3 or 6 . now , i want to be very clear . we could swap these around . there 's actually six ways that you could -- instead of this being the first roll , this roll could be 1 or 4 , and then this one could be 5 or 2 , and then this one could be 3 or 6 . so there 's actually six ways of doing this , i guess you could say . you could permute these six different ways , or 3 times 2 times 1 . but we 'll think about that in a second . but assuming that we want this way , where this first one is going to evaluate to this , and the second one is going to evaluate to this , and the third one is going to evaluate to this , what 's the probability of that happening ? and then we 're going to multiply that 6 by 6 because there are six ways to arrange these terms right over here . so let 's do that . so what 's the probability of that happening ? well , the probability that r1 is a 1 or a 4 , well , that 's two values out of six , so the probability is 1/3 there . the probability that r2 is a 5 or 2 , well , that 's also going to be 1/3 . there 's two values out of a possible of six . the probability that r3 is a 3 or a 6 , only two possibilities there . so two out of six possible faces of the die , so times 1/3 . so the probability that this first one is going to evaluate to this value right over here , the second one is going to evaluate to this value , and the third one is going to evaluate to 1 , is going to be 1/3 times 1/3 times 1/3 , which is 1/27 . and i touched on this already , there 's six ways . you could rearrange this six ways . you have three terms , and you 're putting them in three places . so in the first place , you could put three of the terms . in the second place , you have two terms left that you could put . and in the last place , you only have one term left . so there 's 3 times 2 times 1 ways to arrange these things . we can arrange this 3 times 2 times 1 different ways , so there 's six different arrangements . the probability of each is 1/27 . so the probability under question , this thing over here , there 's six arrangements . there 's six arrangements of getting these things to be added up in this way , and the probability of each of them is 1/27 . so it 's equal to 6/27 , and if you divide the numerator and the denominator by 3 , it 's equal to 2/9 . and we 're done . it was n't too bad , i think . the probability of getting omega to the r1 plus omega to the r2 plus omega to the r3 , where r1 and r2 and r3 are numbers obtained from rolling a fair die , the probability -- when you add all of these , it 's going to be equal to 0 -- is 2/9 . and i thought that was a pretty neat problem .
|
you could rearrange this six ways . you have three terms , and you 're putting them in three places . so in the first place , you could put three of the terms .
|
why is sal taking the three numbers that are obtained upon rolling the die to be different ?
|
so , in this problem , they 're telling us in outer space , the distance an object travels varies directly with the amount of time that it travels . and , that 's of course assuming that it 's not accelerating , and there 's no net force , and all of that on it . so , i guess they 're talking about a specific object . so , some specific object , the amount , the distance that it travels is directly , it varies directly , it varies directly with the amount of time that it travels . so , if we think of in , in , in terms of constants of proportionality , and direct variation , we could say that the distance , we could say that the distance is equal to some constant , times the time , times the time that it travels . the distance varies directly with the amount of time that travels for this particular object . if an asteroid travels 3000 miles , in , if the asteroid travels 3000 miles in 6 hours , what is the constant of variation ? so the distance is 3000 , so we have d is equal to 3000 miles . we have 3,000 miles is the distance , and that 's going to be equal to the constant of variation . the constant of variation times the time , times 6 hours . so , if we wan na solve for the constant of variation , we can just divide both sides by 6 hours . 6 hours , and we divide the right-hand side by 6 hours . and , so , 3,000 divided by 6 is 500 , and 6 divided by 6 is 1 . the hours also cancel out if you care about the units . and , so , the concept of proportionality , the left-hand side is just 500 , 500 , and then we have miles per hour , miles per hour . fired 500 miles per hour , and that is equal to k. so , the constant proportionality is 500 miles per hour , or you could say 500 if you 're not too worried about the units . or , we should say , the constant of variation , to use the terminology that they actually use in the question .
|
so the distance is 3000 , so we have d is equal to 3000 miles . we have 3,000 miles is the distance , and that 's going to be equal to the constant of variation . the constant of variation times the time , times 6 hours . so , if we wan na solve for the constant of variation , we can just divide both sides by 6 hours .
|
in direct variation , as x increases , does y always have to increase ?
|
so , in this problem , they 're telling us in outer space , the distance an object travels varies directly with the amount of time that it travels . and , that 's of course assuming that it 's not accelerating , and there 's no net force , and all of that on it . so , i guess they 're talking about a specific object . so , some specific object , the amount , the distance that it travels is directly , it varies directly , it varies directly with the amount of time that it travels . so , if we think of in , in , in terms of constants of proportionality , and direct variation , we could say that the distance , we could say that the distance is equal to some constant , times the time , times the time that it travels . the distance varies directly with the amount of time that travels for this particular object . if an asteroid travels 3000 miles , in , if the asteroid travels 3000 miles in 6 hours , what is the constant of variation ? so the distance is 3000 , so we have d is equal to 3000 miles . we have 3,000 miles is the distance , and that 's going to be equal to the constant of variation . the constant of variation times the time , times 6 hours . so , if we wan na solve for the constant of variation , we can just divide both sides by 6 hours . 6 hours , and we divide the right-hand side by 6 hours . and , so , 3,000 divided by 6 is 500 , and 6 divided by 6 is 1 . the hours also cancel out if you care about the units . and , so , the concept of proportionality , the left-hand side is just 500 , 500 , and then we have miles per hour , miles per hour . fired 500 miles per hour , and that is equal to k. so , the constant proportionality is 500 miles per hour , or you could say 500 if you 're not too worried about the units . or , we should say , the constant of variation , to use the terminology that they actually use in the question .
|
so the distance is 3000 , so we have d is equal to 3000 miles . we have 3,000 miles is the distance , and that 's going to be equal to the constant of variation . the constant of variation times the time , times 6 hours . so , if we wan na solve for the constant of variation , we can just divide both sides by 6 hours .
|
if the constant is negative , then y will decrease as x increases , right ?
|
so , in this problem , they 're telling us in outer space , the distance an object travels varies directly with the amount of time that it travels . and , that 's of course assuming that it 's not accelerating , and there 's no net force , and all of that on it . so , i guess they 're talking about a specific object . so , some specific object , the amount , the distance that it travels is directly , it varies directly , it varies directly with the amount of time that it travels . so , if we think of in , in , in terms of constants of proportionality , and direct variation , we could say that the distance , we could say that the distance is equal to some constant , times the time , times the time that it travels . the distance varies directly with the amount of time that travels for this particular object . if an asteroid travels 3000 miles , in , if the asteroid travels 3000 miles in 6 hours , what is the constant of variation ? so the distance is 3000 , so we have d is equal to 3000 miles . we have 3,000 miles is the distance , and that 's going to be equal to the constant of variation . the constant of variation times the time , times 6 hours . so , if we wan na solve for the constant of variation , we can just divide both sides by 6 hours . 6 hours , and we divide the right-hand side by 6 hours . and , so , 3,000 divided by 6 is 500 , and 6 divided by 6 is 1 . the hours also cancel out if you care about the units . and , so , the concept of proportionality , the left-hand side is just 500 , 500 , and then we have miles per hour , miles per hour . fired 500 miles per hour , and that is equal to k. so , the constant proportionality is 500 miles per hour , or you could say 500 if you 're not too worried about the units . or , we should say , the constant of variation , to use the terminology that they actually use in the question .
|
so , in this problem , they 're telling us in outer space , the distance an object travels varies directly with the amount of time that it travels . and , that 's of course assuming that it 's not accelerating , and there 's no net force , and all of that on it .
|
how long will the food last if all the soldiers leave ?
|
so , in this problem , they 're telling us in outer space , the distance an object travels varies directly with the amount of time that it travels . and , that 's of course assuming that it 's not accelerating , and there 's no net force , and all of that on it . so , i guess they 're talking about a specific object . so , some specific object , the amount , the distance that it travels is directly , it varies directly , it varies directly with the amount of time that it travels . so , if we think of in , in , in terms of constants of proportionality , and direct variation , we could say that the distance , we could say that the distance is equal to some constant , times the time , times the time that it travels . the distance varies directly with the amount of time that travels for this particular object . if an asteroid travels 3000 miles , in , if the asteroid travels 3000 miles in 6 hours , what is the constant of variation ? so the distance is 3000 , so we have d is equal to 3000 miles . we have 3,000 miles is the distance , and that 's going to be equal to the constant of variation . the constant of variation times the time , times 6 hours . so , if we wan na solve for the constant of variation , we can just divide both sides by 6 hours . 6 hours , and we divide the right-hand side by 6 hours . and , so , 3,000 divided by 6 is 500 , and 6 divided by 6 is 1 . the hours also cancel out if you care about the units . and , so , the concept of proportionality , the left-hand side is just 500 , 500 , and then we have miles per hour , miles per hour . fired 500 miles per hour , and that is equal to k. so , the constant proportionality is 500 miles per hour , or you could say 500 if you 're not too worried about the units . or , we should say , the constant of variation , to use the terminology that they actually use in the question .
|
fired 500 miles per hour , and that is equal to k. so , the constant proportionality is 500 miles per hour , or you could say 500 if you 're not too worried about the units . or , we should say , the constant of variation , to use the terminology that they actually use in the question .
|
how would someone answer a question that is asking something like , if some factor changed a part of the direct variation , would it still stay a direct variation ?
|
so , in this problem , they 're telling us in outer space , the distance an object travels varies directly with the amount of time that it travels . and , that 's of course assuming that it 's not accelerating , and there 's no net force , and all of that on it . so , i guess they 're talking about a specific object . so , some specific object , the amount , the distance that it travels is directly , it varies directly , it varies directly with the amount of time that it travels . so , if we think of in , in , in terms of constants of proportionality , and direct variation , we could say that the distance , we could say that the distance is equal to some constant , times the time , times the time that it travels . the distance varies directly with the amount of time that travels for this particular object . if an asteroid travels 3000 miles , in , if the asteroid travels 3000 miles in 6 hours , what is the constant of variation ? so the distance is 3000 , so we have d is equal to 3000 miles . we have 3,000 miles is the distance , and that 's going to be equal to the constant of variation . the constant of variation times the time , times 6 hours . so , if we wan na solve for the constant of variation , we can just divide both sides by 6 hours . 6 hours , and we divide the right-hand side by 6 hours . and , so , 3,000 divided by 6 is 500 , and 6 divided by 6 is 1 . the hours also cancel out if you care about the units . and , so , the concept of proportionality , the left-hand side is just 500 , 500 , and then we have miles per hour , miles per hour . fired 500 miles per hour , and that is equal to k. so , the constant proportionality is 500 miles per hour , or you could say 500 if you 're not too worried about the units . or , we should say , the constant of variation , to use the terminology that they actually use in the question .
|
so the distance is 3000 , so we have d is equal to 3000 miles . we have 3,000 miles is the distance , and that 's going to be equal to the constant of variation . the constant of variation times the time , times 6 hours . so , if we wan na solve for the constant of variation , we can just divide both sides by 6 hours .
|
what exactly is `` constant of variation '' ?
|
so , in this problem , they 're telling us in outer space , the distance an object travels varies directly with the amount of time that it travels . and , that 's of course assuming that it 's not accelerating , and there 's no net force , and all of that on it . so , i guess they 're talking about a specific object . so , some specific object , the amount , the distance that it travels is directly , it varies directly , it varies directly with the amount of time that it travels . so , if we think of in , in , in terms of constants of proportionality , and direct variation , we could say that the distance , we could say that the distance is equal to some constant , times the time , times the time that it travels . the distance varies directly with the amount of time that travels for this particular object . if an asteroid travels 3000 miles , in , if the asteroid travels 3000 miles in 6 hours , what is the constant of variation ? so the distance is 3000 , so we have d is equal to 3000 miles . we have 3,000 miles is the distance , and that 's going to be equal to the constant of variation . the constant of variation times the time , times 6 hours . so , if we wan na solve for the constant of variation , we can just divide both sides by 6 hours . 6 hours , and we divide the right-hand side by 6 hours . and , so , 3,000 divided by 6 is 500 , and 6 divided by 6 is 1 . the hours also cancel out if you care about the units . and , so , the concept of proportionality , the left-hand side is just 500 , 500 , and then we have miles per hour , miles per hour . fired 500 miles per hour , and that is equal to k. so , the constant proportionality is 500 miles per hour , or you could say 500 if you 're not too worried about the units . or , we should say , the constant of variation , to use the terminology that they actually use in the question .
|
so the distance is 3000 , so we have d is equal to 3000 miles . we have 3,000 miles is the distance , and that 's going to be equal to the constant of variation . the constant of variation times the time , times 6 hours . so , if we wan na solve for the constant of variation , we can just divide both sides by 6 hours .
|
can someone tell me does inverse variation and partial variation means the same thing ?
|
so , in this problem , they 're telling us in outer space , the distance an object travels varies directly with the amount of time that it travels . and , that 's of course assuming that it 's not accelerating , and there 's no net force , and all of that on it . so , i guess they 're talking about a specific object . so , some specific object , the amount , the distance that it travels is directly , it varies directly , it varies directly with the amount of time that it travels . so , if we think of in , in , in terms of constants of proportionality , and direct variation , we could say that the distance , we could say that the distance is equal to some constant , times the time , times the time that it travels . the distance varies directly with the amount of time that travels for this particular object . if an asteroid travels 3000 miles , in , if the asteroid travels 3000 miles in 6 hours , what is the constant of variation ? so the distance is 3000 , so we have d is equal to 3000 miles . we have 3,000 miles is the distance , and that 's going to be equal to the constant of variation . the constant of variation times the time , times 6 hours . so , if we wan na solve for the constant of variation , we can just divide both sides by 6 hours . 6 hours , and we divide the right-hand side by 6 hours . and , so , 3,000 divided by 6 is 500 , and 6 divided by 6 is 1 . the hours also cancel out if you care about the units . and , so , the concept of proportionality , the left-hand side is just 500 , 500 , and then we have miles per hour , miles per hour . fired 500 miles per hour , and that is equal to k. so , the constant proportionality is 500 miles per hour , or you could say 500 if you 're not too worried about the units . or , we should say , the constant of variation , to use the terminology that they actually use in the question .
|
so , some specific object , the amount , the distance that it travels is directly , it varies directly , it varies directly with the amount of time that it travels . so , if we think of in , in , in terms of constants of proportionality , and direct variation , we could say that the distance , we could say that the distance is equal to some constant , times the time , times the time that it travels . the distance varies directly with the amount of time that travels for this particular object .
|
could someone please explain how direct and direct variation works when there is a square root or squared variable ?
|
so , in this problem , they 're telling us in outer space , the distance an object travels varies directly with the amount of time that it travels . and , that 's of course assuming that it 's not accelerating , and there 's no net force , and all of that on it . so , i guess they 're talking about a specific object . so , some specific object , the amount , the distance that it travels is directly , it varies directly , it varies directly with the amount of time that it travels . so , if we think of in , in , in terms of constants of proportionality , and direct variation , we could say that the distance , we could say that the distance is equal to some constant , times the time , times the time that it travels . the distance varies directly with the amount of time that travels for this particular object . if an asteroid travels 3000 miles , in , if the asteroid travels 3000 miles in 6 hours , what is the constant of variation ? so the distance is 3000 , so we have d is equal to 3000 miles . we have 3,000 miles is the distance , and that 's going to be equal to the constant of variation . the constant of variation times the time , times 6 hours . so , if we wan na solve for the constant of variation , we can just divide both sides by 6 hours . 6 hours , and we divide the right-hand side by 6 hours . and , so , 3,000 divided by 6 is 500 , and 6 divided by 6 is 1 . the hours also cancel out if you care about the units . and , so , the concept of proportionality , the left-hand side is just 500 , 500 , and then we have miles per hour , miles per hour . fired 500 miles per hour , and that is equal to k. so , the constant proportionality is 500 miles per hour , or you could say 500 if you 're not too worried about the units . or , we should say , the constant of variation , to use the terminology that they actually use in the question .
|
so , i guess they 're talking about a specific object . so , some specific object , the amount , the distance that it travels is directly , it varies directly , it varies directly with the amount of time that it travels . so , if we think of in , in , in terms of constants of proportionality , and direct variation , we could say that the distance , we could say that the distance is equal to some constant , times the time , times the time that it travels .
|
if the cost of a telephone conversation varies directly as the length of the time of conversation , and if the cost of six minutes is $ 0.90 , what would be the cost for a nine-minute call ?
|
so , in this problem , they 're telling us in outer space , the distance an object travels varies directly with the amount of time that it travels . and , that 's of course assuming that it 's not accelerating , and there 's no net force , and all of that on it . so , i guess they 're talking about a specific object . so , some specific object , the amount , the distance that it travels is directly , it varies directly , it varies directly with the amount of time that it travels . so , if we think of in , in , in terms of constants of proportionality , and direct variation , we could say that the distance , we could say that the distance is equal to some constant , times the time , times the time that it travels . the distance varies directly with the amount of time that travels for this particular object . if an asteroid travels 3000 miles , in , if the asteroid travels 3000 miles in 6 hours , what is the constant of variation ? so the distance is 3000 , so we have d is equal to 3000 miles . we have 3,000 miles is the distance , and that 's going to be equal to the constant of variation . the constant of variation times the time , times 6 hours . so , if we wan na solve for the constant of variation , we can just divide both sides by 6 hours . 6 hours , and we divide the right-hand side by 6 hours . and , so , 3,000 divided by 6 is 500 , and 6 divided by 6 is 1 . the hours also cancel out if you care about the units . and , so , the concept of proportionality , the left-hand side is just 500 , 500 , and then we have miles per hour , miles per hour . fired 500 miles per hour , and that is equal to k. so , the constant proportionality is 500 miles per hour , or you could say 500 if you 're not too worried about the units . or , we should say , the constant of variation , to use the terminology that they actually use in the question .
|
6 hours , and we divide the right-hand side by 6 hours . and , so , 3,000 divided by 6 is 500 , and 6 divided by 6 is 1 . the hours also cancel out if you care about the units .
|
if 4 men and 2 boys do a piece of work in 8 days and 2 men and 4 boys do the same work in 6 days , then how much time would 1 man and 1 boy take to complete the work ?
|
so , in this problem , they 're telling us in outer space , the distance an object travels varies directly with the amount of time that it travels . and , that 's of course assuming that it 's not accelerating , and there 's no net force , and all of that on it . so , i guess they 're talking about a specific object . so , some specific object , the amount , the distance that it travels is directly , it varies directly , it varies directly with the amount of time that it travels . so , if we think of in , in , in terms of constants of proportionality , and direct variation , we could say that the distance , we could say that the distance is equal to some constant , times the time , times the time that it travels . the distance varies directly with the amount of time that travels for this particular object . if an asteroid travels 3000 miles , in , if the asteroid travels 3000 miles in 6 hours , what is the constant of variation ? so the distance is 3000 , so we have d is equal to 3000 miles . we have 3,000 miles is the distance , and that 's going to be equal to the constant of variation . the constant of variation times the time , times 6 hours . so , if we wan na solve for the constant of variation , we can just divide both sides by 6 hours . 6 hours , and we divide the right-hand side by 6 hours . and , so , 3,000 divided by 6 is 500 , and 6 divided by 6 is 1 . the hours also cancel out if you care about the units . and , so , the concept of proportionality , the left-hand side is just 500 , 500 , and then we have miles per hour , miles per hour . fired 500 miles per hour , and that is equal to k. so , the constant proportionality is 500 miles per hour , or you could say 500 if you 're not too worried about the units . or , we should say , the constant of variation , to use the terminology that they actually use in the question .
|
and , so , the concept of proportionality , the left-hand side is just 500 , 500 , and then we have miles per hour , miles per hour . fired 500 miles per hour , and that is equal to k. so , the constant proportionality is 500 miles per hour , or you could say 500 if you 're not too worried about the units . or , we should say , the constant of variation , to use the terminology that they actually use in the question .
|
how do i know which is x , y , or k ?
|
so , in this problem , they 're telling us in outer space , the distance an object travels varies directly with the amount of time that it travels . and , that 's of course assuming that it 's not accelerating , and there 's no net force , and all of that on it . so , i guess they 're talking about a specific object . so , some specific object , the amount , the distance that it travels is directly , it varies directly , it varies directly with the amount of time that it travels . so , if we think of in , in , in terms of constants of proportionality , and direct variation , we could say that the distance , we could say that the distance is equal to some constant , times the time , times the time that it travels . the distance varies directly with the amount of time that travels for this particular object . if an asteroid travels 3000 miles , in , if the asteroid travels 3000 miles in 6 hours , what is the constant of variation ? so the distance is 3000 , so we have d is equal to 3000 miles . we have 3,000 miles is the distance , and that 's going to be equal to the constant of variation . the constant of variation times the time , times 6 hours . so , if we wan na solve for the constant of variation , we can just divide both sides by 6 hours . 6 hours , and we divide the right-hand side by 6 hours . and , so , 3,000 divided by 6 is 500 , and 6 divided by 6 is 1 . the hours also cancel out if you care about the units . and , so , the concept of proportionality , the left-hand side is just 500 , 500 , and then we have miles per hour , miles per hour . fired 500 miles per hour , and that is equal to k. so , the constant proportionality is 500 miles per hour , or you could say 500 if you 're not too worried about the units . or , we should say , the constant of variation , to use the terminology that they actually use in the question .
|
so , in this problem , they 're telling us in outer space , the distance an object travels varies directly with the amount of time that it travels . and , that 's of course assuming that it 's not accelerating , and there 's no net force , and all of that on it .
|
if x increases by 20 % , what will be the corresponding change in y ?
|
so , in this problem , they 're telling us in outer space , the distance an object travels varies directly with the amount of time that it travels . and , that 's of course assuming that it 's not accelerating , and there 's no net force , and all of that on it . so , i guess they 're talking about a specific object . so , some specific object , the amount , the distance that it travels is directly , it varies directly , it varies directly with the amount of time that it travels . so , if we think of in , in , in terms of constants of proportionality , and direct variation , we could say that the distance , we could say that the distance is equal to some constant , times the time , times the time that it travels . the distance varies directly with the amount of time that travels for this particular object . if an asteroid travels 3000 miles , in , if the asteroid travels 3000 miles in 6 hours , what is the constant of variation ? so the distance is 3000 , so we have d is equal to 3000 miles . we have 3,000 miles is the distance , and that 's going to be equal to the constant of variation . the constant of variation times the time , times 6 hours . so , if we wan na solve for the constant of variation , we can just divide both sides by 6 hours . 6 hours , and we divide the right-hand side by 6 hours . and , so , 3,000 divided by 6 is 500 , and 6 divided by 6 is 1 . the hours also cancel out if you care about the units . and , so , the concept of proportionality , the left-hand side is just 500 , 500 , and then we have miles per hour , miles per hour . fired 500 miles per hour , and that is equal to k. so , the constant proportionality is 500 miles per hour , or you could say 500 if you 're not too worried about the units . or , we should say , the constant of variation , to use the terminology that they actually use in the question .
|
so the distance is 3000 , so we have d is equal to 3000 miles . we have 3,000 miles is the distance , and that 's going to be equal to the constant of variation . the constant of variation times the time , times 6 hours . so , if we wan na solve for the constant of variation , we can just divide both sides by 6 hours .
|
what is the constant variation of y=3x ?
|
consider the following coordinate pairs . and they give us a bunch right over here . which of those pairs is not graphed below ? so let 's see , 3 comma negative 2 . so 3 comma negative 2 , well , actually , that looks like that first one is not graphed . so 3 comma negative 2 is n't graphed . and you can verify that all of these others do seem to be graphed . 4 comma negative 8 is right there . negative 8 comma 3 is right over here . 4 comma 6 is right there . and negative 1 comma 0 is right there . so let 's do a couple more of these . so is negative 5 comma 0 graphed ? yep . it 's right over there . negative 4 comma positive 5 should be there . so that 's not graphed . so let me just select that one . let 's do one more of these . negative 8 comma 4 , so negative 8 comma 4 , we got lucky . the first one is not graphed -- negative 8 comma 4 . and we 're done .
|
which of those pairs is not graphed below ? so let 's see , 3 comma negative 2 . so 3 comma negative 2 , well , actually , that looks like that first one is not graphed .
|
where would 2 1/2 go on the plane ?
|
consider the following coordinate pairs . and they give us a bunch right over here . which of those pairs is not graphed below ? so let 's see , 3 comma negative 2 . so 3 comma negative 2 , well , actually , that looks like that first one is not graphed . so 3 comma negative 2 is n't graphed . and you can verify that all of these others do seem to be graphed . 4 comma negative 8 is right there . negative 8 comma 3 is right over here . 4 comma 6 is right there . and negative 1 comma 0 is right there . so let 's do a couple more of these . so is negative 5 comma 0 graphed ? yep . it 's right over there . negative 4 comma positive 5 should be there . so that 's not graphed . so let me just select that one . let 's do one more of these . negative 8 comma 4 , so negative 8 comma 4 , we got lucky . the first one is not graphed -- negative 8 comma 4 . and we 're done .
|
so let 's do a couple more of these . so is negative 5 comma 0 graphed ? yep .
|
how does this skill apply in real life ?
|
consider the following coordinate pairs . and they give us a bunch right over here . which of those pairs is not graphed below ? so let 's see , 3 comma negative 2 . so 3 comma negative 2 , well , actually , that looks like that first one is not graphed . so 3 comma negative 2 is n't graphed . and you can verify that all of these others do seem to be graphed . 4 comma negative 8 is right there . negative 8 comma 3 is right over here . 4 comma 6 is right there . and negative 1 comma 0 is right there . so let 's do a couple more of these . so is negative 5 comma 0 graphed ? yep . it 's right over there . negative 4 comma positive 5 should be there . so that 's not graphed . so let me just select that one . let 's do one more of these . negative 8 comma 4 , so negative 8 comma 4 , we got lucky . the first one is not graphed -- negative 8 comma 4 . and we 're done .
|
consider the following coordinate pairs . and they give us a bunch right over here .
|
how do you do a coordinate pair that is in the middle of 2 numbers ?
|
consider the following coordinate pairs . and they give us a bunch right over here . which of those pairs is not graphed below ? so let 's see , 3 comma negative 2 . so 3 comma negative 2 , well , actually , that looks like that first one is not graphed . so 3 comma negative 2 is n't graphed . and you can verify that all of these others do seem to be graphed . 4 comma negative 8 is right there . negative 8 comma 3 is right over here . 4 comma 6 is right there . and negative 1 comma 0 is right there . so let 's do a couple more of these . so is negative 5 comma 0 graphed ? yep . it 's right over there . negative 4 comma positive 5 should be there . so that 's not graphed . so let me just select that one . let 's do one more of these . negative 8 comma 4 , so negative 8 comma 4 , we got lucky . the first one is not graphed -- negative 8 comma 4 . and we 're done .
|
let 's do one more of these . negative 8 comma 4 , so negative 8 comma 4 , we got lucky . the first one is not graphed -- negative 8 comma 4 .
|
which quadrant would ( 0 , -4 ) go in ?
|
consider the following coordinate pairs . and they give us a bunch right over here . which of those pairs is not graphed below ? so let 's see , 3 comma negative 2 . so 3 comma negative 2 , well , actually , that looks like that first one is not graphed . so 3 comma negative 2 is n't graphed . and you can verify that all of these others do seem to be graphed . 4 comma negative 8 is right there . negative 8 comma 3 is right over here . 4 comma 6 is right there . and negative 1 comma 0 is right there . so let 's do a couple more of these . so is negative 5 comma 0 graphed ? yep . it 's right over there . negative 4 comma positive 5 should be there . so that 's not graphed . so let me just select that one . let 's do one more of these . negative 8 comma 4 , so negative 8 comma 4 , we got lucky . the first one is not graphed -- negative 8 comma 4 . and we 're done .
|
4 comma 6 is right there . and negative 1 comma 0 is right there . so let 's do a couple more of these .
|
and which quadrant would ( 1,1/2 ) go in ?
|
consider the following coordinate pairs . and they give us a bunch right over here . which of those pairs is not graphed below ? so let 's see , 3 comma negative 2 . so 3 comma negative 2 , well , actually , that looks like that first one is not graphed . so 3 comma negative 2 is n't graphed . and you can verify that all of these others do seem to be graphed . 4 comma negative 8 is right there . negative 8 comma 3 is right over here . 4 comma 6 is right there . and negative 1 comma 0 is right there . so let 's do a couple more of these . so is negative 5 comma 0 graphed ? yep . it 's right over there . negative 4 comma positive 5 should be there . so that 's not graphed . so let me just select that one . let 's do one more of these . negative 8 comma 4 , so negative 8 comma 4 , we got lucky . the first one is not graphed -- negative 8 comma 4 . and we 're done .
|
so let 's do a couple more of these . so is negative 5 comma 0 graphed ? yep .
|
i understand the four quadrants already but where would the point ( 0,0 ) lie in ?
|
consider the following coordinate pairs . and they give us a bunch right over here . which of those pairs is not graphed below ? so let 's see , 3 comma negative 2 . so 3 comma negative 2 , well , actually , that looks like that first one is not graphed . so 3 comma negative 2 is n't graphed . and you can verify that all of these others do seem to be graphed . 4 comma negative 8 is right there . negative 8 comma 3 is right over here . 4 comma 6 is right there . and negative 1 comma 0 is right there . so let 's do a couple more of these . so is negative 5 comma 0 graphed ? yep . it 's right over there . negative 4 comma positive 5 should be there . so that 's not graphed . so let me just select that one . let 's do one more of these . negative 8 comma 4 , so negative 8 comma 4 , we got lucky . the first one is not graphed -- negative 8 comma 4 . and we 're done .
|
negative 8 comma 4 , so negative 8 comma 4 , we got lucky . the first one is not graphed -- negative 8 comma 4 . and we 're done .
|
how do you know which number to put first in the pair ?
|
consider the following coordinate pairs . and they give us a bunch right over here . which of those pairs is not graphed below ? so let 's see , 3 comma negative 2 . so 3 comma negative 2 , well , actually , that looks like that first one is not graphed . so 3 comma negative 2 is n't graphed . and you can verify that all of these others do seem to be graphed . 4 comma negative 8 is right there . negative 8 comma 3 is right over here . 4 comma 6 is right there . and negative 1 comma 0 is right there . so let 's do a couple more of these . so is negative 5 comma 0 graphed ? yep . it 's right over there . negative 4 comma positive 5 should be there . so that 's not graphed . so let me just select that one . let 's do one more of these . negative 8 comma 4 , so negative 8 comma 4 , we got lucky . the first one is not graphed -- negative 8 comma 4 . and we 're done .
|
consider the following coordinate pairs . and they give us a bunch right over here .
|
hoe do you place fractions on a coordinate grid ?
|
consider the following coordinate pairs . and they give us a bunch right over here . which of those pairs is not graphed below ? so let 's see , 3 comma negative 2 . so 3 comma negative 2 , well , actually , that looks like that first one is not graphed . so 3 comma negative 2 is n't graphed . and you can verify that all of these others do seem to be graphed . 4 comma negative 8 is right there . negative 8 comma 3 is right over here . 4 comma 6 is right there . and negative 1 comma 0 is right there . so let 's do a couple more of these . so is negative 5 comma 0 graphed ? yep . it 's right over there . negative 4 comma positive 5 should be there . so that 's not graphed . so let me just select that one . let 's do one more of these . negative 8 comma 4 , so negative 8 comma 4 , we got lucky . the first one is not graphed -- negative 8 comma 4 . and we 're done .
|
and you can verify that all of these others do seem to be graphed . 4 comma negative 8 is right there . negative 8 comma 3 is right over here .
|
and when i clicked on check the answer it said i was wrong and i do n't know why i have to drag the orange dot to a specific negative or positive line for my answer to be right why cant i just plot the orange dot on a random line and not get my answer right ?
|
consider the following coordinate pairs . and they give us a bunch right over here . which of those pairs is not graphed below ? so let 's see , 3 comma negative 2 . so 3 comma negative 2 , well , actually , that looks like that first one is not graphed . so 3 comma negative 2 is n't graphed . and you can verify that all of these others do seem to be graphed . 4 comma negative 8 is right there . negative 8 comma 3 is right over here . 4 comma 6 is right there . and negative 1 comma 0 is right there . so let 's do a couple more of these . so is negative 5 comma 0 graphed ? yep . it 's right over there . negative 4 comma positive 5 should be there . so that 's not graphed . so let me just select that one . let 's do one more of these . negative 8 comma 4 , so negative 8 comma 4 , we got lucky . the first one is not graphed -- negative 8 comma 4 . and we 're done .
|
let 's do one more of these . negative 8 comma 4 , so negative 8 comma 4 , we got lucky . the first one is not graphed -- negative 8 comma 4 .
|
what quadrant for ( -4 1/2,7 ) be in ?
|
consider the following coordinate pairs . and they give us a bunch right over here . which of those pairs is not graphed below ? so let 's see , 3 comma negative 2 . so 3 comma negative 2 , well , actually , that looks like that first one is not graphed . so 3 comma negative 2 is n't graphed . and you can verify that all of these others do seem to be graphed . 4 comma negative 8 is right there . negative 8 comma 3 is right over here . 4 comma 6 is right there . and negative 1 comma 0 is right there . so let 's do a couple more of these . so is negative 5 comma 0 graphed ? yep . it 's right over there . negative 4 comma positive 5 should be there . so that 's not graphed . so let me just select that one . let 's do one more of these . negative 8 comma 4 , so negative 8 comma 4 , we got lucky . the first one is not graphed -- negative 8 comma 4 . and we 're done .
|
it 's right over there . negative 4 comma positive 5 should be there . so that 's not graphed .
|
how do know were the negative and the positive are ?
|
consider the following coordinate pairs . and they give us a bunch right over here . which of those pairs is not graphed below ? so let 's see , 3 comma negative 2 . so 3 comma negative 2 , well , actually , that looks like that first one is not graphed . so 3 comma negative 2 is n't graphed . and you can verify that all of these others do seem to be graphed . 4 comma negative 8 is right there . negative 8 comma 3 is right over here . 4 comma 6 is right there . and negative 1 comma 0 is right there . so let 's do a couple more of these . so is negative 5 comma 0 graphed ? yep . it 's right over there . negative 4 comma positive 5 should be there . so that 's not graphed . so let me just select that one . let 's do one more of these . negative 8 comma 4 , so negative 8 comma 4 , we got lucky . the first one is not graphed -- negative 8 comma 4 . and we 're done .
|
negative 8 comma 4 , so negative 8 comma 4 , we got lucky . the first one is not graphed -- negative 8 comma 4 . and we 're done .
|
how do you know which number goes first ?
|
consider the following coordinate pairs . and they give us a bunch right over here . which of those pairs is not graphed below ? so let 's see , 3 comma negative 2 . so 3 comma negative 2 , well , actually , that looks like that first one is not graphed . so 3 comma negative 2 is n't graphed . and you can verify that all of these others do seem to be graphed . 4 comma negative 8 is right there . negative 8 comma 3 is right over here . 4 comma 6 is right there . and negative 1 comma 0 is right there . so let 's do a couple more of these . so is negative 5 comma 0 graphed ? yep . it 's right over there . negative 4 comma positive 5 should be there . so that 's not graphed . so let me just select that one . let 's do one more of these . negative 8 comma 4 , so negative 8 comma 4 , we got lucky . the first one is not graphed -- negative 8 comma 4 . and we 're done .
|
so that 's not graphed . so let me just select that one . let 's do one more of these .
|
how is one supposed to be good at math ?
|
consider the following coordinate pairs . and they give us a bunch right over here . which of those pairs is not graphed below ? so let 's see , 3 comma negative 2 . so 3 comma negative 2 , well , actually , that looks like that first one is not graphed . so 3 comma negative 2 is n't graphed . and you can verify that all of these others do seem to be graphed . 4 comma negative 8 is right there . negative 8 comma 3 is right over here . 4 comma 6 is right there . and negative 1 comma 0 is right there . so let 's do a couple more of these . so is negative 5 comma 0 graphed ? yep . it 's right over there . negative 4 comma positive 5 should be there . so that 's not graphed . so let me just select that one . let 's do one more of these . negative 8 comma 4 , so negative 8 comma 4 , we got lucky . the first one is not graphed -- negative 8 comma 4 . and we 're done .
|
consider the following coordinate pairs . and they give us a bunch right over here .
|
btw how do you make a ''play '' symbel ?
|
consider the following coordinate pairs . and they give us a bunch right over here . which of those pairs is not graphed below ? so let 's see , 3 comma negative 2 . so 3 comma negative 2 , well , actually , that looks like that first one is not graphed . so 3 comma negative 2 is n't graphed . and you can verify that all of these others do seem to be graphed . 4 comma negative 8 is right there . negative 8 comma 3 is right over here . 4 comma 6 is right there . and negative 1 comma 0 is right there . so let 's do a couple more of these . so is negative 5 comma 0 graphed ? yep . it 's right over there . negative 4 comma positive 5 should be there . so that 's not graphed . so let me just select that one . let 's do one more of these . negative 8 comma 4 , so negative 8 comma 4 , we got lucky . the first one is not graphed -- negative 8 comma 4 . and we 're done .
|
so let 's do a couple more of these . so is negative 5 comma 0 graphed ? yep .
|
which quadrant would the origin ( 0,0 ) be in ?
|
consider the following coordinate pairs . and they give us a bunch right over here . which of those pairs is not graphed below ? so let 's see , 3 comma negative 2 . so 3 comma negative 2 , well , actually , that looks like that first one is not graphed . so 3 comma negative 2 is n't graphed . and you can verify that all of these others do seem to be graphed . 4 comma negative 8 is right there . negative 8 comma 3 is right over here . 4 comma 6 is right there . and negative 1 comma 0 is right there . so let 's do a couple more of these . so is negative 5 comma 0 graphed ? yep . it 's right over there . negative 4 comma positive 5 should be there . so that 's not graphed . so let me just select that one . let 's do one more of these . negative 8 comma 4 , so negative 8 comma 4 , we got lucky . the first one is not graphed -- negative 8 comma 4 . and we 're done .
|
consider the following coordinate pairs . and they give us a bunch right over here .
|
what if the x and y coordinates are in the middle of a number ?
|
consider the following coordinate pairs . and they give us a bunch right over here . which of those pairs is not graphed below ? so let 's see , 3 comma negative 2 . so 3 comma negative 2 , well , actually , that looks like that first one is not graphed . so 3 comma negative 2 is n't graphed . and you can verify that all of these others do seem to be graphed . 4 comma negative 8 is right there . negative 8 comma 3 is right over here . 4 comma 6 is right there . and negative 1 comma 0 is right there . so let 's do a couple more of these . so is negative 5 comma 0 graphed ? yep . it 's right over there . negative 4 comma positive 5 should be there . so that 's not graphed . so let me just select that one . let 's do one more of these . negative 8 comma 4 , so negative 8 comma 4 , we got lucky . the first one is not graphed -- negative 8 comma 4 . and we 're done .
|
consider the following coordinate pairs . and they give us a bunch right over here .
|
were is the fraction coordinate plane at ?
|
consider the following coordinate pairs . and they give us a bunch right over here . which of those pairs is not graphed below ? so let 's see , 3 comma negative 2 . so 3 comma negative 2 , well , actually , that looks like that first one is not graphed . so 3 comma negative 2 is n't graphed . and you can verify that all of these others do seem to be graphed . 4 comma negative 8 is right there . negative 8 comma 3 is right over here . 4 comma 6 is right there . and negative 1 comma 0 is right there . so let 's do a couple more of these . so is negative 5 comma 0 graphed ? yep . it 's right over there . negative 4 comma positive 5 should be there . so that 's not graphed . so let me just select that one . let 's do one more of these . negative 8 comma 4 , so negative 8 comma 4 , we got lucky . the first one is not graphed -- negative 8 comma 4 . and we 're done .
|
consider the following coordinate pairs . and they give us a bunch right over here .
|
how many quadrants can a line graph have ?
|
consider the following coordinate pairs . and they give us a bunch right over here . which of those pairs is not graphed below ? so let 's see , 3 comma negative 2 . so 3 comma negative 2 , well , actually , that looks like that first one is not graphed . so 3 comma negative 2 is n't graphed . and you can verify that all of these others do seem to be graphed . 4 comma negative 8 is right there . negative 8 comma 3 is right over here . 4 comma 6 is right there . and negative 1 comma 0 is right there . so let 's do a couple more of these . so is negative 5 comma 0 graphed ? yep . it 's right over there . negative 4 comma positive 5 should be there . so that 's not graphed . so let me just select that one . let 's do one more of these . negative 8 comma 4 , so negative 8 comma 4 , we got lucky . the first one is not graphed -- negative 8 comma 4 . and we 're done .
|
consider the following coordinate pairs . and they give us a bunch right over here .
|
re ordered pairs : when letters of the alphabet are used in an equation , is it always the case that the letters are expressed as an ordered pair in the same order as they are in the alphabet ?
|
consider the following coordinate pairs . and they give us a bunch right over here . which of those pairs is not graphed below ? so let 's see , 3 comma negative 2 . so 3 comma negative 2 , well , actually , that looks like that first one is not graphed . so 3 comma negative 2 is n't graphed . and you can verify that all of these others do seem to be graphed . 4 comma negative 8 is right there . negative 8 comma 3 is right over here . 4 comma 6 is right there . and negative 1 comma 0 is right there . so let 's do a couple more of these . so is negative 5 comma 0 graphed ? yep . it 's right over there . negative 4 comma positive 5 should be there . so that 's not graphed . so let me just select that one . let 's do one more of these . negative 8 comma 4 , so negative 8 comma 4 , we got lucky . the first one is not graphed -- negative 8 comma 4 . and we 're done .
|
negative 8 comma 4 , so negative 8 comma 4 , we got lucky . the first one is not graphed -- negative 8 comma 4 . and we 're done .
|
is y ever considered the first component in the ordered pair ?
|
consider the following coordinate pairs . and they give us a bunch right over here . which of those pairs is not graphed below ? so let 's see , 3 comma negative 2 . so 3 comma negative 2 , well , actually , that looks like that first one is not graphed . so 3 comma negative 2 is n't graphed . and you can verify that all of these others do seem to be graphed . 4 comma negative 8 is right there . negative 8 comma 3 is right over here . 4 comma 6 is right there . and negative 1 comma 0 is right there . so let 's do a couple more of these . so is negative 5 comma 0 graphed ? yep . it 's right over there . negative 4 comma positive 5 should be there . so that 's not graphed . so let me just select that one . let 's do one more of these . negative 8 comma 4 , so negative 8 comma 4 , we got lucky . the first one is not graphed -- negative 8 comma 4 . and we 're done .
|
consider the following coordinate pairs . and they give us a bunch right over here .
|
how do you know which box you need to go in ?
|
consider the following coordinate pairs . and they give us a bunch right over here . which of those pairs is not graphed below ? so let 's see , 3 comma negative 2 . so 3 comma negative 2 , well , actually , that looks like that first one is not graphed . so 3 comma negative 2 is n't graphed . and you can verify that all of these others do seem to be graphed . 4 comma negative 8 is right there . negative 8 comma 3 is right over here . 4 comma 6 is right there . and negative 1 comma 0 is right there . so let 's do a couple more of these . so is negative 5 comma 0 graphed ? yep . it 's right over there . negative 4 comma positive 5 should be there . so that 's not graphed . so let me just select that one . let 's do one more of these . negative 8 comma 4 , so negative 8 comma 4 , we got lucky . the first one is not graphed -- negative 8 comma 4 . and we 're done .
|
consider the following coordinate pairs . and they give us a bunch right over here .
|
when the coordinate pairs are not in order , does that change the way the problem is made ?
|
consider the following coordinate pairs . and they give us a bunch right over here . which of those pairs is not graphed below ? so let 's see , 3 comma negative 2 . so 3 comma negative 2 , well , actually , that looks like that first one is not graphed . so 3 comma negative 2 is n't graphed . and you can verify that all of these others do seem to be graphed . 4 comma negative 8 is right there . negative 8 comma 3 is right over here . 4 comma 6 is right there . and negative 1 comma 0 is right there . so let 's do a couple more of these . so is negative 5 comma 0 graphed ? yep . it 's right over there . negative 4 comma positive 5 should be there . so that 's not graphed . so let me just select that one . let 's do one more of these . negative 8 comma 4 , so negative 8 comma 4 , we got lucky . the first one is not graphed -- negative 8 comma 4 . and we 're done .
|
it 's right over there . negative 4 comma positive 5 should be there . so that 's not graphed .
|
so will anything on the positive axis be in quadrant 1 , anything on the negative y axis on quadrant 2 , anything on the positive x axis on quadrant 1 , and anything on the negative x axis be in quadrant 4 ?
|
consider the following coordinate pairs . and they give us a bunch right over here . which of those pairs is not graphed below ? so let 's see , 3 comma negative 2 . so 3 comma negative 2 , well , actually , that looks like that first one is not graphed . so 3 comma negative 2 is n't graphed . and you can verify that all of these others do seem to be graphed . 4 comma negative 8 is right there . negative 8 comma 3 is right over here . 4 comma 6 is right there . and negative 1 comma 0 is right there . so let 's do a couple more of these . so is negative 5 comma 0 graphed ? yep . it 's right over there . negative 4 comma positive 5 should be there . so that 's not graphed . so let me just select that one . let 's do one more of these . negative 8 comma 4 , so negative 8 comma 4 , we got lucky . the first one is not graphed -- negative 8 comma 4 . and we 're done .
|
so that 's not graphed . so let me just select that one . let 's do one more of these .
|
how do you know witch is witch if you think there are two correct ansewers to you , but it says that there is only one ?
|
consider the following coordinate pairs . and they give us a bunch right over here . which of those pairs is not graphed below ? so let 's see , 3 comma negative 2 . so 3 comma negative 2 , well , actually , that looks like that first one is not graphed . so 3 comma negative 2 is n't graphed . and you can verify that all of these others do seem to be graphed . 4 comma negative 8 is right there . negative 8 comma 3 is right over here . 4 comma 6 is right there . and negative 1 comma 0 is right there . so let 's do a couple more of these . so is negative 5 comma 0 graphed ? yep . it 's right over there . negative 4 comma positive 5 should be there . so that 's not graphed . so let me just select that one . let 's do one more of these . negative 8 comma 4 , so negative 8 comma 4 , we got lucky . the first one is not graphed -- negative 8 comma 4 . and we 're done .
|
consider the following coordinate pairs . and they give us a bunch right over here .
|
how do you find the negitves ?
|
( piano jazz music ) we 're in the galleries at the crystal bridges museum of american art . i 'm seeing this beautiful , luminous mark rothko . it 's number 210 , number 211 , orange and it dates to 1960 . it is hard for me to verbalize my relationship with this painting . it just makes me want to be quiet . it surrounds me even though it is a flat plain where these orange rectangles and squares hover and vibrate against this lavendery but dark purple field . it makes my whole body feel like it 's vibrating . quiet , contemplative , is exactly how i feel . it almost feels like an intrusion that we 're speaking in front of the painting . there 's something about the horizontals of the forms that make everything feel as if they 're moving ever so slowly , almost the way the clouds form and un-form . and the way in which those forms fill the space but then push out forward and then recede also simultaneously back into the pictorial space is slow and gentle and densely aesthetic . how can something painted so flatly , though we see a lot of brushstrokes in it , it creates this deep illusionistic space . it really seems to be basically two colors and yet each of those colors are seen infinitely modulated . there are so many yellows and oranges within those spaces and then even the purple that functions both as a space that the orange can occupy but then somehow also as a frame . it 's got an infinite set of variations . rothko , by the time he painted this in 1960 had been painting abstractly for 20 years and yet in that practice there 's similarities but no picture is the same . and in this particular one , you see these shifting shapes and there are places where the orange is more densely painted and other places where it 's really thin so that because it is painted entirely purple underneath , that you also get the sense of a veil . it 's really instructive to look at the decisions that rothko made and i find especially intriguing the edges of the orange , the way in which they feather and the complexity of the relationship that he draws between the purple and the orange . this idea that pure color in pure form could resonate in a way that was spiritual , that was profound was central to some of the thinking of the abstract expressionists and i think especially important to rothko . the idea that this was a painting that would elicit deep human emotion . in the mid 20th century there is less conversation around spirituality in art and rothko was throughout his career concerned with thinking about painting and its relationship to the spiritual . and not being connected to any kind of specific religious dogma , but rather , that much larger idea about there being something larger than us and where do we or how do we stand in relationship to it . this is painting that develops in the post war era at a moment when society had some fundamental questions in front of it . this was the aftermath of the holocaust , this was the aftermath of atomic weaponry , this is a moment when important philosophical questions are being asked and rothko is confronting those but is not using the visual vocabulary of a past era . he 's not showing angels . he 's thinking about how is it possible to touch the spiritual in our modern age . and thinking about the year of this painting , 1960 , this is a fiery orange painting and this is just as the civil rights movement and so much activism was literally catching fire . and i think that we ca n't ignore that combination and its possibilities of being on rothko 's mind . so this is a spiritual and transcendent painting but it is very much a product of this moment . ( piano jazz music )
|
( piano jazz music ) we 're in the galleries at the crystal bridges museum of american art . i 'm seeing this beautiful , luminous mark rothko .
|
or the heart of a volcano ?
|
there are four different types of animal tissue that are all made up of eukaryotic cells . epithelial tissue , connective tissue , muscle tissue and nervous tissue . in this video we 're gon na talk about epithelial tissue and connective tissue . when you think about epithelial tissue you can think about it as a lining . both an inner lining and an outer lining . so for example , epithelial tissue makes up the outer layer of our skin . it makes up the outer layer of organs . it lines organs so the lumen of organs will be lined with epithelial tissue and it also lines the inside of cavities , inside of the cavities of the organism . epithelial tissue also make up glands so that would include both exocrine glands and endocrine glands . and just to remind you , exocrine glands will release their substances directly to the target organ . whereas endocrine glands usually release hormones but into the bloodstream , not to the target organ directly . and epithelial tissue comes in two forms . it can be simple and that means it 's one layer thick . or it can be stratified which means it can have two or more layers . and where will you expect to find simple epithelium versus stratified epithelium . well , you 'll find simple epithelium in places where substances need to diffuse from two different places . for example the alveoli of the lungs are lined with simple epithelium because carbon dioxide and oxygen need to diffuse from the alveoli into the bloodstream and vice versa . and of course that will be pretty difficult if you had a thick layer of cells . and you 'd expect to find stratified epithelium in places that need to resist chemical or a mechanical stress . for example , the esophagus is lined with stratified epithelium . that 's because the esophagus will have food coming through it . the food might be sharp , it might be hot and we want a thick layer of cells to protect the underlying tissue of the esophagus . a stratified layer epithelium acts as that protective layer . let 's take a look at a section of simple epithelium and epithelial cells are attached to something known as the basement membrane . the basement membrane is not made up of cells but rather it 's made up of different types of fibers . for example one fiber that can be found in the basement membrane is collagen . and the basement membrane is semipermeable to certain substances and that 's pretty important because epithelial tissue is avascular . that means that epithelial cells have no blood vessels which then makes us ask the question of how do they get nutrients ? they get nutrients from the underlying tissue . what happens is that nutrients will diffuse from the underlying tissue through the basement membrane to the epithelial cells . and that 's how epithelial cells get their nutrients . let 's just recap some of the places that you 'd expect to find epithelial cells . we already mentioned the outer layer of the skin , the tissue lining the mouth , esophagus and gi tract and of course this is not an exhaust of list . in the tissue lining the kidney tubules , and the tissue lining blood and lymphatic vessels . and in fact the tissue that lines blood vessels and lymphatic vessels has a special name . it 's known as endothelium . let 's talk about connective tissue . connective tissue supports tissues , connects tissues and separates different types of tissues from each other and then there are different types of connective tissue that do n't necessarily fall into these neat categories . what are some examples of connective tissue ? bones , cartilage , blood , lymph , adipose tissue which is fat . the membranes covering the brain and the spinal cord and other types of tissues . what does connective tissue look like ? what are some characteristics of connective tissue ? basically it has three components . it has cells . it has what 's known as a ground substance and then it has fibers . the ground substance and the fibers together make up a matrix . let 's see what this looks like . here we have the ground substance which is usually a viscous type of fluid . then interspersed in the ground substance are fibers and then we have cells , and these cells are usually what is producing the matrix . let 's look at some connective tissue in more detail . the first we 'll talk about is areolar tissue which is this tissue right over here . areolar tissue is a very common type of connective tissue . it binds together different types of tissue and it provides flexibility and cushioning , and we can actually see the structure pretty clearly in this picture . you can see the cells over there , those little dots . there 's no cell over here . you can see the fibers running through it . over here and over here . and then the ground substance is the kind of background yellow , viscous liquid that you 're seeing . then we have adipose tissue . adipose tissue is basically fat , tissue is a fat . it provides cushioning for the body , it stored energy and it actually is an exception to the rule . it does not have fibers like most other connective tissue . then we have what 's called fibrous connective tissue . fibrous connective tissue is pretty strong . it provides support and shock absorption for bones and organs , and you find it in the dermis which is the middle layer of the skin , tendons and ligaments . here are some more types of connective tissue . we have blood . blood is also an exception like adipose tissue and that it does not contain fibers . and the matrix of blood is the plasma and you can see the matrix , this yellowish liquid in which the blood cells are suspended . then we have osseous tissue or bone tissue . these cells in osseous tissue are known as osteocytes . those are those brown cells that are kind of forming a pattern and the matrix in osseous tissue is what 's known as bone mineral or hydroxyapatite , which is basically collagen fibers with different minerals like phosphates , magnesium , calcium , et cetera . and then we have hyaline cartilage . the cells in hyaline cartilage are chondrocytes . you can see them over here , there are a bunch of these cells . and they 're found in surfaces of joints . these are all examples of different types of connective tissue and many of them provide some form or another of support for tissues and organs .
|
there are four different types of animal tissue that are all made up of eukaryotic cells . epithelial tissue , connective tissue , muscle tissue and nervous tissue . in this video we 're gon na talk about epithelial tissue and connective tissue .
|
which type of epithelial tissue is found in kidney tubules and why ?
|
there are four different types of animal tissue that are all made up of eukaryotic cells . epithelial tissue , connective tissue , muscle tissue and nervous tissue . in this video we 're gon na talk about epithelial tissue and connective tissue . when you think about epithelial tissue you can think about it as a lining . both an inner lining and an outer lining . so for example , epithelial tissue makes up the outer layer of our skin . it makes up the outer layer of organs . it lines organs so the lumen of organs will be lined with epithelial tissue and it also lines the inside of cavities , inside of the cavities of the organism . epithelial tissue also make up glands so that would include both exocrine glands and endocrine glands . and just to remind you , exocrine glands will release their substances directly to the target organ . whereas endocrine glands usually release hormones but into the bloodstream , not to the target organ directly . and epithelial tissue comes in two forms . it can be simple and that means it 's one layer thick . or it can be stratified which means it can have two or more layers . and where will you expect to find simple epithelium versus stratified epithelium . well , you 'll find simple epithelium in places where substances need to diffuse from two different places . for example the alveoli of the lungs are lined with simple epithelium because carbon dioxide and oxygen need to diffuse from the alveoli into the bloodstream and vice versa . and of course that will be pretty difficult if you had a thick layer of cells . and you 'd expect to find stratified epithelium in places that need to resist chemical or a mechanical stress . for example , the esophagus is lined with stratified epithelium . that 's because the esophagus will have food coming through it . the food might be sharp , it might be hot and we want a thick layer of cells to protect the underlying tissue of the esophagus . a stratified layer epithelium acts as that protective layer . let 's take a look at a section of simple epithelium and epithelial cells are attached to something known as the basement membrane . the basement membrane is not made up of cells but rather it 's made up of different types of fibers . for example one fiber that can be found in the basement membrane is collagen . and the basement membrane is semipermeable to certain substances and that 's pretty important because epithelial tissue is avascular . that means that epithelial cells have no blood vessels which then makes us ask the question of how do they get nutrients ? they get nutrients from the underlying tissue . what happens is that nutrients will diffuse from the underlying tissue through the basement membrane to the epithelial cells . and that 's how epithelial cells get their nutrients . let 's just recap some of the places that you 'd expect to find epithelial cells . we already mentioned the outer layer of the skin , the tissue lining the mouth , esophagus and gi tract and of course this is not an exhaust of list . in the tissue lining the kidney tubules , and the tissue lining blood and lymphatic vessels . and in fact the tissue that lines blood vessels and lymphatic vessels has a special name . it 's known as endothelium . let 's talk about connective tissue . connective tissue supports tissues , connects tissues and separates different types of tissues from each other and then there are different types of connective tissue that do n't necessarily fall into these neat categories . what are some examples of connective tissue ? bones , cartilage , blood , lymph , adipose tissue which is fat . the membranes covering the brain and the spinal cord and other types of tissues . what does connective tissue look like ? what are some characteristics of connective tissue ? basically it has three components . it has cells . it has what 's known as a ground substance and then it has fibers . the ground substance and the fibers together make up a matrix . let 's see what this looks like . here we have the ground substance which is usually a viscous type of fluid . then interspersed in the ground substance are fibers and then we have cells , and these cells are usually what is producing the matrix . let 's look at some connective tissue in more detail . the first we 'll talk about is areolar tissue which is this tissue right over here . areolar tissue is a very common type of connective tissue . it binds together different types of tissue and it provides flexibility and cushioning , and we can actually see the structure pretty clearly in this picture . you can see the cells over there , those little dots . there 's no cell over here . you can see the fibers running through it . over here and over here . and then the ground substance is the kind of background yellow , viscous liquid that you 're seeing . then we have adipose tissue . adipose tissue is basically fat , tissue is a fat . it provides cushioning for the body , it stored energy and it actually is an exception to the rule . it does not have fibers like most other connective tissue . then we have what 's called fibrous connective tissue . fibrous connective tissue is pretty strong . it provides support and shock absorption for bones and organs , and you find it in the dermis which is the middle layer of the skin , tendons and ligaments . here are some more types of connective tissue . we have blood . blood is also an exception like adipose tissue and that it does not contain fibers . and the matrix of blood is the plasma and you can see the matrix , this yellowish liquid in which the blood cells are suspended . then we have osseous tissue or bone tissue . these cells in osseous tissue are known as osteocytes . those are those brown cells that are kind of forming a pattern and the matrix in osseous tissue is what 's known as bone mineral or hydroxyapatite , which is basically collagen fibers with different minerals like phosphates , magnesium , calcium , et cetera . and then we have hyaline cartilage . the cells in hyaline cartilage are chondrocytes . you can see them over here , there are a bunch of these cells . and they 're found in surfaces of joints . these are all examples of different types of connective tissue and many of them provide some form or another of support for tissues and organs .
|
basically it has three components . it has cells . it has what 's known as a ground substance and then it has fibers .
|
is the matrix made out of cells ?
|
there are four different types of animal tissue that are all made up of eukaryotic cells . epithelial tissue , connective tissue , muscle tissue and nervous tissue . in this video we 're gon na talk about epithelial tissue and connective tissue . when you think about epithelial tissue you can think about it as a lining . both an inner lining and an outer lining . so for example , epithelial tissue makes up the outer layer of our skin . it makes up the outer layer of organs . it lines organs so the lumen of organs will be lined with epithelial tissue and it also lines the inside of cavities , inside of the cavities of the organism . epithelial tissue also make up glands so that would include both exocrine glands and endocrine glands . and just to remind you , exocrine glands will release their substances directly to the target organ . whereas endocrine glands usually release hormones but into the bloodstream , not to the target organ directly . and epithelial tissue comes in two forms . it can be simple and that means it 's one layer thick . or it can be stratified which means it can have two or more layers . and where will you expect to find simple epithelium versus stratified epithelium . well , you 'll find simple epithelium in places where substances need to diffuse from two different places . for example the alveoli of the lungs are lined with simple epithelium because carbon dioxide and oxygen need to diffuse from the alveoli into the bloodstream and vice versa . and of course that will be pretty difficult if you had a thick layer of cells . and you 'd expect to find stratified epithelium in places that need to resist chemical or a mechanical stress . for example , the esophagus is lined with stratified epithelium . that 's because the esophagus will have food coming through it . the food might be sharp , it might be hot and we want a thick layer of cells to protect the underlying tissue of the esophagus . a stratified layer epithelium acts as that protective layer . let 's take a look at a section of simple epithelium and epithelial cells are attached to something known as the basement membrane . the basement membrane is not made up of cells but rather it 's made up of different types of fibers . for example one fiber that can be found in the basement membrane is collagen . and the basement membrane is semipermeable to certain substances and that 's pretty important because epithelial tissue is avascular . that means that epithelial cells have no blood vessels which then makes us ask the question of how do they get nutrients ? they get nutrients from the underlying tissue . what happens is that nutrients will diffuse from the underlying tissue through the basement membrane to the epithelial cells . and that 's how epithelial cells get their nutrients . let 's just recap some of the places that you 'd expect to find epithelial cells . we already mentioned the outer layer of the skin , the tissue lining the mouth , esophagus and gi tract and of course this is not an exhaust of list . in the tissue lining the kidney tubules , and the tissue lining blood and lymphatic vessels . and in fact the tissue that lines blood vessels and lymphatic vessels has a special name . it 's known as endothelium . let 's talk about connective tissue . connective tissue supports tissues , connects tissues and separates different types of tissues from each other and then there are different types of connective tissue that do n't necessarily fall into these neat categories . what are some examples of connective tissue ? bones , cartilage , blood , lymph , adipose tissue which is fat . the membranes covering the brain and the spinal cord and other types of tissues . what does connective tissue look like ? what are some characteristics of connective tissue ? basically it has three components . it has cells . it has what 's known as a ground substance and then it has fibers . the ground substance and the fibers together make up a matrix . let 's see what this looks like . here we have the ground substance which is usually a viscous type of fluid . then interspersed in the ground substance are fibers and then we have cells , and these cells are usually what is producing the matrix . let 's look at some connective tissue in more detail . the first we 'll talk about is areolar tissue which is this tissue right over here . areolar tissue is a very common type of connective tissue . it binds together different types of tissue and it provides flexibility and cushioning , and we can actually see the structure pretty clearly in this picture . you can see the cells over there , those little dots . there 's no cell over here . you can see the fibers running through it . over here and over here . and then the ground substance is the kind of background yellow , viscous liquid that you 're seeing . then we have adipose tissue . adipose tissue is basically fat , tissue is a fat . it provides cushioning for the body , it stored energy and it actually is an exception to the rule . it does not have fibers like most other connective tissue . then we have what 's called fibrous connective tissue . fibrous connective tissue is pretty strong . it provides support and shock absorption for bones and organs , and you find it in the dermis which is the middle layer of the skin , tendons and ligaments . here are some more types of connective tissue . we have blood . blood is also an exception like adipose tissue and that it does not contain fibers . and the matrix of blood is the plasma and you can see the matrix , this yellowish liquid in which the blood cells are suspended . then we have osseous tissue or bone tissue . these cells in osseous tissue are known as osteocytes . those are those brown cells that are kind of forming a pattern and the matrix in osseous tissue is what 's known as bone mineral or hydroxyapatite , which is basically collagen fibers with different minerals like phosphates , magnesium , calcium , et cetera . and then we have hyaline cartilage . the cells in hyaline cartilage are chondrocytes . you can see them over here , there are a bunch of these cells . and they 're found in surfaces of joints . these are all examples of different types of connective tissue and many of them provide some form or another of support for tissues and organs .
|
blood is also an exception like adipose tissue and that it does not contain fibers . and the matrix of blood is the plasma and you can see the matrix , this yellowish liquid in which the blood cells are suspended . then we have osseous tissue or bone tissue .
|
and what exactly are these `` fibres '' that constitute the matrix ?
|
there are four different types of animal tissue that are all made up of eukaryotic cells . epithelial tissue , connective tissue , muscle tissue and nervous tissue . in this video we 're gon na talk about epithelial tissue and connective tissue . when you think about epithelial tissue you can think about it as a lining . both an inner lining and an outer lining . so for example , epithelial tissue makes up the outer layer of our skin . it makes up the outer layer of organs . it lines organs so the lumen of organs will be lined with epithelial tissue and it also lines the inside of cavities , inside of the cavities of the organism . epithelial tissue also make up glands so that would include both exocrine glands and endocrine glands . and just to remind you , exocrine glands will release their substances directly to the target organ . whereas endocrine glands usually release hormones but into the bloodstream , not to the target organ directly . and epithelial tissue comes in two forms . it can be simple and that means it 's one layer thick . or it can be stratified which means it can have two or more layers . and where will you expect to find simple epithelium versus stratified epithelium . well , you 'll find simple epithelium in places where substances need to diffuse from two different places . for example the alveoli of the lungs are lined with simple epithelium because carbon dioxide and oxygen need to diffuse from the alveoli into the bloodstream and vice versa . and of course that will be pretty difficult if you had a thick layer of cells . and you 'd expect to find stratified epithelium in places that need to resist chemical or a mechanical stress . for example , the esophagus is lined with stratified epithelium . that 's because the esophagus will have food coming through it . the food might be sharp , it might be hot and we want a thick layer of cells to protect the underlying tissue of the esophagus . a stratified layer epithelium acts as that protective layer . let 's take a look at a section of simple epithelium and epithelial cells are attached to something known as the basement membrane . the basement membrane is not made up of cells but rather it 's made up of different types of fibers . for example one fiber that can be found in the basement membrane is collagen . and the basement membrane is semipermeable to certain substances and that 's pretty important because epithelial tissue is avascular . that means that epithelial cells have no blood vessels which then makes us ask the question of how do they get nutrients ? they get nutrients from the underlying tissue . what happens is that nutrients will diffuse from the underlying tissue through the basement membrane to the epithelial cells . and that 's how epithelial cells get their nutrients . let 's just recap some of the places that you 'd expect to find epithelial cells . we already mentioned the outer layer of the skin , the tissue lining the mouth , esophagus and gi tract and of course this is not an exhaust of list . in the tissue lining the kidney tubules , and the tissue lining blood and lymphatic vessels . and in fact the tissue that lines blood vessels and lymphatic vessels has a special name . it 's known as endothelium . let 's talk about connective tissue . connective tissue supports tissues , connects tissues and separates different types of tissues from each other and then there are different types of connective tissue that do n't necessarily fall into these neat categories . what are some examples of connective tissue ? bones , cartilage , blood , lymph , adipose tissue which is fat . the membranes covering the brain and the spinal cord and other types of tissues . what does connective tissue look like ? what are some characteristics of connective tissue ? basically it has three components . it has cells . it has what 's known as a ground substance and then it has fibers . the ground substance and the fibers together make up a matrix . let 's see what this looks like . here we have the ground substance which is usually a viscous type of fluid . then interspersed in the ground substance are fibers and then we have cells , and these cells are usually what is producing the matrix . let 's look at some connective tissue in more detail . the first we 'll talk about is areolar tissue which is this tissue right over here . areolar tissue is a very common type of connective tissue . it binds together different types of tissue and it provides flexibility and cushioning , and we can actually see the structure pretty clearly in this picture . you can see the cells over there , those little dots . there 's no cell over here . you can see the fibers running through it . over here and over here . and then the ground substance is the kind of background yellow , viscous liquid that you 're seeing . then we have adipose tissue . adipose tissue is basically fat , tissue is a fat . it provides cushioning for the body , it stored energy and it actually is an exception to the rule . it does not have fibers like most other connective tissue . then we have what 's called fibrous connective tissue . fibrous connective tissue is pretty strong . it provides support and shock absorption for bones and organs , and you find it in the dermis which is the middle layer of the skin , tendons and ligaments . here are some more types of connective tissue . we have blood . blood is also an exception like adipose tissue and that it does not contain fibers . and the matrix of blood is the plasma and you can see the matrix , this yellowish liquid in which the blood cells are suspended . then we have osseous tissue or bone tissue . these cells in osseous tissue are known as osteocytes . those are those brown cells that are kind of forming a pattern and the matrix in osseous tissue is what 's known as bone mineral or hydroxyapatite , which is basically collagen fibers with different minerals like phosphates , magnesium , calcium , et cetera . and then we have hyaline cartilage . the cells in hyaline cartilage are chondrocytes . you can see them over here , there are a bunch of these cells . and they 're found in surfaces of joints . these are all examples of different types of connective tissue and many of them provide some form or another of support for tissues and organs .
|
there are four different types of animal tissue that are all made up of eukaryotic cells . epithelial tissue , connective tissue , muscle tissue and nervous tissue . in this video we 're gon na talk about epithelial tissue and connective tissue .
|
when the blood has the cell far away from each other , how can it be a connective tissue ?
|
there are four different types of animal tissue that are all made up of eukaryotic cells . epithelial tissue , connective tissue , muscle tissue and nervous tissue . in this video we 're gon na talk about epithelial tissue and connective tissue . when you think about epithelial tissue you can think about it as a lining . both an inner lining and an outer lining . so for example , epithelial tissue makes up the outer layer of our skin . it makes up the outer layer of organs . it lines organs so the lumen of organs will be lined with epithelial tissue and it also lines the inside of cavities , inside of the cavities of the organism . epithelial tissue also make up glands so that would include both exocrine glands and endocrine glands . and just to remind you , exocrine glands will release their substances directly to the target organ . whereas endocrine glands usually release hormones but into the bloodstream , not to the target organ directly . and epithelial tissue comes in two forms . it can be simple and that means it 's one layer thick . or it can be stratified which means it can have two or more layers . and where will you expect to find simple epithelium versus stratified epithelium . well , you 'll find simple epithelium in places where substances need to diffuse from two different places . for example the alveoli of the lungs are lined with simple epithelium because carbon dioxide and oxygen need to diffuse from the alveoli into the bloodstream and vice versa . and of course that will be pretty difficult if you had a thick layer of cells . and you 'd expect to find stratified epithelium in places that need to resist chemical or a mechanical stress . for example , the esophagus is lined with stratified epithelium . that 's because the esophagus will have food coming through it . the food might be sharp , it might be hot and we want a thick layer of cells to protect the underlying tissue of the esophagus . a stratified layer epithelium acts as that protective layer . let 's take a look at a section of simple epithelium and epithelial cells are attached to something known as the basement membrane . the basement membrane is not made up of cells but rather it 's made up of different types of fibers . for example one fiber that can be found in the basement membrane is collagen . and the basement membrane is semipermeable to certain substances and that 's pretty important because epithelial tissue is avascular . that means that epithelial cells have no blood vessels which then makes us ask the question of how do they get nutrients ? they get nutrients from the underlying tissue . what happens is that nutrients will diffuse from the underlying tissue through the basement membrane to the epithelial cells . and that 's how epithelial cells get their nutrients . let 's just recap some of the places that you 'd expect to find epithelial cells . we already mentioned the outer layer of the skin , the tissue lining the mouth , esophagus and gi tract and of course this is not an exhaust of list . in the tissue lining the kidney tubules , and the tissue lining blood and lymphatic vessels . and in fact the tissue that lines blood vessels and lymphatic vessels has a special name . it 's known as endothelium . let 's talk about connective tissue . connective tissue supports tissues , connects tissues and separates different types of tissues from each other and then there are different types of connective tissue that do n't necessarily fall into these neat categories . what are some examples of connective tissue ? bones , cartilage , blood , lymph , adipose tissue which is fat . the membranes covering the brain and the spinal cord and other types of tissues . what does connective tissue look like ? what are some characteristics of connective tissue ? basically it has three components . it has cells . it has what 's known as a ground substance and then it has fibers . the ground substance and the fibers together make up a matrix . let 's see what this looks like . here we have the ground substance which is usually a viscous type of fluid . then interspersed in the ground substance are fibers and then we have cells , and these cells are usually what is producing the matrix . let 's look at some connective tissue in more detail . the first we 'll talk about is areolar tissue which is this tissue right over here . areolar tissue is a very common type of connective tissue . it binds together different types of tissue and it provides flexibility and cushioning , and we can actually see the structure pretty clearly in this picture . you can see the cells over there , those little dots . there 's no cell over here . you can see the fibers running through it . over here and over here . and then the ground substance is the kind of background yellow , viscous liquid that you 're seeing . then we have adipose tissue . adipose tissue is basically fat , tissue is a fat . it provides cushioning for the body , it stored energy and it actually is an exception to the rule . it does not have fibers like most other connective tissue . then we have what 's called fibrous connective tissue . fibrous connective tissue is pretty strong . it provides support and shock absorption for bones and organs , and you find it in the dermis which is the middle layer of the skin , tendons and ligaments . here are some more types of connective tissue . we have blood . blood is also an exception like adipose tissue and that it does not contain fibers . and the matrix of blood is the plasma and you can see the matrix , this yellowish liquid in which the blood cells are suspended . then we have osseous tissue or bone tissue . these cells in osseous tissue are known as osteocytes . those are those brown cells that are kind of forming a pattern and the matrix in osseous tissue is what 's known as bone mineral or hydroxyapatite , which is basically collagen fibers with different minerals like phosphates , magnesium , calcium , et cetera . and then we have hyaline cartilage . the cells in hyaline cartilage are chondrocytes . you can see them over here , there are a bunch of these cells . and they 're found in surfaces of joints . these are all examples of different types of connective tissue and many of them provide some form or another of support for tissues and organs .
|
there are four different types of animal tissue that are all made up of eukaryotic cells . epithelial tissue , connective tissue , muscle tissue and nervous tissue . in this video we 're gon na talk about epithelial tissue and connective tissue .
|
how is bone an example of connective tissue ?
|
there are four different types of animal tissue that are all made up of eukaryotic cells . epithelial tissue , connective tissue , muscle tissue and nervous tissue . in this video we 're gon na talk about epithelial tissue and connective tissue . when you think about epithelial tissue you can think about it as a lining . both an inner lining and an outer lining . so for example , epithelial tissue makes up the outer layer of our skin . it makes up the outer layer of organs . it lines organs so the lumen of organs will be lined with epithelial tissue and it also lines the inside of cavities , inside of the cavities of the organism . epithelial tissue also make up glands so that would include both exocrine glands and endocrine glands . and just to remind you , exocrine glands will release their substances directly to the target organ . whereas endocrine glands usually release hormones but into the bloodstream , not to the target organ directly . and epithelial tissue comes in two forms . it can be simple and that means it 's one layer thick . or it can be stratified which means it can have two or more layers . and where will you expect to find simple epithelium versus stratified epithelium . well , you 'll find simple epithelium in places where substances need to diffuse from two different places . for example the alveoli of the lungs are lined with simple epithelium because carbon dioxide and oxygen need to diffuse from the alveoli into the bloodstream and vice versa . and of course that will be pretty difficult if you had a thick layer of cells . and you 'd expect to find stratified epithelium in places that need to resist chemical or a mechanical stress . for example , the esophagus is lined with stratified epithelium . that 's because the esophagus will have food coming through it . the food might be sharp , it might be hot and we want a thick layer of cells to protect the underlying tissue of the esophagus . a stratified layer epithelium acts as that protective layer . let 's take a look at a section of simple epithelium and epithelial cells are attached to something known as the basement membrane . the basement membrane is not made up of cells but rather it 's made up of different types of fibers . for example one fiber that can be found in the basement membrane is collagen . and the basement membrane is semipermeable to certain substances and that 's pretty important because epithelial tissue is avascular . that means that epithelial cells have no blood vessels which then makes us ask the question of how do they get nutrients ? they get nutrients from the underlying tissue . what happens is that nutrients will diffuse from the underlying tissue through the basement membrane to the epithelial cells . and that 's how epithelial cells get their nutrients . let 's just recap some of the places that you 'd expect to find epithelial cells . we already mentioned the outer layer of the skin , the tissue lining the mouth , esophagus and gi tract and of course this is not an exhaust of list . in the tissue lining the kidney tubules , and the tissue lining blood and lymphatic vessels . and in fact the tissue that lines blood vessels and lymphatic vessels has a special name . it 's known as endothelium . let 's talk about connective tissue . connective tissue supports tissues , connects tissues and separates different types of tissues from each other and then there are different types of connective tissue that do n't necessarily fall into these neat categories . what are some examples of connective tissue ? bones , cartilage , blood , lymph , adipose tissue which is fat . the membranes covering the brain and the spinal cord and other types of tissues . what does connective tissue look like ? what are some characteristics of connective tissue ? basically it has three components . it has cells . it has what 's known as a ground substance and then it has fibers . the ground substance and the fibers together make up a matrix . let 's see what this looks like . here we have the ground substance which is usually a viscous type of fluid . then interspersed in the ground substance are fibers and then we have cells , and these cells are usually what is producing the matrix . let 's look at some connective tissue in more detail . the first we 'll talk about is areolar tissue which is this tissue right over here . areolar tissue is a very common type of connective tissue . it binds together different types of tissue and it provides flexibility and cushioning , and we can actually see the structure pretty clearly in this picture . you can see the cells over there , those little dots . there 's no cell over here . you can see the fibers running through it . over here and over here . and then the ground substance is the kind of background yellow , viscous liquid that you 're seeing . then we have adipose tissue . adipose tissue is basically fat , tissue is a fat . it provides cushioning for the body , it stored energy and it actually is an exception to the rule . it does not have fibers like most other connective tissue . then we have what 's called fibrous connective tissue . fibrous connective tissue is pretty strong . it provides support and shock absorption for bones and organs , and you find it in the dermis which is the middle layer of the skin , tendons and ligaments . here are some more types of connective tissue . we have blood . blood is also an exception like adipose tissue and that it does not contain fibers . and the matrix of blood is the plasma and you can see the matrix , this yellowish liquid in which the blood cells are suspended . then we have osseous tissue or bone tissue . these cells in osseous tissue are known as osteocytes . those are those brown cells that are kind of forming a pattern and the matrix in osseous tissue is what 's known as bone mineral or hydroxyapatite , which is basically collagen fibers with different minerals like phosphates , magnesium , calcium , et cetera . and then we have hyaline cartilage . the cells in hyaline cartilage are chondrocytes . you can see them over here , there are a bunch of these cells . and they 're found in surfaces of joints . these are all examples of different types of connective tissue and many of them provide some form or another of support for tissues and organs .
|
those are those brown cells that are kind of forming a pattern and the matrix in osseous tissue is what 's known as bone mineral or hydroxyapatite , which is basically collagen fibers with different minerals like phosphates , magnesium , calcium , et cetera . and then we have hyaline cartilage . the cells in hyaline cartilage are chondrocytes .
|
can you please clearly explain the differences among tendon , ligament and cartilage ?
|
there are four different types of animal tissue that are all made up of eukaryotic cells . epithelial tissue , connective tissue , muscle tissue and nervous tissue . in this video we 're gon na talk about epithelial tissue and connective tissue . when you think about epithelial tissue you can think about it as a lining . both an inner lining and an outer lining . so for example , epithelial tissue makes up the outer layer of our skin . it makes up the outer layer of organs . it lines organs so the lumen of organs will be lined with epithelial tissue and it also lines the inside of cavities , inside of the cavities of the organism . epithelial tissue also make up glands so that would include both exocrine glands and endocrine glands . and just to remind you , exocrine glands will release their substances directly to the target organ . whereas endocrine glands usually release hormones but into the bloodstream , not to the target organ directly . and epithelial tissue comes in two forms . it can be simple and that means it 's one layer thick . or it can be stratified which means it can have two or more layers . and where will you expect to find simple epithelium versus stratified epithelium . well , you 'll find simple epithelium in places where substances need to diffuse from two different places . for example the alveoli of the lungs are lined with simple epithelium because carbon dioxide and oxygen need to diffuse from the alveoli into the bloodstream and vice versa . and of course that will be pretty difficult if you had a thick layer of cells . and you 'd expect to find stratified epithelium in places that need to resist chemical or a mechanical stress . for example , the esophagus is lined with stratified epithelium . that 's because the esophagus will have food coming through it . the food might be sharp , it might be hot and we want a thick layer of cells to protect the underlying tissue of the esophagus . a stratified layer epithelium acts as that protective layer . let 's take a look at a section of simple epithelium and epithelial cells are attached to something known as the basement membrane . the basement membrane is not made up of cells but rather it 's made up of different types of fibers . for example one fiber that can be found in the basement membrane is collagen . and the basement membrane is semipermeable to certain substances and that 's pretty important because epithelial tissue is avascular . that means that epithelial cells have no blood vessels which then makes us ask the question of how do they get nutrients ? they get nutrients from the underlying tissue . what happens is that nutrients will diffuse from the underlying tissue through the basement membrane to the epithelial cells . and that 's how epithelial cells get their nutrients . let 's just recap some of the places that you 'd expect to find epithelial cells . we already mentioned the outer layer of the skin , the tissue lining the mouth , esophagus and gi tract and of course this is not an exhaust of list . in the tissue lining the kidney tubules , and the tissue lining blood and lymphatic vessels . and in fact the tissue that lines blood vessels and lymphatic vessels has a special name . it 's known as endothelium . let 's talk about connective tissue . connective tissue supports tissues , connects tissues and separates different types of tissues from each other and then there are different types of connective tissue that do n't necessarily fall into these neat categories . what are some examples of connective tissue ? bones , cartilage , blood , lymph , adipose tissue which is fat . the membranes covering the brain and the spinal cord and other types of tissues . what does connective tissue look like ? what are some characteristics of connective tissue ? basically it has three components . it has cells . it has what 's known as a ground substance and then it has fibers . the ground substance and the fibers together make up a matrix . let 's see what this looks like . here we have the ground substance which is usually a viscous type of fluid . then interspersed in the ground substance are fibers and then we have cells , and these cells are usually what is producing the matrix . let 's look at some connective tissue in more detail . the first we 'll talk about is areolar tissue which is this tissue right over here . areolar tissue is a very common type of connective tissue . it binds together different types of tissue and it provides flexibility and cushioning , and we can actually see the structure pretty clearly in this picture . you can see the cells over there , those little dots . there 's no cell over here . you can see the fibers running through it . over here and over here . and then the ground substance is the kind of background yellow , viscous liquid that you 're seeing . then we have adipose tissue . adipose tissue is basically fat , tissue is a fat . it provides cushioning for the body , it stored energy and it actually is an exception to the rule . it does not have fibers like most other connective tissue . then we have what 's called fibrous connective tissue . fibrous connective tissue is pretty strong . it provides support and shock absorption for bones and organs , and you find it in the dermis which is the middle layer of the skin , tendons and ligaments . here are some more types of connective tissue . we have blood . blood is also an exception like adipose tissue and that it does not contain fibers . and the matrix of blood is the plasma and you can see the matrix , this yellowish liquid in which the blood cells are suspended . then we have osseous tissue or bone tissue . these cells in osseous tissue are known as osteocytes . those are those brown cells that are kind of forming a pattern and the matrix in osseous tissue is what 's known as bone mineral or hydroxyapatite , which is basically collagen fibers with different minerals like phosphates , magnesium , calcium , et cetera . and then we have hyaline cartilage . the cells in hyaline cartilage are chondrocytes . you can see them over here , there are a bunch of these cells . and they 're found in surfaces of joints . these are all examples of different types of connective tissue and many of them provide some form or another of support for tissues and organs .
|
a stratified layer epithelium acts as that protective layer . let 's take a look at a section of simple epithelium and epithelial cells are attached to something known as the basement membrane . the basement membrane is not made up of cells but rather it 's made up of different types of fibers . for example one fiber that can be found in the basement membrane is collagen . and the basement membrane is semipermeable to certain substances and that 's pretty important because epithelial tissue is avascular .
|
why the membrane of the membranous organelles is same the structure of cell membrane ?
|
there are four different types of animal tissue that are all made up of eukaryotic cells . epithelial tissue , connective tissue , muscle tissue and nervous tissue . in this video we 're gon na talk about epithelial tissue and connective tissue . when you think about epithelial tissue you can think about it as a lining . both an inner lining and an outer lining . so for example , epithelial tissue makes up the outer layer of our skin . it makes up the outer layer of organs . it lines organs so the lumen of organs will be lined with epithelial tissue and it also lines the inside of cavities , inside of the cavities of the organism . epithelial tissue also make up glands so that would include both exocrine glands and endocrine glands . and just to remind you , exocrine glands will release their substances directly to the target organ . whereas endocrine glands usually release hormones but into the bloodstream , not to the target organ directly . and epithelial tissue comes in two forms . it can be simple and that means it 's one layer thick . or it can be stratified which means it can have two or more layers . and where will you expect to find simple epithelium versus stratified epithelium . well , you 'll find simple epithelium in places where substances need to diffuse from two different places . for example the alveoli of the lungs are lined with simple epithelium because carbon dioxide and oxygen need to diffuse from the alveoli into the bloodstream and vice versa . and of course that will be pretty difficult if you had a thick layer of cells . and you 'd expect to find stratified epithelium in places that need to resist chemical or a mechanical stress . for example , the esophagus is lined with stratified epithelium . that 's because the esophagus will have food coming through it . the food might be sharp , it might be hot and we want a thick layer of cells to protect the underlying tissue of the esophagus . a stratified layer epithelium acts as that protective layer . let 's take a look at a section of simple epithelium and epithelial cells are attached to something known as the basement membrane . the basement membrane is not made up of cells but rather it 's made up of different types of fibers . for example one fiber that can be found in the basement membrane is collagen . and the basement membrane is semipermeable to certain substances and that 's pretty important because epithelial tissue is avascular . that means that epithelial cells have no blood vessels which then makes us ask the question of how do they get nutrients ? they get nutrients from the underlying tissue . what happens is that nutrients will diffuse from the underlying tissue through the basement membrane to the epithelial cells . and that 's how epithelial cells get their nutrients . let 's just recap some of the places that you 'd expect to find epithelial cells . we already mentioned the outer layer of the skin , the tissue lining the mouth , esophagus and gi tract and of course this is not an exhaust of list . in the tissue lining the kidney tubules , and the tissue lining blood and lymphatic vessels . and in fact the tissue that lines blood vessels and lymphatic vessels has a special name . it 's known as endothelium . let 's talk about connective tissue . connective tissue supports tissues , connects tissues and separates different types of tissues from each other and then there are different types of connective tissue that do n't necessarily fall into these neat categories . what are some examples of connective tissue ? bones , cartilage , blood , lymph , adipose tissue which is fat . the membranes covering the brain and the spinal cord and other types of tissues . what does connective tissue look like ? what are some characteristics of connective tissue ? basically it has three components . it has cells . it has what 's known as a ground substance and then it has fibers . the ground substance and the fibers together make up a matrix . let 's see what this looks like . here we have the ground substance which is usually a viscous type of fluid . then interspersed in the ground substance are fibers and then we have cells , and these cells are usually what is producing the matrix . let 's look at some connective tissue in more detail . the first we 'll talk about is areolar tissue which is this tissue right over here . areolar tissue is a very common type of connective tissue . it binds together different types of tissue and it provides flexibility and cushioning , and we can actually see the structure pretty clearly in this picture . you can see the cells over there , those little dots . there 's no cell over here . you can see the fibers running through it . over here and over here . and then the ground substance is the kind of background yellow , viscous liquid that you 're seeing . then we have adipose tissue . adipose tissue is basically fat , tissue is a fat . it provides cushioning for the body , it stored energy and it actually is an exception to the rule . it does not have fibers like most other connective tissue . then we have what 's called fibrous connective tissue . fibrous connective tissue is pretty strong . it provides support and shock absorption for bones and organs , and you find it in the dermis which is the middle layer of the skin , tendons and ligaments . here are some more types of connective tissue . we have blood . blood is also an exception like adipose tissue and that it does not contain fibers . and the matrix of blood is the plasma and you can see the matrix , this yellowish liquid in which the blood cells are suspended . then we have osseous tissue or bone tissue . these cells in osseous tissue are known as osteocytes . those are those brown cells that are kind of forming a pattern and the matrix in osseous tissue is what 's known as bone mineral or hydroxyapatite , which is basically collagen fibers with different minerals like phosphates , magnesium , calcium , et cetera . and then we have hyaline cartilage . the cells in hyaline cartilage are chondrocytes . you can see them over here , there are a bunch of these cells . and they 're found in surfaces of joints . these are all examples of different types of connective tissue and many of them provide some form or another of support for tissues and organs .
|
there are four different types of animal tissue that are all made up of eukaryotic cells . epithelial tissue , connective tissue , muscle tissue and nervous tissue . in this video we 're gon na talk about epithelial tissue and connective tissue .
|
what attaches the basement membrane to epithelium tissue ?
|
there are four different types of animal tissue that are all made up of eukaryotic cells . epithelial tissue , connective tissue , muscle tissue and nervous tissue . in this video we 're gon na talk about epithelial tissue and connective tissue . when you think about epithelial tissue you can think about it as a lining . both an inner lining and an outer lining . so for example , epithelial tissue makes up the outer layer of our skin . it makes up the outer layer of organs . it lines organs so the lumen of organs will be lined with epithelial tissue and it also lines the inside of cavities , inside of the cavities of the organism . epithelial tissue also make up glands so that would include both exocrine glands and endocrine glands . and just to remind you , exocrine glands will release their substances directly to the target organ . whereas endocrine glands usually release hormones but into the bloodstream , not to the target organ directly . and epithelial tissue comes in two forms . it can be simple and that means it 's one layer thick . or it can be stratified which means it can have two or more layers . and where will you expect to find simple epithelium versus stratified epithelium . well , you 'll find simple epithelium in places where substances need to diffuse from two different places . for example the alveoli of the lungs are lined with simple epithelium because carbon dioxide and oxygen need to diffuse from the alveoli into the bloodstream and vice versa . and of course that will be pretty difficult if you had a thick layer of cells . and you 'd expect to find stratified epithelium in places that need to resist chemical or a mechanical stress . for example , the esophagus is lined with stratified epithelium . that 's because the esophagus will have food coming through it . the food might be sharp , it might be hot and we want a thick layer of cells to protect the underlying tissue of the esophagus . a stratified layer epithelium acts as that protective layer . let 's take a look at a section of simple epithelium and epithelial cells are attached to something known as the basement membrane . the basement membrane is not made up of cells but rather it 's made up of different types of fibers . for example one fiber that can be found in the basement membrane is collagen . and the basement membrane is semipermeable to certain substances and that 's pretty important because epithelial tissue is avascular . that means that epithelial cells have no blood vessels which then makes us ask the question of how do they get nutrients ? they get nutrients from the underlying tissue . what happens is that nutrients will diffuse from the underlying tissue through the basement membrane to the epithelial cells . and that 's how epithelial cells get their nutrients . let 's just recap some of the places that you 'd expect to find epithelial cells . we already mentioned the outer layer of the skin , the tissue lining the mouth , esophagus and gi tract and of course this is not an exhaust of list . in the tissue lining the kidney tubules , and the tissue lining blood and lymphatic vessels . and in fact the tissue that lines blood vessels and lymphatic vessels has a special name . it 's known as endothelium . let 's talk about connective tissue . connective tissue supports tissues , connects tissues and separates different types of tissues from each other and then there are different types of connective tissue that do n't necessarily fall into these neat categories . what are some examples of connective tissue ? bones , cartilage , blood , lymph , adipose tissue which is fat . the membranes covering the brain and the spinal cord and other types of tissues . what does connective tissue look like ? what are some characteristics of connective tissue ? basically it has three components . it has cells . it has what 's known as a ground substance and then it has fibers . the ground substance and the fibers together make up a matrix . let 's see what this looks like . here we have the ground substance which is usually a viscous type of fluid . then interspersed in the ground substance are fibers and then we have cells , and these cells are usually what is producing the matrix . let 's look at some connective tissue in more detail . the first we 'll talk about is areolar tissue which is this tissue right over here . areolar tissue is a very common type of connective tissue . it binds together different types of tissue and it provides flexibility and cushioning , and we can actually see the structure pretty clearly in this picture . you can see the cells over there , those little dots . there 's no cell over here . you can see the fibers running through it . over here and over here . and then the ground substance is the kind of background yellow , viscous liquid that you 're seeing . then we have adipose tissue . adipose tissue is basically fat , tissue is a fat . it provides cushioning for the body , it stored energy and it actually is an exception to the rule . it does not have fibers like most other connective tissue . then we have what 's called fibrous connective tissue . fibrous connective tissue is pretty strong . it provides support and shock absorption for bones and organs , and you find it in the dermis which is the middle layer of the skin , tendons and ligaments . here are some more types of connective tissue . we have blood . blood is also an exception like adipose tissue and that it does not contain fibers . and the matrix of blood is the plasma and you can see the matrix , this yellowish liquid in which the blood cells are suspended . then we have osseous tissue or bone tissue . these cells in osseous tissue are known as osteocytes . those are those brown cells that are kind of forming a pattern and the matrix in osseous tissue is what 's known as bone mineral or hydroxyapatite , which is basically collagen fibers with different minerals like phosphates , magnesium , calcium , et cetera . and then we have hyaline cartilage . the cells in hyaline cartilage are chondrocytes . you can see them over here , there are a bunch of these cells . and they 're found in surfaces of joints . these are all examples of different types of connective tissue and many of them provide some form or another of support for tissues and organs .
|
here are some more types of connective tissue . we have blood . blood is also an exception like adipose tissue and that it does not contain fibers .
|
why does n't blood have fibers ?
|
there are four different types of animal tissue that are all made up of eukaryotic cells . epithelial tissue , connective tissue , muscle tissue and nervous tissue . in this video we 're gon na talk about epithelial tissue and connective tissue . when you think about epithelial tissue you can think about it as a lining . both an inner lining and an outer lining . so for example , epithelial tissue makes up the outer layer of our skin . it makes up the outer layer of organs . it lines organs so the lumen of organs will be lined with epithelial tissue and it also lines the inside of cavities , inside of the cavities of the organism . epithelial tissue also make up glands so that would include both exocrine glands and endocrine glands . and just to remind you , exocrine glands will release their substances directly to the target organ . whereas endocrine glands usually release hormones but into the bloodstream , not to the target organ directly . and epithelial tissue comes in two forms . it can be simple and that means it 's one layer thick . or it can be stratified which means it can have two or more layers . and where will you expect to find simple epithelium versus stratified epithelium . well , you 'll find simple epithelium in places where substances need to diffuse from two different places . for example the alveoli of the lungs are lined with simple epithelium because carbon dioxide and oxygen need to diffuse from the alveoli into the bloodstream and vice versa . and of course that will be pretty difficult if you had a thick layer of cells . and you 'd expect to find stratified epithelium in places that need to resist chemical or a mechanical stress . for example , the esophagus is lined with stratified epithelium . that 's because the esophagus will have food coming through it . the food might be sharp , it might be hot and we want a thick layer of cells to protect the underlying tissue of the esophagus . a stratified layer epithelium acts as that protective layer . let 's take a look at a section of simple epithelium and epithelial cells are attached to something known as the basement membrane . the basement membrane is not made up of cells but rather it 's made up of different types of fibers . for example one fiber that can be found in the basement membrane is collagen . and the basement membrane is semipermeable to certain substances and that 's pretty important because epithelial tissue is avascular . that means that epithelial cells have no blood vessels which then makes us ask the question of how do they get nutrients ? they get nutrients from the underlying tissue . what happens is that nutrients will diffuse from the underlying tissue through the basement membrane to the epithelial cells . and that 's how epithelial cells get their nutrients . let 's just recap some of the places that you 'd expect to find epithelial cells . we already mentioned the outer layer of the skin , the tissue lining the mouth , esophagus and gi tract and of course this is not an exhaust of list . in the tissue lining the kidney tubules , and the tissue lining blood and lymphatic vessels . and in fact the tissue that lines blood vessels and lymphatic vessels has a special name . it 's known as endothelium . let 's talk about connective tissue . connective tissue supports tissues , connects tissues and separates different types of tissues from each other and then there are different types of connective tissue that do n't necessarily fall into these neat categories . what are some examples of connective tissue ? bones , cartilage , blood , lymph , adipose tissue which is fat . the membranes covering the brain and the spinal cord and other types of tissues . what does connective tissue look like ? what are some characteristics of connective tissue ? basically it has three components . it has cells . it has what 's known as a ground substance and then it has fibers . the ground substance and the fibers together make up a matrix . let 's see what this looks like . here we have the ground substance which is usually a viscous type of fluid . then interspersed in the ground substance are fibers and then we have cells , and these cells are usually what is producing the matrix . let 's look at some connective tissue in more detail . the first we 'll talk about is areolar tissue which is this tissue right over here . areolar tissue is a very common type of connective tissue . it binds together different types of tissue and it provides flexibility and cushioning , and we can actually see the structure pretty clearly in this picture . you can see the cells over there , those little dots . there 's no cell over here . you can see the fibers running through it . over here and over here . and then the ground substance is the kind of background yellow , viscous liquid that you 're seeing . then we have adipose tissue . adipose tissue is basically fat , tissue is a fat . it provides cushioning for the body , it stored energy and it actually is an exception to the rule . it does not have fibers like most other connective tissue . then we have what 's called fibrous connective tissue . fibrous connective tissue is pretty strong . it provides support and shock absorption for bones and organs , and you find it in the dermis which is the middle layer of the skin , tendons and ligaments . here are some more types of connective tissue . we have blood . blood is also an exception like adipose tissue and that it does not contain fibers . and the matrix of blood is the plasma and you can see the matrix , this yellowish liquid in which the blood cells are suspended . then we have osseous tissue or bone tissue . these cells in osseous tissue are known as osteocytes . those are those brown cells that are kind of forming a pattern and the matrix in osseous tissue is what 's known as bone mineral or hydroxyapatite , which is basically collagen fibers with different minerals like phosphates , magnesium , calcium , et cetera . and then we have hyaline cartilage . the cells in hyaline cartilage are chondrocytes . you can see them over here , there are a bunch of these cells . and they 're found in surfaces of joints . these are all examples of different types of connective tissue and many of them provide some form or another of support for tissues and organs .
|
there are four different types of animal tissue that are all made up of eukaryotic cells . epithelial tissue , connective tissue , muscle tissue and nervous tissue . in this video we 're gon na talk about epithelial tissue and connective tissue .
|
why would cuboidal tissue line tubules be associated with secretion ?
|
there are four different types of animal tissue that are all made up of eukaryotic cells . epithelial tissue , connective tissue , muscle tissue and nervous tissue . in this video we 're gon na talk about epithelial tissue and connective tissue . when you think about epithelial tissue you can think about it as a lining . both an inner lining and an outer lining . so for example , epithelial tissue makes up the outer layer of our skin . it makes up the outer layer of organs . it lines organs so the lumen of organs will be lined with epithelial tissue and it also lines the inside of cavities , inside of the cavities of the organism . epithelial tissue also make up glands so that would include both exocrine glands and endocrine glands . and just to remind you , exocrine glands will release their substances directly to the target organ . whereas endocrine glands usually release hormones but into the bloodstream , not to the target organ directly . and epithelial tissue comes in two forms . it can be simple and that means it 's one layer thick . or it can be stratified which means it can have two or more layers . and where will you expect to find simple epithelium versus stratified epithelium . well , you 'll find simple epithelium in places where substances need to diffuse from two different places . for example the alveoli of the lungs are lined with simple epithelium because carbon dioxide and oxygen need to diffuse from the alveoli into the bloodstream and vice versa . and of course that will be pretty difficult if you had a thick layer of cells . and you 'd expect to find stratified epithelium in places that need to resist chemical or a mechanical stress . for example , the esophagus is lined with stratified epithelium . that 's because the esophagus will have food coming through it . the food might be sharp , it might be hot and we want a thick layer of cells to protect the underlying tissue of the esophagus . a stratified layer epithelium acts as that protective layer . let 's take a look at a section of simple epithelium and epithelial cells are attached to something known as the basement membrane . the basement membrane is not made up of cells but rather it 's made up of different types of fibers . for example one fiber that can be found in the basement membrane is collagen . and the basement membrane is semipermeable to certain substances and that 's pretty important because epithelial tissue is avascular . that means that epithelial cells have no blood vessels which then makes us ask the question of how do they get nutrients ? they get nutrients from the underlying tissue . what happens is that nutrients will diffuse from the underlying tissue through the basement membrane to the epithelial cells . and that 's how epithelial cells get their nutrients . let 's just recap some of the places that you 'd expect to find epithelial cells . we already mentioned the outer layer of the skin , the tissue lining the mouth , esophagus and gi tract and of course this is not an exhaust of list . in the tissue lining the kidney tubules , and the tissue lining blood and lymphatic vessels . and in fact the tissue that lines blood vessels and lymphatic vessels has a special name . it 's known as endothelium . let 's talk about connective tissue . connective tissue supports tissues , connects tissues and separates different types of tissues from each other and then there are different types of connective tissue that do n't necessarily fall into these neat categories . what are some examples of connective tissue ? bones , cartilage , blood , lymph , adipose tissue which is fat . the membranes covering the brain and the spinal cord and other types of tissues . what does connective tissue look like ? what are some characteristics of connective tissue ? basically it has three components . it has cells . it has what 's known as a ground substance and then it has fibers . the ground substance and the fibers together make up a matrix . let 's see what this looks like . here we have the ground substance which is usually a viscous type of fluid . then interspersed in the ground substance are fibers and then we have cells , and these cells are usually what is producing the matrix . let 's look at some connective tissue in more detail . the first we 'll talk about is areolar tissue which is this tissue right over here . areolar tissue is a very common type of connective tissue . it binds together different types of tissue and it provides flexibility and cushioning , and we can actually see the structure pretty clearly in this picture . you can see the cells over there , those little dots . there 's no cell over here . you can see the fibers running through it . over here and over here . and then the ground substance is the kind of background yellow , viscous liquid that you 're seeing . then we have adipose tissue . adipose tissue is basically fat , tissue is a fat . it provides cushioning for the body , it stored energy and it actually is an exception to the rule . it does not have fibers like most other connective tissue . then we have what 's called fibrous connective tissue . fibrous connective tissue is pretty strong . it provides support and shock absorption for bones and organs , and you find it in the dermis which is the middle layer of the skin , tendons and ligaments . here are some more types of connective tissue . we have blood . blood is also an exception like adipose tissue and that it does not contain fibers . and the matrix of blood is the plasma and you can see the matrix , this yellowish liquid in which the blood cells are suspended . then we have osseous tissue or bone tissue . these cells in osseous tissue are known as osteocytes . those are those brown cells that are kind of forming a pattern and the matrix in osseous tissue is what 's known as bone mineral or hydroxyapatite , which is basically collagen fibers with different minerals like phosphates , magnesium , calcium , et cetera . and then we have hyaline cartilage . the cells in hyaline cartilage are chondrocytes . you can see them over here , there are a bunch of these cells . and they 're found in surfaces of joints . these are all examples of different types of connective tissue and many of them provide some form or another of support for tissues and organs .
|
let 's talk about connective tissue . connective tissue supports tissues , connects tissues and separates different types of tissues from each other and then there are different types of connective tissue that do n't necessarily fall into these neat categories . what are some examples of connective tissue ?
|
the four tissues consist of body ?
|
there are four different types of animal tissue that are all made up of eukaryotic cells . epithelial tissue , connective tissue , muscle tissue and nervous tissue . in this video we 're gon na talk about epithelial tissue and connective tissue . when you think about epithelial tissue you can think about it as a lining . both an inner lining and an outer lining . so for example , epithelial tissue makes up the outer layer of our skin . it makes up the outer layer of organs . it lines organs so the lumen of organs will be lined with epithelial tissue and it also lines the inside of cavities , inside of the cavities of the organism . epithelial tissue also make up glands so that would include both exocrine glands and endocrine glands . and just to remind you , exocrine glands will release their substances directly to the target organ . whereas endocrine glands usually release hormones but into the bloodstream , not to the target organ directly . and epithelial tissue comes in two forms . it can be simple and that means it 's one layer thick . or it can be stratified which means it can have two or more layers . and where will you expect to find simple epithelium versus stratified epithelium . well , you 'll find simple epithelium in places where substances need to diffuse from two different places . for example the alveoli of the lungs are lined with simple epithelium because carbon dioxide and oxygen need to diffuse from the alveoli into the bloodstream and vice versa . and of course that will be pretty difficult if you had a thick layer of cells . and you 'd expect to find stratified epithelium in places that need to resist chemical or a mechanical stress . for example , the esophagus is lined with stratified epithelium . that 's because the esophagus will have food coming through it . the food might be sharp , it might be hot and we want a thick layer of cells to protect the underlying tissue of the esophagus . a stratified layer epithelium acts as that protective layer . let 's take a look at a section of simple epithelium and epithelial cells are attached to something known as the basement membrane . the basement membrane is not made up of cells but rather it 's made up of different types of fibers . for example one fiber that can be found in the basement membrane is collagen . and the basement membrane is semipermeable to certain substances and that 's pretty important because epithelial tissue is avascular . that means that epithelial cells have no blood vessels which then makes us ask the question of how do they get nutrients ? they get nutrients from the underlying tissue . what happens is that nutrients will diffuse from the underlying tissue through the basement membrane to the epithelial cells . and that 's how epithelial cells get their nutrients . let 's just recap some of the places that you 'd expect to find epithelial cells . we already mentioned the outer layer of the skin , the tissue lining the mouth , esophagus and gi tract and of course this is not an exhaust of list . in the tissue lining the kidney tubules , and the tissue lining blood and lymphatic vessels . and in fact the tissue that lines blood vessels and lymphatic vessels has a special name . it 's known as endothelium . let 's talk about connective tissue . connective tissue supports tissues , connects tissues and separates different types of tissues from each other and then there are different types of connective tissue that do n't necessarily fall into these neat categories . what are some examples of connective tissue ? bones , cartilage , blood , lymph , adipose tissue which is fat . the membranes covering the brain and the spinal cord and other types of tissues . what does connective tissue look like ? what are some characteristics of connective tissue ? basically it has three components . it has cells . it has what 's known as a ground substance and then it has fibers . the ground substance and the fibers together make up a matrix . let 's see what this looks like . here we have the ground substance which is usually a viscous type of fluid . then interspersed in the ground substance are fibers and then we have cells , and these cells are usually what is producing the matrix . let 's look at some connective tissue in more detail . the first we 'll talk about is areolar tissue which is this tissue right over here . areolar tissue is a very common type of connective tissue . it binds together different types of tissue and it provides flexibility and cushioning , and we can actually see the structure pretty clearly in this picture . you can see the cells over there , those little dots . there 's no cell over here . you can see the fibers running through it . over here and over here . and then the ground substance is the kind of background yellow , viscous liquid that you 're seeing . then we have adipose tissue . adipose tissue is basically fat , tissue is a fat . it provides cushioning for the body , it stored energy and it actually is an exception to the rule . it does not have fibers like most other connective tissue . then we have what 's called fibrous connective tissue . fibrous connective tissue is pretty strong . it provides support and shock absorption for bones and organs , and you find it in the dermis which is the middle layer of the skin , tendons and ligaments . here are some more types of connective tissue . we have blood . blood is also an exception like adipose tissue and that it does not contain fibers . and the matrix of blood is the plasma and you can see the matrix , this yellowish liquid in which the blood cells are suspended . then we have osseous tissue or bone tissue . these cells in osseous tissue are known as osteocytes . those are those brown cells that are kind of forming a pattern and the matrix in osseous tissue is what 's known as bone mineral or hydroxyapatite , which is basically collagen fibers with different minerals like phosphates , magnesium , calcium , et cetera . and then we have hyaline cartilage . the cells in hyaline cartilage are chondrocytes . you can see them over here , there are a bunch of these cells . and they 're found in surfaces of joints . these are all examples of different types of connective tissue and many of them provide some form or another of support for tissues and organs .
|
let 's talk about connective tissue . connective tissue supports tissues , connects tissues and separates different types of tissues from each other and then there are different types of connective tissue that do n't necessarily fall into these neat categories . what are some examples of connective tissue ?
|
which of the four tissues include bone and endothelial ?
|
there are four different types of animal tissue that are all made up of eukaryotic cells . epithelial tissue , connective tissue , muscle tissue and nervous tissue . in this video we 're gon na talk about epithelial tissue and connective tissue . when you think about epithelial tissue you can think about it as a lining . both an inner lining and an outer lining . so for example , epithelial tissue makes up the outer layer of our skin . it makes up the outer layer of organs . it lines organs so the lumen of organs will be lined with epithelial tissue and it also lines the inside of cavities , inside of the cavities of the organism . epithelial tissue also make up glands so that would include both exocrine glands and endocrine glands . and just to remind you , exocrine glands will release their substances directly to the target organ . whereas endocrine glands usually release hormones but into the bloodstream , not to the target organ directly . and epithelial tissue comes in two forms . it can be simple and that means it 's one layer thick . or it can be stratified which means it can have two or more layers . and where will you expect to find simple epithelium versus stratified epithelium . well , you 'll find simple epithelium in places where substances need to diffuse from two different places . for example the alveoli of the lungs are lined with simple epithelium because carbon dioxide and oxygen need to diffuse from the alveoli into the bloodstream and vice versa . and of course that will be pretty difficult if you had a thick layer of cells . and you 'd expect to find stratified epithelium in places that need to resist chemical or a mechanical stress . for example , the esophagus is lined with stratified epithelium . that 's because the esophagus will have food coming through it . the food might be sharp , it might be hot and we want a thick layer of cells to protect the underlying tissue of the esophagus . a stratified layer epithelium acts as that protective layer . let 's take a look at a section of simple epithelium and epithelial cells are attached to something known as the basement membrane . the basement membrane is not made up of cells but rather it 's made up of different types of fibers . for example one fiber that can be found in the basement membrane is collagen . and the basement membrane is semipermeable to certain substances and that 's pretty important because epithelial tissue is avascular . that means that epithelial cells have no blood vessels which then makes us ask the question of how do they get nutrients ? they get nutrients from the underlying tissue . what happens is that nutrients will diffuse from the underlying tissue through the basement membrane to the epithelial cells . and that 's how epithelial cells get their nutrients . let 's just recap some of the places that you 'd expect to find epithelial cells . we already mentioned the outer layer of the skin , the tissue lining the mouth , esophagus and gi tract and of course this is not an exhaust of list . in the tissue lining the kidney tubules , and the tissue lining blood and lymphatic vessels . and in fact the tissue that lines blood vessels and lymphatic vessels has a special name . it 's known as endothelium . let 's talk about connective tissue . connective tissue supports tissues , connects tissues and separates different types of tissues from each other and then there are different types of connective tissue that do n't necessarily fall into these neat categories . what are some examples of connective tissue ? bones , cartilage , blood , lymph , adipose tissue which is fat . the membranes covering the brain and the spinal cord and other types of tissues . what does connective tissue look like ? what are some characteristics of connective tissue ? basically it has three components . it has cells . it has what 's known as a ground substance and then it has fibers . the ground substance and the fibers together make up a matrix . let 's see what this looks like . here we have the ground substance which is usually a viscous type of fluid . then interspersed in the ground substance are fibers and then we have cells , and these cells are usually what is producing the matrix . let 's look at some connective tissue in more detail . the first we 'll talk about is areolar tissue which is this tissue right over here . areolar tissue is a very common type of connective tissue . it binds together different types of tissue and it provides flexibility and cushioning , and we can actually see the structure pretty clearly in this picture . you can see the cells over there , those little dots . there 's no cell over here . you can see the fibers running through it . over here and over here . and then the ground substance is the kind of background yellow , viscous liquid that you 're seeing . then we have adipose tissue . adipose tissue is basically fat , tissue is a fat . it provides cushioning for the body , it stored energy and it actually is an exception to the rule . it does not have fibers like most other connective tissue . then we have what 's called fibrous connective tissue . fibrous connective tissue is pretty strong . it provides support and shock absorption for bones and organs , and you find it in the dermis which is the middle layer of the skin , tendons and ligaments . here are some more types of connective tissue . we have blood . blood is also an exception like adipose tissue and that it does not contain fibers . and the matrix of blood is the plasma and you can see the matrix , this yellowish liquid in which the blood cells are suspended . then we have osseous tissue or bone tissue . these cells in osseous tissue are known as osteocytes . those are those brown cells that are kind of forming a pattern and the matrix in osseous tissue is what 's known as bone mineral or hydroxyapatite , which is basically collagen fibers with different minerals like phosphates , magnesium , calcium , et cetera . and then we have hyaline cartilage . the cells in hyaline cartilage are chondrocytes . you can see them over here , there are a bunch of these cells . and they 're found in surfaces of joints . these are all examples of different types of connective tissue and many of them provide some form or another of support for tissues and organs .
|
and the matrix of blood is the plasma and you can see the matrix , this yellowish liquid in which the blood cells are suspended . then we have osseous tissue or bone tissue . these cells in osseous tissue are known as osteocytes .
|
bone and endothelial important function ?
|
there are four different types of animal tissue that are all made up of eukaryotic cells . epithelial tissue , connective tissue , muscle tissue and nervous tissue . in this video we 're gon na talk about epithelial tissue and connective tissue . when you think about epithelial tissue you can think about it as a lining . both an inner lining and an outer lining . so for example , epithelial tissue makes up the outer layer of our skin . it makes up the outer layer of organs . it lines organs so the lumen of organs will be lined with epithelial tissue and it also lines the inside of cavities , inside of the cavities of the organism . epithelial tissue also make up glands so that would include both exocrine glands and endocrine glands . and just to remind you , exocrine glands will release their substances directly to the target organ . whereas endocrine glands usually release hormones but into the bloodstream , not to the target organ directly . and epithelial tissue comes in two forms . it can be simple and that means it 's one layer thick . or it can be stratified which means it can have two or more layers . and where will you expect to find simple epithelium versus stratified epithelium . well , you 'll find simple epithelium in places where substances need to diffuse from two different places . for example the alveoli of the lungs are lined with simple epithelium because carbon dioxide and oxygen need to diffuse from the alveoli into the bloodstream and vice versa . and of course that will be pretty difficult if you had a thick layer of cells . and you 'd expect to find stratified epithelium in places that need to resist chemical or a mechanical stress . for example , the esophagus is lined with stratified epithelium . that 's because the esophagus will have food coming through it . the food might be sharp , it might be hot and we want a thick layer of cells to protect the underlying tissue of the esophagus . a stratified layer epithelium acts as that protective layer . let 's take a look at a section of simple epithelium and epithelial cells are attached to something known as the basement membrane . the basement membrane is not made up of cells but rather it 's made up of different types of fibers . for example one fiber that can be found in the basement membrane is collagen . and the basement membrane is semipermeable to certain substances and that 's pretty important because epithelial tissue is avascular . that means that epithelial cells have no blood vessels which then makes us ask the question of how do they get nutrients ? they get nutrients from the underlying tissue . what happens is that nutrients will diffuse from the underlying tissue through the basement membrane to the epithelial cells . and that 's how epithelial cells get their nutrients . let 's just recap some of the places that you 'd expect to find epithelial cells . we already mentioned the outer layer of the skin , the tissue lining the mouth , esophagus and gi tract and of course this is not an exhaust of list . in the tissue lining the kidney tubules , and the tissue lining blood and lymphatic vessels . and in fact the tissue that lines blood vessels and lymphatic vessels has a special name . it 's known as endothelium . let 's talk about connective tissue . connective tissue supports tissues , connects tissues and separates different types of tissues from each other and then there are different types of connective tissue that do n't necessarily fall into these neat categories . what are some examples of connective tissue ? bones , cartilage , blood , lymph , adipose tissue which is fat . the membranes covering the brain and the spinal cord and other types of tissues . what does connective tissue look like ? what are some characteristics of connective tissue ? basically it has three components . it has cells . it has what 's known as a ground substance and then it has fibers . the ground substance and the fibers together make up a matrix . let 's see what this looks like . here we have the ground substance which is usually a viscous type of fluid . then interspersed in the ground substance are fibers and then we have cells , and these cells are usually what is producing the matrix . let 's look at some connective tissue in more detail . the first we 'll talk about is areolar tissue which is this tissue right over here . areolar tissue is a very common type of connective tissue . it binds together different types of tissue and it provides flexibility and cushioning , and we can actually see the structure pretty clearly in this picture . you can see the cells over there , those little dots . there 's no cell over here . you can see the fibers running through it . over here and over here . and then the ground substance is the kind of background yellow , viscous liquid that you 're seeing . then we have adipose tissue . adipose tissue is basically fat , tissue is a fat . it provides cushioning for the body , it stored energy and it actually is an exception to the rule . it does not have fibers like most other connective tissue . then we have what 's called fibrous connective tissue . fibrous connective tissue is pretty strong . it provides support and shock absorption for bones and organs , and you find it in the dermis which is the middle layer of the skin , tendons and ligaments . here are some more types of connective tissue . we have blood . blood is also an exception like adipose tissue and that it does not contain fibers . and the matrix of blood is the plasma and you can see the matrix , this yellowish liquid in which the blood cells are suspended . then we have osseous tissue or bone tissue . these cells in osseous tissue are known as osteocytes . those are those brown cells that are kind of forming a pattern and the matrix in osseous tissue is what 's known as bone mineral or hydroxyapatite , which is basically collagen fibers with different minerals like phosphates , magnesium , calcium , et cetera . and then we have hyaline cartilage . the cells in hyaline cartilage are chondrocytes . you can see them over here , there are a bunch of these cells . and they 're found in surfaces of joints . these are all examples of different types of connective tissue and many of them provide some form or another of support for tissues and organs .
|
here are some more types of connective tissue . we have blood . blood is also an exception like adipose tissue and that it does not contain fibers .
|
does the basement membrane consists of blood capillaries ?
|
there are four different types of animal tissue that are all made up of eukaryotic cells . epithelial tissue , connective tissue , muscle tissue and nervous tissue . in this video we 're gon na talk about epithelial tissue and connective tissue . when you think about epithelial tissue you can think about it as a lining . both an inner lining and an outer lining . so for example , epithelial tissue makes up the outer layer of our skin . it makes up the outer layer of organs . it lines organs so the lumen of organs will be lined with epithelial tissue and it also lines the inside of cavities , inside of the cavities of the organism . epithelial tissue also make up glands so that would include both exocrine glands and endocrine glands . and just to remind you , exocrine glands will release their substances directly to the target organ . whereas endocrine glands usually release hormones but into the bloodstream , not to the target organ directly . and epithelial tissue comes in two forms . it can be simple and that means it 's one layer thick . or it can be stratified which means it can have two or more layers . and where will you expect to find simple epithelium versus stratified epithelium . well , you 'll find simple epithelium in places where substances need to diffuse from two different places . for example the alveoli of the lungs are lined with simple epithelium because carbon dioxide and oxygen need to diffuse from the alveoli into the bloodstream and vice versa . and of course that will be pretty difficult if you had a thick layer of cells . and you 'd expect to find stratified epithelium in places that need to resist chemical or a mechanical stress . for example , the esophagus is lined with stratified epithelium . that 's because the esophagus will have food coming through it . the food might be sharp , it might be hot and we want a thick layer of cells to protect the underlying tissue of the esophagus . a stratified layer epithelium acts as that protective layer . let 's take a look at a section of simple epithelium and epithelial cells are attached to something known as the basement membrane . the basement membrane is not made up of cells but rather it 's made up of different types of fibers . for example one fiber that can be found in the basement membrane is collagen . and the basement membrane is semipermeable to certain substances and that 's pretty important because epithelial tissue is avascular . that means that epithelial cells have no blood vessels which then makes us ask the question of how do they get nutrients ? they get nutrients from the underlying tissue . what happens is that nutrients will diffuse from the underlying tissue through the basement membrane to the epithelial cells . and that 's how epithelial cells get their nutrients . let 's just recap some of the places that you 'd expect to find epithelial cells . we already mentioned the outer layer of the skin , the tissue lining the mouth , esophagus and gi tract and of course this is not an exhaust of list . in the tissue lining the kidney tubules , and the tissue lining blood and lymphatic vessels . and in fact the tissue that lines blood vessels and lymphatic vessels has a special name . it 's known as endothelium . let 's talk about connective tissue . connective tissue supports tissues , connects tissues and separates different types of tissues from each other and then there are different types of connective tissue that do n't necessarily fall into these neat categories . what are some examples of connective tissue ? bones , cartilage , blood , lymph , adipose tissue which is fat . the membranes covering the brain and the spinal cord and other types of tissues . what does connective tissue look like ? what are some characteristics of connective tissue ? basically it has three components . it has cells . it has what 's known as a ground substance and then it has fibers . the ground substance and the fibers together make up a matrix . let 's see what this looks like . here we have the ground substance which is usually a viscous type of fluid . then interspersed in the ground substance are fibers and then we have cells , and these cells are usually what is producing the matrix . let 's look at some connective tissue in more detail . the first we 'll talk about is areolar tissue which is this tissue right over here . areolar tissue is a very common type of connective tissue . it binds together different types of tissue and it provides flexibility and cushioning , and we can actually see the structure pretty clearly in this picture . you can see the cells over there , those little dots . there 's no cell over here . you can see the fibers running through it . over here and over here . and then the ground substance is the kind of background yellow , viscous liquid that you 're seeing . then we have adipose tissue . adipose tissue is basically fat , tissue is a fat . it provides cushioning for the body , it stored energy and it actually is an exception to the rule . it does not have fibers like most other connective tissue . then we have what 's called fibrous connective tissue . fibrous connective tissue is pretty strong . it provides support and shock absorption for bones and organs , and you find it in the dermis which is the middle layer of the skin , tendons and ligaments . here are some more types of connective tissue . we have blood . blood is also an exception like adipose tissue and that it does not contain fibers . and the matrix of blood is the plasma and you can see the matrix , this yellowish liquid in which the blood cells are suspended . then we have osseous tissue or bone tissue . these cells in osseous tissue are known as osteocytes . those are those brown cells that are kind of forming a pattern and the matrix in osseous tissue is what 's known as bone mineral or hydroxyapatite , which is basically collagen fibers with different minerals like phosphates , magnesium , calcium , et cetera . and then we have hyaline cartilage . the cells in hyaline cartilage are chondrocytes . you can see them over here , there are a bunch of these cells . and they 're found in surfaces of joints . these are all examples of different types of connective tissue and many of them provide some form or another of support for tissues and organs .
|
you can see the cells over there , those little dots . there 's no cell over here . you can see the fibers running through it .
|
can someone give a short and sweet definition of an epithelial cell ?
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things . and so the first thing i want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale . and i 'll give you some hints . we know that they have equal mass . so maybe you can set up some type of relationship using an equal sign , somehow showing that this right over here is equal to that . and i 'll give you a few seconds to do that . so let 's think about it a little bit . what do we have on this side ? well , we have our mystery mass . and i 'll represent that mystery mass by the question mark right over here . but that 's not the only thing that we have on the left-hand side . we also have these other 3 kilograms . so let me write over here . we 'll assume that we 're dealing with kilograms . so we have the mystery mass in kilograms plus 3 more kilograms . that 's what we have here on the left-hand side . now , what do we have here on the right-hand side ? well , we just have 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 kilograms . so we just have 10 . we just have 10 on the right-hand side . and what else do we know ? well , we know that this scale is balanced , that the mass here is equal to the mass here . because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown . we do n't know what this mystery mass is . if we add 3 kilograms to it , then we see that it has the exact same mass as 10 kilograms . now my question to you is , what can we do to this equation so that we can essentially solve for the unknown , so that we can figure out what the unknown is ? well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right . in order to say they 're equal , the stuff has to actually be balanced . so in the last video , we removed 3 of these . we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here . we will remove 3 , not from one side . if we remove 3 from one side , then it would n't be equal anymore . we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark . and on the right-hand side , we 're left with 10 minus 3 , which is 7 . and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark .
|
3 and the yellow blocks were all unknowns ?
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things . and so the first thing i want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale . and i 'll give you some hints . we know that they have equal mass . so maybe you can set up some type of relationship using an equal sign , somehow showing that this right over here is equal to that . and i 'll give you a few seconds to do that . so let 's think about it a little bit . what do we have on this side ? well , we have our mystery mass . and i 'll represent that mystery mass by the question mark right over here . but that 's not the only thing that we have on the left-hand side . we also have these other 3 kilograms . so let me write over here . we 'll assume that we 're dealing with kilograms . so we have the mystery mass in kilograms plus 3 more kilograms . that 's what we have here on the left-hand side . now , what do we have here on the right-hand side ? well , we just have 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 kilograms . so we just have 10 . we just have 10 on the right-hand side . and what else do we know ? well , we know that this scale is balanced , that the mass here is equal to the mass here . because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown . we do n't know what this mystery mass is . if we add 3 kilograms to it , then we see that it has the exact same mass as 10 kilograms . now my question to you is , what can we do to this equation so that we can essentially solve for the unknown , so that we can figure out what the unknown is ? well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right . in order to say they 're equal , the stuff has to actually be balanced . so in the last video , we removed 3 of these . we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here . we will remove 3 , not from one side . if we remove 3 from one side , then it would n't be equal anymore . we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark . and on the right-hand side , we 're left with 10 minus 3 , which is 7 . and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced .
|
why is learning geometry so important if all we need is algebra to prosper ?
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things . and so the first thing i want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale . and i 'll give you some hints . we know that they have equal mass . so maybe you can set up some type of relationship using an equal sign , somehow showing that this right over here is equal to that . and i 'll give you a few seconds to do that . so let 's think about it a little bit . what do we have on this side ? well , we have our mystery mass . and i 'll represent that mystery mass by the question mark right over here . but that 's not the only thing that we have on the left-hand side . we also have these other 3 kilograms . so let me write over here . we 'll assume that we 're dealing with kilograms . so we have the mystery mass in kilograms plus 3 more kilograms . that 's what we have here on the left-hand side . now , what do we have here on the right-hand side ? well , we just have 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 kilograms . so we just have 10 . we just have 10 on the right-hand side . and what else do we know ? well , we know that this scale is balanced , that the mass here is equal to the mass here . because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown . we do n't know what this mystery mass is . if we add 3 kilograms to it , then we see that it has the exact same mass as 10 kilograms . now my question to you is , what can we do to this equation so that we can essentially solve for the unknown , so that we can figure out what the unknown is ? well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right . in order to say they 're equal , the stuff has to actually be balanced . so in the last video , we removed 3 of these . we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here . we will remove 3 , not from one side . if we remove 3 from one side , then it would n't be equal anymore . we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark . and on the right-hand side , we 're left with 10 minus 3 , which is 7 . and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark .
|
so the equation is x+3=10 ?
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things . and so the first thing i want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale . and i 'll give you some hints . we know that they have equal mass . so maybe you can set up some type of relationship using an equal sign , somehow showing that this right over here is equal to that . and i 'll give you a few seconds to do that . so let 's think about it a little bit . what do we have on this side ? well , we have our mystery mass . and i 'll represent that mystery mass by the question mark right over here . but that 's not the only thing that we have on the left-hand side . we also have these other 3 kilograms . so let me write over here . we 'll assume that we 're dealing with kilograms . so we have the mystery mass in kilograms plus 3 more kilograms . that 's what we have here on the left-hand side . now , what do we have here on the right-hand side ? well , we just have 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 kilograms . so we just have 10 . we just have 10 on the right-hand side . and what else do we know ? well , we know that this scale is balanced , that the mass here is equal to the mass here . because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown . we do n't know what this mystery mass is . if we add 3 kilograms to it , then we see that it has the exact same mass as 10 kilograms . now my question to you is , what can we do to this equation so that we can essentially solve for the unknown , so that we can figure out what the unknown is ? well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right . in order to say they 're equal , the stuff has to actually be balanced . so in the last video , we removed 3 of these . we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here . we will remove 3 , not from one side . if we remove 3 from one side , then it would n't be equal anymore . we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark . and on the right-hand side , we 're left with 10 minus 3 , which is 7 . and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things .
|
what is the average grade level for algebra ?
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things . and so the first thing i want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale . and i 'll give you some hints . we know that they have equal mass . so maybe you can set up some type of relationship using an equal sign , somehow showing that this right over here is equal to that . and i 'll give you a few seconds to do that . so let 's think about it a little bit . what do we have on this side ? well , we have our mystery mass . and i 'll represent that mystery mass by the question mark right over here . but that 's not the only thing that we have on the left-hand side . we also have these other 3 kilograms . so let me write over here . we 'll assume that we 're dealing with kilograms . so we have the mystery mass in kilograms plus 3 more kilograms . that 's what we have here on the left-hand side . now , what do we have here on the right-hand side ? well , we just have 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 kilograms . so we just have 10 . we just have 10 on the right-hand side . and what else do we know ? well , we know that this scale is balanced , that the mass here is equal to the mass here . because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown . we do n't know what this mystery mass is . if we add 3 kilograms to it , then we see that it has the exact same mass as 10 kilograms . now my question to you is , what can we do to this equation so that we can essentially solve for the unknown , so that we can figure out what the unknown is ? well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right . in order to say they 're equal , the stuff has to actually be balanced . so in the last video , we removed 3 of these . we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here . we will remove 3 , not from one side . if we remove 3 from one side , then it would n't be equal anymore . we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark . and on the right-hand side , we 're left with 10 minus 3 , which is 7 . and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
now , what do we have here on the right-hand side ? well , we just have 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 kilograms . so we just have 10 .
|
how many percent for 1.5 ?
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things . and so the first thing i want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale . and i 'll give you some hints . we know that they have equal mass . so maybe you can set up some type of relationship using an equal sign , somehow showing that this right over here is equal to that . and i 'll give you a few seconds to do that . so let 's think about it a little bit . what do we have on this side ? well , we have our mystery mass . and i 'll represent that mystery mass by the question mark right over here . but that 's not the only thing that we have on the left-hand side . we also have these other 3 kilograms . so let me write over here . we 'll assume that we 're dealing with kilograms . so we have the mystery mass in kilograms plus 3 more kilograms . that 's what we have here on the left-hand side . now , what do we have here on the right-hand side ? well , we just have 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 kilograms . so we just have 10 . we just have 10 on the right-hand side . and what else do we know ? well , we know that this scale is balanced , that the mass here is equal to the mass here . because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown . we do n't know what this mystery mass is . if we add 3 kilograms to it , then we see that it has the exact same mass as 10 kilograms . now my question to you is , what can we do to this equation so that we can essentially solve for the unknown , so that we can figure out what the unknown is ? well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right . in order to say they 're equal , the stuff has to actually be balanced . so in the last video , we removed 3 of these . we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here . we will remove 3 , not from one side . if we remove 3 from one side , then it would n't be equal anymore . we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark . and on the right-hand side , we 're left with 10 minus 3 , which is 7 . and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things .
|
who invented log and why ?
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things . and so the first thing i want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale . and i 'll give you some hints . we know that they have equal mass . so maybe you can set up some type of relationship using an equal sign , somehow showing that this right over here is equal to that . and i 'll give you a few seconds to do that . so let 's think about it a little bit . what do we have on this side ? well , we have our mystery mass . and i 'll represent that mystery mass by the question mark right over here . but that 's not the only thing that we have on the left-hand side . we also have these other 3 kilograms . so let me write over here . we 'll assume that we 're dealing with kilograms . so we have the mystery mass in kilograms plus 3 more kilograms . that 's what we have here on the left-hand side . now , what do we have here on the right-hand side ? well , we just have 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 kilograms . so we just have 10 . we just have 10 on the right-hand side . and what else do we know ? well , we know that this scale is balanced , that the mass here is equal to the mass here . because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown . we do n't know what this mystery mass is . if we add 3 kilograms to it , then we see that it has the exact same mass as 10 kilograms . now my question to you is , what can we do to this equation so that we can essentially solve for the unknown , so that we can figure out what the unknown is ? well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right . in order to say they 're equal , the stuff has to actually be balanced . so in the last video , we removed 3 of these . we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here . we will remove 3 , not from one side . if we remove 3 from one side , then it would n't be equal anymore . we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark . and on the right-hand side , we 're left with 10 minus 3 , which is 7 . and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ?
|
why do we need to use a scale in alegbra ?
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things . and so the first thing i want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale . and i 'll give you some hints . we know that they have equal mass . so maybe you can set up some type of relationship using an equal sign , somehow showing that this right over here is equal to that . and i 'll give you a few seconds to do that . so let 's think about it a little bit . what do we have on this side ? well , we have our mystery mass . and i 'll represent that mystery mass by the question mark right over here . but that 's not the only thing that we have on the left-hand side . we also have these other 3 kilograms . so let me write over here . we 'll assume that we 're dealing with kilograms . so we have the mystery mass in kilograms plus 3 more kilograms . that 's what we have here on the left-hand side . now , what do we have here on the right-hand side ? well , we just have 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 kilograms . so we just have 10 . we just have 10 on the right-hand side . and what else do we know ? well , we know that this scale is balanced , that the mass here is equal to the mass here . because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown . we do n't know what this mystery mass is . if we add 3 kilograms to it , then we see that it has the exact same mass as 10 kilograms . now my question to you is , what can we do to this equation so that we can essentially solve for the unknown , so that we can figure out what the unknown is ? well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right . in order to say they 're equal , the stuff has to actually be balanced . so in the last video , we removed 3 of these . we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here . we will remove 3 , not from one side . if we remove 3 from one side , then it would n't be equal anymore . we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark . and on the right-hand side , we 're left with 10 minus 3 , which is 7 . and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
would the question mark be the same as any variable ?
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things . and so the first thing i want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale . and i 'll give you some hints . we know that they have equal mass . so maybe you can set up some type of relationship using an equal sign , somehow showing that this right over here is equal to that . and i 'll give you a few seconds to do that . so let 's think about it a little bit . what do we have on this side ? well , we have our mystery mass . and i 'll represent that mystery mass by the question mark right over here . but that 's not the only thing that we have on the left-hand side . we also have these other 3 kilograms . so let me write over here . we 'll assume that we 're dealing with kilograms . so we have the mystery mass in kilograms plus 3 more kilograms . that 's what we have here on the left-hand side . now , what do we have here on the right-hand side ? well , we just have 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 kilograms . so we just have 10 . we just have 10 on the right-hand side . and what else do we know ? well , we know that this scale is balanced , that the mass here is equal to the mass here . because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown . we do n't know what this mystery mass is . if we add 3 kilograms to it , then we see that it has the exact same mass as 10 kilograms . now my question to you is , what can we do to this equation so that we can essentially solve for the unknown , so that we can figure out what the unknown is ? well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right . in order to say they 're equal , the stuff has to actually be balanced . so in the last video , we removed 3 of these . we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here . we will remove 3 , not from one side . if we remove 3 from one side , then it would n't be equal anymore . we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark . and on the right-hand side , we 're left with 10 minus 3 , which is 7 . and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown .
|
how might i ever use this sort of algebraic equation in a real life problem ?
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things . and so the first thing i want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale . and i 'll give you some hints . we know that they have equal mass . so maybe you can set up some type of relationship using an equal sign , somehow showing that this right over here is equal to that . and i 'll give you a few seconds to do that . so let 's think about it a little bit . what do we have on this side ? well , we have our mystery mass . and i 'll represent that mystery mass by the question mark right over here . but that 's not the only thing that we have on the left-hand side . we also have these other 3 kilograms . so let me write over here . we 'll assume that we 're dealing with kilograms . so we have the mystery mass in kilograms plus 3 more kilograms . that 's what we have here on the left-hand side . now , what do we have here on the right-hand side ? well , we just have 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 kilograms . so we just have 10 . we just have 10 on the right-hand side . and what else do we know ? well , we know that this scale is balanced , that the mass here is equal to the mass here . because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown . we do n't know what this mystery mass is . if we add 3 kilograms to it , then we see that it has the exact same mass as 10 kilograms . now my question to you is , what can we do to this equation so that we can essentially solve for the unknown , so that we can figure out what the unknown is ? well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right . in order to say they 're equal , the stuff has to actually be balanced . so in the last video , we removed 3 of these . we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here . we will remove 3 , not from one side . if we remove 3 from one side , then it would n't be equal anymore . we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark . and on the right-hand side , we 're left with 10 minus 3 , which is 7 . and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
what is the question in the blue box ?
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things . and so the first thing i want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale . and i 'll give you some hints . we know that they have equal mass . so maybe you can set up some type of relationship using an equal sign , somehow showing that this right over here is equal to that . and i 'll give you a few seconds to do that . so let 's think about it a little bit . what do we have on this side ? well , we have our mystery mass . and i 'll represent that mystery mass by the question mark right over here . but that 's not the only thing that we have on the left-hand side . we also have these other 3 kilograms . so let me write over here . we 'll assume that we 're dealing with kilograms . so we have the mystery mass in kilograms plus 3 more kilograms . that 's what we have here on the left-hand side . now , what do we have here on the right-hand side ? well , we just have 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 kilograms . so we just have 10 . we just have 10 on the right-hand side . and what else do we know ? well , we know that this scale is balanced , that the mass here is equal to the mass here . because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown . we do n't know what this mystery mass is . if we add 3 kilograms to it , then we see that it has the exact same mass as 10 kilograms . now my question to you is , what can we do to this equation so that we can essentially solve for the unknown , so that we can figure out what the unknown is ? well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right . in order to say they 're equal , the stuff has to actually be balanced . so in the last video , we removed 3 of these . we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here . we will remove 3 , not from one side . if we remove 3 from one side , then it would n't be equal anymore . we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark . and on the right-hand side , we 're left with 10 minus 3 , which is 7 . and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things .
|
whats the different between y2-x3 ?
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things . and so the first thing i want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale . and i 'll give you some hints . we know that they have equal mass . so maybe you can set up some type of relationship using an equal sign , somehow showing that this right over here is equal to that . and i 'll give you a few seconds to do that . so let 's think about it a little bit . what do we have on this side ? well , we have our mystery mass . and i 'll represent that mystery mass by the question mark right over here . but that 's not the only thing that we have on the left-hand side . we also have these other 3 kilograms . so let me write over here . we 'll assume that we 're dealing with kilograms . so we have the mystery mass in kilograms plus 3 more kilograms . that 's what we have here on the left-hand side . now , what do we have here on the right-hand side ? well , we just have 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 kilograms . so we just have 10 . we just have 10 on the right-hand side . and what else do we know ? well , we know that this scale is balanced , that the mass here is equal to the mass here . because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown . we do n't know what this mystery mass is . if we add 3 kilograms to it , then we see that it has the exact same mass as 10 kilograms . now my question to you is , what can we do to this equation so that we can essentially solve for the unknown , so that we can figure out what the unknown is ? well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right . in order to say they 're equal , the stuff has to actually be balanced . so in the last video , we removed 3 of these . we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here . we will remove 3 , not from one side . if we remove 3 from one side , then it would n't be equal anymore . we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark . and on the right-hand side , we 're left with 10 minus 3 , which is 7 . and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark .
|
is x > 2=x is greater than or equal to 3 ?
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things . and so the first thing i want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale . and i 'll give you some hints . we know that they have equal mass . so maybe you can set up some type of relationship using an equal sign , somehow showing that this right over here is equal to that . and i 'll give you a few seconds to do that . so let 's think about it a little bit . what do we have on this side ? well , we have our mystery mass . and i 'll represent that mystery mass by the question mark right over here . but that 's not the only thing that we have on the left-hand side . we also have these other 3 kilograms . so let me write over here . we 'll assume that we 're dealing with kilograms . so we have the mystery mass in kilograms plus 3 more kilograms . that 's what we have here on the left-hand side . now , what do we have here on the right-hand side ? well , we just have 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 kilograms . so we just have 10 . we just have 10 on the right-hand side . and what else do we know ? well , we know that this scale is balanced , that the mass here is equal to the mass here . because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown . we do n't know what this mystery mass is . if we add 3 kilograms to it , then we see that it has the exact same mass as 10 kilograms . now my question to you is , what can we do to this equation so that we can essentially solve for the unknown , so that we can figure out what the unknown is ? well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right . in order to say they 're equal , the stuff has to actually be balanced . so in the last video , we removed 3 of these . we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here . we will remove 3 , not from one side . if we remove 3 from one side , then it would n't be equal anymore . we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark . and on the right-hand side , we 're left with 10 minus 3 , which is 7 . and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
so in the last video , we removed 3 of these . we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here .
|
how did you do to keep the scale balance ?
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things . and so the first thing i want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale . and i 'll give you some hints . we know that they have equal mass . so maybe you can set up some type of relationship using an equal sign , somehow showing that this right over here is equal to that . and i 'll give you a few seconds to do that . so let 's think about it a little bit . what do we have on this side ? well , we have our mystery mass . and i 'll represent that mystery mass by the question mark right over here . but that 's not the only thing that we have on the left-hand side . we also have these other 3 kilograms . so let me write over here . we 'll assume that we 're dealing with kilograms . so we have the mystery mass in kilograms plus 3 more kilograms . that 's what we have here on the left-hand side . now , what do we have here on the right-hand side ? well , we just have 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 kilograms . so we just have 10 . we just have 10 on the right-hand side . and what else do we know ? well , we know that this scale is balanced , that the mass here is equal to the mass here . because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown . we do n't know what this mystery mass is . if we add 3 kilograms to it , then we see that it has the exact same mass as 10 kilograms . now my question to you is , what can we do to this equation so that we can essentially solve for the unknown , so that we can figure out what the unknown is ? well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right . in order to say they 're equal , the stuff has to actually be balanced . so in the last video , we removed 3 of these . we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here . we will remove 3 , not from one side . if we remove 3 from one side , then it would n't be equal anymore . we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark . and on the right-hand side , we 're left with 10 minus 3 , which is 7 . and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right .
|
why does n't the scale move when he erases the squares ?
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things . and so the first thing i want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale . and i 'll give you some hints . we know that they have equal mass . so maybe you can set up some type of relationship using an equal sign , somehow showing that this right over here is equal to that . and i 'll give you a few seconds to do that . so let 's think about it a little bit . what do we have on this side ? well , we have our mystery mass . and i 'll represent that mystery mass by the question mark right over here . but that 's not the only thing that we have on the left-hand side . we also have these other 3 kilograms . so let me write over here . we 'll assume that we 're dealing with kilograms . so we have the mystery mass in kilograms plus 3 more kilograms . that 's what we have here on the left-hand side . now , what do we have here on the right-hand side ? well , we just have 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 kilograms . so we just have 10 . we just have 10 on the right-hand side . and what else do we know ? well , we know that this scale is balanced , that the mass here is equal to the mass here . because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown . we do n't know what this mystery mass is . if we add 3 kilograms to it , then we see that it has the exact same mass as 10 kilograms . now my question to you is , what can we do to this equation so that we can essentially solve for the unknown , so that we can figure out what the unknown is ? well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right . in order to say they 're equal , the stuff has to actually be balanced . so in the last video , we removed 3 of these . we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here . we will remove 3 , not from one side . if we remove 3 from one side , then it would n't be equal anymore . we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark . and on the right-hand side , we 're left with 10 minus 3 , which is 7 . and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things .
|
why is x the most popular variable ?
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things . and so the first thing i want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale . and i 'll give you some hints . we know that they have equal mass . so maybe you can set up some type of relationship using an equal sign , somehow showing that this right over here is equal to that . and i 'll give you a few seconds to do that . so let 's think about it a little bit . what do we have on this side ? well , we have our mystery mass . and i 'll represent that mystery mass by the question mark right over here . but that 's not the only thing that we have on the left-hand side . we also have these other 3 kilograms . so let me write over here . we 'll assume that we 're dealing with kilograms . so we have the mystery mass in kilograms plus 3 more kilograms . that 's what we have here on the left-hand side . now , what do we have here on the right-hand side ? well , we just have 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 kilograms . so we just have 10 . we just have 10 on the right-hand side . and what else do we know ? well , we know that this scale is balanced , that the mass here is equal to the mass here . because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown . we do n't know what this mystery mass is . if we add 3 kilograms to it , then we see that it has the exact same mass as 10 kilograms . now my question to you is , what can we do to this equation so that we can essentially solve for the unknown , so that we can figure out what the unknown is ? well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right . in order to say they 're equal , the stuff has to actually be balanced . so in the last video , we removed 3 of these . we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here . we will remove 3 , not from one side . if we remove 3 from one side , then it would n't be equal anymore . we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark . and on the right-hand side , we 're left with 10 minus 3 , which is 7 . and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things .
|
why is math so important ?
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things . and so the first thing i want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale . and i 'll give you some hints . we know that they have equal mass . so maybe you can set up some type of relationship using an equal sign , somehow showing that this right over here is equal to that . and i 'll give you a few seconds to do that . so let 's think about it a little bit . what do we have on this side ? well , we have our mystery mass . and i 'll represent that mystery mass by the question mark right over here . but that 's not the only thing that we have on the left-hand side . we also have these other 3 kilograms . so let me write over here . we 'll assume that we 're dealing with kilograms . so we have the mystery mass in kilograms plus 3 more kilograms . that 's what we have here on the left-hand side . now , what do we have here on the right-hand side ? well , we just have 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 kilograms . so we just have 10 . we just have 10 on the right-hand side . and what else do we know ? well , we know that this scale is balanced , that the mass here is equal to the mass here . because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown . we do n't know what this mystery mass is . if we add 3 kilograms to it , then we see that it has the exact same mass as 10 kilograms . now my question to you is , what can we do to this equation so that we can essentially solve for the unknown , so that we can figure out what the unknown is ? well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right . in order to say they 're equal , the stuff has to actually be balanced . so in the last video , we removed 3 of these . we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here . we will remove 3 , not from one side . if we remove 3 from one side , then it would n't be equal anymore . we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark . and on the right-hand side , we 're left with 10 minus 3 , which is 7 . and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things .
|
why is algebra used so much in science ?
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things . and so the first thing i want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale . and i 'll give you some hints . we know that they have equal mass . so maybe you can set up some type of relationship using an equal sign , somehow showing that this right over here is equal to that . and i 'll give you a few seconds to do that . so let 's think about it a little bit . what do we have on this side ? well , we have our mystery mass . and i 'll represent that mystery mass by the question mark right over here . but that 's not the only thing that we have on the left-hand side . we also have these other 3 kilograms . so let me write over here . we 'll assume that we 're dealing with kilograms . so we have the mystery mass in kilograms plus 3 more kilograms . that 's what we have here on the left-hand side . now , what do we have here on the right-hand side ? well , we just have 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 kilograms . so we just have 10 . we just have 10 on the right-hand side . and what else do we know ? well , we know that this scale is balanced , that the mass here is equal to the mass here . because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown . we do n't know what this mystery mass is . if we add 3 kilograms to it , then we see that it has the exact same mass as 10 kilograms . now my question to you is , what can we do to this equation so that we can essentially solve for the unknown , so that we can figure out what the unknown is ? well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right . in order to say they 're equal , the stuff has to actually be balanced . so in the last video , we removed 3 of these . we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here . we will remove 3 , not from one side . if we remove 3 from one side , then it would n't be equal anymore . we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark . and on the right-hand side , we 're left with 10 minus 3 , which is 7 . and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things .
|
why is algebra needed to measure some object ?
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things . and so the first thing i want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale . and i 'll give you some hints . we know that they have equal mass . so maybe you can set up some type of relationship using an equal sign , somehow showing that this right over here is equal to that . and i 'll give you a few seconds to do that . so let 's think about it a little bit . what do we have on this side ? well , we have our mystery mass . and i 'll represent that mystery mass by the question mark right over here . but that 's not the only thing that we have on the left-hand side . we also have these other 3 kilograms . so let me write over here . we 'll assume that we 're dealing with kilograms . so we have the mystery mass in kilograms plus 3 more kilograms . that 's what we have here on the left-hand side . now , what do we have here on the right-hand side ? well , we just have 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 kilograms . so we just have 10 . we just have 10 on the right-hand side . and what else do we know ? well , we know that this scale is balanced , that the mass here is equal to the mass here . because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown . we do n't know what this mystery mass is . if we add 3 kilograms to it , then we see that it has the exact same mass as 10 kilograms . now my question to you is , what can we do to this equation so that we can essentially solve for the unknown , so that we can figure out what the unknown is ? well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right . in order to say they 're equal , the stuff has to actually be balanced . so in the last video , we removed 3 of these . we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here . we will remove 3 , not from one side . if we remove 3 from one side , then it would n't be equal anymore . we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark . and on the right-hand side , we 're left with 10 minus 3 , which is 7 . and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right .
|
how come the scale dose n't move ?
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things . and so the first thing i want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale . and i 'll give you some hints . we know that they have equal mass . so maybe you can set up some type of relationship using an equal sign , somehow showing that this right over here is equal to that . and i 'll give you a few seconds to do that . so let 's think about it a little bit . what do we have on this side ? well , we have our mystery mass . and i 'll represent that mystery mass by the question mark right over here . but that 's not the only thing that we have on the left-hand side . we also have these other 3 kilograms . so let me write over here . we 'll assume that we 're dealing with kilograms . so we have the mystery mass in kilograms plus 3 more kilograms . that 's what we have here on the left-hand side . now , what do we have here on the right-hand side ? well , we just have 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 kilograms . so we just have 10 . we just have 10 on the right-hand side . and what else do we know ? well , we know that this scale is balanced , that the mass here is equal to the mass here . because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown . we do n't know what this mystery mass is . if we add 3 kilograms to it , then we see that it has the exact same mass as 10 kilograms . now my question to you is , what can we do to this equation so that we can essentially solve for the unknown , so that we can figure out what the unknown is ? well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right . in order to say they 're equal , the stuff has to actually be balanced . so in the last video , we removed 3 of these . we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here . we will remove 3 , not from one side . if we remove 3 from one side , then it would n't be equal anymore . we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark . and on the right-hand side , we 're left with 10 minus 3 , which is 7 . and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark .
|
so , when we have an unknown mass , we take however much away from side # 1 , and then we do the same to the other side ( # 2 ) , then what is left on side # 2 is how much the unknown mass weighs ?
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things . and so the first thing i want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale . and i 'll give you some hints . we know that they have equal mass . so maybe you can set up some type of relationship using an equal sign , somehow showing that this right over here is equal to that . and i 'll give you a few seconds to do that . so let 's think about it a little bit . what do we have on this side ? well , we have our mystery mass . and i 'll represent that mystery mass by the question mark right over here . but that 's not the only thing that we have on the left-hand side . we also have these other 3 kilograms . so let me write over here . we 'll assume that we 're dealing with kilograms . so we have the mystery mass in kilograms plus 3 more kilograms . that 's what we have here on the left-hand side . now , what do we have here on the right-hand side ? well , we just have 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 kilograms . so we just have 10 . we just have 10 on the right-hand side . and what else do we know ? well , we know that this scale is balanced , that the mass here is equal to the mass here . because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown . we do n't know what this mystery mass is . if we add 3 kilograms to it , then we see that it has the exact same mass as 10 kilograms . now my question to you is , what can we do to this equation so that we can essentially solve for the unknown , so that we can figure out what the unknown is ? well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right . in order to say they 're equal , the stuff has to actually be balanced . so in the last video , we removed 3 of these . we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here . we will remove 3 , not from one side . if we remove 3 from one side , then it would n't be equal anymore . we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark . and on the right-hand side , we 're left with 10 minus 3 , which is 7 . and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things .
|
why is algebra so important ?
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things . and so the first thing i want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale . and i 'll give you some hints . we know that they have equal mass . so maybe you can set up some type of relationship using an equal sign , somehow showing that this right over here is equal to that . and i 'll give you a few seconds to do that . so let 's think about it a little bit . what do we have on this side ? well , we have our mystery mass . and i 'll represent that mystery mass by the question mark right over here . but that 's not the only thing that we have on the left-hand side . we also have these other 3 kilograms . so let me write over here . we 'll assume that we 're dealing with kilograms . so we have the mystery mass in kilograms plus 3 more kilograms . that 's what we have here on the left-hand side . now , what do we have here on the right-hand side ? well , we just have 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 kilograms . so we just have 10 . we just have 10 on the right-hand side . and what else do we know ? well , we know that this scale is balanced , that the mass here is equal to the mass here . because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown . we do n't know what this mystery mass is . if we add 3 kilograms to it , then we see that it has the exact same mass as 10 kilograms . now my question to you is , what can we do to this equation so that we can essentially solve for the unknown , so that we can figure out what the unknown is ? well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right . in order to say they 're equal , the stuff has to actually be balanced . so in the last video , we removed 3 of these . we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here . we will remove 3 , not from one side . if we remove 3 from one side , then it would n't be equal anymore . we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark . and on the right-hand side , we 're left with 10 minus 3 , which is 7 . and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
we just have 10 on the right-hand side . and what else do we know ? well , we know that this scale is balanced , that the mass here is equal to the mass here .
|
why do we need relationships to understand the problem , even if we know that the answer would be an integer ?
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things . and so the first thing i want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale . and i 'll give you some hints . we know that they have equal mass . so maybe you can set up some type of relationship using an equal sign , somehow showing that this right over here is equal to that . and i 'll give you a few seconds to do that . so let 's think about it a little bit . what do we have on this side ? well , we have our mystery mass . and i 'll represent that mystery mass by the question mark right over here . but that 's not the only thing that we have on the left-hand side . we also have these other 3 kilograms . so let me write over here . we 'll assume that we 're dealing with kilograms . so we have the mystery mass in kilograms plus 3 more kilograms . that 's what we have here on the left-hand side . now , what do we have here on the right-hand side ? well , we just have 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 kilograms . so we just have 10 . we just have 10 on the right-hand side . and what else do we know ? well , we know that this scale is balanced , that the mass here is equal to the mass here . because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown . we do n't know what this mystery mass is . if we add 3 kilograms to it , then we see that it has the exact same mass as 10 kilograms . now my question to you is , what can we do to this equation so that we can essentially solve for the unknown , so that we can figure out what the unknown is ? well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right . in order to say they 're equal , the stuff has to actually be balanced . so in the last video , we removed 3 of these . we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here . we will remove 3 , not from one side . if we remove 3 from one side , then it would n't be equal anymore . we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark . and on the right-hand side , we 're left with 10 minus 3 , which is 7 . and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark .
|
why do we even have to remove the three squares from the left side ?
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things . and so the first thing i want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale . and i 'll give you some hints . we know that they have equal mass . so maybe you can set up some type of relationship using an equal sign , somehow showing that this right over here is equal to that . and i 'll give you a few seconds to do that . so let 's think about it a little bit . what do we have on this side ? well , we have our mystery mass . and i 'll represent that mystery mass by the question mark right over here . but that 's not the only thing that we have on the left-hand side . we also have these other 3 kilograms . so let me write over here . we 'll assume that we 're dealing with kilograms . so we have the mystery mass in kilograms plus 3 more kilograms . that 's what we have here on the left-hand side . now , what do we have here on the right-hand side ? well , we just have 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 kilograms . so we just have 10 . we just have 10 on the right-hand side . and what else do we know ? well , we know that this scale is balanced , that the mass here is equal to the mass here . because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown . we do n't know what this mystery mass is . if we add 3 kilograms to it , then we see that it has the exact same mass as 10 kilograms . now my question to you is , what can we do to this equation so that we can essentially solve for the unknown , so that we can figure out what the unknown is ? well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right . in order to say they 're equal , the stuff has to actually be balanced . so in the last video , we removed 3 of these . we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here . we will remove 3 , not from one side . if we remove 3 from one side , then it would n't be equal anymore . we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark . and on the right-hand side , we 're left with 10 minus 3 , which is 7 . and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
why the box in blue has a question mark , instead of a x ?
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things . and so the first thing i want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale . and i 'll give you some hints . we know that they have equal mass . so maybe you can set up some type of relationship using an equal sign , somehow showing that this right over here is equal to that . and i 'll give you a few seconds to do that . so let 's think about it a little bit . what do we have on this side ? well , we have our mystery mass . and i 'll represent that mystery mass by the question mark right over here . but that 's not the only thing that we have on the left-hand side . we also have these other 3 kilograms . so let me write over here . we 'll assume that we 're dealing with kilograms . so we have the mystery mass in kilograms plus 3 more kilograms . that 's what we have here on the left-hand side . now , what do we have here on the right-hand side ? well , we just have 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 kilograms . so we just have 10 . we just have 10 on the right-hand side . and what else do we know ? well , we know that this scale is balanced , that the mass here is equal to the mass here . because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown . we do n't know what this mystery mass is . if we add 3 kilograms to it , then we see that it has the exact same mass as 10 kilograms . now my question to you is , what can we do to this equation so that we can essentially solve for the unknown , so that we can figure out what the unknown is ? well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right . in order to say they 're equal , the stuff has to actually be balanced . so in the last video , we removed 3 of these . we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here . we will remove 3 , not from one side . if we remove 3 from one side , then it would n't be equal anymore . we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark . and on the right-hand side , we 're left with 10 minus 3 , which is 7 . and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown .
|
how does linear equation work ?
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things . and so the first thing i want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale . and i 'll give you some hints . we know that they have equal mass . so maybe you can set up some type of relationship using an equal sign , somehow showing that this right over here is equal to that . and i 'll give you a few seconds to do that . so let 's think about it a little bit . what do we have on this side ? well , we have our mystery mass . and i 'll represent that mystery mass by the question mark right over here . but that 's not the only thing that we have on the left-hand side . we also have these other 3 kilograms . so let me write over here . we 'll assume that we 're dealing with kilograms . so we have the mystery mass in kilograms plus 3 more kilograms . that 's what we have here on the left-hand side . now , what do we have here on the right-hand side ? well , we just have 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 kilograms . so we just have 10 . we just have 10 on the right-hand side . and what else do we know ? well , we know that this scale is balanced , that the mass here is equal to the mass here . because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown . we do n't know what this mystery mass is . if we add 3 kilograms to it , then we see that it has the exact same mass as 10 kilograms . now my question to you is , what can we do to this equation so that we can essentially solve for the unknown , so that we can figure out what the unknown is ? well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right . in order to say they 're equal , the stuff has to actually be balanced . so in the last video , we removed 3 of these . we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here . we will remove 3 , not from one side . if we remove 3 from one side , then it would n't be equal anymore . we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark . and on the right-hand side , we 're left with 10 minus 3 , which is 7 . and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things .
|
why is math so important ?
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things . and so the first thing i want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale . and i 'll give you some hints . we know that they have equal mass . so maybe you can set up some type of relationship using an equal sign , somehow showing that this right over here is equal to that . and i 'll give you a few seconds to do that . so let 's think about it a little bit . what do we have on this side ? well , we have our mystery mass . and i 'll represent that mystery mass by the question mark right over here . but that 's not the only thing that we have on the left-hand side . we also have these other 3 kilograms . so let me write over here . we 'll assume that we 're dealing with kilograms . so we have the mystery mass in kilograms plus 3 more kilograms . that 's what we have here on the left-hand side . now , what do we have here on the right-hand side ? well , we just have 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 kilograms . so we just have 10 . we just have 10 on the right-hand side . and what else do we know ? well , we know that this scale is balanced , that the mass here is equal to the mass here . because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown . we do n't know what this mystery mass is . if we add 3 kilograms to it , then we see that it has the exact same mass as 10 kilograms . now my question to you is , what can we do to this equation so that we can essentially solve for the unknown , so that we can figure out what the unknown is ? well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right . in order to say they 're equal , the stuff has to actually be balanced . so in the last video , we removed 3 of these . we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here . we will remove 3 , not from one side . if we remove 3 from one side , then it would n't be equal anymore . we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark . and on the right-hand side , we 're left with 10 minus 3 , which is 7 . and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things . and so the first thing i want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale .
|
how is math the same as ideas ?
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things . and so the first thing i want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale . and i 'll give you some hints . we know that they have equal mass . so maybe you can set up some type of relationship using an equal sign , somehow showing that this right over here is equal to that . and i 'll give you a few seconds to do that . so let 's think about it a little bit . what do we have on this side ? well , we have our mystery mass . and i 'll represent that mystery mass by the question mark right over here . but that 's not the only thing that we have on the left-hand side . we also have these other 3 kilograms . so let me write over here . we 'll assume that we 're dealing with kilograms . so we have the mystery mass in kilograms plus 3 more kilograms . that 's what we have here on the left-hand side . now , what do we have here on the right-hand side ? well , we just have 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 kilograms . so we just have 10 . we just have 10 on the right-hand side . and what else do we know ? well , we know that this scale is balanced , that the mass here is equal to the mass here . because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown . we do n't know what this mystery mass is . if we add 3 kilograms to it , then we see that it has the exact same mass as 10 kilograms . now my question to you is , what can we do to this equation so that we can essentially solve for the unknown , so that we can figure out what the unknown is ? well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right . in order to say they 're equal , the stuff has to actually be balanced . so in the last video , we removed 3 of these . we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here . we will remove 3 , not from one side . if we remove 3 from one side , then it would n't be equal anymore . we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark . and on the right-hand side , we 're left with 10 minus 3 , which is 7 . and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here . we will remove 3 , not from one side .
|
what is most important thing to learn in math ?
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things . and so the first thing i want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale . and i 'll give you some hints . we know that they have equal mass . so maybe you can set up some type of relationship using an equal sign , somehow showing that this right over here is equal to that . and i 'll give you a few seconds to do that . so let 's think about it a little bit . what do we have on this side ? well , we have our mystery mass . and i 'll represent that mystery mass by the question mark right over here . but that 's not the only thing that we have on the left-hand side . we also have these other 3 kilograms . so let me write over here . we 'll assume that we 're dealing with kilograms . so we have the mystery mass in kilograms plus 3 more kilograms . that 's what we have here on the left-hand side . now , what do we have here on the right-hand side ? well , we just have 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 kilograms . so we just have 10 . we just have 10 on the right-hand side . and what else do we know ? well , we know that this scale is balanced , that the mass here is equal to the mass here . because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown . we do n't know what this mystery mass is . if we add 3 kilograms to it , then we see that it has the exact same mass as 10 kilograms . now my question to you is , what can we do to this equation so that we can essentially solve for the unknown , so that we can figure out what the unknown is ? well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right . in order to say they 're equal , the stuff has to actually be balanced . so in the last video , we removed 3 of these . we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here . we will remove 3 , not from one side . if we remove 3 from one side , then it would n't be equal anymore . we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark . and on the right-hand side , we 're left with 10 minus 3 , which is 7 . and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things .
|
what is algebra and what is the difference between algebra and math ?
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things . and so the first thing i want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale . and i 'll give you some hints . we know that they have equal mass . so maybe you can set up some type of relationship using an equal sign , somehow showing that this right over here is equal to that . and i 'll give you a few seconds to do that . so let 's think about it a little bit . what do we have on this side ? well , we have our mystery mass . and i 'll represent that mystery mass by the question mark right over here . but that 's not the only thing that we have on the left-hand side . we also have these other 3 kilograms . so let me write over here . we 'll assume that we 're dealing with kilograms . so we have the mystery mass in kilograms plus 3 more kilograms . that 's what we have here on the left-hand side . now , what do we have here on the right-hand side ? well , we just have 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 kilograms . so we just have 10 . we just have 10 on the right-hand side . and what else do we know ? well , we know that this scale is balanced , that the mass here is equal to the mass here . because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown . we do n't know what this mystery mass is . if we add 3 kilograms to it , then we see that it has the exact same mass as 10 kilograms . now my question to you is , what can we do to this equation so that we can essentially solve for the unknown , so that we can figure out what the unknown is ? well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right . in order to say they 're equal , the stuff has to actually be balanced . so in the last video , we removed 3 of these . we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here . we will remove 3 , not from one side . if we remove 3 from one side , then it would n't be equal anymore . we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark . and on the right-hand side , we 're left with 10 minus 3 , which is 7 . and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
if we remove 3 from one side , then it would n't be equal anymore . we need to remove 3 from both sides . so we need to remove 3 .
|
what if we had a mystery block on both sides and only knew the weight of both sides put together ?
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things . and so the first thing i want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale . and i 'll give you some hints . we know that they have equal mass . so maybe you can set up some type of relationship using an equal sign , somehow showing that this right over here is equal to that . and i 'll give you a few seconds to do that . so let 's think about it a little bit . what do we have on this side ? well , we have our mystery mass . and i 'll represent that mystery mass by the question mark right over here . but that 's not the only thing that we have on the left-hand side . we also have these other 3 kilograms . so let me write over here . we 'll assume that we 're dealing with kilograms . so we have the mystery mass in kilograms plus 3 more kilograms . that 's what we have here on the left-hand side . now , what do we have here on the right-hand side ? well , we just have 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 kilograms . so we just have 10 . we just have 10 on the right-hand side . and what else do we know ? well , we know that this scale is balanced , that the mass here is equal to the mass here . because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown . we do n't know what this mystery mass is . if we add 3 kilograms to it , then we see that it has the exact same mass as 10 kilograms . now my question to you is , what can we do to this equation so that we can essentially solve for the unknown , so that we can figure out what the unknown is ? well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right . in order to say they 're equal , the stuff has to actually be balanced . so in the last video , we removed 3 of these . we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here . we will remove 3 , not from one side . if we remove 3 from one side , then it would n't be equal anymore . we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark . and on the right-hand side , we 're left with 10 minus 3 , which is 7 . and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things .
|
why is everything out of date ?
|
i now want to refigure out what this mystery mass is , but we 're going to start using a little bit more of mathematics . and mathematics really are just a language , symbols for representing ideas , for representing relationships between things . and so the first thing i want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale . and i 'll give you some hints . we know that they have equal mass . so maybe you can set up some type of relationship using an equal sign , somehow showing that this right over here is equal to that . and i 'll give you a few seconds to do that . so let 's think about it a little bit . what do we have on this side ? well , we have our mystery mass . and i 'll represent that mystery mass by the question mark right over here . but that 's not the only thing that we have on the left-hand side . we also have these other 3 kilograms . so let me write over here . we 'll assume that we 're dealing with kilograms . so we have the mystery mass in kilograms plus 3 more kilograms . that 's what we have here on the left-hand side . now , what do we have here on the right-hand side ? well , we just have 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 kilograms . so we just have 10 . we just have 10 on the right-hand side . and what else do we know ? well , we know that this scale is balanced , that the mass here is equal to the mass here . because the scale is balanced the way it 's been drawn , we know that these two things are equal . so we have just set up an equation . we 're using question mark as our unknown . we do n't know what this mystery mass is . if we add 3 kilograms to it , then we see that it has the exact same mass as 10 kilograms . now my question to you is , what can we do to this equation so that we can essentially solve for the unknown , so that we can figure out what the unknown is ? well , we saw in the last little problem that we had that if we wanted to figure out this mystery mass , we had to remove 3 kilograms from both sides . if we just removed 3 kilograms from one side , then the scale would n't be balanced anymore . and we really would n't be able to say that the mystery mass is equal to the thing on the right . in order to say they 're equal , the stuff has to actually be balanced . so in the last video , we removed 3 of these . we removed 3 kilograms from both sides in order to keep the scale balanced . so mathematically , we 'll do the exact same thing over here . we will remove 3 , not from one side . if we remove 3 from one side , then it would n't be equal anymore . we need to remove 3 from both sides . so we need to remove 3 . we need to subtract 3 from both sides of this equation in order to keep the scale balanced . so on the left-hand side , what are we left with ? well , just like over here , we 're left with just the question mark . 3 minus 3 is 0 . so on the left-hand side , we 're left with just the question mark . and on the right-hand side , we 're left with 10 minus 3 , which is 7 . and we get the exact same result . question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
question mark is equal to 7 . and if we 're dealing with kilograms , then this is 7 kilograms .
|
why is it that we need to learn math in the first place ?
|
( music ) ( `` in the sky with diamonds '' by scalding lucy ) steven : we 're in the louvre and we 're looking at a nicholas poussin , et in arcadia ego . we have four figures . we see ancient shepherds and a very classical female figure . beth : clearly based on ancient greek and roman sculpture , as are all the figures , actually . and that treatment of the drapery that looks back to ancient greece and the classical period . steven : right in the center , the largest , most dominant form is a tomb . this huge solid block of masonry . beth : and a figure who 's pointing at it and looks back at the female figure , almost alarmed at what they 're reading . steven : there 's a little ambiguity . is it possible they 're having difficulty reading ? do they not know this language ? or you 're right , are they disturbed by the message ? beth : `` i too am in arcadia '' meaning even death is in arcadia . the landscape has a setting sun . there 's a strong shadow on the tomb cast by the kneeling figure and there 's a real sense of a poetic passage of time . steven : that initial time is important . if you look at the tomb , it 's not new . although it 's stone , it 's been harmed over time and we get a sense that it is even more ancient than these ancient people . this is a bridge back in time . poussin was so interested in the archaeology of the past . beth : that 's right . steven : resurrecting it through color , through form , through style and through subject . beth : one gets a sense that in looking back by poussin to ancient greek and roman culture , he must have had a sense of ... steven : longing for the past . beth : and also a sense of the transience of human life and of what human being make . steven : in a sense , the power of art to transcend time this way , both in terms of what 's represented , this tomb as a kind of art . but then also , of course , this painting itself . ( music ) ( `` in the sky with diamonds '' by scalding lucy )
|
is it possible they 're having difficulty reading ? do they not know this language ? or you 're right , are they disturbed by the message ?
|
does anyone know what kind of footwear this is ?
|
( music ) ( `` in the sky with diamonds '' by scalding lucy ) steven : we 're in the louvre and we 're looking at a nicholas poussin , et in arcadia ego . we have four figures . we see ancient shepherds and a very classical female figure . beth : clearly based on ancient greek and roman sculpture , as are all the figures , actually . and that treatment of the drapery that looks back to ancient greece and the classical period . steven : right in the center , the largest , most dominant form is a tomb . this huge solid block of masonry . beth : and a figure who 's pointing at it and looks back at the female figure , almost alarmed at what they 're reading . steven : there 's a little ambiguity . is it possible they 're having difficulty reading ? do they not know this language ? or you 're right , are they disturbed by the message ? beth : `` i too am in arcadia '' meaning even death is in arcadia . the landscape has a setting sun . there 's a strong shadow on the tomb cast by the kneeling figure and there 's a real sense of a poetic passage of time . steven : that initial time is important . if you look at the tomb , it 's not new . although it 's stone , it 's been harmed over time and we get a sense that it is even more ancient than these ancient people . this is a bridge back in time . poussin was so interested in the archaeology of the past . beth : that 's right . steven : resurrecting it through color , through form , through style and through subject . beth : one gets a sense that in looking back by poussin to ancient greek and roman culture , he must have had a sense of ... steven : longing for the past . beth : and also a sense of the transience of human life and of what human being make . steven : in a sense , the power of art to transcend time this way , both in terms of what 's represented , this tomb as a kind of art . but then also , of course , this painting itself . ( music ) ( `` in the sky with diamonds '' by scalding lucy )
|
steven : that initial time is important . if you look at the tomb , it 's not new . although it 's stone , it 's been harmed over time and we get a sense that it is even more ancient than these ancient people .
|
is n't that a strange looking tomb ?
|
( music ) ( `` in the sky with diamonds '' by scalding lucy ) steven : we 're in the louvre and we 're looking at a nicholas poussin , et in arcadia ego . we have four figures . we see ancient shepherds and a very classical female figure . beth : clearly based on ancient greek and roman sculpture , as are all the figures , actually . and that treatment of the drapery that looks back to ancient greece and the classical period . steven : right in the center , the largest , most dominant form is a tomb . this huge solid block of masonry . beth : and a figure who 's pointing at it and looks back at the female figure , almost alarmed at what they 're reading . steven : there 's a little ambiguity . is it possible they 're having difficulty reading ? do they not know this language ? or you 're right , are they disturbed by the message ? beth : `` i too am in arcadia '' meaning even death is in arcadia . the landscape has a setting sun . there 's a strong shadow on the tomb cast by the kneeling figure and there 's a real sense of a poetic passage of time . steven : that initial time is important . if you look at the tomb , it 's not new . although it 's stone , it 's been harmed over time and we get a sense that it is even more ancient than these ancient people . this is a bridge back in time . poussin was so interested in the archaeology of the past . beth : that 's right . steven : resurrecting it through color , through form , through style and through subject . beth : one gets a sense that in looking back by poussin to ancient greek and roman culture , he must have had a sense of ... steven : longing for the past . beth : and also a sense of the transience of human life and of what human being make . steven : in a sense , the power of art to transcend time this way , both in terms of what 's represented , this tomb as a kind of art . but then also , of course , this painting itself . ( music ) ( `` in the sky with diamonds '' by scalding lucy )
|
if you look at the tomb , it 's not new . although it 's stone , it 's been harmed over time and we get a sense that it is even more ancient than these ancient people . this is a bridge back in time .
|
as did the greeks or ancient romans have tombs like that ?
|
( music ) ( `` in the sky with diamonds '' by scalding lucy ) steven : we 're in the louvre and we 're looking at a nicholas poussin , et in arcadia ego . we have four figures . we see ancient shepherds and a very classical female figure . beth : clearly based on ancient greek and roman sculpture , as are all the figures , actually . and that treatment of the drapery that looks back to ancient greece and the classical period . steven : right in the center , the largest , most dominant form is a tomb . this huge solid block of masonry . beth : and a figure who 's pointing at it and looks back at the female figure , almost alarmed at what they 're reading . steven : there 's a little ambiguity . is it possible they 're having difficulty reading ? do they not know this language ? or you 're right , are they disturbed by the message ? beth : `` i too am in arcadia '' meaning even death is in arcadia . the landscape has a setting sun . there 's a strong shadow on the tomb cast by the kneeling figure and there 's a real sense of a poetic passage of time . steven : that initial time is important . if you look at the tomb , it 's not new . although it 's stone , it 's been harmed over time and we get a sense that it is even more ancient than these ancient people . this is a bridge back in time . poussin was so interested in the archaeology of the past . beth : that 's right . steven : resurrecting it through color , through form , through style and through subject . beth : one gets a sense that in looking back by poussin to ancient greek and roman culture , he must have had a sense of ... steven : longing for the past . beth : and also a sense of the transience of human life and of what human being make . steven : in a sense , the power of art to transcend time this way , both in terms of what 's represented , this tomb as a kind of art . but then also , of course , this painting itself . ( music ) ( `` in the sky with diamonds '' by scalding lucy )
|
steven : in a sense , the power of art to transcend time this way , both in terms of what 's represented , this tomb as a kind of art . but then also , of course , this painting itself . ( music ) ( `` in the sky with diamonds '' by scalding lucy )
|
is the painting baroque style ?
|
hybridization can have a large effect on the stabilization of a conjugate base . so if we start off with ethane , here 's the ethane molecule , we know the hybridization of this carbon , we know this carbon is sp3 hybridized . so let 's say that ethane donates a proton and let 's make it this proton right here . so the electrons in this bond , the electrons in magenta are left behind on that carbon to form the conjugate base . so here are the electrons in magenta and this carbon is sp3 hybridized which means the electrons in magenta occupy an sp3 hybrid orbital . so that 's meant to represent an sp3 hybrid orbital . we know from the videos on hybridization that an sp3 hybridized orbital has 25 % s character and 75 % p character . so i 'm just going to write down here 25 % s character . let 's more on to ethene or ethylene . this carbon is sp2 hybridized so we know that this carbon in ethene is sp2 hybridized . if ethene donates this proton , the electrons in magenta are left behind . so here are the electrons in magenta . this is the conjugate base to ethene and this carbon is sp2 hybridized . so the lone pair of electrons , the electrons in magenta occupy an sp2 hybridized orbital . so that 's supposed to represent an sp2 hybrid orbital . an sp2 hybridized orbital has approximately 33 % s character . so , i 'm gon na write down here 33 % s character . finally , we have acetylene . this carbon in acetylene is sp hybridized . so if acetylene donates a proton , if acetylene donates this proton , then these electrons are left behind . so the electrons in magenta are these electrons and this carbon is sp hybridized so the electrons in magenta occupy an sp hybrid orbital . an sp hybrid orbital is 50 % s character . so this is 50 % s character . now , let 's look at pka values . so the pka for this proton on ethane is approximately 50 . the pka value for this proton on ethene is approximately 44 . and the pka value for this proton on acetylene is about 25 . we know the lower the pka value , the stronger the acid . so as we move to the right , we see a decrease in pka values . and therefore , that 's an increase in the acidity . so we 're talking about increase in the acid strength . so acetylene is the strongest acid out of these three . if acetylene is the strongest acid , that must mean it has the most stable conjugate base . so this conjugate base here to acetylene must be the most stable out of these three . so as we move to the right , we are increasing in stability . so increasing in the stability of the conjugate base . so how do we explain the increased stability of the conjugate base in terms of hybridization ? well , let 's look at the hybrid orbitals that we were talking about here . for the first conjugate base , our lone pair of electrons occupy an sp3 hybridized orbital and that was 25 % s character . and as we went to the right for our conjugate bases , we increased in s character to 33 % to 50 % . so as we move to the right , we increase in stability . we also increase in s character . so increasing in s character increases the stability of the conjugate base and we can explain that by thinking about s and p orbitals . on average , an s orbital has electron density closer to the nucleus than a p orbital . so as you increase in s character , you 're increasing in electron density closest to the nucleus . so let me go ahead and point out what i mean here . so let 's look at this lone pair of electrons in the conjugate base to ethane . we think about the distance of those electrons to the nucleus . an sp3 hybridized orbital has the smallest amount of s character therefore those electrons are on average further away from the nucleus . that 's less stable , that 's higher in energy . as we move to the right , we can see that that distance decreases . so the distance decreases . and finally , for an sp hybridized orbital , that 's the shortest distance between that lone pair of electrons and the positively charged nucleus . if you decrease the distance between the positively charged nucleus and the electrons , that means you increase the force of attraction . so this conjugate base is the most stable because there 's a greater attraction to the nucleus for those electrons . so the nucleus is better able to hold onto those electrons , is a greater force and that means increased stability or lower energy . so this is the most stable conjugate base . if that 's the most stable conjugate base , then acetylene is the most acidic compound out of those three . so this also has an effect on electronegativity . if an sp hybridized carbon is better able to attract electrons , well think about our definition for electronegativity . it 's the power of an atom to attract electrons to itself . so since the electrons are closer to the positively charged nucleus in an sp hybridized carbon so that must mean that sp hybridized carbons are more electronegative . so an sp hybridized carbon is more electronegative than an sp2 hybridized carbon and an sp2 hybridized carbon is more electronegative than an sp3 hybridized carbon . so it has to do with the amount of s character . and that might seem weird because so far we 've said that carbon has a certain value for the electronegativity and we 've always assumed that it 's the same but now we can see that it 's different . an sp hybridized carbon is actually the most electronegative .
|
so this is the most stable conjugate base . if that 's the most stable conjugate base , then acetylene is the most acidic compound out of those three . so this also has an effect on electronegativity .
|
so consider , i take a compound having many chlorines - 2 at the middle carbons ( as they have 2 valencies each ) and three for the last carbon - is n't this gon na exert too much inductive effect which may possibly cause the compound to be somewhat unstable ?
|
hybridization can have a large effect on the stabilization of a conjugate base . so if we start off with ethane , here 's the ethane molecule , we know the hybridization of this carbon , we know this carbon is sp3 hybridized . so let 's say that ethane donates a proton and let 's make it this proton right here . so the electrons in this bond , the electrons in magenta are left behind on that carbon to form the conjugate base . so here are the electrons in magenta and this carbon is sp3 hybridized which means the electrons in magenta occupy an sp3 hybrid orbital . so that 's meant to represent an sp3 hybrid orbital . we know from the videos on hybridization that an sp3 hybridized orbital has 25 % s character and 75 % p character . so i 'm just going to write down here 25 % s character . let 's more on to ethene or ethylene . this carbon is sp2 hybridized so we know that this carbon in ethene is sp2 hybridized . if ethene donates this proton , the electrons in magenta are left behind . so here are the electrons in magenta . this is the conjugate base to ethene and this carbon is sp2 hybridized . so the lone pair of electrons , the electrons in magenta occupy an sp2 hybridized orbital . so that 's supposed to represent an sp2 hybrid orbital . an sp2 hybridized orbital has approximately 33 % s character . so , i 'm gon na write down here 33 % s character . finally , we have acetylene . this carbon in acetylene is sp hybridized . so if acetylene donates a proton , if acetylene donates this proton , then these electrons are left behind . so the electrons in magenta are these electrons and this carbon is sp hybridized so the electrons in magenta occupy an sp hybrid orbital . an sp hybrid orbital is 50 % s character . so this is 50 % s character . now , let 's look at pka values . so the pka for this proton on ethane is approximately 50 . the pka value for this proton on ethene is approximately 44 . and the pka value for this proton on acetylene is about 25 . we know the lower the pka value , the stronger the acid . so as we move to the right , we see a decrease in pka values . and therefore , that 's an increase in the acidity . so we 're talking about increase in the acid strength . so acetylene is the strongest acid out of these three . if acetylene is the strongest acid , that must mean it has the most stable conjugate base . so this conjugate base here to acetylene must be the most stable out of these three . so as we move to the right , we are increasing in stability . so increasing in the stability of the conjugate base . so how do we explain the increased stability of the conjugate base in terms of hybridization ? well , let 's look at the hybrid orbitals that we were talking about here . for the first conjugate base , our lone pair of electrons occupy an sp3 hybridized orbital and that was 25 % s character . and as we went to the right for our conjugate bases , we increased in s character to 33 % to 50 % . so as we move to the right , we increase in stability . we also increase in s character . so increasing in s character increases the stability of the conjugate base and we can explain that by thinking about s and p orbitals . on average , an s orbital has electron density closer to the nucleus than a p orbital . so as you increase in s character , you 're increasing in electron density closest to the nucleus . so let me go ahead and point out what i mean here . so let 's look at this lone pair of electrons in the conjugate base to ethane . we think about the distance of those electrons to the nucleus . an sp3 hybridized orbital has the smallest amount of s character therefore those electrons are on average further away from the nucleus . that 's less stable , that 's higher in energy . as we move to the right , we can see that that distance decreases . so the distance decreases . and finally , for an sp hybridized orbital , that 's the shortest distance between that lone pair of electrons and the positively charged nucleus . if you decrease the distance between the positively charged nucleus and the electrons , that means you increase the force of attraction . so this conjugate base is the most stable because there 's a greater attraction to the nucleus for those electrons . so the nucleus is better able to hold onto those electrons , is a greater force and that means increased stability or lower energy . so this is the most stable conjugate base . if that 's the most stable conjugate base , then acetylene is the most acidic compound out of those three . so this also has an effect on electronegativity . if an sp hybridized carbon is better able to attract electrons , well think about our definition for electronegativity . it 's the power of an atom to attract electrons to itself . so since the electrons are closer to the positively charged nucleus in an sp hybridized carbon so that must mean that sp hybridized carbons are more electronegative . so an sp hybridized carbon is more electronegative than an sp2 hybridized carbon and an sp2 hybridized carbon is more electronegative than an sp3 hybridized carbon . so it has to do with the amount of s character . and that might seem weird because so far we 've said that carbon has a certain value for the electronegativity and we 've always assumed that it 's the same but now we can see that it 's different . an sp hybridized carbon is actually the most electronegative .
|
and as we went to the right for our conjugate bases , we increased in s character to 33 % to 50 % . so as we move to the right , we increase in stability . we also increase in s character .
|
this idea seems to contradict the idea of delocalizing electrons to increase stability ?
|
hybridization can have a large effect on the stabilization of a conjugate base . so if we start off with ethane , here 's the ethane molecule , we know the hybridization of this carbon , we know this carbon is sp3 hybridized . so let 's say that ethane donates a proton and let 's make it this proton right here . so the electrons in this bond , the electrons in magenta are left behind on that carbon to form the conjugate base . so here are the electrons in magenta and this carbon is sp3 hybridized which means the electrons in magenta occupy an sp3 hybrid orbital . so that 's meant to represent an sp3 hybrid orbital . we know from the videos on hybridization that an sp3 hybridized orbital has 25 % s character and 75 % p character . so i 'm just going to write down here 25 % s character . let 's more on to ethene or ethylene . this carbon is sp2 hybridized so we know that this carbon in ethene is sp2 hybridized . if ethene donates this proton , the electrons in magenta are left behind . so here are the electrons in magenta . this is the conjugate base to ethene and this carbon is sp2 hybridized . so the lone pair of electrons , the electrons in magenta occupy an sp2 hybridized orbital . so that 's supposed to represent an sp2 hybrid orbital . an sp2 hybridized orbital has approximately 33 % s character . so , i 'm gon na write down here 33 % s character . finally , we have acetylene . this carbon in acetylene is sp hybridized . so if acetylene donates a proton , if acetylene donates this proton , then these electrons are left behind . so the electrons in magenta are these electrons and this carbon is sp hybridized so the electrons in magenta occupy an sp hybrid orbital . an sp hybrid orbital is 50 % s character . so this is 50 % s character . now , let 's look at pka values . so the pka for this proton on ethane is approximately 50 . the pka value for this proton on ethene is approximately 44 . and the pka value for this proton on acetylene is about 25 . we know the lower the pka value , the stronger the acid . so as we move to the right , we see a decrease in pka values . and therefore , that 's an increase in the acidity . so we 're talking about increase in the acid strength . so acetylene is the strongest acid out of these three . if acetylene is the strongest acid , that must mean it has the most stable conjugate base . so this conjugate base here to acetylene must be the most stable out of these three . so as we move to the right , we are increasing in stability . so increasing in the stability of the conjugate base . so how do we explain the increased stability of the conjugate base in terms of hybridization ? well , let 's look at the hybrid orbitals that we were talking about here . for the first conjugate base , our lone pair of electrons occupy an sp3 hybridized orbital and that was 25 % s character . and as we went to the right for our conjugate bases , we increased in s character to 33 % to 50 % . so as we move to the right , we increase in stability . we also increase in s character . so increasing in s character increases the stability of the conjugate base and we can explain that by thinking about s and p orbitals . on average , an s orbital has electron density closer to the nucleus than a p orbital . so as you increase in s character , you 're increasing in electron density closest to the nucleus . so let me go ahead and point out what i mean here . so let 's look at this lone pair of electrons in the conjugate base to ethane . we think about the distance of those electrons to the nucleus . an sp3 hybridized orbital has the smallest amount of s character therefore those electrons are on average further away from the nucleus . that 's less stable , that 's higher in energy . as we move to the right , we can see that that distance decreases . so the distance decreases . and finally , for an sp hybridized orbital , that 's the shortest distance between that lone pair of electrons and the positively charged nucleus . if you decrease the distance between the positively charged nucleus and the electrons , that means you increase the force of attraction . so this conjugate base is the most stable because there 's a greater attraction to the nucleus for those electrons . so the nucleus is better able to hold onto those electrons , is a greater force and that means increased stability or lower energy . so this is the most stable conjugate base . if that 's the most stable conjugate base , then acetylene is the most acidic compound out of those three . so this also has an effect on electronegativity . if an sp hybridized carbon is better able to attract electrons , well think about our definition for electronegativity . it 's the power of an atom to attract electrons to itself . so since the electrons are closer to the positively charged nucleus in an sp hybridized carbon so that must mean that sp hybridized carbons are more electronegative . so an sp hybridized carbon is more electronegative than an sp2 hybridized carbon and an sp2 hybridized carbon is more electronegative than an sp3 hybridized carbon . so it has to do with the amount of s character . and that might seem weird because so far we 've said that carbon has a certain value for the electronegativity and we 've always assumed that it 's the same but now we can see that it 's different . an sp hybridized carbon is actually the most electronegative .
|
so as we move to the right , we increase in stability . we also increase in s character . so increasing in s character increases the stability of the conjugate base and we can explain that by thinking about s and p orbitals .
|
does the sp3 character also confer an inductive effect ?
|
hybridization can have a large effect on the stabilization of a conjugate base . so if we start off with ethane , here 's the ethane molecule , we know the hybridization of this carbon , we know this carbon is sp3 hybridized . so let 's say that ethane donates a proton and let 's make it this proton right here . so the electrons in this bond , the electrons in magenta are left behind on that carbon to form the conjugate base . so here are the electrons in magenta and this carbon is sp3 hybridized which means the electrons in magenta occupy an sp3 hybrid orbital . so that 's meant to represent an sp3 hybrid orbital . we know from the videos on hybridization that an sp3 hybridized orbital has 25 % s character and 75 % p character . so i 'm just going to write down here 25 % s character . let 's more on to ethene or ethylene . this carbon is sp2 hybridized so we know that this carbon in ethene is sp2 hybridized . if ethene donates this proton , the electrons in magenta are left behind . so here are the electrons in magenta . this is the conjugate base to ethene and this carbon is sp2 hybridized . so the lone pair of electrons , the electrons in magenta occupy an sp2 hybridized orbital . so that 's supposed to represent an sp2 hybrid orbital . an sp2 hybridized orbital has approximately 33 % s character . so , i 'm gon na write down here 33 % s character . finally , we have acetylene . this carbon in acetylene is sp hybridized . so if acetylene donates a proton , if acetylene donates this proton , then these electrons are left behind . so the electrons in magenta are these electrons and this carbon is sp hybridized so the electrons in magenta occupy an sp hybrid orbital . an sp hybrid orbital is 50 % s character . so this is 50 % s character . now , let 's look at pka values . so the pka for this proton on ethane is approximately 50 . the pka value for this proton on ethene is approximately 44 . and the pka value for this proton on acetylene is about 25 . we know the lower the pka value , the stronger the acid . so as we move to the right , we see a decrease in pka values . and therefore , that 's an increase in the acidity . so we 're talking about increase in the acid strength . so acetylene is the strongest acid out of these three . if acetylene is the strongest acid , that must mean it has the most stable conjugate base . so this conjugate base here to acetylene must be the most stable out of these three . so as we move to the right , we are increasing in stability . so increasing in the stability of the conjugate base . so how do we explain the increased stability of the conjugate base in terms of hybridization ? well , let 's look at the hybrid orbitals that we were talking about here . for the first conjugate base , our lone pair of electrons occupy an sp3 hybridized orbital and that was 25 % s character . and as we went to the right for our conjugate bases , we increased in s character to 33 % to 50 % . so as we move to the right , we increase in stability . we also increase in s character . so increasing in s character increases the stability of the conjugate base and we can explain that by thinking about s and p orbitals . on average , an s orbital has electron density closer to the nucleus than a p orbital . so as you increase in s character , you 're increasing in electron density closest to the nucleus . so let me go ahead and point out what i mean here . so let 's look at this lone pair of electrons in the conjugate base to ethane . we think about the distance of those electrons to the nucleus . an sp3 hybridized orbital has the smallest amount of s character therefore those electrons are on average further away from the nucleus . that 's less stable , that 's higher in energy . as we move to the right , we can see that that distance decreases . so the distance decreases . and finally , for an sp hybridized orbital , that 's the shortest distance between that lone pair of electrons and the positively charged nucleus . if you decrease the distance between the positively charged nucleus and the electrons , that means you increase the force of attraction . so this conjugate base is the most stable because there 's a greater attraction to the nucleus for those electrons . so the nucleus is better able to hold onto those electrons , is a greater force and that means increased stability or lower energy . so this is the most stable conjugate base . if that 's the most stable conjugate base , then acetylene is the most acidic compound out of those three . so this also has an effect on electronegativity . if an sp hybridized carbon is better able to attract electrons , well think about our definition for electronegativity . it 's the power of an atom to attract electrons to itself . so since the electrons are closer to the positively charged nucleus in an sp hybridized carbon so that must mean that sp hybridized carbons are more electronegative . so an sp hybridized carbon is more electronegative than an sp2 hybridized carbon and an sp2 hybridized carbon is more electronegative than an sp3 hybridized carbon . so it has to do with the amount of s character . and that might seem weird because so far we 've said that carbon has a certain value for the electronegativity and we 've always assumed that it 's the same but now we can see that it 's different . an sp hybridized carbon is actually the most electronegative .
|
so since the electrons are closer to the positively charged nucleus in an sp hybridized carbon so that must mean that sp hybridized carbons are more electronegative . so an sp hybridized carbon is more electronegative than an sp2 hybridized carbon and an sp2 hybridized carbon is more electronegative than an sp3 hybridized carbon . so it has to do with the amount of s character .
|
that is to say , if we have a carbon double or triple bond not necessarily on the carbon to which the hydrogen is connected , but somewhere else on the same molecule , will that also increase the acidity , and decrease with distance from the hydrogen in question ?
|
hybridization can have a large effect on the stabilization of a conjugate base . so if we start off with ethane , here 's the ethane molecule , we know the hybridization of this carbon , we know this carbon is sp3 hybridized . so let 's say that ethane donates a proton and let 's make it this proton right here . so the electrons in this bond , the electrons in magenta are left behind on that carbon to form the conjugate base . so here are the electrons in magenta and this carbon is sp3 hybridized which means the electrons in magenta occupy an sp3 hybrid orbital . so that 's meant to represent an sp3 hybrid orbital . we know from the videos on hybridization that an sp3 hybridized orbital has 25 % s character and 75 % p character . so i 'm just going to write down here 25 % s character . let 's more on to ethene or ethylene . this carbon is sp2 hybridized so we know that this carbon in ethene is sp2 hybridized . if ethene donates this proton , the electrons in magenta are left behind . so here are the electrons in magenta . this is the conjugate base to ethene and this carbon is sp2 hybridized . so the lone pair of electrons , the electrons in magenta occupy an sp2 hybridized orbital . so that 's supposed to represent an sp2 hybrid orbital . an sp2 hybridized orbital has approximately 33 % s character . so , i 'm gon na write down here 33 % s character . finally , we have acetylene . this carbon in acetylene is sp hybridized . so if acetylene donates a proton , if acetylene donates this proton , then these electrons are left behind . so the electrons in magenta are these electrons and this carbon is sp hybridized so the electrons in magenta occupy an sp hybrid orbital . an sp hybrid orbital is 50 % s character . so this is 50 % s character . now , let 's look at pka values . so the pka for this proton on ethane is approximately 50 . the pka value for this proton on ethene is approximately 44 . and the pka value for this proton on acetylene is about 25 . we know the lower the pka value , the stronger the acid . so as we move to the right , we see a decrease in pka values . and therefore , that 's an increase in the acidity . so we 're talking about increase in the acid strength . so acetylene is the strongest acid out of these three . if acetylene is the strongest acid , that must mean it has the most stable conjugate base . so this conjugate base here to acetylene must be the most stable out of these three . so as we move to the right , we are increasing in stability . so increasing in the stability of the conjugate base . so how do we explain the increased stability of the conjugate base in terms of hybridization ? well , let 's look at the hybrid orbitals that we were talking about here . for the first conjugate base , our lone pair of electrons occupy an sp3 hybridized orbital and that was 25 % s character . and as we went to the right for our conjugate bases , we increased in s character to 33 % to 50 % . so as we move to the right , we increase in stability . we also increase in s character . so increasing in s character increases the stability of the conjugate base and we can explain that by thinking about s and p orbitals . on average , an s orbital has electron density closer to the nucleus than a p orbital . so as you increase in s character , you 're increasing in electron density closest to the nucleus . so let me go ahead and point out what i mean here . so let 's look at this lone pair of electrons in the conjugate base to ethane . we think about the distance of those electrons to the nucleus . an sp3 hybridized orbital has the smallest amount of s character therefore those electrons are on average further away from the nucleus . that 's less stable , that 's higher in energy . as we move to the right , we can see that that distance decreases . so the distance decreases . and finally , for an sp hybridized orbital , that 's the shortest distance between that lone pair of electrons and the positively charged nucleus . if you decrease the distance between the positively charged nucleus and the electrons , that means you increase the force of attraction . so this conjugate base is the most stable because there 's a greater attraction to the nucleus for those electrons . so the nucleus is better able to hold onto those electrons , is a greater force and that means increased stability or lower energy . so this is the most stable conjugate base . if that 's the most stable conjugate base , then acetylene is the most acidic compound out of those three . so this also has an effect on electronegativity . if an sp hybridized carbon is better able to attract electrons , well think about our definition for electronegativity . it 's the power of an atom to attract electrons to itself . so since the electrons are closer to the positively charged nucleus in an sp hybridized carbon so that must mean that sp hybridized carbons are more electronegative . so an sp hybridized carbon is more electronegative than an sp2 hybridized carbon and an sp2 hybridized carbon is more electronegative than an sp3 hybridized carbon . so it has to do with the amount of s character . and that might seem weird because so far we 've said that carbon has a certain value for the electronegativity and we 've always assumed that it 's the same but now we can see that it 's different . an sp hybridized carbon is actually the most electronegative .
|
so since the electrons are closer to the positively charged nucleus in an sp hybridized carbon so that must mean that sp hybridized carbons are more electronegative . so an sp hybridized carbon is more electronegative than an sp2 hybridized carbon and an sp2 hybridized carbon is more electronegative than an sp3 hybridized carbon . so it has to do with the amount of s character .
|
why exactly does he say the greater en on the hybridized carbon with the greatest % of s character directly relates to acidity then ?
|
- let 's talk about polarization of light . we know what light waves are ; they 're electromagnetic waves . so they 're made out of electric fields . and that 's not good enough . we know there 's not just electric fields . that could n't sustain itself . there 's got to be magnetic fields there , as well , that are changing . those are perpendicular , so you can kind of draw them . it 's hard , on something two-dimensional , but you can kind of imagine those looking something like this . and those magnetic fields would point at a right angle to the electric fields . but this gets really messy if i try to draw both the electric and magnetic fields at the same time . so we 're going to leave the magnetic fields out . it 's often good enough to just know the direction of the electric field when we focus on the electric field . so what does polarization mean ? polarization refers to the fact that , if this light ray was heading straight toward your eye , or a detector , over here , what would you see ? well , if i draw an axis over here , and this point here , in the middle , this is this line -- so imagine we 're looking straight down that line -- and then up and down is up and down , and then left and right , that direction i have the magnetic field , would be this way and that way . what would my eye see ? well , my eye 's only going to see electric fields that either point up or electric fields that point down . they might have different values , but i 'm only going to see electric fields that point up or down . because of that , this light ray is polarized . so polarized light is light where the electric field is only oscillating in one direction . up or down , that 's one direction -- vertically . or it could be polarized horizontally . or it could be polarized diagonally . but either way , you could have this wave polarized along any direction . i mean , a light ray like this , if we had it coming in diagonal , this light ray that 's oscillating like this , where the electric field oscillates like that , that also polarized . these are both polarized because there 's only one direction that the electric field is oscillating in . and you might thing , `` pff , how could you ever have `` a light ray that 's not polarized ? '' easy . most light that you get is not polarized . that is to say , light that 's coming from the sun , straight from the sun -- typically not polarized . light from a lightbulb , an old incandescent light bulb , this thing 's hot . you can get light polarized in any direction , all at once , all overlapping . so if we draw this case for a light bulb , just a random incandescent light bulb , you might get light , some of the light , hitting you eye , you can get some light that 's got that direction , you got light that 's got this direction , you got light in all these directions at any given moment . i mean , you 'd have to add these up to get the total , and they might not all be the same value . but what i 'm trying to say is , at any given moment , you do n't know what direction the electric field 's going to be hitting your eye at from a random source . it could be in any direction . so this is not polarized . this diagram represents light that is not polarized . at some point , the field might be pointing this way , at some later point it 's this way ; it 's just random . you never know which way the electric field 's going to be pointing . whereas these over here , these are polarized . so how could you polarize this light ? let 's say you wanted light that was polarized . you were doing an experiment . you needed polarized light . well , that 's easy . you can use what 's called a polarizer . and this is a material that lets light through , but it only lets light through in one orientation , so you 're going to have a polarizer that , for instance , only lets through vertically polarized light . so this is a polarizer . these are cheap : thin , plastic , configured in a way so that it only lets light through that 's vertically polarized . any light coming in here that 's not vertically polarized gets blocked , or absorbed . so what that means is , if you used this polarizer and held it in between your eye and this light bulb , you would only get this light . all the rest of it would get blocked . or you could just rotate this thing and imagine a polarizer that only lets through horizontal light . now it would only let through light that was this way , and so you would only get this part of the light . or you could just orient it at any angle you want and block everything but the certain angle that this polarizer is defined as letting light through . so you can do this . and once you hold this up , you get polarized light , light that 's only got one orientation . so that 's what polarization means . but why do we care about polarization ? well , let me get rid of this for a minute . you 've heard of polarized sunglasses . so imagine you 're standing near water , or maybe you 're standing on ice or snow or something reflective . there 's a problem . say the sun 's out . it 's shining . it 's a beautiful day -- except there 's going to be glare . let 's say you 're looking down at something here on the ground . it 's going to get light reflecting off of it from just ... you know , light 's coming in from all direction . but it also gets this direct light from the sun . so it gets light from reflected off the clouds and whatever , whatever 's nearby , ambient light . and there 's also this direct sunlight . that 's harsh . if that reflects straight up to your eye , that hurts . you do n't like that . it blocks our vision . it 's hard to see , it 's glare . we do n't want this glare . so what can we do ? well , it just so happens that , when light reflects off of a surface , even though the light from the sun is not polarized , once it reflects , it does get polarized or at least partially polarized . so this surface here , once this light reflects , it 's coming in at all orientations . you got electric field ... you never know what electric field you 're going to get straight from the sun . and when it reflects , though , you mostly get , upon reflection , the direction of polarization defined by the plane of the surface that it hit . so because the floor is horizontal , when this light ray hits the ground and reflects , that reflected light gets partially polarized . this horizontal component of the electric field is going to be more present than the other components . maybe not completely . sometimes it could be . it could be completely polarized , but often it 's just partially polarized . but that 's pretty cool , because now you know what we can do . i know how to block this . we should get some sunglasses . we put some sunglasses on and we make our glasses so that these are polarized . and how do we want these polarized ? i want to get rid of the glare . so what i do is , i make sure my sunglasses only let through vertically polarized light . here 's some polarizers . that way , a lot of this glare gets blocked because it does not have a vertical orientation , it has a horizontal orientation . and then we can block it . so that 's one good thing that polarization does for us , and understanding it , we can get rid of glare . also , fishermen like it because , if you 're trying to look in the water at fish , you want to see in through the water , you want to see this light from the fish getting to you . you do n't want to see the glare off of the sun getting to you . so polarized sunglasses are useful . also , we can play a trick on our eye , if we really wanted to . you could take one of these , make one eye have a vertical orientation for the polarization , have the other eye with a horizontal ... and you 're thinking , `` this is stupid . `` why would you do this for ? '' `` this eye 's going to get a lot of glare . '' we would n't use these outside , when you 're , like , skiing or fishing , but you could play a trick on your eyes if you went to the movies and you went and watched a movie . well , the reason our eyes see 3d is because they 're spaced a little bit apart . they each get a different , slightly different image . that makes us see in 3d . we can play the same trick on our eye if we have the polarization like this . if light , if some of the light from the movie theater screen is coming in with one polarization , and the other light 's coming in with the other polarization , we can send two different images to our eyes at the same time . if you took these off , it 'd look like garbage because you 'd be getting both of these slightly different images , it 'd look all blurry . and it does . if you take off your 3d glasses and look at a 3d movie , looks terrible , because now both eyes are getting both images . but if you put your glasses back on , now this eye only gets the orientation that it 's supposed to get , and this eye only gets the orientation that it 's supposed to get , and you get a 3d image . so it 's useful in many ways . let me show you one more thing here . let 's come back here . this light was polarized vertically . so that 's called linear polarization . any time ... same with these . these are all linear polarization because , just up and down , one linear direction , just diagonal . this is also linear . all of these are linear . you can get circular polarized light . so if we come back to here , we 've got our electric field pointing up , like that . now let 's say we sent in another light ray , another light ray that also had a polarization , but not in this direction . let 's say our other light ray had polarization in this direction , so it looks like this , kind of like what our magnetic field would have looked like . but this is a completely different light ray with its own polarization and its own magnetic field . so we send this in . what would happen ? well , at this point , you 'd have a electric field that points this way . at this point , you 'd have a electric field that points that way . what would your eye see if you were over here ? let 's see . if i draw our axis here . all right , when this point right here gets to your eye , what am i going to see ? well , i 'm going to have a light ray that 's one part of a light ray . one component points up . that 's this electric field . one component points left . that 's this electric field . so the total , my total electric field , would point this way . i could to the pythagorean theorem if i wanted to figure out the size of it , but i just want to know the direction for now . and then it gets to here , and look at it : they both have zero . this light ray has zero electric field , this one has zero electric fields . so then it 'd just be at zero . now what happens over here ? well , i 've got light . this one points to the right at that point , this pink one , and then this red one would be pointing down . so what would i have at that point ? i 'd have light that went this way , and it would just be doing this over and over . it would just be ... i 'd just have diagonally polarized light . this is n't giving me anything new . you might think this is dumb . why do this ? why send in two different waves to just get diagonally polarized light ? i could have just sent in one wave that was diagonally polarized and got the same thing . the reason is , if you shift this purple wave , this pink wave , by 90 degrees of phase , by pi over two in phase , something magical happens . let me show you what happens here , if we move this to here . now we do n't just get diagonally linear polarized light . what we 're going to get is ... let me get rid of this . okay , so we start off with red , right ? the red electric field points up , and then this pink wave 's electric field is zero at that point . so this is all i have . my total electric field would just be up . i 'm going to draw it right here . the green 'll be the total . now i come over to here , and at this point , there 's some red electric field that points up , but there 's some of this other electric field that points this way . so i 'd have a total electric field that would point that way . and then i get over to here , and i 'd have all of the electric field from the pink one , none from the red one . it would point all left then . look what 's happening . the polarization of this light , if i shift this , if i 'm sitting here , looking with my eye , as my eye receives this light , i 'm going to see this light rotate its polarization . the polarization i 'm going to notice swings around in a circular pattern . and because of this , we call this circular polarization . so this is another type of polarization , where the actual angle of polarization rotates smoothly as this light ray enters your eye . and you know what ? er , drrr ... all right , actually , i sent you to receive this one first . that makes no sense . you 're going to receive the ones closes to you first in this light ray going this way . so you 'd actually receive this one first , then that one , then this one , then this one . because of that , you would n't see this going in a counterclockwise way , you 'd see this going in a clockwise circularly polarized way . sorry about that . you might think , `` okay , why ? `` why even bother with circular polarization ? '' well , i kind of lied earlier . turns out , in the movie theater example , they do n't actually do it like this , typically . oftentimes in the movie theaters , we do n't have just linearly polarized sunglasses . this would be a problem because , when you look at the movie theater screen , and if you were to tilt your head just a little bit ... think about it . this one 's not really going to get the right image anymore . it 's going to get some of both . and this one 's going to get some of both . it 's going to be blurry . your head would have to be perfectly level the whole time , which might be annoying . so what we do is , instead , we create circular polarized glasses , so that this one would only get one polarization , this one would get the other direction . this way , even if you tilt your head a little bit ... shoot , clockwise is clockwise , counterclockwise is counterclockwise . by using circular polarization for 3d movies , it can make it a little easier on you eyes to see a better 3d image , even if your head 's tilted a little bit .
|
so this is a polarizer . these are cheap : thin , plastic , configured in a way so that it only lets light through that 's vertically polarized . any light coming in here that 's not vertically polarized gets blocked , or absorbed .
|
how does the plastic sheet limit the polarity ?
|
- let 's talk about polarization of light . we know what light waves are ; they 're electromagnetic waves . so they 're made out of electric fields . and that 's not good enough . we know there 's not just electric fields . that could n't sustain itself . there 's got to be magnetic fields there , as well , that are changing . those are perpendicular , so you can kind of draw them . it 's hard , on something two-dimensional , but you can kind of imagine those looking something like this . and those magnetic fields would point at a right angle to the electric fields . but this gets really messy if i try to draw both the electric and magnetic fields at the same time . so we 're going to leave the magnetic fields out . it 's often good enough to just know the direction of the electric field when we focus on the electric field . so what does polarization mean ? polarization refers to the fact that , if this light ray was heading straight toward your eye , or a detector , over here , what would you see ? well , if i draw an axis over here , and this point here , in the middle , this is this line -- so imagine we 're looking straight down that line -- and then up and down is up and down , and then left and right , that direction i have the magnetic field , would be this way and that way . what would my eye see ? well , my eye 's only going to see electric fields that either point up or electric fields that point down . they might have different values , but i 'm only going to see electric fields that point up or down . because of that , this light ray is polarized . so polarized light is light where the electric field is only oscillating in one direction . up or down , that 's one direction -- vertically . or it could be polarized horizontally . or it could be polarized diagonally . but either way , you could have this wave polarized along any direction . i mean , a light ray like this , if we had it coming in diagonal , this light ray that 's oscillating like this , where the electric field oscillates like that , that also polarized . these are both polarized because there 's only one direction that the electric field is oscillating in . and you might thing , `` pff , how could you ever have `` a light ray that 's not polarized ? '' easy . most light that you get is not polarized . that is to say , light that 's coming from the sun , straight from the sun -- typically not polarized . light from a lightbulb , an old incandescent light bulb , this thing 's hot . you can get light polarized in any direction , all at once , all overlapping . so if we draw this case for a light bulb , just a random incandescent light bulb , you might get light , some of the light , hitting you eye , you can get some light that 's got that direction , you got light that 's got this direction , you got light in all these directions at any given moment . i mean , you 'd have to add these up to get the total , and they might not all be the same value . but what i 'm trying to say is , at any given moment , you do n't know what direction the electric field 's going to be hitting your eye at from a random source . it could be in any direction . so this is not polarized . this diagram represents light that is not polarized . at some point , the field might be pointing this way , at some later point it 's this way ; it 's just random . you never know which way the electric field 's going to be pointing . whereas these over here , these are polarized . so how could you polarize this light ? let 's say you wanted light that was polarized . you were doing an experiment . you needed polarized light . well , that 's easy . you can use what 's called a polarizer . and this is a material that lets light through , but it only lets light through in one orientation , so you 're going to have a polarizer that , for instance , only lets through vertically polarized light . so this is a polarizer . these are cheap : thin , plastic , configured in a way so that it only lets light through that 's vertically polarized . any light coming in here that 's not vertically polarized gets blocked , or absorbed . so what that means is , if you used this polarizer and held it in between your eye and this light bulb , you would only get this light . all the rest of it would get blocked . or you could just rotate this thing and imagine a polarizer that only lets through horizontal light . now it would only let through light that was this way , and so you would only get this part of the light . or you could just orient it at any angle you want and block everything but the certain angle that this polarizer is defined as letting light through . so you can do this . and once you hold this up , you get polarized light , light that 's only got one orientation . so that 's what polarization means . but why do we care about polarization ? well , let me get rid of this for a minute . you 've heard of polarized sunglasses . so imagine you 're standing near water , or maybe you 're standing on ice or snow or something reflective . there 's a problem . say the sun 's out . it 's shining . it 's a beautiful day -- except there 's going to be glare . let 's say you 're looking down at something here on the ground . it 's going to get light reflecting off of it from just ... you know , light 's coming in from all direction . but it also gets this direct light from the sun . so it gets light from reflected off the clouds and whatever , whatever 's nearby , ambient light . and there 's also this direct sunlight . that 's harsh . if that reflects straight up to your eye , that hurts . you do n't like that . it blocks our vision . it 's hard to see , it 's glare . we do n't want this glare . so what can we do ? well , it just so happens that , when light reflects off of a surface , even though the light from the sun is not polarized , once it reflects , it does get polarized or at least partially polarized . so this surface here , once this light reflects , it 's coming in at all orientations . you got electric field ... you never know what electric field you 're going to get straight from the sun . and when it reflects , though , you mostly get , upon reflection , the direction of polarization defined by the plane of the surface that it hit . so because the floor is horizontal , when this light ray hits the ground and reflects , that reflected light gets partially polarized . this horizontal component of the electric field is going to be more present than the other components . maybe not completely . sometimes it could be . it could be completely polarized , but often it 's just partially polarized . but that 's pretty cool , because now you know what we can do . i know how to block this . we should get some sunglasses . we put some sunglasses on and we make our glasses so that these are polarized . and how do we want these polarized ? i want to get rid of the glare . so what i do is , i make sure my sunglasses only let through vertically polarized light . here 's some polarizers . that way , a lot of this glare gets blocked because it does not have a vertical orientation , it has a horizontal orientation . and then we can block it . so that 's one good thing that polarization does for us , and understanding it , we can get rid of glare . also , fishermen like it because , if you 're trying to look in the water at fish , you want to see in through the water , you want to see this light from the fish getting to you . you do n't want to see the glare off of the sun getting to you . so polarized sunglasses are useful . also , we can play a trick on our eye , if we really wanted to . you could take one of these , make one eye have a vertical orientation for the polarization , have the other eye with a horizontal ... and you 're thinking , `` this is stupid . `` why would you do this for ? '' `` this eye 's going to get a lot of glare . '' we would n't use these outside , when you 're , like , skiing or fishing , but you could play a trick on your eyes if you went to the movies and you went and watched a movie . well , the reason our eyes see 3d is because they 're spaced a little bit apart . they each get a different , slightly different image . that makes us see in 3d . we can play the same trick on our eye if we have the polarization like this . if light , if some of the light from the movie theater screen is coming in with one polarization , and the other light 's coming in with the other polarization , we can send two different images to our eyes at the same time . if you took these off , it 'd look like garbage because you 'd be getting both of these slightly different images , it 'd look all blurry . and it does . if you take off your 3d glasses and look at a 3d movie , looks terrible , because now both eyes are getting both images . but if you put your glasses back on , now this eye only gets the orientation that it 's supposed to get , and this eye only gets the orientation that it 's supposed to get , and you get a 3d image . so it 's useful in many ways . let me show you one more thing here . let 's come back here . this light was polarized vertically . so that 's called linear polarization . any time ... same with these . these are all linear polarization because , just up and down , one linear direction , just diagonal . this is also linear . all of these are linear . you can get circular polarized light . so if we come back to here , we 've got our electric field pointing up , like that . now let 's say we sent in another light ray , another light ray that also had a polarization , but not in this direction . let 's say our other light ray had polarization in this direction , so it looks like this , kind of like what our magnetic field would have looked like . but this is a completely different light ray with its own polarization and its own magnetic field . so we send this in . what would happen ? well , at this point , you 'd have a electric field that points this way . at this point , you 'd have a electric field that points that way . what would your eye see if you were over here ? let 's see . if i draw our axis here . all right , when this point right here gets to your eye , what am i going to see ? well , i 'm going to have a light ray that 's one part of a light ray . one component points up . that 's this electric field . one component points left . that 's this electric field . so the total , my total electric field , would point this way . i could to the pythagorean theorem if i wanted to figure out the size of it , but i just want to know the direction for now . and then it gets to here , and look at it : they both have zero . this light ray has zero electric field , this one has zero electric fields . so then it 'd just be at zero . now what happens over here ? well , i 've got light . this one points to the right at that point , this pink one , and then this red one would be pointing down . so what would i have at that point ? i 'd have light that went this way , and it would just be doing this over and over . it would just be ... i 'd just have diagonally polarized light . this is n't giving me anything new . you might think this is dumb . why do this ? why send in two different waves to just get diagonally polarized light ? i could have just sent in one wave that was diagonally polarized and got the same thing . the reason is , if you shift this purple wave , this pink wave , by 90 degrees of phase , by pi over two in phase , something magical happens . let me show you what happens here , if we move this to here . now we do n't just get diagonally linear polarized light . what we 're going to get is ... let me get rid of this . okay , so we start off with red , right ? the red electric field points up , and then this pink wave 's electric field is zero at that point . so this is all i have . my total electric field would just be up . i 'm going to draw it right here . the green 'll be the total . now i come over to here , and at this point , there 's some red electric field that points up , but there 's some of this other electric field that points this way . so i 'd have a total electric field that would point that way . and then i get over to here , and i 'd have all of the electric field from the pink one , none from the red one . it would point all left then . look what 's happening . the polarization of this light , if i shift this , if i 'm sitting here , looking with my eye , as my eye receives this light , i 'm going to see this light rotate its polarization . the polarization i 'm going to notice swings around in a circular pattern . and because of this , we call this circular polarization . so this is another type of polarization , where the actual angle of polarization rotates smoothly as this light ray enters your eye . and you know what ? er , drrr ... all right , actually , i sent you to receive this one first . that makes no sense . you 're going to receive the ones closes to you first in this light ray going this way . so you 'd actually receive this one first , then that one , then this one , then this one . because of that , you would n't see this going in a counterclockwise way , you 'd see this going in a clockwise circularly polarized way . sorry about that . you might think , `` okay , why ? `` why even bother with circular polarization ? '' well , i kind of lied earlier . turns out , in the movie theater example , they do n't actually do it like this , typically . oftentimes in the movie theaters , we do n't have just linearly polarized sunglasses . this would be a problem because , when you look at the movie theater screen , and if you were to tilt your head just a little bit ... think about it . this one 's not really going to get the right image anymore . it 's going to get some of both . and this one 's going to get some of both . it 's going to be blurry . your head would have to be perfectly level the whole time , which might be annoying . so what we do is , instead , we create circular polarized glasses , so that this one would only get one polarization , this one would get the other direction . this way , even if you tilt your head a little bit ... shoot , clockwise is clockwise , counterclockwise is counterclockwise . by using circular polarization for 3d movies , it can make it a little easier on you eyes to see a better 3d image , even if your head 's tilted a little bit .
|
one component points up . that 's this electric field . one component points left .
|
hey , why is the phenomena of `` polarization '' focus so much importance to the orientation of electric field but not the magnetic field ?
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.