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hello grammarians , hello paige . hi , david . so , today we 're gon na learn about hyphens . and what a hyphen is , it 's a little stick , like this , as opposed to a dash , which is about twice as long . and people confuse them a lot , but they have very different functions . so what a hyphen is used to do is it '... | and people confuse them a lot , but they have very different functions . so what a hyphen is used to do is it 's used to join two words into one . all right . | how can you tell the difference between a hyphen and a dash if they are both used in a sentence ? |
hello grammarians , hello paige . hi , david . so , today we 're gon na learn about hyphens . and what a hyphen is , it 's a little stick , like this , as opposed to a dash , which is about twice as long . and people confuse them a lot , but they have very different functions . so what a hyphen is used to do is it '... | it became closed , cause everyone knows what that means . right , so you would use hyphenated compounds when you 're kind of in this intermediary stage of acceptedness . so like , maybe one day , in the future , yellow-green will be a super common color . right , it 's everyone 's favorite color , so it 'll just be s... | is there anything in english that would make such distintion , or one simply has to use the whole sentence to describe difference between shade of color and stripes of two colors ? |
hello grammarians , hello paige . hi , david . so , today we 're gon na learn about hyphens . and what a hyphen is , it 's a little stick , like this , as opposed to a dash , which is about twice as long . and people confuse them a lot , but they have very different functions . so what a hyphen is used to do is it '... | so yeah , so a hyphen is joining these two things . but let 's say we had a sentence like , `` her hair was yellow -- green were her eyes . '' you know , and so we 're still separating the words yellow and green with a stick , but a dash is longer , and instead of uniting yellow-green , it 's separating them the way th... | it says '' her hair was yellow -- green were her eyes '' if i were to g=change the sentience to `` her hair was yellow -- her eyes were green '' does it still work like so or does it change all completely to a new sentience ? |
hello grammarians , hello paige . hi , david . so , today we 're gon na learn about hyphens . and what a hyphen is , it 's a little stick , like this , as opposed to a dash , which is about twice as long . and people confuse them a lot , but they have very different functions . so what a hyphen is used to do is it '... | right . or my co-op from the co-op , or co-op from the coop , or something . so , in order to be clear , it really helps to put in that little hyphen . | is the dash preferable to the umlaut for words like cooperative or co-op , and other words such as reintegrate ( which is n't pronounced with `` rein '' as one syllable ) or reexamine ? |
hello grammarians , hello paige . hi , david . so , today we 're gon na learn about hyphens . and what a hyphen is , it 's a little stick , like this , as opposed to a dash , which is about twice as long . and people confuse them a lot , but they have very different functions . so what a hyphen is used to do is it '... | and people confuse them a lot , but they have very different functions . so what a hyphen is used to do is it 's used to join two words into one . all right . | how do you know when to put a hyphen or not or make the to words one ? |
so this is an example from the khan academy exercise , graphing solutions to two variable linear equations . and they tell us to complete the table so each row represents a solution of the following equation . and they give us the equation , and then they want us to figure out , what does y equal when x is equal to ne... | so this is an example from the khan academy exercise , graphing solutions to two variable linear equations . and they tell us to complete the table so each row represents a solution of the following equation . | what is the proof that euclid has discovered the axioms ? |
so this is an example from the khan academy exercise , graphing solutions to two variable linear equations . and they tell us to complete the table so each row represents a solution of the following equation . and they give us the equation , and then they want us to figure out , what does y equal when x is equal to ne... | and then , let 's see , 16 minus 16 is zero . five x plus three x is equal to eight x . we get eight x is equal to 40 . | given : a= ( x/x is a whole number less than or equal to 20 ) questions : 1 ) list the elements of a given set 2 ) how many of these elements are even ? |
so this is an example from the khan academy exercise , graphing solutions to two variable linear equations . and they tell us to complete the table so each row represents a solution of the following equation . and they give us the equation , and then they want us to figure out , what does y equal when x is equal to ne... | so this is an example from the khan academy exercise , graphing solutions to two variable linear equations . and they tell us to complete the table so each row represents a solution of the following equation . | 3 ) how many of these are prime ? |
so this is an example from the khan academy exercise , graphing solutions to two variable linear equations . and they tell us to complete the table so each row represents a solution of the following equation . and they give us the equation , and then they want us to figure out , what does y equal when x is equal to ne... | now let 's say i wan na get all my ys on the left and all my xs on the right . so i do n't want this negative three x on the left , so i 'd wan na add three x . adding three x would cancel this out , but i ca n't just do it on the left hand side , i have to do it on the right hand side as well . | 5 ) how many of these elements are three digit number ? |
so this is an example from the khan academy exercise , graphing solutions to two variable linear equations . and they tell us to complete the table so each row represents a solution of the following equation . and they give us the equation , and then they want us to figure out , what does y equal when x is equal to ne... | and then i have five x plus three x is eight x . two y minus two y is zero . and then if i wanted to , i could solve for y , i could divide both sides by five and i 'd get y is equal to 8/5 x . | why is n't xy=4 a linear equation in two variables ? |
so this is an example from the khan academy exercise , graphing solutions to two variable linear equations . and they tell us to complete the table so each row represents a solution of the following equation . and they give us the equation , and then they want us to figure out , what does y equal when x is equal to ne... | and then , let 's see , 16 minus 16 is zero . five x plus three x is equal to eight x . we get eight x is equal to 40 . | why does 5y=8 x become y= 8/5x ? |
so this is an example from the khan academy exercise , graphing solutions to two variable linear equations . and they tell us to complete the table so each row represents a solution of the following equation . and they give us the equation , and then they want us to figure out , what does y equal when x is equal to ne... | and then , let 's see , 16 minus 16 is zero . five x plus three x is equal to eight x . we get eight x is equal to 40 . | why did sal put the x 's on the right and not the left ? |
so this is an example from the khan academy exercise , graphing solutions to two variable linear equations . and they tell us to complete the table so each row represents a solution of the following equation . and they give us the equation , and then they want us to figure out , what does y equal when x is equal to ne... | so this is an example from the khan academy exercise , graphing solutions to two variable linear equations . and they tell us to complete the table so each row represents a solution of the following equation . | what do you do when y=0 ? |
so this is an example from the khan academy exercise , graphing solutions to two variable linear equations . and they tell us to complete the table so each row represents a solution of the following equation . and they give us the equation , and then they want us to figure out , what does y equal when x is equal to ne... | so when y is positive eight , x is positive five . now they ask us , `` use your two solutions `` to graph the equation . '' so let 's see if we can do , oh , whoops , let me , let me use my mouse now . | patience p , patience ... why did n't you use what we 've learned in previous lessons and simplified the equation before substituting the values for variables ? |
so this is an example from the khan academy exercise , graphing solutions to two variable linear equations . and they tell us to complete the table so each row represents a solution of the following equation . and they give us the equation , and then they want us to figure out , what does y equal when x is equal to ne... | and they give us the equation , and then they want us to figure out , what does y equal when x is equal to negative five ? and what does x equal when y is equal to eight . and to figure this out , i 've actually copied and pasted this part of the problem onto my scratchpad , so let me get that out . | how would solve ( 2x+3y=5x+y ) if y was equal to 0 ? |
so this is an example from the khan academy exercise , graphing solutions to two variable linear equations . and they tell us to complete the table so each row represents a solution of the following equation . and they give us the equation , and then they want us to figure out , what does y equal when x is equal to ne... | and then , let 's see , 16 minus 16 is zero . five x plus three x is equal to eight x . we get eight x is equal to 40 . | how can you solve the equation when there is no x or y values are displayed and there is only a graph ? |
- the n plus one rule allows us to predict how many peaks we would expect to see for a signal in an nmr spectrum . so if we think about the signal for one proton , if that proton has n neighboring protons , we would expect to see n plus one peaks on the nmr spectrum . the n plus one rule only applies when the neighbori... | so n is equal to two . we would expect n plus one peaks . so two plus one is equal to three . | would n't oxygen deshield the proton nearby more than chlorine would ( since oxygen is more electronegative ) ? |
- the n plus one rule allows us to predict how many peaks we would expect to see for a signal in an nmr spectrum . so if we think about the signal for one proton , if that proton has n neighboring protons , we would expect to see n plus one peaks on the nmr spectrum . the n plus one rule only applies when the neighbori... | let 's think about the signal for the red protons first . how many neighboring protons do the red protons have ? we go to the carbon next door and this is the carbon next door for both of those red protons and there 's one neighbor . | why do the equivalent protons not change the effect of the magnetic field ? |
- the n plus one rule allows us to predict how many peaks we would expect to see for a signal in an nmr spectrum . so if we think about the signal for one proton , if that proton has n neighboring protons , we would expect to see n plus one peaks on the nmr spectrum . the n plus one rule only applies when the neighbori... | we expect one signal for the blue proton and we would expect one signal for these red protons here . let 's think about the red protons first . so how many neighboring protons do we have ? | in the first example , why is the blue h more downfield than the red h ? |
- the n plus one rule allows us to predict how many peaks we would expect to see for a signal in an nmr spectrum . so if we think about the signal for one proton , if that proton has n neighboring protons , we would expect to see n plus one peaks on the nmr spectrum . the n plus one rule only applies when the neighbori... | let 's think about the signal for the red protons first . how many neighboring protons do the red protons have ? we go to the carbon next door and this is the carbon next door for both of those red protons and there 's one neighbor . so one neighbor , n is equal to one . so one plus one is equal to two , we would expec... | the red h is next to o , which is more electronegative than cl , so should n't it be more deshielded and thus further downfield ? |
- the n plus one rule allows us to predict how many peaks we would expect to see for a signal in an nmr spectrum . so if we think about the signal for one proton , if that proton has n neighboring protons , we would expect to see n plus one peaks on the nmr spectrum . the n plus one rule only applies when the neighbori... | and let 's talk a little bit more about spin-spin splitting and when to expect a signal . so if you have chemically equivalent protons , they do n't show spin-spin splitting . so if i look at these two protons right here . | ~ are n't the red and blue hydrogens chemically equivalent ? |
- the n plus one rule allows us to predict how many peaks we would expect to see for a signal in an nmr spectrum . so if we think about the signal for one proton , if that proton has n neighboring protons , we would expect to see n plus one peaks on the nmr spectrum . the n plus one rule only applies when the neighbori... | so two plus one is equal to three . we would expect a triplet for this signal and here is our triplet . one , two and three peaks for that one . | is this proton nmr how you can tell triplet o2 and singlet o2 apart ? |
- the n plus one rule allows us to predict how many peaks we would expect to see for a signal in an nmr spectrum . so if we think about the signal for one proton , if that proton has n neighboring protons , we would expect to see n plus one peaks on the nmr spectrum . the n plus one rule only applies when the neighbori... | so how many neighboring protons do we have ? we go to the carbon next door and then we have one proton . so one neighbor . | at around 7 mn how come the proton varies in the frequency that it reads out at when both times its a hydrogen attached next to a bromide ion ? |
- the n plus one rule allows us to predict how many peaks we would expect to see for a signal in an nmr spectrum . so if we think about the signal for one proton , if that proton has n neighboring protons , we would expect to see n plus one peaks on the nmr spectrum . the n plus one rule only applies when the neighbori... | so n is equal to two . we would expect n plus one peaks . so two plus one is equal to three . | would n't the protons have to be sharing different environments to have an effect on one another in terms of coupling ? |
- the n plus one rule allows us to predict how many peaks we would expect to see for a signal in an nmr spectrum . so if we think about the signal for one proton , if that proton has n neighboring protons , we would expect to see n plus one peaks on the nmr spectrum . the n plus one rule only applies when the neighbori... | there are no protons on that carbon . so we have a total of only one neighboring proton for the red proton . so one neighboring proton , so n is equal to one . | the red proton is next to the oxygen which is more electronegative than chlorine so should n't the red proton be at a lower position because the more electronegative oxygen will de-shield it ? |
- the n plus one rule allows us to predict how many peaks we would expect to see for a signal in an nmr spectrum . so if we think about the signal for one proton , if that proton has n neighboring protons , we would expect to see n plus one peaks on the nmr spectrum . the n plus one rule only applies when the neighbori... | so this one right here , so there 's one peak and there 's the second peak so we get a doublet . what about the signal for the blue proton ? so we get a signal for the blue proton . how many neighboring protons do we have ? | in the very first example , why does the red proton give the signal to the right ( lower chemical shift ) and the blue proton give the signal to the left ( higher chemical shift ) ? |
- the n plus one rule allows us to predict how many peaks we would expect to see for a signal in an nmr spectrum . so if we think about the signal for one proton , if that proton has n neighboring protons , we would expect to see n plus one peaks on the nmr spectrum . the n plus one rule only applies when the neighbori... | so n is equal to two . we would expect n plus one peaks . so two plus one is equal to three . | i would imagine being close to a methoxy group would deshield the proton more than being close to a chlorine group would , because oxygen is more electronegative than chlorine ? |
- the n plus one rule allows us to predict how many peaks we would expect to see for a signal in an nmr spectrum . so if we think about the signal for one proton , if that proton has n neighboring protons , we would expect to see n plus one peaks on the nmr spectrum . the n plus one rule only applies when the neighbori... | so that 's that signal . what about the blue proton ? so how many neighbors does the blue proton have ? | how do we know which peak is red and which is blue ? |
- the n plus one rule allows us to predict how many peaks we would expect to see for a signal in an nmr spectrum . so if we think about the signal for one proton , if that proton has n neighboring protons , we would expect to see n plus one peaks on the nmr spectrum . the n plus one rule only applies when the neighbori... | there are no protons on that carbon . so we have a total of only one neighboring proton for the red proton . so one neighboring proton , so n is equal to one . | does a proton need to be equivalent in order to be considered a `` neighboring proton '' ? |
- the n plus one rule allows us to predict how many peaks we would expect to see for a signal in an nmr spectrum . so if we think about the signal for one proton , if that proton has n neighboring protons , we would expect to see n plus one peaks on the nmr spectrum . the n plus one rule only applies when the neighbori... | no neighbors so n is equal to zero . n plus one peaks . so zero plus one is equal to one . | how come that molecule has 7 peaks ? |
- the n plus one rule allows us to predict how many peaks we would expect to see for a signal in an nmr spectrum . so if we think about the signal for one proton , if that proton has n neighboring protons , we would expect to see n plus one peaks on the nmr spectrum . the n plus one rule only applies when the neighbori... | so here are the three protons . on this carbon there are three protons and on this carbon , there would only be one proton , so here 's this one . let 's think about how many signals we would expect to see . | it looks chemically equivalent to me ... is that proton on the carbon attached to the bromine preferential on one side causing chemical inequivalence ? |
- the n plus one rule allows us to predict how many peaks we would expect to see for a signal in an nmr spectrum . so if we think about the signal for one proton , if that proton has n neighboring protons , we would expect to see n plus one peaks on the nmr spectrum . the n plus one rule only applies when the neighbori... | let 's think about the signal for the red protons first . how many neighboring protons do the red protons have ? we go to the carbon next door and this is the carbon next door for both of those red protons and there 's one neighbor . | are n't the two red protons not equivalent ? |
- the n plus one rule allows us to predict how many peaks we would expect to see for a signal in an nmr spectrum . so if we think about the signal for one proton , if that proton has n neighboring protons , we would expect to see n plus one peaks on the nmr spectrum . the n plus one rule only applies when the neighbori... | so that 's that signal . what about the blue proton ? so how many neighbors does the blue proton have ? | would the blue proton discussed near the 7 min mark have an integration value equal to 4 ? |
we ’ re on the fourth floor of museum of modern art looking at the painting by pablo picasso from 1909 from the summer of 1909 ’ horta de ebro ’ . it ’ s one of picasso ’ s critical early cubist paintings . it looks very cubist already . i mean it already looks like a radical departure from cezanne , but this is two ye... | they become a synthetic whole and actually he ’ s willing something else that i think further resist that . if you look at shadow and reflection they become almost objects and space themselves rather than just sort of an optical phenomena . what you mean ? | why is there a..sort of green shadow in the centre of the painting ? |
we ’ re on the fourth floor of museum of modern art looking at the painting by pablo picasso from 1909 from the summer of 1909 ’ horta de ebro ’ . it ’ s one of picasso ’ s critical early cubist paintings . it looks very cubist already . i mean it already looks like a radical departure from cezanne , but this is two ye... | we ’ re looking at the hilltop pound , there ’ s a little water collect down at the bottom , right , and actually we can even see the reflection in the surface of the water there . of course what most people find so interesting by this painting is his willingness to pull and push perspective . so that we ’ re looking s... | i looked in to it briefly , and it seems that it means that moma currently owns a percentage stake in the painting , shares exhibition/physical ownership with the benefactor , and then will eventually take full possession at a future date ... is that about the gist of it ? |
we ’ re on the fourth floor of museum of modern art looking at the painting by pablo picasso from 1909 from the summer of 1909 ’ horta de ebro ’ . it ’ s one of picasso ’ s critical early cubist paintings . it looks very cubist already . i mean it already looks like a radical departure from cezanne , but this is two ye... | we ’ re on the fourth floor of museum of modern art looking at the painting by pablo picasso from 1909 from the summer of 1909 ’ horta de ebro ’ . it ’ s one of picasso ’ s critical early cubist paintings . | what state is the museum of modern art in ? |
we ’ re on the fourth floor of museum of modern art looking at the painting by pablo picasso from 1909 from the summer of 1909 ’ horta de ebro ’ . it ’ s one of picasso ’ s critical early cubist paintings . it looks very cubist already . i mean it already looks like a radical departure from cezanne , but this is two ye... | there are historical chronology is usually that after demoiselle braque really begins to explore cezanne in very serious ways . picasso ’ s response to… follows braque . yeah , by the way of cezanne , exactly , right . | why is picasso more well known for his portraits ? |
we ’ re on the fourth floor of museum of modern art looking at the painting by pablo picasso from 1909 from the summer of 1909 ’ horta de ebro ’ . it ’ s one of picasso ’ s critical early cubist paintings . it looks very cubist already . i mean it already looks like a radical departure from cezanne , but this is two ye... | we ’ re on the fourth floor of museum of modern art looking at the painting by pablo picasso from 1909 from the summer of 1909 ’ horta de ebro ’ . it ’ s one of picasso ’ s critical early cubist paintings . | what twist does this painting gives us about 1909 ? |
in the last video , we showed you the cauchy-schwarz inequality . i think it 's worth rewriting because this is something that 's going to show up a lot . it 's a very useful tool . and that just told us if i have two vectors , x and y , they 're both members of rn . and they 're both nonzero vectors . and that was an ... | you took from the tail of x to the head of y . so this vector right here is the vector x plus y . and that 's why it 's called the triangle inequality . | what about ||vector x||-||vector y|| < =||vector ( x+y ) || ? |
in the last video , we showed you the cauchy-schwarz inequality . i think it 's worth rewriting because this is something that 's going to show up a lot . it 's a very useful tool . and that just told us if i have two vectors , x and y , they 're both members of rn . and they 're both nonzero vectors . and that was an ... | and the only way that i can ensure that this expression right here is equal to the absolute value of x dot y , the only way i can assure this is that c is positive . if c is negative , then this is going to be a negative number while this is a positive . so if i assume that this is positive , then i can say that x dot ... | what happens when c is negative ? |
in the last video , we showed you the cauchy-schwarz inequality . i think it 's worth rewriting because this is something that 's going to show up a lot . it 's a very useful tool . and that just told us if i have two vectors , x and y , they 're both members of rn . and they 're both nonzero vectors . and that was an ... | you took from the tail of x to the head of y . so this vector right here is the vector x plus y . and that 's why it 's called the triangle inequality . | does the equality work if vector x or y are zero ? |
in the last video , we showed you the cauchy-schwarz inequality . i think it 's worth rewriting because this is something that 's going to show up a lot . it 's a very useful tool . and that just told us if i have two vectors , x and y , they 're both members of rn . and they 're both nonzero vectors . and that was an ... | so let me write this is just equal to the magnitude of our vector x. i should stop using the word magnitude . the length of our vector x squared . and then i have two terms here . | what is the difference between the length and the magnitude of a vector ? |
in the last video , we showed you the cauchy-schwarz inequality . i think it 's worth rewriting because this is something that 's going to show up a lot . it 's a very useful tool . and that just told us if i have two vectors , x and y , they 're both members of rn . and they 're both nonzero vectors . and that was an ... | maybe this was a little bit overkill , but i think it 's good to see that this is n't just some magic here . and we 're just using the exact properties that we proved with the dot product . so that 's that right there . | what is the difference when using |a| and ||a|| ? |
in the last video , we showed you the cauchy-schwarz inequality . i think it 's worth rewriting because this is something that 's going to show up a lot . it 's a very useful tool . and that just told us if i have two vectors , x and y , they 're both members of rn . and they 're both nonzero vectors . and that was an ... | you took from the tail of x to the head of y . so this vector right here is the vector x plus y . and that 's why it 's called the triangle inequality . | when adding two vectors in n-space , do n't the three points that define this addition ( the tail of the first vector , the head of the first vector/tail of the second vector , and the head of the second vector ) just define another plane ( or set of planes along the same line for the degenerative case ) that 's in som... |
in the last video , we showed you the cauchy-schwarz inequality . i think it 's worth rewriting because this is something that 's going to show up a lot . it 's a very useful tool . and that just told us if i have two vectors , x and y , they 're both members of rn . and they 're both nonzero vectors . and that was an ... | and that just told us if i have two vectors , x and y , they 're both members of rn . and they 're both nonzero vectors . and that was an assumption we had to make when we did the proof , otherwise there was a potential of dividing by one of their magnitudes . | what are that angles between vectors ? |
in the last video , we showed you the cauchy-schwarz inequality . i think it 's worth rewriting because this is something that 's going to show up a lot . it 's a very useful tool . and that just told us if i have two vectors , x and y , they 're both members of rn . and they 're both nonzero vectors . and that was an ... | we know that x dot y and y dot x are really the same thing . we showed that order does n't matter when you take the dot product , just like it does n't matter with regular multiplication . so these are really the same terms . | how come sal does n't use inner product ? |
in the last video , we showed you the cauchy-schwarz inequality . i think it 's worth rewriting because this is something that 's going to show up a lot . it 's a very useful tool . and that just told us if i have two vectors , x and y , they 're both members of rn . and they 're both nonzero vectors . and that was an ... | these are n't just numbers . and this is the dot product . it 's just not normal multiplication . | is n't inner product a stronger , more general form of the dot product ? |
in the last video , we showed you the cauchy-schwarz inequality . i think it 's worth rewriting because this is something that 's going to show up a lot . it 's a very useful tool . and that just told us if i have two vectors , x and y , they 're both members of rn . and they 're both nonzero vectors . and that was an ... | you took from the tail of x to the head of y . so this vector right here is the vector x plus y . and that 's why it 's called the triangle inequality . | why do you go back to the factor 2 ( vector x dot vector y ) in the equation ? |
in the last video , we showed you the cauchy-schwarz inequality . i think it 's worth rewriting because this is something that 's going to show up a lot . it 's a very useful tool . and that just told us if i have two vectors , x and y , they 're both members of rn . and they 're both nonzero vectors . and that was an ... | but this is just to give you the idea . so then this is their sum , right ? you took from the tail of x to the head of y . | is it right to say that the square of the absolute value of the sum of vectors a and b is equal to the square of the sum of the two vectors ? |
in the last video , we showed you the cauchy-schwarz inequality . i think it 's worth rewriting because this is something that 's going to show up a lot . it 's a very useful tool . and that just told us if i have two vectors , x and y , they 're both members of rn . and they 're both nonzero vectors . and that was an ... | so this equals that and all of that -- what does this equal ? this is equal to x dot x . what 's x dot x ? x dot x is just the magnitude . | why is x dot y replaced with the product of length x and length y ? |
in the last video , we showed you the cauchy-schwarz inequality . i think it 's worth rewriting because this is something that 's going to show up a lot . it 's a very useful tool . and that just told us if i have two vectors , x and y , they 're both members of rn . and they 're both nonzero vectors . and that was an ... | you took from the tail of x to the head of y . so this vector right here is the vector x plus y . and that 's why it 's called the triangle inequality . | what is the difference in mag of vector x and absolute value of vector x ? |
in the last video , we showed you the cauchy-schwarz inequality . i think it 's worth rewriting because this is something that 's going to show up a lot . it 's a very useful tool . and that just told us if i have two vectors , x and y , they 're both members of rn . and they 're both nonzero vectors . and that was an ... | so this equals that and all of that -- what does this equal ? this is equal to x dot x . what 's x dot x ? x dot x is just the magnitude . | if ||x|| + ||y|| = || x + y || when x = cy , then we must assume c > 0 and that x dot y = |x dot y| , correct ? |
in the last video , we showed you the cauchy-schwarz inequality . i think it 's worth rewriting because this is something that 's going to show up a lot . it 's a very useful tool . and that just told us if i have two vectors , x and y , they 're both members of rn . and they 're both nonzero vectors . and that was an ... | but this is kind of your two-dimensional space that 's going on . what 's interesting or what 's useful about linear algebra is , we 've just defined the triangle inequality for arbitrarily large vectors , or vectors that have an arbitrarily high number of components . each of these , these do n't have to be in r2 . | how to identify type of triangle if sides are represented by vectors ? |
in the last video , we showed you the cauchy-schwarz inequality . i think it 's worth rewriting because this is something that 's going to show up a lot . it 's a very useful tool . and that just told us if i have two vectors , x and y , they 're both members of rn . and they 're both nonzero vectors . and that was an ... | you took from the tail of x to the head of y . so this vector right here is the vector x plus y . and that 's why it 's called the triangle inequality . | ( x + y ) to develop the definition of vector triangle inequality ? |
in the last video , we showed you the cauchy-schwarz inequality . i think it 's worth rewriting because this is something that 's going to show up a lot . it 's a very useful tool . and that just told us if i have two vectors , x and y , they 're both members of rn . and they 're both nonzero vectors . and that was an ... | you took from the tail of x to the head of y . so this vector right here is the vector x plus y . and that 's why it 's called the triangle inequality . | what if , either x or y itself is a negative vector itself ? |
in the last video , we showed you the cauchy-schwarz inequality . i think it 's worth rewriting because this is something that 's going to show up a lot . it 's a very useful tool . and that just told us if i have two vectors , x and y , they 're both members of rn . and they 're both nonzero vectors . and that was an ... | why is that ? well this could be negative . i could show you examples of dot products that are negative . in fact , if x has all positive terms and y has all negative terms , you 're going to have a negative dot product . | at around you talk about dot products being negative but how could a scalar quantity be negative ? |
in the last video , we showed you the cauchy-schwarz inequality . i think it 's worth rewriting because this is something that 's going to show up a lot . it 's a very useful tool . and that just told us if i have two vectors , x and y , they 're both members of rn . and they 're both nonzero vectors . and that was an ... | you took from the tail of x to the head of y . so this vector right here is the vector x plus y . and that 's why it 's called the triangle inequality . | isnt negative just used to specify direction of a vector ? |
in the last video , we showed you the cauchy-schwarz inequality . i think it 's worth rewriting because this is something that 's going to show up a lot . it 's a very useful tool . and that just told us if i have two vectors , x and y , they 're both members of rn . and they 're both nonzero vectors . and that was an ... | this is true if we 're in r100 where every vector has a hundred components to it . we 've just defined some notion of the triangle inequality . we 've abstracted well beyond just our two-dimensional cartesian coordinates . | how do you find the area of a triangle that is defined by vectors ? |
in the last video , we showed you the cauchy-schwarz inequality . i think it 's worth rewriting because this is something that 's going to show up a lot . it 's a very useful tool . and that just told us if i have two vectors , x and y , they 're both members of rn . and they 're both nonzero vectors . and that was an ... | so this equals that and all of that -- what does this equal ? this is equal to x dot x . what 's x dot x ? x dot x is just the magnitude . | the extreme case when x and y are parallel , and x+y lies on top , is that still considered a triangle ? |
in the last video , we showed you the cauchy-schwarz inequality . i think it 's worth rewriting because this is something that 's going to show up a lot . it 's a very useful tool . and that just told us if i have two vectors , x and y , they 're both members of rn . and they 're both nonzero vectors . and that was an ... | and if we just take the square root of both sides of this , you get the length of our vector x plus y is less than or equal to the length of the vector x by itself plus the length of the vector y . and we call this the triangle inequality , which you might have remembered from geometry . now why is it called the triang... | isnt it obvious that the triangle inequality can also work in n dimensions ? |
in the last video , we showed you the cauchy-schwarz inequality . i think it 's worth rewriting because this is something that 's going to show up a lot . it 's a very useful tool . and that just told us if i have two vectors , x and y , they 're both members of rn . and they 're both nonzero vectors . and that was an ... | we 've abstracted well beyond just our two-dimensional cartesian coordinates . well beyond even our three dimensions to essentially , n dimensional space . and i have n't defined dimensions yet , but i think you 're starting to appreciate what they are . | can any 2d geometry object property be prove to extend to n dimensions using vectors ? |
in the last video , we showed you the cauchy-schwarz inequality . i think it 's worth rewriting because this is something that 's going to show up a lot . it 's a very useful tool . and that just told us if i have two vectors , x and y , they 're both members of rn . and they 're both nonzero vectors . and that was an ... | no absolute value here . so the only way that i can assure that this is a positive quantity , that this is the same thing as the absolute value of x dot y is to enforce -- if i 'm kind of going to go down this road , is to enforce that this term right here , that c be positive . because if c is positive , then x dot y ... | around 1; why do you necessarily know that the y-vector is also positive ? |
in the last video , we showed you the cauchy-schwarz inequality . i think it 's worth rewriting because this is something that 's going to show up a lot . it 's a very useful tool . and that just told us if i have two vectors , x and y , they 're both members of rn . and they 're both nonzero vectors . and that was an ... | but i do n't have the absolute value of x dot y here . i do n't know that this is positive . i can say definitively that this is a positive quantity because i took the absolute value of it . | obviously , c needs to be positive ; but , again ; why is it a given that the y-vector is positive ? |
in the last video , we showed you the cauchy-schwarz inequality . i think it 's worth rewriting because this is something that 's going to show up a lot . it 's a very useful tool . and that just told us if i have two vectors , x and y , they 're both members of rn . and they 're both nonzero vectors . and that was an ... | what does x plus y look like ? and remember , i ca n't necessarily draw any two vectors on a two-dimensional space like this . i 'm just assuming that these are in r2 . | what does it mean when we divide two vectors ? |
in the last video , we showed you the cauchy-schwarz inequality . i think it 's worth rewriting because this is something that 's going to show up a lot . it 's a very useful tool . and that just told us if i have two vectors , x and y , they 're both members of rn . and they 're both nonzero vectors . and that was an ... | so that is definitely less than or equal to -- i 'm just rewriting this x squared and i 'll write the plus 2 there . plus 2 . but i want to make it very clear what i 'm replacing here . | also , how can we cancel 2 vectors ? |
in the last video , we showed you the cauchy-schwarz inequality . i think it 's worth rewriting because this is something that 's going to show up a lot . it 's a very useful tool . and that just told us if i have two vectors , x and y , they 're both members of rn . and they 're both nonzero vectors . and that was an ... | so that is definitely less than or equal to -- i 'm just rewriting this x squared and i 'll write the plus 2 there . plus 2 . but i want to make it very clear what i 'm replacing here . | this is a general form of the expansion of ( a+b ) ^2 , correct ? |
in the last video , we showed you the cauchy-schwarz inequality . i think it 's worth rewriting because this is something that 's going to show up a lot . it 's a very useful tool . and that just told us if i have two vectors , x and y , they 're both members of rn . and they 're both nonzero vectors . and that was an ... | we could say look , we could add a little x dot y is less than or equal to the absolute value of x dot y . which is less than or equal to the length of x times the length of y . so x dot y is definite -- this , the dot product of x with y is definitely less than it 's absolute value of that . | if so , my confusion lies in the 2ab term ; since according to cauchy-swarz , |a.b| = ||a|| ||b|| iff one is a scalar multiple of the other , how does it work to satisfy ( for example in two dimensional space ) that the area of a times b is equal to the length of a times the length of b , but in this case they are perp... |
in the last video , we showed you the cauchy-schwarz inequality . i think it 's worth rewriting because this is something that 's going to show up a lot . it 's a very useful tool . and that just told us if i have two vectors , x and y , they 're both members of rn . and they 're both nonzero vectors . and that was an ... | each of these , these do n't have to be in r2 . this is true if we 're in r100 where every vector has a hundred components to it . we 've just defined some notion of the triangle inequality . | is this true for every vector space or only for cartesian spaces ? |
( piano music ) steven : there is this marvelous way that jan van eyck can create a sense of the real even when he 's representing the impossible . beth : mary is impossibly large within this exceptionally beautiful and perhaps impossibly beautiful gothic church . she fills this space , and is shown here as the queen o... | we see it flooding in the gothic windows , and two pools of sunlight on the floor in front of mary . we know that we 're looking toward the east end of the church ; therefore the light that we see reflected on the floor is coming from the windows on the north , and those spots of light would be impossible in that case ... | in regards to the light source being mystical , is n't it possible the artist simply made a mistake and meant for that to be light pooling from the west windows ? |
( piano music ) steven : there is this marvelous way that jan van eyck can create a sense of the real even when he 's representing the impossible . beth : mary is impossibly large within this exceptionally beautiful and perhaps impossibly beautiful gothic church . she fills this space , and is shown here as the queen o... | steven : this painting is about the way that light passes through the great windows of a gothic cathedral into its sacred interior space , because that functioned , in the medieval mind , as an important symbol of mary 's chastity ; of her virginity . this is an ideal church . this architecture does n't exist in the wo... | how do we know we are facing the east end of the church ? |
( piano music ) steven : there is this marvelous way that jan van eyck can create a sense of the real even when he 's representing the impossible . beth : mary is impossibly large within this exceptionally beautiful and perhaps impossibly beautiful gothic church . she fills this space , and is shown here as the queen o... | this is a way of representing the heavenly sphere in an environment that we can recognize . this painting was stolen in 1877 , and although the panel itself was recovered , its frame was not . the frame , however , had an inscription , which was recorded , and it read as follows . | due to the 1877 theft mentioned in 0 has no one made an attempt to recreate another frame for this painting with the same inscription ? |
( piano music ) steven : there is this marvelous way that jan van eyck can create a sense of the real even when he 's representing the impossible . beth : mary is impossibly large within this exceptionally beautiful and perhaps impossibly beautiful gothic church . she fills this space , and is shown here as the queen o... | we know that we 're looking toward the east end of the church ; therefore the light that we see reflected on the floor is coming from the windows on the north , and those spots of light would be impossible in that case , so the light must be mystical ; supernatural . steven : this painting is about the way that light p... | was mary 's virginity important ? |
( piano music ) steven : there is this marvelous way that jan van eyck can create a sense of the real even when he 's representing the impossible . beth : mary is impossibly large within this exceptionally beautiful and perhaps impossibly beautiful gothic church . she fills this space , and is shown here as the queen o... | this is an ideal church . this architecture does n't exist in the world , but is jan van eyck 's fantasy of the perfect interior for mary , to enthrone mary . this is a way of representing the heavenly sphere in an environment that we can recognize . | does anyone know what the tablet like thing on the pillar near mary is ? |
( piano music ) steven : there is this marvelous way that jan van eyck can create a sense of the real even when he 's representing the impossible . beth : mary is impossibly large within this exceptionally beautiful and perhaps impossibly beautiful gothic church . she fills this space , and is shown here as the queen o... | the frame , however , had an inscription , which was recorded , and it read as follows . `` as the sunbeam through the glass passes but not stains , `` so the virgin as she was , a virgin still remains . '' ( piano music ) | what does that mean `` as the sunbeam through the glass passes but not stains so the virgin as she was a virgin still remains '' mostly the part about the `` virgin as she was a virgin still remains '' ? |
( piano music ) steven : there is this marvelous way that jan van eyck can create a sense of the real even when he 's representing the impossible . beth : mary is impossibly large within this exceptionally beautiful and perhaps impossibly beautiful gothic church . she fills this space , and is shown here as the queen o... | this is a way of representing the heavenly sphere in an environment that we can recognize . this painting was stolen in 1877 , and although the panel itself was recovered , its frame was not . the frame , however , had an inscription , which was recorded , and it read as follows . | where is this painting currently found ? |
( piano music ) steven : there is this marvelous way that jan van eyck can create a sense of the real even when he 's representing the impossible . beth : mary is impossibly large within this exceptionally beautiful and perhaps impossibly beautiful gothic church . she fills this space , and is shown here as the queen o... | this is an ideal church . this architecture does n't exist in the world , but is jan van eyck 's fantasy of the perfect interior for mary , to enthrone mary . this is a way of representing the heavenly sphere in an environment that we can recognize . | would n't it more accurate to compare the delicate stained glass window mullions to be more representative of a woman 's hymen ? |
( piano music ) steven : there is this marvelous way that jan van eyck can create a sense of the real even when he 's representing the impossible . beth : mary is impossibly large within this exceptionally beautiful and perhaps impossibly beautiful gothic church . she fills this space , and is shown here as the queen o... | steven : if we look to the far back , we can see this beautiful tracery , and within that wooden carving , we can actually see stories of the life of the virgin mary . through the doorway we can also see two angels that seem to be singing from a hymnbook , and if we look just over mary 's left shoulder , we can see a s... | mary may have been a virgin at conception , but would this physical condition still remain after giving birth ? |
in the first video on evolution , i drew something that i called an ape , and then i drew a tail on it . and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . there 's obviously other primat... | and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . | why did apes and humans evolve from a common ancestor , but in different paths ? |
in the first video on evolution , i drew something that i called an ape , and then i drew a tail on it . and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . there 's obviously other primat... | and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . | when the instructor refers to `` lesser apes '' what characteristics classify these `` lesser apes '' ? |
in the first video on evolution , i drew something that i called an ape , and then i drew a tail on it . and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . there 's obviously other primat... | and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . | so we are not derived from apes , we are actually an ape species am i right ? |
in the first video on evolution , i drew something that i called an ape , and then i drew a tail on it . and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . there 's obviously other primat... | and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . | can humans reproduce with the other apes ? |
in the first video on evolution , i drew something that i called an ape , and then i drew a tail on it . and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . there 's obviously other primat... | and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . | okay , so we evolve from apes , so if one mated with a human could you see the `` half-way '' of human evolution ? |
in the first video on evolution , i drew something that i called an ape , and then i drew a tail on it . and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . there 's obviously other primat... | and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . | how did the apes eventually change ? |
in the first video on evolution , i drew something that i called an ape , and then i drew a tail on it . and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . there 's obviously other primat... | there 's obviously other primates that also have no tails , but apes definitely have no tails . and just to clarify , there 's kind of two families within apes and their common names are `` the lesser apes '' and `` the great apes . '' and the lesser apes - the lesser apes are things like gibbons , and the great apes a... | does this mean we have common ancestry from amphibians or even fish ? |
in the first video on evolution , i drew something that i called an ape , and then i drew a tail on it . and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . there 's obviously other primat... | and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . | or do other types of apes also have webbing between their fingers like us ? |
in the first video on evolution , i drew something that i called an ape , and then i drew a tail on it . and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . there 's obviously other primat... | and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . | is there a difference between apes and monkeys ? |
in the first video on evolution , i drew something that i called an ape , and then i drew a tail on it . and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . there 's obviously other primat... | and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . | if humans evolved from ancient apes our ancestor ( most probably ) , and referring to the previous video on natural selection , why did the apes did not get extinct ? |
in the first video on evolution , i drew something that i called an ape , and then i drew a tail on it . and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . there 's obviously other primat... | in the first video on evolution , i drew something that i called an ape , and then i drew a tail on it . and what i want to do in this video is clarify that that was absolutely wrong . | will humans evolve even more during the next few decades ? |
in the first video on evolution , i drew something that i called an ape , and then i drew a tail on it . and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . there 's obviously other primat... | and the lesser apes - the lesser apes are things like gibbons , and the great apes are things like chimpanzees and gorillas , and , me , or human beings ! so these right here , these are the great apes . these are the great apes , and clearly this great ape right here did not have a great sense of style in 1994 . | evolution is still taking place today , right ? |
in the first video on evolution , i drew something that i called an ape , and then i drew a tail on it . and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . there 's obviously other primat... | in the first video on evolution , i drew something that i called an ape , and then i drew a tail on it . and what i want to do in this video is clarify that that was absolutely wrong . | so what evolution changes are taking place today ? |
in the first video on evolution , i drew something that i called an ape , and then i drew a tail on it . and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . there 's obviously other primat... | and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . | what is the difference between greater apes and lesser apes ? |
in the first video on evolution , i drew something that i called an ape , and then i drew a tail on it . and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . there 's obviously other primat... | in the first video on evolution , i drew something that i called an ape , and then i drew a tail on it . and what i want to do in this video is clarify that that was absolutely wrong . | in he dinosaur period , we see that in each age , there are quite a few dominant species in each categories ( herbivores , carnivores , air , water et cetera ) .so , in our age , why are we the only dominant species ? |
in the first video on evolution , i drew something that i called an ape , and then i drew a tail on it . and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . there 's obviously other primat... | in the first video on evolution , i drew something that i called an ape , and then i drew a tail on it . and what i want to do in this video is clarify that that was absolutely wrong . | and why are we the first species to become so advanced , and why did we get so advanced ? |
in the first video on evolution , i drew something that i called an ape , and then i drew a tail on it . and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . there 's obviously other primat... | so these right here , these are the great apes . these are the great apes , and clearly this great ape right here did not have a great sense of style in 1994 . and really did n't feel the need to have a haircut ! | how many bones does an ape have ? |
in the first video on evolution , i drew something that i called an ape , and then i drew a tail on it . and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . there 's obviously other primat... | and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . | which primates can be classified as great apes and which ca n't ? |
in the first video on evolution , i drew something that i called an ape , and then i drew a tail on it . and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . there 's obviously other primat... | and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . | what is the difference between great apes and lesser apes ? |
in the first video on evolution , i drew something that i called an ape , and then i drew a tail on it . and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . there 's obviously other primat... | and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . | animals have been gifted with tails so that they can balance themselves during any kind of movements like running or jumping.so how do lesser and greater apes balance themselves without tails ? |
in the first video on evolution , i drew something that i called an ape , and then i drew a tail on it . and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . there 's obviously other primat... | and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . | why are apes so closely related ? |
in the first video on evolution , i drew something that i called an ape , and then i drew a tail on it . and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . there 's obviously other primat... | and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . | is it possible the humans are evolved from something else other than apes ? |
in the first video on evolution , i drew something that i called an ape , and then i drew a tail on it . and what i want to do in this video is clarify that that was absolutely wrong . apes - apes have no tails . and it 's actually one of the main distinguishing characteristics of apes . there 's obviously other primat... | and it 's actually one of the main distinguishing characteristics of apes . there 's obviously other primates that also have no tails , but apes definitely have no tails . and just to clarify , there 's kind of two families within apes and their common names are `` the lesser apes '' and `` the great apes . '' | would the babies be born with or with out tails ? |
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