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 ? |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.