context stringlengths 545 71.9k | questionsrc stringlengths 16 10.2k | question stringlengths 11 563 |
|---|---|---|
sal : let 's see if we can calculate the definite integral from zero to one of x squared times two to the x to the third power d x . like always i encourage you to pause this video and see if you can figure this out on your own . i 'm assuming you 've had a go at it . there 's a couple of interesting things here . the ... | you might be saying , `` okay , look . `` maybe u substitution could be at play here . '' because i have this crazy expression , x to the third times the natural log of two , but what 's the derivative of that ? | is there no simpler substitution that could be made ? |
sal : let 's see if we can calculate the definite integral from zero to one of x squared times two to the x to the third power d x . like always i encourage you to pause this video and see if you can figure this out on your own . i 'm assuming you 've had a go at it . there 's a couple of interesting things here . the ... | you might be saying , `` okay , look . `` maybe u substitution could be at play here . '' because i have this crazy expression , x to the third times the natural log of two , but what 's the derivative of that ? | is there no simpler substitution that could be made ? |
sal : let 's see if we can calculate the definite integral from zero to one of x squared times two to the x to the third power d x . like always i encourage you to pause this video and see if you can figure this out on your own . i 'm assuming you 've had a go at it . there 's a couple of interesting things here . the ... | you might be saying , `` okay , look . `` maybe u substitution could be at play here . '' because i have this crazy expression , x to the third times the natural log of two , but what 's the derivative of that ? | could sal also have made u=x^3 and then do 2^u du ? |
sal : let 's see if we can calculate the definite integral from zero to one of x squared times two to the x to the third power d x . like always i encourage you to pause this video and see if you can figure this out on your own . i 'm assuming you 've had a go at it . there 's a couple of interesting things here . the ... | well that 's going to be three x squared times the natural log of two , or three times the natural log of two times x squared . that 's just a constant times x squared . we already have a x squared here so maybe we can engineer this a little bit to have the constant there as well . | at the very very end why do n't we have to add a possible constant ( + c ) ? |
let 's now tackle a classic thought experiment in probability , called the monte hall problem . and it 's called the monty hall problem because monty hall was the game show host in let 's make a deal , where they would set up a situation very similar to the monte hall problem that we 're about to say . so let 's say th... | and no matter which one you pick , there 'll always be at least one other curtain that does not have the prize . there might be two , if you picked right . but there will always be at least one other curtain that does not have the prize . | what is the probability that you picked the right door out of 100 doors ? |
let 's now tackle a classic thought experiment in probability , called the monte hall problem . and it 's called the monty hall problem because monty hall was the game show host in let 's make a deal , where they would set up a situation very similar to the monte hall problem that we 're about to say . so let 's say th... | and these are the only possibilities , and these add up to one right over here . so do n't switch , 1/3 chance of winning . now let 's think about the switching situation . | - what are your chances of winning if you never switch ? |
let 's now tackle a classic thought experiment in probability , called the monte hall problem . and it 's called the monty hall problem because monty hall was the game show host in let 's make a deal , where they would set up a situation very similar to the monte hall problem that we 're about to say . so let 's say th... | now let 's think about the switching situation . so let 's say always -- when you always switch . let 's think about how this might play out . | - what are your chances of winning if you always switch ? |
let 's now tackle a classic thought experiment in probability , called the monte hall problem . and it 's called the monty hall problem because monty hall was the game show host in let 's make a deal , where they would set up a situation very similar to the monte hall problem that we 're about to say . so let 's say th... | now let 's think about the switching situation . so let 's say always -- when you always switch . let 's think about how this might play out . | are we required to say `` i will always switch '' or `` not switch '' even before choosing the first time ? |
let 's now tackle a classic thought experiment in probability , called the monte hall problem . and it 's called the monty hall problem because monty hall was the game show host in let 's make a deal , where they would set up a situation very similar to the monte hall problem that we 're about to say . so let 's say th... | let 's think about how this might play out . what is your probability of winning ? and before we even think about that , think about how you would win if you always switch . | would the probability still concentrate ? |
let 's now tackle a classic thought experiment in probability , called the monte hall problem . and it 's called the monty hall problem because monty hall was the game show host in let 's make a deal , where they would set up a situation very similar to the monte hall problem that we 're about to say . so let 's say th... | and so your goal is to try to find the cash prize . and they say guess which one , or which one would you like to select ? and so let 's say that you select door number one , or curtain number one . | how does the theory work if there is only one goat ? |
let 's now tackle a classic thought experiment in probability , called the monte hall problem . and it 's called the monty hall problem because monty hall was the game show host in let 's make a deal , where they would set up a situation very similar to the monte hall problem that we 're about to say . so let 's say th... | let 's now tackle a classic thought experiment in probability , called the monte hall problem . and it 's called the monty hall problem because monty hall was the game show host in let 's make a deal , where they would set up a situation very similar to the monte hall problem that we 're about to say . so let 's say th... | how did monty hall become so great and what if your choice is the right prize and you switch ? |
let 's now tackle a classic thought experiment in probability , called the monte hall problem . and it 's called the monty hall problem because monty hall was the game show host in let 's make a deal , where they would set up a situation very similar to the monte hall problem that we 're about to say . so let 's say th... | and the question here is , does it make a difference ? are you better off holding fast , sticking to your guns , staying with the original guess ? are you better off switching to whatever curtain is left ? | did sal mean sticking to your gut instead of guns ? |
let 's now tackle a classic thought experiment in probability , called the monte hall problem . and it 's called the monty hall problem because monty hall was the game show host in let 's make a deal , where they would set up a situation very similar to the monte hall problem that we 're about to say . so let 's say th... | and these are the only possibilities , and these add up to one right over here . so do n't switch , 1/3 chance of winning . now let 's think about the switching situation . | what you had was the first item chosen has a 1/3 chance of winning , but the second item has a 1/2 chance , so 1/2 is bigger than 1/3 , so switching is better , right ? |
let 's now tackle a classic thought experiment in probability , called the monte hall problem . and it 's called the monty hall problem because monty hall was the game show host in let 's make a deal , where they would set up a situation very similar to the monte hall problem that we 're about to say . so let 's say th... | let 's now tackle a classic thought experiment in probability , called the monte hall problem . and it 's called the monty hall problem because monty hall was the game show host in let 's make a deal , where they would set up a situation very similar to the monte hall problem that we 're about to say . | what does p ( w ) mean ? |
let 's now tackle a classic thought experiment in probability , called the monte hall problem . and it 's called the monty hall problem because monty hall was the game show host in let 's make a deal , where they would set up a situation very similar to the monte hall problem that we 're about to say . so let 's say th... | we know this . so the contestant picks door number one right over here . then we ca n't lift door number two because there 's a car back there . | 1- what are my odds of picking the right door ? |
let 's now tackle a classic thought experiment in probability , called the monte hall problem . and it 's called the monty hall problem because monty hall was the game show host in let 's make a deal , where they would set up a situation very similar to the monte hall problem that we 're about to say . so let 's say th... | we 're going to lift door number three , and we 're going to expose this goat . in which case , it probably would be good for the person to switch . if the person picks door number two , then we as the game show can show either door number one or door number three , and then it actually does not make sense for the pers... | what would the probabilities be in the following similar scenario ? |
let 's now tackle a classic thought experiment in probability , called the monte hall problem . and it 's called the monty hall problem because monty hall was the game show host in let 's make a deal , where they would set up a situation very similar to the monte hall problem that we 're about to say . so let 's say th... | let 's think about how this might play out . what is your probability of winning ? and before we even think about that , think about how you would win if you always switch . | how can this square with the idea that switching curtains improves the odds of winning ? |
let 's now tackle a classic thought experiment in probability , called the monte hall problem . and it 's called the monty hall problem because monty hall was the game show host in let 's make a deal , where they would set up a situation very similar to the monte hall problem that we 're about to say . so let 's say th... | are you better off holding fast , sticking to your guns , staying with the original guess ? are you better off switching to whatever curtain is left ? or does it not matter ? | are you saying the act of revealing your choice is what gives switching better odds ? |
let 's now tackle a classic thought experiment in probability , called the monte hall problem . and it 's called the monty hall problem because monty hall was the game show host in let 's make a deal , where they would set up a situation very similar to the monte hall problem that we 're about to say . so let 's say th... | so the only way to lose , if you 're always going to switch , is to pick the right the first time . well , what 's the probability of you picking right the first time ? well , that is only 1/3 . | what is the probability that the marks of the first four persons taken from left are in descending order and the first two persons taken from right are in descending order ? |
i have a square here divided into one , two , three , four , five , six , seven , eight , nine equal sections . and we 've already seen that if we were to shade in one of these sections , if we were to select one of these sections , let 's say the middle one right over here , this is one out of the nine equal sections ... | well , each of these , we 've already seen , each of these represent 1/9 . so that 's 1/9 , that 's 1/9 . when i say 1/9 , i could also say a ninth . | 1/1 is equal to 1 right ? |
i have a square here divided into one , two , three , four , five , six , seven , eight , nine equal sections . and we 've already seen that if we were to shade in one of these sections , if we were to select one of these sections , let 's say the middle one right over here , this is one out of the nine equal sections ... | well , each of these , we 've already seen , each of these represent 1/9 . so that 's 1/9 , that 's 1/9 . when i say 1/9 , i could also say a ninth . | how do you do for exp : find 1/100 of 15 ? |
i have a square here divided into one , two , three , four , five , six , seven , eight , nine equal sections . and we 've already seen that if we were to shade in one of these sections , if we were to select one of these sections , let 's say the middle one right over here , this is one out of the nine equal sections ... | well , you would say , well , that represents 1/9 of the whole . this thing right over here represents 1/9 . now what would happen if we shaded in more than that ? so let 's say we shaded in this one and this one , let me shade it in a little bit better . | if you have 15 squares and you shaded in 13.007 would you have 13 7/100 shaded in , right ? |
i have a square here divided into one , two , three , four , five , six , seven , eight , nine equal sections . and we 've already seen that if we were to shade in one of these sections , if we were to select one of these sections , let 's say the middle one right over here , this is one out of the nine equal sections ... | i have a square here divided into one , two , three , four , five , six , seven , eight , nine equal sections . and we 've already seen that if we were to shade in one of these sections , if we were to select one of these sections , let 's say the middle one right over here , this is one out of the nine equal sections ... | how did the pictures suddenly change and why ? |
i have a square here divided into one , two , three , four , five , six , seven , eight , nine equal sections . and we 've already seen that if we were to shade in one of these sections , if we were to select one of these sections , let 's say the middle one right over here , this is one out of the nine equal sections ... | i have a square here divided into one , two , three , four , five , six , seven , eight , nine equal sections . and we 've already seen that if we were to shade in one of these sections , if we were to select one of these sections , let 's say the middle one right over here , this is one out of the nine equal sections ... | what is a mixed number ? |
i have a square here divided into one , two , three , four , five , six , seven , eight , nine equal sections . and we 've already seen that if we were to shade in one of these sections , if we were to select one of these sections , let 's say the middle one right over here , this is one out of the nine equal sections ... | and you might be saying , wait , wait , if i gave five out of the five equal sections shaded in , if i have 5/5 shaded in , i 've got the whole thing shaded in . and you would be absolutely right . 5/5 is equal to the whole . | would 6/8 be an equivalent fraction to 12/16 ? |
i have a square here divided into one , two , three , four , five , six , seven , eight , nine equal sections . and we 've already seen that if we were to shade in one of these sections , if we were to select one of these sections , let 's say the middle one right over here , this is one out of the nine equal sections ... | now let 's make things a little bit more interesting . let 's shade in . so here i have five equal sections . | does the part of the whole you shade first have to be in the middle ? |
i have a square here divided into one , two , three , four , five , six , seven , eight , nine equal sections . and we 've already seen that if we were to shade in one of these sections , if we were to select one of these sections , let 's say the middle one right over here , this is one out of the nine equal sections ... | well , each of these , we 've already seen , each of these represent 1/9 . so that 's 1/9 , that 's 1/9 . when i say 1/9 , i could also say a ninth . so this is 1/9 or a ninth , so each of these represents a ninth . but how many of these ninths do we have shaded in ? | how did sal call 1/9 , ninth ? |
i have a square here divided into one , two , three , four , five , six , seven , eight , nine equal sections . and we 've already seen that if we were to shade in one of these sections , if we were to select one of these sections , let 's say the middle one right over here , this is one out of the nine equal sections ... | and we 've already seen that if we were to shade in one of these sections , if we were to select one of these sections , let 's say the middle one right over here , this is one out of the nine equal sections . so if someone said , what fraction of the whole does this purple square represent ? well , you would say , wel... | what is the square root of `` pi '' ? |
i have a square here divided into one , two , three , four , five , six , seven , eight , nine equal sections . and we 've already seen that if we were to shade in one of these sections , if we were to select one of these sections , let 's say the middle one right over here , this is one out of the nine equal sections ... | well , each of these , we 've already seen , each of these represent 1/9 . so that 's 1/9 , that 's 1/9 . when i say 1/9 , i could also say a ninth . | what is the decimal number of 1/3 ? |
i have a square here divided into one , two , three , four , five , six , seven , eight , nine equal sections . and we 've already seen that if we were to shade in one of these sections , if we were to select one of these sections , let 's say the middle one right over here , this is one out of the nine equal sections ... | now this one right over here it might be tempting to say , i have one , two , three , four sections and one , two , three have been shaded in so maybe the red represents 3/4 of the figure . but remember , the sections have to be equal sections . and this red section is way bigger . | is there a way to make a fraction out of uneven sections ? |
in order to solve problems and make decisions , you often have to access information already stored in your brain . but how is that information stored ? there are a lot of possibilities , but the one we 're going to focus on in this video is the semantic network approach , which argues that concepts are organized in y... | for example , people tend to verify that a pig is an animal faster than a pig is a mammal . because of this issue and some other problems , collins and loftus proposed a modified version of the semantic network . rather than a hierarchical organization , this model says that every individual semantic network develops b... | is a semantic network still a strong concept in current psychology ? |
in order to solve problems and make decisions , you often have to access information already stored in your brain . but how is that information stored ? there are a lot of possibilities , but the one we 're going to focus on in this video is the semantic network approach , which argues that concepts are organized in y... | so when you activate one concept , you 're pulling up related concepts along with it . this general elevation and availability is called spreading activation . for example , if i say `` fire engine , '' not only do you think of a fire engine , but related concepts such as trucks , fire , even the color red become activ... | so in the modified semantic networks and spreading activation , are these phenomenons affected by our schemas ? |
in order to solve problems and make decisions , you often have to access information already stored in your brain . but how is that information stored ? there are a lot of possibilities , but the one we 're going to focus on in this video is the semantic network approach , which argues that concepts are organized in y... | so when you activate one concept , you 're pulling up related concepts along with it . this general elevation and availability is called spreading activation . for example , if i say `` fire engine , '' not only do you think of a fire engine , but related concepts such as trucks , fire , even the color red become activ... | what is the difference between spreading activation and priming ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | and now he 's tripling his marbles . so we want to multiply 3 times the total number of marbles he has now -- times 4 plus 5 . so this right over here is the numerical expression that models the situation without performing any operations . | what does `` x '' after a number mean ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | so we can add the 4 marbles to the 5 marbles . so 4 marbles plus the 5 marbles . so that 's what happens after the first sentence . | at 0.07 , why did sal write marmoles instead of marbles ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | and now he 's tripling his marbles . so we want to multiply 3 times the total number of marbles he has now -- times 4 plus 5 . so this right over here is the numerical expression that models the situation without performing any operations . | will the product change if you put the 3 in 3 ( 4+5 ) on the other side , like this : ( 4+5 ) 3 ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | he has 9 marbles before tripling . and then you multiply it by 3 and he has 27 . but this is what they 're asking for . | does it matter what side of the parentheses the 3 goes on ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . | is n't the '+ ' sign an operation ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | and now he 's tripling his marbles . so we want to multiply 3 times the total number of marbles he has now -- times 4 plus 5 . so this right over here is the numerical expression that models the situation without performing any operations . | is 16x+10 a reasonable way to represent the number of shells that heather has left to make necklaces with ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | but this is what they 're asking for . they want us to write this expression . | why does n't sal write x or * to multiply ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | so let 's think about what 's going on . so he already had 5 marbles in his pocket . and then he found 4 more marbles to add to that . | how is the moon large enough to block the sun ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | he has 9 marbles before tripling . and then you multiply it by 3 and he has 27 . but this is what they 're asking for . | why is it 3 is triple means 3 ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . | do n't you have to put the multiplication sign ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | so we can add the 4 marbles to the 5 marbles . so 4 marbles plus the 5 marbles . so that 's what happens after the first sentence . | why does the equation just say 3 ( 4+5 ) without the multiplication sign ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . | what is the multiplecation sign on a computer ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | he has 9 marbles before tripling . and then you multiply it by 3 and he has 27 . but this is what they 're asking for . | is there another ways to solve 3 ( 37-2 ) -1 ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . | what does numerical expression mean ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | but this is what they 're asking for . they want us to write this expression . | can you write the 3 at the end of the expression ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | but this is what they 're asking for . they want us to write this expression . | for your expression , how can you write 3 ( tripled ) and not add a multiplication sign after ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . | is constructing numerical expressions just adding the numbers and then multiplying the numbers ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | so we want to multiply 3 times the total number of marbles he has now -- times 4 plus 5 . so this right over here is the numerical expression that models the situation without performing any operations . we , of course , could then actually calculate this . he has 9 marbles before tripling . | how come sal uses `` * '' and `` + '' but the problem does n't actually say to use the operations ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . | what is the difference between a numerical expression and an algebraic expression ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | but this is what they 're asking for . they want us to write this expression . | how do you write in base ten numeral form ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | so we can add the 4 marbles to the 5 marbles . so 4 marbles plus the 5 marbles . so that 's what happens after the first sentence . | why did you put 4 & 5 in brackets ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . | what is algebraic all about ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . | how do i write a numerical expression representing 1 item at $ 60 , 2 items at $ 70 and 1 item at $ 20 ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | so let 's think about what 's going on . so he already had 5 marbles in his pocket . and then he found 4 more marbles to add to that . | what is a word problem for 5+3x2-6 ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | but this is what they 're asking for . they want us to write this expression . | hey sal , i wanted you to put '' write an expression of ex 12 doubed from 132 '' please ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . | what is the length of an edge of the cube ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . | is there an end to the universe ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | we , of course , could then actually calculate this . he has 9 marbles before tripling . and then you multiply it by 3 and he has 27 . | should n't you put a multiplication sign after the 9 ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . | what is the difference between braces and parentheses ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . | what are the energy points for ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | and now he 's tripling his marbles . so we want to multiply 3 times the total number of marbles he has now -- times 4 plus 5 . so this right over here is the numerical expression that models the situation without performing any operations . | why does n't sal put an x sign after the 3 in 3 ( 4+5 ) ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | but this is what they 're asking for . they want us to write this expression . | hey what did alan want ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . | wait so how do you know when to put the brackets around which numbers ? |
alan found 4 marbles to add to his 5 marbles currently in his pocket . he then had a competition with his friends and tripled his marbles . write a numerical expression to model the situation without performing any operations . so let 's think about what 's going on . so he already had 5 marbles in his pocket . and the... | he has 9 marbles before tripling . and then you multiply it by 3 and he has 27 . but this is what they 're asking for . | so should you put a x after the 3 ? |
- in the last two videos , we talked about our theme and how to break your story into beats using the story spine . the next step is to divide your story spine into larger sections , which we call acts . throughout history , storytellers have experimented with everything from one act to eight acts or more , but the mos... | - in the last two videos , we talked about our theme and how to break your story into beats using the story spine . the next step is to divide your story spine into larger sections , which we call acts . | does your story have to have an antagonist ? |
- in the last two videos , we talked about our theme and how to break your story into beats using the story spine . the next step is to divide your story spine into larger sections , which we call acts . throughout history , storytellers have experimented with everything from one act to eight acts or more , but the mos... | you probably know this as a character we sometimes call the villain , but it can take many forms . generally , the antagonist is a force that gets in the way of your character 's wants and needs . marlin 's antagonist is something , something that stands in his way , the ocean and his fear of it . | how is the antagonist , which is the force that gets in the way , different from the obstacles that affects the character 's journey ? |
- in the last two videos , we talked about our theme and how to break your story into beats using the story spine . the next step is to divide your story spine into larger sections , which we call acts . throughout history , storytellers have experimented with everything from one act to eight acts or more , but the mos... | in order to save him , marlin is forced to face his biggest fear , the open ocean . the first act can also introduce something called the antagonist . you probably know this as a character we sometimes call the villain , but it can take many forms . | would dory be an antagonist ? |
by this point , you may be getting kind of sick of these pressure volume loops . but i assure you they 're very , very worthwhile getting to know . in fact , let 's learn one more thing out of these pressure volume loops . let 's try to squeeze all the knowledge we can out of these things . so i 'm going to draw one fo... | it 's just going to continue to be contracted if i can somehow fill this with calcium and not allow it to go into relaxation . so my heart cell 's completely contracted . that 's the key , right ? | if the heart muscle is contracted , would n't the aorta have the blood and not the ventricle ? |
you 've opened up a shoe factory and you 're trying to figure out how many thousands of pairs of shoes to produce in order to optimize your profit . and so let 's let x equal the thousands of pairs produced . now let 's think about how much money you 're going to make per pair . actually , let me say how much revenue ,... | and once again , this is also going to be in thousands of dollars . now , given these functions of x for revenue and cost , what is profit as a function of x going to be ? well , your profit as a function of x is just going to be equal to your revenue as a function of x minus your cost as a function of x . | all of the optimization videos are cool and everything , but i have one question : how do you find the equation for profit , cost , or stuff like that using real world data ? |
you 've opened up a shoe factory and you 're trying to figure out how many thousands of pairs of shoes to produce in order to optimize your profit . and so let 's let x equal the thousands of pairs produced . now let 's think about how much money you 're going to make per pair . actually , let me say how much revenue ,... | if you produce a certain amount and let 's say you bring in , i do n't know , $ 10,000 of revenue and it costs you $ 5,000 to produce those shoes , you 'll have $ 5,000 in profit . those numbers are n't the ones that would actually you would get from this right here . i 'm just giving you an example . | without plugging in random numbers ? |
you 've opened up a shoe factory and you 're trying to figure out how many thousands of pairs of shoes to produce in order to optimize your profit . and so let 's let x equal the thousands of pairs produced . now let 's think about how much money you 're going to make per pair . actually , let me say how much revenue ,... | now if we want to optimize this profit function analytically , the easiest way is to think about what are the critical points of this profit function and are any of those critical points minimum points or maximum points ? and if one of them is a maximum point , then we can say , well , let 's produce that many . that i... | why does sal write the first critical point to the thousandths but the second one to the ten-thousandths ? |
you 've opened up a shoe factory and you 're trying to figure out how many thousands of pairs of shoes to produce in order to optimize your profit . and so let 's let x equal the thousands of pairs produced . now let 's think about how much money you 're going to make per pair . actually , let me say how much revenue ,... | so let 's figure out what these two are . and i 'll use a calculator . i 'll use the calculator for this one . | can we use calculus to optimize a relation between workforce and profit ? |
you 've opened up a shoe factory and you 're trying to figure out how many thousands of pairs of shoes to produce in order to optimize your profit . and so let 's let x equal the thousands of pairs produced . now let 's think about how much money you 're going to make per pair . actually , let me say how much revenue ,... | now let 's think about how much money you 're going to make per pair . actually , let me say how much revenue , which is how much you actually get to sell those shoes for . so let 's write a function right here . | like for example with 100 workers how much shoes need to be manufactured for maximum profit ? |
you 've opened up a shoe factory and you 're trying to figure out how many thousands of pairs of shoes to produce in order to optimize your profit . and so let 's let x equal the thousands of pairs produced . now let 's think about how much money you 're going to make per pair . actually , let me say how much revenue ,... | and if this was 4 it 'd be even more negative , so this thing is going to be less than 0 . do n't even have to use my calculator to evaluate it . now what about this thing right over here ? | should n't sal have checked the end behaviour of the graph first to see if there even was a maximum profit ? |
you 've opened up a shoe factory and you 're trying to figure out how many thousands of pairs of shoes to produce in order to optimize your profit . and so let 's let x equal the thousands of pairs produced . now let 's think about how much money you 're going to make per pair . actually , let me say how much revenue ,... | yep . all right . now these are all we know about these , or these are both critical points . | if the graph tended towards infinity this method could have given an incorrect result right ? |
you 've opened up a shoe factory and you 're trying to figure out how many thousands of pairs of shoes to produce in order to optimize your profit . and so let 's let x equal the thousands of pairs produced . now let 's think about how much money you 're going to make per pair . actually , let me say how much revenue ,... | so what is it ? i 've just said it here in abstract terms , but we know what r of x is and what 's c of x . this is 10x minus all of this business . | while i agree with the solution derived in the video , why does n't setting r ( x ) = c ( x ) work ? |
you 've opened up a shoe factory and you 're trying to figure out how many thousands of pairs of shoes to produce in order to optimize your profit . and so let 's let x equal the thousands of pairs produced . now let 's think about how much money you 're going to make per pair . actually , let me say how much revenue ,... | so now we just have to solve for x . and so we just are essentially solving a quadratic equation . just so that i do n't have as many negatives , let 's multiply both sides by negative 1 . | do optimization questions often use the quadratic equation ? |
you 've opened up a shoe factory and you 're trying to figure out how many thousands of pairs of shoes to produce in order to optimize your profit . and so let 's let x equal the thousands of pairs produced . now let 's think about how much money you 're going to make per pair . actually , let me say how much revenue ,... | if you produce a certain amount and let 's say you bring in , i do n't know , $ 10,000 of revenue and it costs you $ 5,000 to produce those shoes , you 'll have $ 5,000 in profit . those numbers are n't the ones that would actually you would get from this right here . i 'm just giving you an example . | in reality would there ever be a cost equation be that perfect for differentiation ? |
you 've opened up a shoe factory and you 're trying to figure out how many thousands of pairs of shoes to produce in order to optimize your profit . and so let 's let x equal the thousands of pairs produced . now let 's think about how much money you 're going to make per pair . actually , let me say how much revenue ,... | and once again , this is also going to be in thousands of dollars . now , given these functions of x for revenue and cost , what is profit as a function of x going to be ? well , your profit as a function of x is just going to be equal to your revenue as a function of x minus your cost as a function of x . | in this problem will it also be correct if the amount of quantity to be produced that is x is found by equating marginal revenue ( mr ) and marginal cost ( mc ) functions ? |
you 've opened up a shoe factory and you 're trying to figure out how many thousands of pairs of shoes to produce in order to optimize your profit . and so let 's let x equal the thousands of pairs produced . now let 's think about how much money you 're going to make per pair . actually , let me say how much revenue ,... | to do that , i 'll use the second derivative test to figure out if our function is concave upwards or concave downwards or neither at one of these points . so let 's look at the second derivative . so p prime prime of x is going to be equal to negative 6x plus 12 . | when he checks the second derivative , ca n't you just plug the values back into the original equation and see which result is greater ? |
you 've opened up a shoe factory and you 're trying to figure out how many thousands of pairs of shoes to produce in order to optimize your profit . and so let 's let x equal the thousands of pairs produced . now let 's think about how much money you 're going to make per pair . actually , let me say how much revenue ,... | so let 's write a function right here . revenue as a function of x . well , you have a wholesaler who 's willing to pay you $ 10 per pair for as many pairs as you 're willing to give him . | do n't you have to plug the x-value into the revenue and cost equations and find the distance ? |
you 've opened up a shoe factory and you 're trying to figure out how many thousands of pairs of shoes to produce in order to optimize your profit . and so let 's let x equal the thousands of pairs produced . now let 's think about how much money you 're going to make per pair . actually , let me say how much revenue ,... | so what is it ? i 've just said it here in abstract terms , but we know what r of x is and what 's c of x . this is 10x minus all of this business . | only one thing i 'd like to know , how did you get the equation p ( x ) = r ( x ) c ( x ) = x^3 - 6x^2 + 15x ? |
you 've opened up a shoe factory and you 're trying to figure out how many thousands of pairs of shoes to produce in order to optimize your profit . and so let 's let x equal the thousands of pairs produced . now let 's think about how much money you 're going to make per pair . actually , let me say how much revenue ,... | these are points at which our derivative is equal to 0 . but we do n't know whether they 're minimum points , they 're points at which the function takes on a minimum value , a maximum value , or neither . to do that , i 'll use the second derivative test to figure out if our function is concave upwards or concave down... | is n't it much easier ( to remember and apply ) to use the first derivative test and find out whether the critical point is maximum or minimum ? |
you 've opened up a shoe factory and you 're trying to figure out how many thousands of pairs of shoes to produce in order to optimize your profit . and so let 's let x equal the thousands of pairs produced . now let 's think about how much money you 're going to make per pair . actually , let me say how much revenue ,... | so i get my calculator out . so my original profit function is right over there . so i want to be able to see that and that . | when do we substitue the profit and when we do n't need to substitute ? |
you 've opened up a shoe factory and you 're trying to figure out how many thousands of pairs of shoes to produce in order to optimize your profit . and so let 's let x equal the thousands of pairs produced . now let 's think about how much money you 're going to make per pair . actually , let me say how much revenue ,... | so let 's figure out what these two are . and i 'll use a calculator . i 'll use the calculator for this one . | how can i use optimization in regard to the relationship between distance , rate , and time or cost , distance , and rate ? |
you 've opened up a shoe factory and you 're trying to figure out how many thousands of pairs of shoes to produce in order to optimize your profit . and so let 's let x equal the thousands of pairs produced . now let 's think about how much money you 're going to make per pair . actually , let me say how much revenue ,... | you 've opened up a shoe factory and you 're trying to figure out how many thousands of pairs of shoes to produce in order to optimize your profit . and so let 's let x equal the thousands of pairs produced . | why is a shoe factory making pears ? |
you 've opened up a shoe factory and you 're trying to figure out how many thousands of pairs of shoes to produce in order to optimize your profit . and so let 's let x equal the thousands of pairs produced . now let 's think about how much money you 're going to make per pair . actually , let me say how much revenue ,... | so if you have an interval where the slope is decreasing and you know the point where the slope is exactly 0 , which is where x is equal to 3.528 , it must be a maximum . so we actually do take on a maximum value when x is 3.528 . on the other side we see that over here we 're concave upwards . | why change -x^3 to x^3 ? |
you 've opened up a shoe factory and you 're trying to figure out how many thousands of pairs of shoes to produce in order to optimize your profit . and so let 's let x equal the thousands of pairs produced . now let 's think about how much money you 're going to make per pair . actually , let me say how much revenue ,... | and once again , this is also going to be in thousands of dollars . now , given these functions of x for revenue and cost , what is profit as a function of x going to be ? well , your profit as a function of x is just going to be equal to your revenue as a function of x minus your cost as a function of x . if you produ... | does any cost actually exist as a polynomial function ? |
you 've opened up a shoe factory and you 're trying to figure out how many thousands of pairs of shoes to produce in order to optimize your profit . and so let 's let x equal the thousands of pairs produced . now let 's think about how much money you 're going to make per pair . actually , let me say how much revenue ,... | that is going to be -- we will have optimized or we will figure out the quantity we need to produce in order to optimize our profit . so to figure out critical points , we essentially have to find the derivative of our function and figure out when does that derivative equal 0 or when is that derivative undefined ? that... | can we take the 3rd derivative here instead to find the shape of the concave ? |
man in glasses : hello , there . here at crash course hq we like to start out each day with a nice healthy dose of water in all its 3 forms . it 's the only substance on all of our planet earth that occurs naturally in solid , liquid and gas forms . to celebrate this magical bond between two hydrogen atoms and one oxyg... | when you get one of these polar substances in water , it 's strong enough that it breaks all the little cohesive forces , all those little hydrogen bonds . instead of hydrogen bonding to each other , the water will hydrogen bond around these polar substances . table salt is ionic , and right now it 's being separated i... | what exactly happens when oxygen and hydrogen bond to make water so dense ( compared to the two gasses that form it ) ? |
man in glasses : hello , there . here at crash course hq we like to start out each day with a nice healthy dose of water in all its 3 forms . it 's the only substance on all of our planet earth that occurs naturally in solid , liquid and gas forms . to celebrate this magical bond between two hydrogen atoms and one oxyg... | these molecules lack charged poles . they are non-polar and are not dissolving in water because essentially they 're being pushed out of the water by water 's cohesive forces . water , we may call it the universal solvent , but that does not mean that it dissolves everything . | why does water `` bead up '' on certain wax papers or plants ? |
man in glasses : hello , there . here at crash course hq we like to start out each day with a nice healthy dose of water in all its 3 forms . it 's the only substance on all of our planet earth that occurs naturally in solid , liquid and gas forms . to celebrate this magical bond between two hydrogen atoms and one oxyg... | thanks to adhesion , the water molecules are attracted to the molecules in the straw . as the water molecules adhere to the straw , other molecules are drawn in by cohesion following those fellow water molecules . thank you cohesion . | if ice is less dense than water , and the ice molecules are spread out , would that mean that part of the reason why it floats is not only from low density , but from the molecules are spread out more , spreading the density equally , too ? |
man in glasses : hello , there . here at crash course hq we like to start out each day with a nice healthy dose of water in all its 3 forms . it 's the only substance on all of our planet earth that occurs naturally in solid , liquid and gas forms . to celebrate this magical bond between two hydrogen atoms and one oxyg... | that 's the principle behind sweating , which is an extremely effective , though somewhat embarrassing , part of life . this is an example of another incredibly cool thing about water . when my body gets hot and it sweats , that heat excites some of the water molecules on my skin to the point where they break those hyd... | why is water the only thing on earth that exists in three different forms ? |
man in glasses : hello , there . here at crash course hq we like to start out each day with a nice healthy dose of water in all its 3 forms . it 's the only substance on all of our planet earth that occurs naturally in solid , liquid and gas forms . to celebrate this magical bond between two hydrogen atoms and one oxyg... | why ? why do we think that water is necessary for life ? why does water on other planets get us so freaking excited ? | how did earth produce so much water to support life ? |
man in glasses : hello , there . here at crash course hq we like to start out each day with a nice healthy dose of water in all its 3 forms . it 's the only substance on all of our planet earth that occurs naturally in solid , liquid and gas forms . to celebrate this magical bond between two hydrogen atoms and one oxyg... | why is it so hot in here ? heat capacity ! yes , water has a very high heat capacity and probably that means nothing to you . | is heat capacity , as mentioned another term for specific heat or is there a difference between the two ? |
man in glasses : hello , there . here at crash course hq we like to start out each day with a nice healthy dose of water in all its 3 forms . it 's the only substance on all of our planet earth that occurs naturally in solid , liquid and gas forms . to celebrate this magical bond between two hydrogen atoms and one oxyg... | aside from artificially warming your bed , it 's also very important that it 's hard to heat up and cool down the oceans significantly . they become giant heat sinks that regulate the temperature and the climate of our planet , which is why , for example , it 's so much nicer in los angeles where the ocean is constantl... | how does a boat or ship float on the ocean ? |
man in glasses : hello , there . here at crash course hq we like to start out each day with a nice healthy dose of water in all its 3 forms . it 's the only substance on all of our planet earth that occurs naturally in solid , liquid and gas forms . to celebrate this magical bond between two hydrogen atoms and one oxyg... | these molecules lack charged poles . they are non-polar and are not dissolving in water because essentially they 're being pushed out of the water by water 's cohesive forces . water , we may call it the universal solvent , but that does not mean that it dissolves everything . | where did all the water come from ? |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.