context
stringlengths
545
71.9k
questionsrc
stringlengths
16
10.2k
question
stringlengths
11
563
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 ?