context
stringlengths
545
71.9k
questionsrc
stringlengths
16
10.2k
question
stringlengths
11
563
welcome to the presentation on averages . averages is probably a concept that you 've already used before , maybe not in a mathematical way . but people will talk in terms of , the average voter wants a politician to do this , or the average student in a class wants to get out early . so you 're probably already famili...
like the mode . you 'll also the mean , which we 'll talk about later , is actually the same thing as the average . but the average is just one number that you can use to represent a set of numbers .
how changing the value effects the mean and median ?
welcome to the presentation on averages . averages is probably a concept that you 've already used before , maybe not in a mathematical way . but people will talk in terms of , the average voter wants a politician to do this , or the average student in a class wants to get out early . so you 're probably already famili...
but 6 goes into 53 , 8 times . 48 . 56 .
32,44,45,49,56 , what will happen if 45 becomes 48 ?
welcome to the presentation on averages . averages is probably a concept that you 've already used before , maybe not in a mathematical way . but people will talk in terms of , the average voter wants a politician to do this , or the average student in a class wants to get out early . so you 're probably already famili...
so 4 goes into 29 . and it goes , 7 , 7 , 28 . and then we have 10 , i did n't have to do that decimal there , oh well .
if you have a average rating of 2.7 and you want to determine the total rating and there were 100 people who gave ratings that would just be a rate problem involving average so it would be 2.7 rating/ person *100 people= 270 total ratings then right ?
welcome to the presentation on averages . averages is probably a concept that you 've already used before , maybe not in a mathematical way . but people will talk in terms of , the average voter wants a politician to do this , or the average student in a class wants to get out early . so you 're probably already famili...
so that 's 200 . and what 's this average ? well , 4 times 84 , we already said , is 336 .
what is the difference between the average and the mean ?
welcome to the presentation on averages . averages is probably a concept that you 've already used before , maybe not in a mathematical way . but people will talk in terms of , the average voter wants a politician to do this , or the average student in a class wants to get out early . so you 're probably already famili...
and i said that i need to get in an 88 in the class . and now we solve for x . let me make some space here .
if you have two groups with respective averages x and y , and the average of the groups added together is something closer to x than to y , does that mean that the number of samples in the first group ( x ) is necessarily larger than the number of samples in the second group ( y ) ?
welcome to the presentation on averages . averages is probably a concept that you 've already used before , maybe not in a mathematical way . but people will talk in terms of , the average voter wants a politician to do this , or the average student in a class wants to get out early . so you 're probably already famili...
so 4 goes into 29 7.25 times . so the average of these four numbers is equal to 7.25 . and that might make sense to you because 7.25 is someplace in between these numbers .
if the average of 7 numbers is 12 , what is their sum ?
welcome to the presentation on averages . averages is probably a concept that you 've already used before , maybe not in a mathematical way . but people will talk in terms of , the average voter wants a politician to do this , or the average student in a class wants to get out early . so you 're probably already famili...
33 minus 32 is 1 , 16 . 4 . so the average is equal to 84 .
so you just add all the numbers together and then divide by how ever many numbers there are so like 2+4+6+8=20 then divide 20/4=5 so 5 would be the average of 2,4,6,8 right ?
welcome to the presentation on averages . averages is probably a concept that you 've already used before , maybe not in a mathematical way . but people will talk in terms of , the average voter wants a politician to do this , or the average student in a class wants to get out early . so you 're probably already famili...
we said , after 4 exams we had an 84 . what do i have to get on that next exam to average an 88 in the class after 5 exams ? and that 's what we solved for when we got x .
how did you get the 440 during the average exam score ?
welcome to the presentation on averages . averages is probably a concept that you 've already used before , maybe not in a mathematical way . but people will talk in terms of , the average voter wants a politician to do this , or the average student in a class wants to get out early . so you 're probably already famili...
so that 's 200 . and what 's this average ? well , 4 times 84 , we already said , is 336 .
what is the difference between mean and average ?
welcome to the presentation on averages . averages is probably a concept that you 've already used before , maybe not in a mathematical way . but people will talk in terms of , the average voter wants a politician to do this , or the average student in a class wants to get out early . so you 're probably already famili...
let me make some space here . so , 5 times 88 is , let 's see . 5 times 80 is 400 , so it 's 440 .
why sal multiples 5.88 ( min ) ?
welcome to the presentation on averages . averages is probably a concept that you 've already used before , maybe not in a mathematical way . but people will talk in terms of , the average voter wants a politician to do this , or the average student in a class wants to get out early . so you 're probably already famili...
because there 's 6 exams in the class . and i 'm going to get 100 in each . so that 's 200 .
how did you get to be so good at math ?
welcome to the presentation on averages . averages is probably a concept that you 've already used before , maybe not in a mathematical way . but people will talk in terms of , the average voter wants a politician to do this , or the average student in a class wants to get out early . so you 're probably already famili...
welcome to the presentation on averages . averages is probably a concept that you 've already used before , maybe not in a mathematical way .
is averages how they grade your tests and sports skills ?
welcome to the presentation on averages . averages is probably a concept that you 've already used before , maybe not in a mathematical way . but people will talk in terms of , the average voter wants a politician to do this , or the average student in a class wants to get out early . so you 're probably already famili...
33 minus 32 is 1 , 16 . 4 . so the average is equal to 84 .
why sal does n't make a shortcut , and use the average of the past 4 exams as is ?
welcome to the presentation on averages . averages is probably a concept that you 've already used before , maybe not in a mathematical way . but people will talk in terms of , the average voter wants a politician to do this , or the average student in a class wants to get out early . so you 're probably already famili...
so that 's 200 . and what 's this average ? well , 4 times 84 , we already said , is 336 .
how do you do average of averages ?
welcome to the presentation on averages . averages is probably a concept that you 've already used before , maybe not in a mathematical way . but people will talk in terms of , the average voter wants a politician to do this , or the average student in a class wants to get out early . so you 're probably already famili...
i said after four exams , after four exams , i had an 84 average . if i said that there are 6 exams in the class , and the highest score i could get on an exam is 100 , what is the highest average i can finish in the class if i were to really study hard and get 100 on the next 2 exams ? well , once again , what we 'll ...
what is the minimum number of tests that zack has to score a 100 on to get the average score to at least 93 ?
welcome to the presentation on averages . averages is probably a concept that you 've already used before , maybe not in a mathematical way . but people will talk in terms of , the average voter wants a politician to do this , or the average student in a class wants to get out early . so you 're probably already famili...
440 equals 4 times 84 , we just saw that , is 320 plus 16 is 336 . 336 plus x is equal to 440 . well , it turns out if you subtract 336 from both sides , you get x is equal to 104 .
how did you get the 440 in the 3rd equation ?
welcome to the presentation on averages . averages is probably a concept that you 've already used before , maybe not in a mathematical way . but people will talk in terms of , the average voter wants a politician to do this , or the average student in a class wants to get out early . so you 're probably already famili...
so the average is equal to 84 . so depending on what school you go to that 's either a b or a c. so , so far my average after the first four exams is an 84 . now let 's make this a little bit more difficult .
is math mr. khan 's favorite subject is school ?
welcome to the presentation on averages . averages is probably a concept that you 've already used before , maybe not in a mathematical way . but people will talk in terms of , the average voter wants a politician to do this , or the average student in a class wants to get out early . so you 're probably already famili...
so now what we can say is , is that the first four exams , i could either list out the first four exams that i took . or i already know what the average is . so i know the sum of the first four exams is going to 4 times 84 .
why would you need to know percentages ?
welcome to the presentation on averages . averages is probably a concept that you 've already used before , maybe not in a mathematical way . but people will talk in terms of , the average voter wants a politician to do this , or the average student in a class wants to get out early . so you 're probably already famili...
so that 's 200 . and what 's this average ? well , 4 times 84 , we already said , is 336 .
can an average be negative ?
welcome to the presentation on averages . averages is probably a concept that you 've already used before , maybe not in a mathematical way . but people will talk in terms of , the average voter wants a politician to do this , or the average student in a class wants to get out early . so you 're probably already famili...
so that 's 200 . and what 's this average ? well , 4 times 84 , we already said , is 336 .
if the average weight of the cartons is 10 , the heavier carton weighs how much more than the lighter carton ?
welcome to the presentation on averages . averages is probably a concept that you 've already used before , maybe not in a mathematical way . but people will talk in terms of , the average voter wants a politician to do this , or the average student in a class wants to get out early . so you 're probably already famili...
so that 's 200 . and what 's this average ? well , 4 times 84 , we already said , is 336 .
is an average the same as the arithmatic mean ?
welcome to the presentation on averages . averages is probably a concept that you 've already used before , maybe not in a mathematical way . but people will talk in terms of , the average voter wants a politician to do this , or the average student in a class wants to get out early . so you 're probably already famili...
33 minus 32 is 1 , 16 . 4 . so the average is equal to 84 .
why does sal use `` 4 x 84 '' ?
welcome to the presentation on averages . averages is probably a concept that you 've already used before , maybe not in a mathematical way . but people will talk in terms of , the average voter wants a politician to do this , or the average student in a class wants to get out early . so you 're probably already famili...
1 plus 3 plus 5 plus 20 equals , let 's see , 1 plus 3 is 4 . 4 plus 5 is 9 . 9 plus 20 is 29 .
ex : 5 consecutive integers equals 523 , what is the smallest of these integers ?
welcome to the presentation on averages . averages is probably a concept that you 've already used before , maybe not in a mathematical way . but people will talk in terms of , the average voter wants a politician to do this , or the average student in a class wants to get out early . so you 're probably already famili...
1 plus 3 plus 5 plus 20 equals , let 's see , 1 plus 3 is 4 . 4 plus 5 is 9 . 9 plus 20 is 29 .
what does x stand for 3 ?
welcome to the presentation on averages . averages is probably a concept that you 've already used before , maybe not in a mathematical way . but people will talk in terms of , the average voter wants a politician to do this , or the average student in a class wants to get out early . so you 're probably already famili...
33 minus 32 is 1 , 16 . 4 . so the average is equal to 84 .
why is 4 ( 84 ) +x to get the average ?
welcome to the presentation on averages . averages is probably a concept that you 've already used before , maybe not in a mathematical way . but people will talk in terms of , the average voter wants a politician to do this , or the average student in a class wants to get out early . so you 're probably already famili...
so that 's 200 . and what 's this average ? well , 4 times 84 , we already said , is 336 .
what is the astigmatism of 5x -y of the average when the hypotenuse is less than the decimal of the denominator ?
welcome to the presentation on averages . averages is probably a concept that you 've already used before , maybe not in a mathematical way . but people will talk in terms of , the average voter wants a politician to do this , or the average student in a class wants to get out early . so you 're probably already famili...
and then we have 10 , i did n't have to do that decimal there , oh well . 2 , 8 , 25 . so 4 goes into 29 7.25 times .
a car travelled 25 km at an average speed of xkm/h.if ti speed was increased by 5 km/h , it would complete same journey 15 minutes earlier.what is the original speed of car ?
welcome to the presentation on averages . averages is probably a concept that you 've already used before , maybe not in a mathematical way . but people will talk in terms of , the average voter wants a politician to do this , or the average student in a class wants to get out early . so you 're probably already famili...
1 plus 3 plus 5 plus 20 equals , let 's see , 1 plus 3 is 4 . 4 plus 5 is 9 . 9 plus 20 is 29 .
: the sum of 5 consecutive odd integers is 345.what is the smallest of 5 integers ?
: i want to make it super clear , what the difference is between a lot of these words that sound really similar , but their subtly different from each other . so , the first one is molarity , and we know that means moles in one liter of solution . keeping the numerator the same , but tweaking the denominator you get m...
actually , let me make it a little permeable membrane . this cell is usually going to be setting in some solution , and that solution could be the blood , or it could be the interstitial fluid , or some solution . when we talk about these four terms , and especially , tinicity , we 're talking about the relationship be...
how to calculate a 1 molar solution ?
: i want to make it super clear , what the difference is between a lot of these words that sound really similar , but their subtly different from each other . so , the first one is molarity , and we know that means moles in one liter of solution . keeping the numerator the same , but tweaking the denominator you get m...
actually , let me make it a little permeable membrane . this cell is usually going to be setting in some solution , and that solution could be the blood , or it could be the interstitial fluid , or some solution . when we talk about these four terms , and especially , tinicity , we 're talking about the relationship be...
how do you find molality of solution `` x '' when the new solute is mixed in with a solution that has 2 different substances such as water and something else ?
: let 's see how to form imines and enamines and start with the formation of an imine we start with an aldehyde or a ketone . and you add an amine to it and you need an acid catalyst and over here on the right if your y is equal to hydrogen or an alkyl group which is a r double prime you will form an imine . so let 's...
and i 've seen two different ways to start off , the mechanism and so i 'll present both ways and you can choose which one you want to use . and so one way would be to think about an acid being present right , so we 'll say it 's h-a plus the generic acid and you think about this as protonating your imine . so you have...
the amine is basic , wo n't it take a h+ from the acid and thereby become unreactive ?
: let 's see how to form imines and enamines and start with the formation of an imine we start with an aldehyde or a ketone . and you add an amine to it and you need an acid catalyst and over here on the right if your y is equal to hydrogen or an alkyl group which is a r double prime you will form an imine . so let 's...
so you take that proton and leave those electrons in magenta behind on your nitrogen . so we also have an o-h group bonded to our carbon here , and then we also have our alkyl group , so r and r prime . so this intermediate is called a carbinolamine .
in general , what is the difference between the `` y '' group of the imine and the `` r '' groups ?
: let 's see how to form imines and enamines and start with the formation of an imine we start with an aldehyde or a ketone . and you add an amine to it and you need an acid catalyst and over here on the right if your y is equal to hydrogen or an alkyl group which is a r double prime you will form an imine . so let 's...
so deprotonation for our last step will form an imine . and this is once again done with a primary amine right here . and so that 's a little bit different from what we 're going to talk about next , we 're going to talk about formation of an enamine , and formation of an enamine is , it starts off the same way in term...
is it possible to deprotonate cyclic ring in primary amine ?
: let 's see how to form imines and enamines and start with the formation of an imine we start with an aldehyde or a ketone . and you add an amine to it and you need an acid catalyst and over here on the right if your y is equal to hydrogen or an alkyl group which is a r double prime you will form an imine . so let 's...
so this lone pair of electrons here on the oxygen picks up this proton and that forms this bond right here . we 've talked about in previous videos how protonation of the carbonyl oxygen makes the carbonyl carbon more electrophilic . and so we have a good electrophile , this carbon here is a good electrophile and the i...
does it matter if the acid catalyst was added before or after the amine attacks the carbonyl carbon ?
: let 's see how to form imines and enamines and start with the formation of an imine we start with an aldehyde or a ketone . and you add an amine to it and you need an acid catalyst and over here on the right if your y is equal to hydrogen or an alkyl group which is a r double prime you will form an imine . so let 's...
so partial negative oxygen , partial positive carbon this is our electrophile and then a lone pair of electrons on our nitrogen right makes our imine a good nucleophile so they can just attack directly . right , attack this carbon push these electrons off onto your oxygen . so let 's go ahead and draw the result of tha...
and anyway , should n't the ammine attack the c from both sides ( from the top and from the bottom ) forming a racemic mixture ?
: let 's see how to form imines and enamines and start with the formation of an imine we start with an aldehyde or a ketone . and you add an amine to it and you need an acid catalyst and over here on the right if your y is equal to hydrogen or an alkyl group which is a r double prime you will form an imine . so let 's...
and so one way would be to think about an acid being present right , so we 'll say it 's h-a plus the generic acid and you think about this as protonating your imine . so you have an imine and protons , you 're protonating your imine to form this generic acid here . and then your carbonyl oxygen is going to be protonat...
if i wanted to use an imine and form an aldehyde with an animo acid , i would simply follow these steps backwards ?
: let 's see how to form imines and enamines and start with the formation of an imine we start with an aldehyde or a ketone . and you add an amine to it and you need an acid catalyst and over here on the right if your y is equal to hydrogen or an alkyl group which is a r double prime you will form an imine . so let 's...
and i 've seen two different ways to start off , the mechanism and so i 'll present both ways and you can choose which one you want to use . and so one way would be to think about an acid being present right , so we 'll say it 's h-a plus the generic acid and you think about this as protonating your imine . so you have...
why is the acid written as h-a+ ?
: let 's see how to form imines and enamines and start with the formation of an imine we start with an aldehyde or a ketone . and you add an amine to it and you need an acid catalyst and over here on the right if your y is equal to hydrogen or an alkyl group which is a r double prime you will form an imine . so let 's...
and so that 's one way to start off your mechanism and of course there is another way to do it . so let 's talk about just using our nitrogen as a nucleophile straightaway so the imine is a pretty good nucleophile and so we can just show our nucleophile attacking our electrophile directly . so partial negative oxygen ,...
can an ammonium salt e.g nh4cl , ammonium succinate , ammonium oxalate etc act as a nucleophile ( in place of ammonia , amines ) & kick-on this reaction ?
: let 's see how to form imines and enamines and start with the formation of an imine we start with an aldehyde or a ketone . and you add an amine to it and you need an acid catalyst and over here on the right if your y is equal to hydrogen or an alkyl group which is a r double prime you will form an imine . so let 's...
and so that 's a little bit different from what we 're going to talk about next , we 're going to talk about formation of an enamine , and formation of an enamine is , it starts off the same way in terms of the mechanism but it 's this iminium ion step that changes a little bit . so let 's look at reacting a ketone wit...
do enamines only form from ketone + 2o amine ?
: let 's see how to form imines and enamines and start with the formation of an imine we start with an aldehyde or a ketone . and you add an amine to it and you need an acid catalyst and over here on the right if your y is equal to hydrogen or an alkyl group which is a r double prime you will form an imine . so let 's...
: let 's see how to form imines and enamines and start with the formation of an imine we start with an aldehyde or a ketone . and you add an amine to it and you need an acid catalyst and over here on the right if your y is equal to hydrogen or an alkyl group which is a r double prime you will form an imine .
why is the carbinoleamine not stable ?
: let 's see how to form imines and enamines and start with the formation of an imine we start with an aldehyde or a ketone . and you add an amine to it and you need an acid catalyst and over here on the right if your y is equal to hydrogen or an alkyl group which is a r double prime you will form an imine . so let 's...
and so formation of an enamine happens because once again we do n't have the same iminium ion that we had before because of the fact that we started with a secondary amine . so that 's why it 's important to recognize the kind of amine that you were reacting with your aldehyde or a ketone . and if it 's secondary , you...
what would be the product of ammonia reacting with aldehyde or ketone ( basic conditions ) ?
: let 's see how to form imines and enamines and start with the formation of an imine we start with an aldehyde or a ketone . and you add an amine to it and you need an acid catalyst and over here on the right if your y is equal to hydrogen or an alkyl group which is a r double prime you will form an imine . so let 's...
and so we ca n't deprotonate in the same place , we have to pick a carbon adjacent over here . so here 's a proton over here on this carbon and our base could come along . so let 's go ahead and draw out our amine base with a lone pair of electrons right here .
when the base picks up that specific proton , could have taken even the other one ?
: let 's see how to form imines and enamines and start with the formation of an imine we start with an aldehyde or a ketone . and you add an amine to it and you need an acid catalyst and over here on the right if your y is equal to hydrogen or an alkyl group which is a r double prime you will form an imine . so let 's...
so the nitrogen is bonded to one carbon . so this is a reaction with a primary amine and then we 're going to use sulphuric acid as our catalyst here . so to figure out the product of this reaction since it 's kind of a long mechanism so it does n't really makes sense to run through the entire mechanism but we could th...
can you use the protonated acid or the amine as a source of h ?
: let 's see how to form imines and enamines and start with the formation of an imine we start with an aldehyde or a ketone . and you add an amine to it and you need an acid catalyst and over here on the right if your y is equal to hydrogen or an alkyl group which is a r double prime you will form an imine . so let 's...
our nitrogen is bonded to two hydrogens and our y group and that would make our nitrogen a plus one formal charge and then our oxygen this time would be a negative one formal charge . so negative one formal charge here . we have our alkyl groups down here , so let 's once again show our electrons .
does a formal charge of -1 mean an actual charge of -2 ?
: let 's see how to form imines and enamines and start with the formation of an imine we start with an aldehyde or a ketone . and you add an amine to it and you need an acid catalyst and over here on the right if your y is equal to hydrogen or an alkyl group which is a r double prime you will form an imine . so let 's...
and i 've seen two different ways to start off , the mechanism and so i 'll present both ways and you can choose which one you want to use . and so one way would be to think about an acid being present right , so we 'll say it 's h-a plus the generic acid and you think about this as protonating your imine . so you have...
why is the acid written as h-a+ ?
in this video we 're going to introduce ourselves to the idea of adding decimals . and i encourage you as we work through these problems to keep pausing the video and seeing if you can think about it on your own before we work through it together . now we 're going to build up slowly , and in future videos we 're gon ...
but the way we 're learning it in this video in the next view is to really make sure we understand what is happening . so let 's say we wanted to add 0.1 to 0.8 . or you could say we 're adding 1/10 to 8/10 .
do we say like 0 point 1 or 0 and 1 because my teacher would say and ?
in this video we 're going to introduce ourselves to the idea of adding decimals . and i encourage you as we work through these problems to keep pausing the video and seeing if you can think about it on your own before we work through it together . now we 're going to build up slowly , and in future videos we 're gon ...
so let me color these in really fast . use that light blue color . that is 1/10 .
why did sal use his pen to color the parts instead of the color tool he used last time ?
imagine if it was pitch black in your room . would you be able to walk ? as long as nothing got in your way , you 'd probably be able to walk perfectly fine . but why is this ? when walking in a pitch black room , you rely on your sense of balance . you know exactly where you are in space . you know whether or not you ...
and this is known as kinesthesia . so let me write that down -- kinesthesia . and so if we talk about proprioception to include your body 's position in space as well as your ability to balance , so your sense of balance would be included under proprioception , kinesthesia is talking more about the movement of your bod...
so , both proprioception and kinesthesia rely on spindles in the muscles to determine where the body is in space , balance , and movement ?
imagine if it was pitch black in your room . would you be able to walk ? as long as nothing got in your way , you 'd probably be able to walk perfectly fine . but why is this ? when walking in a pitch black room , you rely on your sense of balance . you know exactly where you are in space . you know whether or not you ...
there 's another word that 's commonly used to talk about your body 's movements . and this is known as kinesthesia . so let me write that down -- kinesthesia .
can kinesthesia be thought of muscle memory ?
imagine if it was pitch black in your room . would you be able to walk ? as long as nothing got in your way , you 'd probably be able to walk perfectly fine . but why is this ? when walking in a pitch black room , you rely on your sense of balance . you know exactly where you are in space . you know whether or not you ...
and the big difference is , just to kind of summarize , is that proprioception is concerned with position while kinesthesia is concerned with movement . and proprioception includes your sense of balance , while kinesthesia does not .
is it possible for proprioception sense to adapt to kinesthesia sense ?
imagine if it was pitch black in your room . would you be able to walk ? as long as nothing got in your way , you 'd probably be able to walk perfectly fine . but why is this ? when walking in a pitch black room , you rely on your sense of balance . you know exactly where you are in space . you know whether or not you ...
and the big difference is , just to kind of summarize , is that proprioception is concerned with position while kinesthesia is concerned with movement . and proprioception includes your sense of balance , while kinesthesia does not .
are the receptors for proprioception and kinesthesia the same ?
let 's see if we might be able to make some use of the divergence theorem . so i have this region , this simple solid right over here . x can go between negative 1 and 1. z , this kind of arch part right over here , is going to be a function of x . that 's the upper bound on z . the lower bound on z is just 0 . and the...
so let 's see , can i simplify a little bit ? i have 2 minus 1/2 , which is 3/2 . so i have 3/2 .
is n't the height ( z ) of the region not always z=1-x^2 ?
let 's see if we might be able to make some use of the divergence theorem . so i have this region , this simple solid right over here . x can go between negative 1 and 1. z , this kind of arch part right over here , is going to be a function of x . that 's the upper bound on z . the lower bound on z is just 0 . and the...
so let 's see , can i simplify a little bit ? i have 2 minus 1/2 , which is 3/2 . so i have 3/2 .
sometimes it is z=1-x^2 and sometimes it is the plane y=2-z ?
let 's see if we might be able to make some use of the divergence theorem . so i have this region , this simple solid right over here . x can go between negative 1 and 1. z , this kind of arch part right over here , is going to be a function of x . that 's the upper bound on z . the lower bound on z is just 0 . and the...
and we are going to get , if we simplify this , we get 2 minus 2x squared minus 1/2 , and then plus -- so this is negative 1/2 times negative 2x squared . so it 's going to be positive x squared minus 1/2 x to the fourth . now , let 's see , can we simplify this part ?
because the function ( a*x^2 + b*x^4 + c*x^6 ) is even , should n't we multiply it by 2 and change the limit of integration of x to be from 0 to 1 ?
let 's see if we might be able to make some use of the divergence theorem . so i have this region , this simple solid right over here . x can go between negative 1 and 1. z , this kind of arch part right over here , is going to be a function of x . that 's the upper bound on z . the lower bound on z is just 0 . and the...
the divergence of f simplified down to 2x . and so now we can restate the flux across the surface as a triple integral of 2x . so let me just write 2x here .
at the beginning of the video , should n't the surface integral also be dotted with the normal vector of the surface in order to get the flux ?
let 's see if we might be able to make some use of the divergence theorem . so i have this region , this simple solid right over here . x can go between negative 1 and 1. z , this kind of arch part right over here , is going to be a function of x . that 's the upper bound on z . the lower bound on z is just 0 . and the...
so the divergence of f is going to be the partial of the x component , or the partial of the -- you could say the i component or the x component with respect to x . well , the derivative of this with respect to x is just x . the derivative of this with respect to x , luckily , is just 0 .
so should n't div f be x+y ?
let 's see if we might be able to make some use of the divergence theorem . so i have this region , this simple solid right over here . x can go between negative 1 and 1. z , this kind of arch part right over here , is going to be a function of x . that 's the upper bound on z . the lower bound on z is just 0 . and the...
and surface integrals are messy as is , especially when you have a crazy vector field like this . but you could imagine that there might be a way to simplify this , perhaps using the divergence theorem . the divergence theorem tells us that the flux across the boundary of this simple solid region is going to be the sam...
does that triple integral in the divergence theorem count as a volume integral ?
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
so , what will the formula be if the observer is in an angle from the source 's direction of motion ( not exactly in front of or behind the source ) ?
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
can the observer sitting in the source emitting sound , if traveling faster than the speed of sound , hear the source sound normally ?
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
what happens if the observer is traveling at the exact same speed as the wave from the source or the source itself ?
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
he 'll be blue . so this is the observer . so when we started off , our source was right here .
what does the observer experience ?
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
this guy is going to see the wave crest more frequently . he 's going to observe a higher frequency . if this is a sound , a higher pitch .
how can we observe the doppler effect in objects moving faster than the speed of sound ?
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
the velocity of the wave times the period from the perspective of the source plus the velocity of the source , because the source has gotten that much further away from him , velocity of the source times the period of the source , so that 's how far the next crest is . and then you divide it by the speed of the wave , ...
why speed of the source does n't affect speed of the wave ?
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
and we were able to do that by doing a thought experiment . saying , ok , my object starts here . after one period -- a period is just a measure of time , but it 's the measure of time over which the source emits a cycle , so it emits a cycle every period .
why does the frequency of an approaching object seem to be increasing gradually , and then decrease gradually ?
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
why is the doppler effect of sound different in cases in which observer is moving and in which source is moving ?
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
that 's going to be equal to this distance . the velocity of the wave times the period from the perspective of the source plus the velocity of the source , because the source has gotten that much further away from him , velocity of the source times the period of the source , so that 's how far the next crest is . and t...
we can predict the doppler effect if we are straight in the path of the wave source , but what about when we are at an angle to the direction of the velocity of the wave source ?
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
so the frequency of the source is going to be 1 cycle per second , 1 hertz . the velocity of the wave is 10 meters per second . let me write this .
is velocity of the wave the same thing as velocity of the obsever ?
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
is n't the source constantly moving ?
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
why is the apparent frequency greater than the actual frequency in case the source is moving towards the stationary object ?
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
will the same formula hold true if the observer is not exactly in the path of source but sideways ?
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
1 cycle per second . the velocity of the wave is 10 meters per second . the velocity of the wave is 10 meters per second minus the velocity of the source is 5 meters per second . so what 's this going to be equal to ?
but why are n't the velocities added to get a net velocity ?
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
he 's going to observe a higher frequency . if this is a sound , a higher pitch . this guy , since each crest or the cycles are getting spread out , he 's going to see them less frequently , and if this is sound , he 's going to observe a lower pitch .
do sound waves not act like physical objects where velocities can be added ?
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
here in case of source moving , we are considering the movement of source first wave next ... but they take place at-a-time ... so wave must be in an elliptical path ... is n't it ?
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
so the amount of time it takes for him to see the next crest or the same point in the next cycle , that 's the period . that 's the observed period . that 's going to be equal to this distance .
would every observed period be shorter if the frequency be different ?
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
1 cycle per second . the velocity of the wave is 10 meters per second . the velocity of the wave is 10 meters per second minus the velocity of the source is 5 meters per second . so what 's this going to be equal to ?
when the source emits a wave , wo n't the velocity of the source be added to the velocity of the wave ?
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
but after one period , we said , ok , where is that first wave front , or that first pulse , or that first crest ? and where is the source ? because exactly one period has passed by , and the source will be ready to emit another crest or another cycle .
how would you rearrange the doppler equation to find the speed of the source ?
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
so 1 cycle per second , or 1 hertz , which is a cycle per second . so using those numbers , let 's see if we get to the exact same answer we got in that first video where we first learned about the doppler effect . so let 's look at the frequency from the point of view of this gentleman right here .
how does doppler effects related to temperature ?
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
what happens when both the source and observer are moving ?
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
and if you want the observed frequency for that guy over there -- i 'll do it in the same color . the observed frequency for a guy where the source is traveling away from him is just the inverse of that . so one over the period , one over the period , same argument we did there , one over the period from the point of v...
if the frequency observed by someone who is getting further and further away from the source of the wave is always the same , why do people hear lower and lower frequency ( volume ) when an ambulance is getting away from them ?
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
that 's going to be equal to this distance . the velocity of the wave times the period from the perspective of the source plus the velocity of the source , because the source has gotten that much further away from him , velocity of the source times the period of the source , so that 's how far the next crest is . and t...
what will be when source is faster 5 times of sound ?
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
how long will it take for that pulse that 's being emitted right then to also reach him ? and then that tells us the period between two pulses or between two crests . now let 's think about that exact same situation here .
what happens when train is out of circumference and two guys are in motion ?
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
what happens to the observer when the source is moving away ?
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
let me write this . 1 cycle per second . the velocity of the wave is 10 meters per second . the velocity of the wave is 10 meters per second minus the velocity of the source is 5 meters per second .
a listener moves froma to b with a constant velocity u. if the speed of sound is 330m/s , what must be the value of u so that he hears 8 beats per second ?
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
so the amount of time it takes for him to see the next crest or the same point in the next cycle , that 's the period . that 's the observed period . that 's going to be equal to this distance .
what if we wanted the period/frequency if the source had traveled for another period after travelling a period ?
in the last video , we figured out the formulas for the observed period and frequency for an observer sitting in the path of the source . so the source is moving towards the observer . so this is the example where the train is moving towards you , and you perceive the train 's horn as having a higher pitch or a higher ...
and we can just factor out the t sub s 's here and say this is t sub s times v sub w , the velocity of the wave plus the velocity of the source divided by the velocity the wave . so this will be a larger observed period than if this guy was stationary and especially if the observer was in the path of the guy . that mak...
what are stationary or standing waves ?
you know , it 's not unheard of for a guy to have a uti or urinary tract infection , but still , it 's pretty reasonable to say that utis are way more common in women . and in fact , there 's a statistic that i once read that said that one in five women will have a uti at some point in their life . so , yeah , i guess...
but one of the important exceptions to that rule is pregnancy . so a pregnant woman who has bacteria in her urine without any symptoms of uti , which is called asymptomatic , it 's called asymptomatic , so without symptoms , bacteriuria , so when you have bacteria in the urine but do n't have any symptoms , right ? in ...
if a pregnant woman is diagnosed with a uti caused by bacteria ( and not a fungus or a virus ) then since cranberry juice not only prevents more bacteria from getting in like blueberry juice does but also acts as a natural antibiotic could n't the pregnant woman drink cranberry juice for about a week or 2 to naturally ...
you know , it 's not unheard of for a guy to have a uti or urinary tract infection , but still , it 's pretty reasonable to say that utis are way more common in women . and in fact , there 's a statistic that i once read that said that one in five women will have a uti at some point in their life . so , yeah , i guess...
so a pregnant woman who has bacteria in her urine without any symptoms of uti , which is called asymptomatic , it 's called asymptomatic , so without symptoms , bacteriuria , so when you have bacteria in the urine but do n't have any symptoms , right ? in a pregnant woman , that needs to be treated . and the reason for...
how would you treat a pregnant woman who has a uti because of a fungus or a virus ( which is less common but could potentially be more serious than a bacterial uti ) ?
you know , it 's not unheard of for a guy to have a uti or urinary tract infection , but still , it 's pretty reasonable to say that utis are way more common in women . and in fact , there 's a statistic that i once read that said that one in five women will have a uti at some point in their life . so , yeah , i guess...
and we know that folate is really important for neural tube development . so for that reason , it 's usually avoided in the first trimester . and sulfamethoxazole can increase bilirubin levels in the baby , which can be pretty dangerous .
is recommended screening for asymptomatic bacteriuria limited to just once during the first trimester as mentioned ?
you know , it 's not unheard of for a guy to have a uti or urinary tract infection , but still , it 's pretty reasonable to say that utis are way more common in women . and in fact , there 's a statistic that i once read that said that one in five women will have a uti at some point in their life . so , yeah , i guess...
it can lead to kidney dysfunction , premature labor , and even death of the fetus . so that 's why we always , always collect the sample of urine in the very first trimester , even if a woman has absolutely no symptoms of uti , to look for bacteria in the urine . and if there 's evidence of bacteria in the urine , agai...
is there any strip available for uti detection which can detect the whole bacteria cell in urine sample ?
you know , it 's not unheard of for a guy to have a uti or urinary tract infection , but still , it 's pretty reasonable to say that utis are way more common in women . and in fact , there 's a statistic that i once read that said that one in five women will have a uti at some point in their life . so , yeah , i guess...
i know it 's a mouthful . and that 's a very popular treatment . another popular treatment is nitrofurantoin , right ? and a third popular choice is ciprofloxacin .
what are the differences in treatment of urethritis and cystitis ?
you know , it 's not unheard of for a guy to have a uti or urinary tract infection , but still , it 's pretty reasonable to say that utis are way more common in women . and in fact , there 's a statistic that i once read that said that one in five women will have a uti at some point in their life . so , yeah , i guess...
it can lead to kidney dysfunction , premature labor , and even death of the fetus . so that 's why we always , always collect the sample of urine in the very first trimester , even if a woman has absolutely no symptoms of uti , to look for bacteria in the urine . and if there 's evidence of bacteria in the urine , agai...
is there any colorimetric strip which can detect whole bacterial cell in urine sample in case of uti ?
two videos ago we learned about half-lives and we saw that they 're good if we are trying to figure out how much of a compound we have left after one half-life or two half-life or three half-lives . we can just take half of the compound at every period . but it 's not as useful if we 're trying to figure out how much ...
the amount of carbon-14 we 're going to have left is going to be the amount that we started with times `` e '' to the minus `` k '' , `` k '' we just solved for-1.2 times 10 to the minus four , times the amount of time that has passed by . this is our formula for carbon , if we were doing it for carbon-14 . if we were ...
what is the mathematical process of using carbon-14 to calculate the age of very old objects ?
steven zucker : as with many triptychs , viewers could see the exterior of the closed triptych during the weekdays . and on feast days or on the weekends , the painting would be opened up . you would move from the rather prosaic expressions of our world to a brilliantly colored scene of the horrors of limbo and the hor...
the image , in a sense , unfolds as a kind of story , beginning in the left wing . we see god in heaven . he is in majesty , in a kind of brilliant mandorla surrounded by clouds .
what word is used to describe god 's setting ?
steven zucker : as with many triptychs , viewers could see the exterior of the closed triptych during the weekdays . and on feast days or on the weekends , the painting would be opened up . you would move from the rather prosaic expressions of our world to a brilliantly colored scene of the horrors of limbo and the hor...
steven zucker : as well as a horn played by a demon in the back , where the horn actually looks as if it 's an extension of this nose . bosch uses music as one vehicle for sinfulness . beth harris : a kind of sign of indulgence in pleasure .
is there any known history regarding the life of the artist , bosch ?
steven zucker : as with many triptychs , viewers could see the exterior of the closed triptych during the weekdays . and on feast days or on the weekends , the painting would be opened up . you would move from the rather prosaic expressions of our world to a brilliantly colored scene of the horrors of limbo and the hor...
and he 's very much associated with pilgrimage . it is his pilgrimage that so many medieval faithful would follow . beth harris : these wings could have given us clues to the patron of this very large triptych , but unfortunately , the coat of arms is blank .
would a christian of this era not have viewed nature as just a collection of gods creations ?
steven zucker : as with many triptychs , viewers could see the exterior of the closed triptych during the weekdays . and on feast days or on the weekends , the painting would be opened up . you would move from the rather prosaic expressions of our world to a brilliantly colored scene of the horrors of limbo and the hor...
and he 's very much associated with pilgrimage . it is his pilgrimage that so many medieval faithful would follow . beth harris : these wings could have given us clues to the patron of this very large triptych , but unfortunately , the coat of arms is blank .
why are so many art pieces fold-able panels ?
steven zucker : as with many triptychs , viewers could see the exterior of the closed triptych during the weekdays . and on feast days or on the weekends , the painting would be opened up . you would move from the rather prosaic expressions of our world to a brilliantly colored scene of the horrors of limbo and the hor...
then we jump down to the bottom and the creation of eve , then just above that the temptation , and above that the expulsion of adam and even from the garden of eden . and of course , this is the origin of original sin . and after the expulsion of adam and eve from the garden of eden , mankind knows sin and temptation ...
how original is this painting ?
steven zucker : as with many triptychs , viewers could see the exterior of the closed triptych during the weekdays . and on feast days or on the weekends , the painting would be opened up . you would move from the rather prosaic expressions of our world to a brilliantly colored scene of the horrors of limbo and the hor...
steven zucker : as with many triptychs , viewers could see the exterior of the closed triptych during the weekdays . and on feast days or on the weekends , the painting would be opened up . you would move from the rather prosaic expressions of our world to a brilliantly colored scene of the horrors of limbo and the hor...
i can vaguely recall maybe some cruel egyptian hieroglyphs , and some minotaurs , but these torturing figures and excrement seem like a big leap forward to me in terms of painting from the imagination ... who or what influenced bosch to paint this painting full of torture and gross things ?
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a stand...
but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ?
what is the difference between z score and standard deviation ?
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a stand...
well , it 's 83 minus 81 . it 's two grades above the mean . but we want it in terms of standard deviations .
how do i find an area under a normal curve if only two plots are given ?