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use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | and if we have time , i 'll tell you why it makes a lot of sense , or how we can derive it . so the change of base formula just tells us that log -- let me do some colors here -- log base a of b is the exact same thing as log base x , where x is an arbitrary base of b , over log base , that same base , base x over a . ... | is there anything special for log base pi of x ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , which is a natural logarithm , and log base 10 . so you generally have to change your ... | what does log base e mean what is e ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , which is a natural logarithm , and log base 10 . so you generally have to change your ... | are there any calculators that actually have different log base changes other than 10 ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | so this numerator is just equal to 2 . so it simplifies to 2 over log base 10 of 5 . and we can now use our calculator , because the log function on a calculator is log base 10 . so let 's get our calculator out . | 4 , why do you use the base 10 ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , which is a natural logarithm , and log base 10 . so you generally have to change your ... | why is e called the natural base of logarithms ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , which is a natural logarithm , and log base 10 . so you generally have to change your ... | how did you get the log base 10 ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | so this numerator is just equal to 2 . so it simplifies to 2 over log base 10 of 5 . and we can now use our calculator , because the log function on a calculator is log base 10 . so let 's get our calculator out . | will it always be base 10 when you use that formula in 7 ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | does a scientific calculator not allow you to change the base ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | and if we have time , i 'll tell you why it makes a lot of sense , or how we can derive it . so the change of base formula just tells us that log -- let me do some colors here -- log base a of b is the exact same thing as log base x , where x is an arbitrary base of b , over log base , that same base , base x over a . ... | what happens when you have a negative number in the base when doing change of base ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | so it simplifies to 2 over log base 10 of 5 . and we can now use our calculator , because the log function on a calculator is log base 10 . so let 's get our calculator out . | how can we solve logs without calculator ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | and if we have time , i 'll tell you why it makes a lot of sense , or how we can derive it . so the change of base formula just tells us that log -- let me do some colors here -- log base a of b is the exact same thing as log base x , where x is an arbitrary base of b , over log base , that same base , base x over a . ... | what does `` base '' stand for ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | they have functions for log base e , which is a natural logarithm , and log base 10 . so you generally have to change your base . and that 's what the change of base formula is . and if we have time , i 'll tell you why it makes a lot of sense , or how we can derive it . | okay can anyone give me an explanation in words as to what a change of base is ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | we want to clear this . 2 divided by -- when someone just writes log , they mean base 10 . if they press ln , that means base e. so log without any other information is log base 10 . | would n't the solution be written in quotient form since it is being divided ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | this is an exponential way of writing this truth . this is a logarithmic way of writing this truth . this is equal to b . | how do you convert the logbase of a logarithmic expression to another logbase ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | we 've proven the change of base formula . log base a of b is equal to log base x of b divided by log base x of a . in this example , a was 5 , b is 100 , and the base that we switched it to is 10. x is 10 . | how do you find what log base 8 or log base 7 or any number is equal to ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | so this numerator is just equal to 2 . so it simplifies to 2 over log base 10 of 5 . and we can now use our calculator , because the log function on a calculator is log base 10 . so let 's get our calculator out . | we know log base 10 is 1.0 but how can you find the others without a calculator ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | we 've proven the change of base formula . log base a of b is equal to log base x of b divided by log base x of a . in this example , a was 5 , b is 100 , and the base that we switched it to is 10. x is 10 . | 8 in the video , why does the `` log a '' become `` log x '' ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | and if we have time , i 'll tell you why it makes a lot of sense , or how we can derive it . so the change of base formula just tells us that log -- let me do some colors here -- log base a of b is the exact same thing as log base x , where x is an arbitrary base of b , over log base , that same base , base x over a . ... | so i 'm working on base 16 right now and i am getting really confused an my homework is asking for me to change the base 16 numeral into base 10 and it is really confusing can you help me ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | so this numerator is just equal to 2 . so it simplifies to 2 over log base 10 of 5 . and we can now use our calculator , because the log function on a calculator is log base 10 . | from how did sal get that answer from log^5 ( 100 ) ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . | but what happens if log_x ( a ) is zero ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | so it simplifies to 2 over log base 10 of 5 . and we can now use our calculator , because the log function on a calculator is log base 10 . so let 's get our calculator out . | do n't you have to qualify that your log function is only defined when that is non-zero ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | 10 to the same power will be equal to this , because these two things are equal to each other . so let 's take the same logarithm of both sides of this , the logarithm with the same base . and i 'll actually do log base x to prove the general case , here . | when we change the base of logarithm , we lose information about proper input of logarithm ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | so if our calculator has a certain base x function , we can convert to that base . it 's usually e or base 10 . base 10 is an easy way to go . and in general , if you just see someone write a logarithm like this , if they just write log of x , they 're implying -- this implies log base 10 of x . | does the changed base have to be 10 , e or common , could an individual change the base to any number ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | so this is also equal to c. and we 're done . we 've proven the change of base formula . log base a of b is equal to log base x of b divided by log base x of a . | is the definition of inverse the same as the change of base formula ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | and if we have time , i 'll tell you why it makes a lot of sense , or how we can derive it . so the change of base formula just tells us that log -- let me do some colors here -- log base a of b is the exact same thing as log base x , where x is an arbitrary base of b , over log base , that same base , base x over a . ... | why does the base have to be x. why do you have to include a log ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | the second power . so this numerator is just equal to 2 . so it simplifies to 2 over log base 10 of 5 . and we can now use our calculator , because the log function on a calculator is log base 10 . | what is the difference between algebra 1 and algebra 2 ? |
steven zucker : the fading light of the sun is being replaced by the lanterns being held by these children . it is that moment at twilight when artificial light just begins to assert itself against the light of the day . beth harris : it is a wonderful and haunting time of the day . and sargent captured it in his paint... | and it 's easy to see how this becomes important to the beginnings of abstraction , looking at art not for what it 's representing , not for the objects it 's copying from the world , but for the things that art is made of itself . steven zucker : sargent actually painted this plein air . that is , he painted it in a g... | are these sargent 's children ? |
steven zucker : the fading light of the sun is being replaced by the lanterns being held by these children . it is that moment at twilight when artificial light just begins to assert itself against the light of the day . beth harris : it is a wonderful and haunting time of the day . and sargent captured it in his paint... | and it 's easy to see how this becomes important to the beginnings of abstraction , looking at art not for what it 's representing , not for the objects it 's copying from the world , but for the things that art is made of itself . steven zucker : sargent actually painted this plein air . that is , he painted it in a g... | john singer sargent was an american and formally trained in paris -- what makes his artwork distinctly `` late victorian '' ? |
steven zucker : the fading light of the sun is being replaced by the lanterns being held by these children . it is that moment at twilight when artificial light just begins to assert itself against the light of the day . beth harris : it is a wonderful and haunting time of the day . and sargent captured it in his paint... | the parts that are illuminated are these lanterns against this graying , green forms of dusk . steven zucker : look at the way that the canvas is really flat -- clearly , the influence of japanese prints . the way in which , for instance , the flowers are smallest at the feet of the children . | how was there so much japanese influence during this time ? |
: depending on who you speak to , the term pneumonia and the term pneumonitis can be used synomonously , meaning that they can often mean the same thing . what i 'm gon na do - and you see me drawing here - i 'm just going to draw a set of lungs and we 're gon na discuss what the differences are between the two . you ... | : depending on who you speak to , the term pneumonia and the term pneumonitis can be used synomonously , meaning that they can often mean the same thing . what i 'm gon na do - and you see me drawing here - i 'm just going to draw a set of lungs and we 're gon na discuss what the differences are between the two . | what is worse to have ? |
: depending on who you speak to , the term pneumonia and the term pneumonitis can be used synomonously , meaning that they can often mean the same thing . what i 'm gon na do - and you see me drawing here - i 'm just going to draw a set of lungs and we 're gon na discuss what the differences are between the two . you ... | so this is pneumonia . with pneumonitis , if we scoop over here and look at pneumonitis , the issue is not that it is an infection . it 's that it is inflammation . | is asbestosis a type of pneumonitis ? |
so there are situations where you have some type of a function , this is clearly a nonlinear function . f of x is equal to one over x minus one , this is its graph or at least part of its graph right over here . but where you wan na approximate it with a linear function especially around a certain value , and so what ... | so , and that 's actually pretty close to what i drew up here , this should be intersecting the y-axis at negative 3/4 . so there you have it , this , this line , or you could even say , this equation , is going to be a very good linear approximation , about as good as you can get for a linear approximation for that no... | how do you calculate the error and percentage error after finding the linear approximation ? |
so there are situations where you have some type of a function , this is clearly a nonlinear function . f of x is equal to one over x minus one , this is its graph or at least part of its graph right over here . but where you wan na approximate it with a linear function especially around a certain value , and so what ... | so let 's do that . so in order to find the equation of the tangent line , the equation of a line is y is equal to mx plus b where m is a slope and b is the y intercept . there 's other ways that you could think about it . | how would you solve for the y-intercept algebraically ? |
so there are situations where you have some type of a function , this is clearly a nonlinear function . f of x is equal to one over x minus one , this is its graph or at least part of its graph right over here . but where you wan na approximate it with a linear function especially around a certain value , and so what ... | f of x is equal to one over x minus one , this is its graph or at least part of its graph right over here . but where you wan na approximate it with a linear function especially around a certain value , and so what we 're going to do is , we wan na find an approximation , let me write this down , i wan na find an appro... | how should we determine if the approximate value is an overestimate or underestimate of the actual value ? |
in the next few videos , we 're gon na do a very high-level overview of ancient history . we 're literally going to try to cover 3,000 years of history in a handful of videos . and we 're going to focus on not all of the history in the world , and it 's worth noting that there 's going to be history in north and south... | and this is right at around the same time you have folks living in mesopotamia , you have the akkadians . we 're going into deep history now , so we do n't know exactly what was going on in the indus valley , but we believe that there were people there as well , and there were people many , many other places . but now ... | 3 it takes about the jewish exodus , now would n't the egyptians have written about the large group of people they have just enslaved i mean that must have been a large amount of influx in the slave population so why would n't they 've written about it ? |
in the next few videos , we 're gon na do a very high-level overview of ancient history . we 're literally going to try to cover 3,000 years of history in a handful of videos . and we 're going to focus on not all of the history in the world , and it 's worth noting that there 's going to be history in north and south... | in the next few videos , we 're gon na do a very high-level overview of ancient history . we 're literally going to try to cover 3,000 years of history in a handful of videos . | is b.c.e the same as b.c ? |
in the next few videos , we 're gon na do a very high-level overview of ancient history . we 're literally going to try to cover 3,000 years of history in a handful of videos . and we 're going to focus on not all of the history in the world , and it 's worth noting that there 's going to be history in north and south... | we 're gon na go about 500 years . and we associate ancient egypt with the pyramids , and , relatively speaking , the pyramids were built fairly early in the history of ancient egypt . they were built about 2500 bce , or so we 're talking about 4,500-4,600 years ago was the time that , especially the most famous , the ... | how long did the ancient egypt civilization , lasts ? |
in the next few videos , we 're gon na do a very high-level overview of ancient history . we 're literally going to try to cover 3,000 years of history in a handful of videos . and we 're going to focus on not all of the history in the world , and it 's worth noting that there 's going to be history in north and south... | we 're gon na go about 500 years . and we associate ancient egypt with the pyramids , and , relatively speaking , the pyramids were built fairly early in the history of ancient egypt . they were built about 2500 bce , or so we 're talking about 4,500-4,600 years ago was the time that , especially the most famous , the ... | is n't the cheops pyramid the most famous of all pyramids ? |
in the next few videos , we 're gon na do a very high-level overview of ancient history . we 're literally going to try to cover 3,000 years of history in a handful of videos . and we 're going to focus on not all of the history in the world , and it 's worth noting that there 's going to be history in north and south... | so , if we say this is judea , this is mesopotamia . and we will also touch a little bit later on persia , which is that area there . the ancient greece . | also what is a judeo-christian ? |
in the next few videos , we 're gon na do a very high-level overview of ancient history . we 're literally going to try to cover 3,000 years of history in a handful of videos . and we 're going to focus on not all of the history in the world , and it 's worth noting that there 's going to be history in north and south... | so , i 'll just write judea . judea . that 's a little hard to read . | if the akkadian semites decedents of abraham had not made it to judea until the 2000bce , then who where the ancient egyptians if the bedouins had not migrated there yet neither ? |
in the next few videos , we 're gon na do a very high-level overview of ancient history . we 're literally going to try to cover 3,000 years of history in a handful of videos . and we 're going to focus on not all of the history in the world , and it 's worth noting that there 's going to be history in north and south... | and abraham , we believe that he was coincident or maybe came a little bit after hammurabi because a lotta the old testament seems to at least be inspired by some of what we see in hammurabi 's code . and it 's worth noting that even though this seems like a long time ago , around 1700 bce , the time of hammurabi , and... | how important was religion at the time in these empires ? |
in the next few videos , we 're gon na do a very high-level overview of ancient history . we 're literally going to try to cover 3,000 years of history in a handful of videos . and we 're going to focus on not all of the history in the world , and it 's worth noting that there 's going to be history in north and south... | and this is right at around the same time you have folks living in mesopotamia , you have the akkadians . we 're going into deep history now , so we do n't know exactly what was going on in the indus valley , but we believe that there were people there as well , and there were people many , many other places . but now ... | also , how much did leaders of the empires make use of religion , to make people accept things they normally would n't have accepted ? |
in the next few videos , we 're gon na do a very high-level overview of ancient history . we 're literally going to try to cover 3,000 years of history in a handful of videos . and we 're going to focus on not all of the history in the world , and it 's worth noting that there 's going to be history in north and south... | in the next few videos , we 're gon na do a very high-level overview of ancient history . we 're literally going to try to cover 3,000 years of history in a handful of videos . | which nations have the closest dna or are the descendants of the shumerians ? |
in the next few videos , we 're gon na do a very high-level overview of ancient history . we 're literally going to try to cover 3,000 years of history in a handful of videos . and we 're going to focus on not all of the history in the world , and it 's worth noting that there 's going to be history in north and south... | because in 1700 bce , and we 're gon na talk about hammurabi , who lived in , who ruled over babylon , the babylonian empire . so , hammurabi right over here in babylon , famous for the code of hammurabi . he codified a series of laws . | how come sal pronounces hammurabi as if it was written hummurabi ? |
in the next few videos , we 're gon na do a very high-level overview of ancient history . we 're literally going to try to cover 3,000 years of history in a handful of videos . and we 're going to focus on not all of the history in the world , and it 's worth noting that there 's going to be history in north and south... | let me write this . this is 1700 bce . and once again , i 'll put approximately . | was the place which abraham lived around 1700 bce part of shumerians ' land ? |
we 're asked to find a power series for f , and they 've given us f of x is equal to six over one plus x to the third power . now , since they 're letting us pick which power series , you might say , well , let me just find the maclaurin series because the maclaurin series tends to be the simplest to find 'cause we 'r... | but the simplest way to approach it is to say , hey , you know what , this form right over here , this rational expression , it looks similar . it looks like the sum of a geometric series . let 's just remind ourselves what the sum of a geometric series looks like . if i have a plus a times r , so a is my first term , ... | the sum of geometric sequence is a/ ( 1-r ) , but this is only true for |r| < 1 , is n't it ? |
we 're asked to find a power series for f , and they 've given us f of x is equal to six over one plus x to the third power . now , since they 're letting us pick which power series , you might say , well , let me just find the maclaurin series because the maclaurin series tends to be the simplest to find 'cause we 'r... | we 're asked to find a power series for f , and they 've given us f of x is equal to six over one plus x to the third power . now , since they 're letting us pick which power series , you might say , well , let me just find the maclaurin series because the maclaurin series tends to be the simplest to find 'cause we 'r... | does n't the maclaurin series have a factorial denominator in every term ? |
we 're asked to find a power series for f , and they 've given us f of x is equal to six over one plus x to the third power . now , since they 're letting us pick which power series , you might say , well , let me just find the maclaurin series because the maclaurin series tends to be the simplest to find 'cause we 'r... | we 're asked to find a power series for f , and they 've given us f of x is equal to six over one plus x to the third power . now , since they 're letting us pick which power series , you might say , well , let me just find the maclaurin series because the maclaurin series tends to be the simplest to find 'cause we 'r... | the serie is p ( x ) =6 -6x^3 +6x^6 ... ... the funtion is f ( x ) = 6/ ( 1+x^3 ) if x=1 f ( 1 ) =3 and p ( 1 ) =0 or 6 why f and p not equal in a infinite maclaurin 's serie the error is zero ? |
karl filled up the tank of his truck with 400 liters of fuel and set out to deliver a shipment of bananas to alaska . the truck consumed 0.8 liters of fuel or eight-tenths of a liter of fuel for each kilometer driven . graph the amount of fuel remaining in the truck 's tank in liters as a function of distance driven i... | karl filled up the tank of his truck with 400 liters of fuel and set out to deliver a shipment of bananas to alaska . the truck consumed 0.8 liters of fuel or eight-tenths of a liter of fuel for each kilometer driven . graph the amount of fuel remaining in the truck 's tank in liters as a function of distance driven i... | what kind of truck uses 0.8 liters of fuel per km driven ? |
hi everyone . here and in the next few videos i 'm gon na be talking about tangent planes of graphs , and i 'll specify this is tangent planes of graphs and not of some other thing because in different context of multivariable calculus you might be taking a tangent plane of say a parametric surface or something like t... | hi everyone . here and in the next few videos i 'm gon na be talking about tangent planes of graphs , and i 'll specify this is tangent planes of graphs and not of some other thing because in different context of multivariable calculus you might be taking a tangent plane of say a parametric surface or something like t... | would that mean people are just tangent objects of the space-time continuum ? |
find the probability of getting exactly two heads when flipping three coins . so let 's think about the sample space . let 's think about all of the possible outcomes . so i could get all heads . so on flip one i get a head , flip two i get a head , flip three i get a head . i could get two heads and then a tail . i co... | find the probability of getting exactly two heads when flipping three coins . so let 's think about the sample space . | i 'm wondering if you have to always draw out all of the possibilities , or is there a formula that can be used ? |
find the probability of getting exactly two heads when flipping three coins . so let 's think about the sample space . let 's think about all of the possible outcomes . so i could get all heads . so on flip one i get a head , flip two i get a head , flip three i get a head . i could get two heads and then a tail . i co... | find the probability of getting exactly two heads when flipping three coins . so let 's think about the sample space . | a coin has two faces ( heads and tails ) , with a probability of 50 % for each face , but what is the probability that is does not fall on any of it 's faces but on it 's edge ? |
find the probability of getting exactly two heads when flipping three coins . so let 's think about the sample space . let 's think about all of the possible outcomes . so i could get all heads . so on flip one i get a head , flip two i get a head , flip three i get a head . i could get two heads and then a tail . i co... | so the probability of getting exactly two heads when flipping three coins is three outcomes satisfying this event over eight possible outcomes . so it is 3/8 . | how is this different from seating individuals abcd in 3 seats where using combinations would state that abc cba and bca are all the same outcome ? |
find the probability of getting exactly two heads when flipping three coins . so let 's think about the sample space . let 's think about all of the possible outcomes . so i could get all heads . so on flip one i get a head , flip two i get a head , flip three i get a head . i could get two heads and then a tail . i co... | find the probability of getting exactly two heads when flipping three coins . so let 's think about the sample space . | why do you have to draw out the possibilities ? |
find the probability of getting exactly two heads when flipping three coins . so let 's think about the sample space . let 's think about all of the possible outcomes . so i could get all heads . so on flip one i get a head , flip two i get a head , flip three i get a head . i could get two heads and then a tail . i co... | there 's only one head . this is exactly two heads . this is only one head , only one head , no heads . so you have one , two , three of the possible outcomes are associated with this event . | what is the probability that it will come up heads if tossed one more time ? |
find the probability of getting exactly two heads when flipping three coins . so let 's think about the sample space . let 's think about all of the possible outcomes . so i could get all heads . so on flip one i get a head , flip two i get a head , flip three i get a head . i could get two heads and then a tail . i co... | the probability of exactly two heads , well what is the size of our sample space ? i have eight possible outcomes . so eight , this is possible outcomes , or the size of our sample space , possible outcomes . and how many of those possible outcomes are associated with this event ? | is the formula # of outcomes meet the constraint/ # of all outcomes really generated from the real-life experiments and also be tested is true ? |
find the probability of getting exactly two heads when flipping three coins . so let 's think about the sample space . let 's think about all of the possible outcomes . so i could get all heads . so on flip one i get a head , flip two i get a head , flip three i get a head . i could get two heads and then a tail . i co... | these are all of the different ways that i could flip three coins . and you can maybe say that this is the first flip , the second flip , and the third flip . now , so this right over here is the sample space . | what in the question makes the distinction between whether the order of the roll or flip matters in the number of outcomes ? |
find the probability of getting exactly two heads when flipping three coins . so let 's think about the sample space . let 's think about all of the possible outcomes . so i could get all heads . so on flip one i get a head , flip two i get a head , flip three i get a head . i could get two heads and then a tail . i co... | the probability of exactly two heads , well what is the size of our sample space ? i have eight possible outcomes . so eight , this is possible outcomes , or the size of our sample space , possible outcomes . and how many of those possible outcomes are associated with this event ? | where did you get the formula when you did the probability ( exactly 2 `` h '' ) 3 outcomes satisfy over 8 possible outcomes ? |
find the probability of getting exactly two heads when flipping three coins . so let 's think about the sample space . let 's think about all of the possible outcomes . so i could get all heads . so on flip one i get a head , flip two i get a head , flip three i get a head . i could get two heads and then a tail . i co... | find the probability of getting exactly two heads when flipping three coins . so let 's think about the sample space . | is there a difference between hht and hth ? |
find the probability of getting exactly two heads when flipping three coins . so let 's think about the sample space . let 's think about all of the possible outcomes . so i could get all heads . so on flip one i get a head , flip two i get a head , flip three i get a head . i could get two heads and then a tail . i co... | find the probability of getting exactly two heads when flipping three coins . so let 's think about the sample space . | probability of at least 5 heads with 10 coins ? |
let 's say that this circle right over here represents one whole . and we 've divided this circle into one , two , three , four , five equal sections . so each of these sections represents 1/5 of the circle . and we 've seen this already . 1/5 , 1/5 , 1/5 , and 1/5 . and if we were to then color in some of this -- so ,... | we 've essentially taken two of these jumps . each jump is 1/1 . now we are at 2/1 , which is the same thing as 2 . | how can you divide 1 into 6 ? |
let 's say that this circle right over here represents one whole . and we 've divided this circle into one , two , three , four , five equal sections . so each of these sections represents 1/5 of the circle . and we 've seen this already . 1/5 , 1/5 , 1/5 , and 1/5 . and if we were to then color in some of this -- so ,... | let me label it . one whole . and instead of dividing it into five equal sections , i 'm just going to divide it into one equal section . | is one whole one number ? |
let 's say that this circle right over here represents one whole . and we 've divided this circle into one , two , three , four , five equal sections . so each of these sections represents 1/5 of the circle . and we 've seen this already . 1/5 , 1/5 , 1/5 , and 1/5 . and if we were to then color in some of this -- so ,... | we 've essentially taken two of these jumps . each jump is 1/1 . now we are at 2/1 , which is the same thing as 2 . | can a whole number be written as a fraction with a denominator of 1 ? |
let 's say that this circle right over here represents one whole . and we 've divided this circle into one , two , three , four , five equal sections . so each of these sections represents 1/5 of the circle . and we 've seen this already . 1/5 , 1/5 , 1/5 , and 1/5 . and if we were to then color in some of this -- so ,... | but another way of thinking about this fraction symbol is that it 's division . so you could view this as 3 divided by 1 is equal to 3 . or you could say , well , look , 1 over 1 is a whole , and i now have three of them , so this is equal to 3 wholes . | when the numerator is lesser than or equal to the denominator why does the fraction divided always is lesser than or equal to 1 ? |
let 's say that this circle right over here represents one whole . and we 've divided this circle into one , two , three , four , five equal sections . so each of these sections represents 1/5 of the circle . and we 've seen this already . 1/5 , 1/5 , 1/5 , and 1/5 . and if we were to then color in some of this -- so ,... | so 3/1 is the same thing as the number 3 . and let me make sure , let me emphasize that . let me draw this on a number line . | is sal sure that we can write the denominator smaller than the nominator ? |
let 's say that this circle right over here represents one whole . and we 've divided this circle into one , two , three , four , five equal sections . so each of these sections represents 1/5 of the circle . and we 've seen this already . 1/5 , 1/5 , 1/5 , and 1/5 . and if we were to then color in some of this -- so ,... | let me label it . one whole . and instead of dividing it into five equal sections , i 'm just going to divide it into one equal section . | what do you do to determine a whole when you know the number equivalent to a fraction of the whole ? |
let 's say that this circle right over here represents one whole . and we 've divided this circle into one , two , three , four , five equal sections . so each of these sections represents 1/5 of the circle . and we 've seen this already . 1/5 , 1/5 , 1/5 , and 1/5 . and if we were to then color in some of this -- so ,... | let me draw this on a number line . so once again , let me go all the way to 3 . so 0 , 1 , 2 , and 3 . | can a fractions denominator go on until infinity ? |
let 's say that this circle right over here represents one whole . and we 've divided this circle into one , two , three , four , five equal sections . so each of these sections represents 1/5 of the circle . and we 've seen this already . 1/5 , 1/5 , 1/5 , and 1/5 . and if we were to then color in some of this -- so ,... | we 've shaded in 3/5 of the whole . so the fraction that 's actually shaded in now is 3/5 . 3/5 is what 's shaded in . | can a fraction be a negative ? |
let 's say that this circle right over here represents one whole . and we 've divided this circle into one , two , three , four , five equal sections . so each of these sections represents 1/5 of the circle . and we 've seen this already . 1/5 , 1/5 , 1/5 , and 1/5 . and if we were to then color in some of this -- so ,... | let 's say that this circle right over here represents one whole . and we 've divided this circle into one , two , three , four , five equal sections . | are there different kinds of fractions ? |
let 's say that this circle right over here represents one whole . and we 've divided this circle into one , two , three , four , five equal sections . so each of these sections represents 1/5 of the circle . and we 've seen this already . 1/5 , 1/5 , 1/5 , and 1/5 . and if we were to then color in some of this -- so ,... | we 've essentially taken two of these jumps . each jump is 1/1 . now we are at 2/1 , which is the same thing as 2 . | how would you write 1 mile as a fraction in order to subtract the miles already hiked ? |
let 's say that this circle right over here represents one whole . and we 've divided this circle into one , two , three , four , five equal sections . so each of these sections represents 1/5 of the circle . and we 've seen this already . 1/5 , 1/5 , 1/5 , and 1/5 . and if we were to then color in some of this -- so ,... | this right over here is equal to , if i were to take the combination , this is equal to 3 . 3 wholes . or if i were to think of it in terms of numbers , just a number line , literally , this would represent the number 3 . | why is .33333 repeating decimal 1/3 why isnt 3/10 ? |
let 's say that this circle right over here represents one whole . and we 've divided this circle into one , two , three , four , five equal sections . so each of these sections represents 1/5 of the circle . and we 've seen this already . 1/5 , 1/5 , 1/5 , and 1/5 . and if we were to then color in some of this -- so ,... | let me label it . one whole . and instead of dividing it into five equal sections , i 'm just going to divide it into one equal section . | how can whole numbers be represented as fractions ? |
let 's say that this circle right over here represents one whole . and we 've divided this circle into one , two , three , four , five equal sections . so each of these sections represents 1/5 of the circle . and we 've seen this already . 1/5 , 1/5 , 1/5 , and 1/5 . and if we were to then color in some of this -- so ,... | so once again , let me go all the way to 3 . so 0 , 1 , 2 , and 3 . so one whole gets us exactly one jump on the number line . | what is 2/3 equal to in a whole number ? |
let 's say that this circle right over here represents one whole . and we 've divided this circle into one , two , three , four , five equal sections . so each of these sections represents 1/5 of the circle . and we 've seen this already . 1/5 , 1/5 , 1/5 , and 1/5 . and if we were to then color in some of this -- so ,... | notice when i took a 1/5 , another 1/5 , and another 1/5 , i could call that 3/5 . so now if i take one 1/1 , another 1/1 , and another 1/1 , well , i should be able to call this 3/1 , or 3 firsts , or however you want to call it . so i could call this 3 firsts . | how many copies of 1/4 does it take to make 1 whole ? |
let 's say that this circle right over here represents one whole . and we 've divided this circle into one , two , three , four , five equal sections . so each of these sections represents 1/5 of the circle . and we 've seen this already . 1/5 , 1/5 , 1/5 , and 1/5 . and if we were to then color in some of this -- so ,... | and we 've seen this already . 1/5 , 1/5 , 1/5 , and 1/5 . and if we were to then color in some of this -- so , let 's say we were to color in three of these sections . | is 5/5 equal to 6/6 ? |
let 's say that this circle right over here represents one whole . and we 've divided this circle into one , two , three , four , five equal sections . so each of these sections represents 1/5 of the circle . and we 've seen this already . 1/5 , 1/5 , 1/5 , and 1/5 . and if we were to then color in some of this -- so ,... | let me label it . one whole . and instead of dividing it into five equal sections , i 'm just going to divide it into one equal section . | why are whole numbers fractions ? |
let 's say that this circle right over here represents one whole . and we 've divided this circle into one , two , three , four , five equal sections . so each of these sections represents 1/5 of the circle . and we 've seen this already . 1/5 , 1/5 , 1/5 , and 1/5 . and if we were to then color in some of this -- so ,... | this right over here is equal to , if i were to take the combination , this is equal to 3 . 3 wholes . or if i were to think of it in terms of numbers , just a number line , literally , this would represent the number 3 . | how do you turn numbers into wholes ? |
let 's say that this circle right over here represents one whole . and we 've divided this circle into one , two , three , four , five equal sections . so each of these sections represents 1/5 of the circle . and we 've seen this already . 1/5 , 1/5 , 1/5 , and 1/5 . and if we were to then color in some of this -- so ,... | 3 wholes . or if i were to think of it in terms of numbers , just a number line , literally , this would represent the number 3 . but what 's another way i could represent it ? | how do you turn numbers into fractions ? |
let 's say that this circle right over here represents one whole . and we 've divided this circle into one , two , three , four , five equal sections . so each of these sections represents 1/5 of the circle . and we 've seen this already . 1/5 , 1/5 , 1/5 , and 1/5 . and if we were to then color in some of this -- so ,... | this right over here is equal to , if i were to take the combination , this is equal to 3 . 3 wholes . or if i were to think of it in terms of numbers , just a number line , literally , this would represent the number 3 . | is 3/3= to 3 , or is the equivalent of 3 3/1 ? |
let 's say that this circle right over here represents one whole . and we 've divided this circle into one , two , three , four , five equal sections . so each of these sections represents 1/5 of the circle . and we 've seen this already . 1/5 , 1/5 , 1/5 , and 1/5 . and if we were to then color in some of this -- so ,... | let 's say that this circle right over here represents one whole . and we 've divided this circle into one , two , three , four , five equal sections . | does it matter of the numerator is higher than the denominator ? |
let 's say that this circle right over here represents one whole . and we 've divided this circle into one , two , three , four , five equal sections . so each of these sections represents 1/5 of the circle . and we 've seen this already . 1/5 , 1/5 , 1/5 , and 1/5 . and if we were to then color in some of this -- so ,... | let me label it . one whole . and instead of dividing it into five equal sections , i 'm just going to divide it into one equal section . | how are whole numbers as fractions ? |
let 's say that this circle right over here represents one whole . and we 've divided this circle into one , two , three , four , five equal sections . so each of these sections represents 1/5 of the circle . and we 've seen this already . 1/5 , 1/5 , 1/5 , and 1/5 . and if we were to then color in some of this -- so ,... | let me label it . one whole . and instead of dividing it into five equal sections , i 'm just going to divide it into one equal section . | how much is left if u take 9/10 out of one whole ? |
let 's say that this circle right over here represents one whole . and we 've divided this circle into one , two , three , four , five equal sections . so each of these sections represents 1/5 of the circle . and we 've seen this already . 1/5 , 1/5 , 1/5 , and 1/5 . and if we were to then color in some of this -- so ,... | let me label it . one whole . and instead of dividing it into five equal sections , i 'm just going to divide it into one equal section . | when do we need to consider amounts that do n't represent whole numbers ? |
let 's say that this circle right over here represents one whole . and we 've divided this circle into one , two , three , four , five equal sections . so each of these sections represents 1/5 of the circle . and we 've seen this already . 1/5 , 1/5 , 1/5 , and 1/5 . and if we were to then color in some of this -- so ,... | let 's say that this circle right over here represents one whole . and we 've divided this circle into one , two , three , four , five equal sections . | why dose everyone hate me ? |
let 's say that this circle right over here represents one whole . and we 've divided this circle into one , two , three , four , five equal sections . so each of these sections represents 1/5 of the circle . and we 've seen this already . 1/5 , 1/5 , 1/5 , and 1/5 . and if we were to then color in some of this -- so ,... | notice when i took a 1/5 , another 1/5 , and another 1/5 , i could call that 3/5 . so now if i take one 1/1 , another 1/1 , and another 1/1 , well , i should be able to call this 3/1 , or 3 firsts , or however you want to call it . so i could call this 3 firsts . | why would i follow three circles appearing and being called 3/1 ? |
let 's say that this circle right over here represents one whole . and we 've divided this circle into one , two , three , four , five equal sections . so each of these sections represents 1/5 of the circle . and we 've seen this already . 1/5 , 1/5 , 1/5 , and 1/5 . and if we were to then color in some of this -- so ,... | let 's say that this circle right over here represents one whole . and we 've divided this circle into one , two , three , four , five equal sections . | what 's is partial products ? |
okay now , i said in a previous video that triglycerols , and i 'm drawing an example here . triglycerols are hydrolyzable lipids . which means that they 're lipids that can be broken down into smaller pieces in a hydrolysis reaction . so , hydrolysis reaction . and maybe a more general way of looking at this reaction... | so , hydrolysis reaction . and maybe a more general way of looking at this reaction is as an ester hydrolysis . because , really what 's being broken down in here are the individual ester bonds . you see , this is an ester . this carbon is double-bonded to an oxygen and then bonded to an additional or group , as well ,... | where does the na+ go if ester is circle like xiclohexane ? |
okay now , i said in a previous video that triglycerols , and i 'm drawing an example here . triglycerols are hydrolyzable lipids . which means that they 're lipids that can be broken down into smaller pieces in a hydrolysis reaction . so , hydrolysis reaction . and maybe a more general way of looking at this reaction... | and that reaction is hugely significant in our bodies . but , another application for this reaction is actually in the creation of soaps . so soaps and what happens is when you use a strong base like naoh . so maybe like , naoh which is sodium hydroxide , as this base promotion , you end up with a sodium cation at the ... | 2 ) what is the reason behind it that if grease sticks to our clothes we use detergents instead of soaps ? |
okay now , i said in a previous video that triglycerols , and i 'm drawing an example here . triglycerols are hydrolyzable lipids . which means that they 're lipids that can be broken down into smaller pieces in a hydrolysis reaction . so , hydrolysis reaction . and maybe a more general way of looking at this reaction... | and these electrons are going to move back on to this pretty electronegative oxygen which was willing to give up this hydrogen because it 's such a strong acid . you end up with a product of a carboxylate anion . so , we 've got that negative charge , and then our alcohol . so , this would be the base promoted ester hy... | why carboxylate ion is very unreactive toward nucleophilic substitution as well as it has a negative formal charge which makes it a strong nucleophile ... ? |
okay now , i said in a previous video that triglycerols , and i 'm drawing an example here . triglycerols are hydrolyzable lipids . which means that they 're lipids that can be broken down into smaller pieces in a hydrolysis reaction . so , hydrolysis reaction . and maybe a more general way of looking at this reaction... | but , i want to concentrate on the base promoted ester hydrolysis because it has some specific implications for these trigylcerols that we 've been talking about that i want to build towards . so , the base promoted ester hydrolysis . so , to give us a headstart on this base promoted ester hydrolysis , i went ahead and... | meaning of hydrolysis here by base is hydrolysis itself which is formation of alcohol and carboxylic acid or formation of soaps only ... ? |
okay now , i said in a previous video that triglycerols , and i 'm drawing an example here . triglycerols are hydrolyzable lipids . which means that they 're lipids that can be broken down into smaller pieces in a hydrolysis reaction . so , hydrolysis reaction . and maybe a more general way of looking at this reaction... | which means that they 're lipids that can be broken down into smaller pieces in a hydrolysis reaction . so , hydrolysis reaction . and maybe a more general way of looking at this reaction is as an ester hydrolysis . | so , is saponification an sn2 reaction ? |
let 's see if we can use our knowledge of green 's theorem to solve some actual line integrals . and actually , before i show an example , i want to make one clarification on green 's theorem . all of the examples that i did is i had a region like this , and the inside of the region was to the left of what we traversed... | and so using green 's theorem we were able to find the answer to this integral up here . it 's equal to 16/15 . hopefully you found that useful . | is the answer 16/15 representing the area of the region bounded by the closed curve or the volume bounded by the closed curve and the surface f ( x , y ) ? |
let 's see if we can use our knowledge of green 's theorem to solve some actual line integrals . and actually , before i show an example , i want to make one clarification on green 's theorem . all of the examples that i did is i had a region like this , and the inside of the region was to the left of what we traversed... | so minus 24/15 and we get it being equal to 16/15 . and so using green 's theorem we were able to find the answer to this integral up here . it 's equal to 16/15 . | so does that mean that f is not conservative since the answer for the close loop integral is non-zero ? |
let 's see if we can use our knowledge of green 's theorem to solve some actual line integrals . and actually , before i show an example , i want to make one clarification on green 's theorem . all of the examples that i did is i had a region like this , and the inside of the region was to the left of what we traversed... | so all my examples i went counterclockwise and so our region was to the left of -- if you imagined walking along the path in that direction , it was always to our left . and that 's the situation which green 's theorem would apply . so if you were to take a line integral along this path , a closed line integral , maybe... | should i assume that it wants me to go counter clockwise , since that makes green 's theorem positive ? |
let 's see if we can use our knowledge of green 's theorem to solve some actual line integrals . and actually , before i show an example , i want to make one clarification on green 's theorem . all of the examples that i did is i had a region like this , and the inside of the region was to the left of what we traversed... | when you put 1 in there you get -- i 'll do it in a different color . we get 8/5 times 1 to the third , which is 8/5 minus 8/5 minus 8/5 . and then we 're going to have minus -- when you put 0 in here you 're just going to get a bunch of 0 's . | what was the point in him specifying what the f vetor was ? |
let 's see if we can use our knowledge of green 's theorem to solve some actual line integrals . and actually , before i show an example , i want to make one clarification on green 's theorem . all of the examples that i did is i had a region like this , and the inside of the region was to the left of what we traversed... | my y-axis and then my x-axis right there . and let 's see . x goes from 0 to 1 , so if we make -- that 's obviously 0 . | is there any more obvious way to see if your vector field is conservative ? |
let 's see if we can use our knowledge of green 's theorem to solve some actual line integrals . and actually , before i show an example , i want to make one clarification on green 's theorem . all of the examples that i did is i had a region like this , and the inside of the region was to the left of what we traversed... | so minus 24/15 and we get it being equal to 16/15 . and so using green 's theorem we were able to find the answer to this integral up here . it 's equal to 16/15 . | so is green 's theorem just an alternative to parametrizing and then doing the single integral ? |
let 's see if we can use our knowledge of green 's theorem to solve some actual line integrals . and actually , before i show an example , i want to make one clarification on green 's theorem . all of the examples that i did is i had a region like this , and the inside of the region was to the left of what we traversed... | all right . now dx . now this is just a straightforward one-dimensional integral . | dq/dx-dp/dy ) essentially the curl of the vector function ? |
let 's see if we can use our knowledge of green 's theorem to solve some actual line integrals . and actually , before i show an example , i want to make one clarification on green 's theorem . all of the examples that i did is i had a region like this , and the inside of the region was to the left of what we traversed... | and so using green 's theorem we were able to find the answer to this integral up here . it 's equal to 16/15 . hopefully you found that useful . | is 16/15 flow or flux ? |
let 's see if we can use our knowledge of green 's theorem to solve some actual line integrals . and actually , before i show an example , i want to make one clarification on green 's theorem . all of the examples that i did is i had a region like this , and the inside of the region was to the left of what we traversed... | i have to specify that . so our curve , we could start at any point really , but we 're going to go like that . then get to that point and then come back down along that top curve just like that . and so this met the condition that the inside of the region is always going to be our left , so we can just do the straight... | why is the vector field not conservative even though they have the same starting point and ending point ? |
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