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you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | ( so let me write this down in the appropriate colors . ) so 2 to the 3rd power . ( 2^3 . ) | why is anything ( except maybe 0 ) to the 0 power 1 ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . | can you do exponents with division ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . | do exponents go along with scientific notation ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | ( so let me write this down in the appropriate colors . ) so 2 to the 3rd power . ( 2^3 . ) | can there be a number to the infinity power ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . | can you put exponents on negative numbers ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | so 5 to the 4th power ( 5^4 ) is going to be equal to multiplying 4 5 's together . so 5^4 = 5 × 5 × 5 × 5 . notice , we have [ counting : 1 , 2 , 3 ] 4 5 's . | so 5times 3 is 5+5+5=15 and then just add different types of numbers or a specific number ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | so this would be equal to , not 2 + 2 + 2 , but 2 × ... ( and i ’ ll use a little dot to signify multiplication . ) ... 2 × 2 × 2 . well , what 's 2 × 2 × 2 ? | near is that some sort of boat/train ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . | what if the base is zero ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy . | what if the exponent is 0 ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy . | what if you wanted to know if you are squaring the number or using an exponent ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | ( 2 × 2 × 2 = 8 . ) so 2 to the 3rd power is equal to 8 . ( 2^3 = 8 . ) | what is the definition of an exponent and i see that we use exponents in scientific notation but they say it is a power ( ten to the power 8 ) is exponents and powers the same ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy . | if there is a negative number for the exponent then what do you do ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy . | if taking an exponent is manly multiplucation , what else is there to it ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | ( so let me write this down in the appropriate colors . ) so 2 to the 3rd power . ( 2^3 . ) | anyone know what the largest power determined by a computer is ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | ( so let me write this down in the appropriate colors . ) so 2 to the 3rd power . ( 2^3 . ) | how can we multiply if the power is negative ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy . | is there a way to make it less complicated when you have a big exponent ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy . | what is the importance of the base and the exponent ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | what is , say , 5 to the – let 's say – 5 to the 4th power ( 5^4 ) ? and what you 'll see here is this number is going to get large very , very , very fast . so 5 to the 4th power ( 5^4 ) is going to be equal to multiplying 4 5 's together . | would you need an advanced math computer to calculate a really large number , such as 16^1008 ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy . | what if the exponent is 0 ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | ( so let me write this down in the appropriate colors . ) so 2 to the 3rd power . ( 2^3 . ) | so , what would i do with a negative power that makes a ridiculously huge ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | so this would be equal to , not 2 + 2 + 2 , but 2 × ... ( and i ’ ll use a little dot to signify multiplication . ) ... 2 × 2 × 2 . well , what 's 2 × 2 × 2 ? | how on earth did sal get to 625 ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | what is , say , 5 to the – let 's say – 5 to the 4th power ( 5^4 ) ? and what you 'll see here is this number is going to get large very , very , very fast . so 5 to the 4th power ( 5^4 ) is going to be equal to multiplying 4 5 's together . | what is a base number ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | so 2 to the 3rd power is equal to 8 . ( 2^3 = 8 . ) let 's try a few more examples here . | an exponet can have any number right not just 12 and below because2*8 would be 2 times 8 and eveyone knows its 16 ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | so let 's multiply 3 – ( let me do that in yellow . ) let 's multiply 3 × 3 . so this is going to be equal to 9 . | is there a other way to multiply a exponents in different ways ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy . | when using an exponent , what if the result is a too big of a number ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . | # yolo : d what is a variable and why is it important ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . | how do you sknow love for exponents containing x ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy . | what do you do when you have 10a and an exponent ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | ( so let me write this down in the appropriate colors . ) so 2 to the 3rd power . ( 2^3 . ) | how do you do the following : four times 5 to the power of 2 over four to the power of one times fives ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | ( so let me write this down in the appropriate colors . ) so 2 to the 3rd power . ( 2^3 . ) | why is anything to the 0th power 1 ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | we are not adding them . this is not 5 × 4 . this is not 20 . | if the sum of two numbers is 150 and if the larger number is 4 times the smaller number , what are those numbers ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | and what you 'll see here is this number is going to get large very , very , very fast . so 5 to the 4th power ( 5^4 ) is going to be equal to multiplying 4 5 's together . so 5^4 = 5 × 5 × 5 × 5 . | is 4 to the power of 0 equal to 4 or 0 ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | ( so let me write this down in the appropriate colors . ) so 2 to the 3rd power . ( 2^3 . ) | why is everything to the 1st power that number ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | so 5^4 = 5 × 5 × 5 × 5 . notice , we have [ counting : 1 , 2 , 3 ] 4 5 's . and we are multiplying them . | for example , why is x^1=x ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . | how do you tell the difference between order of magnitude and exponents ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy . | what if the exponent is big and is very hard to figure out ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | ( so let me write this down in the appropriate colors . ) so 2 to the 3rd power . ( 2^3 . ) | why is anything to the 0th power 1 ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | ( 2^3 . ) so you might be tempted to say , `` hey , maybe this is 2 × 3 , which would be 6 . '' but remember , i just said this is repeated multiplication . | would n't be 0 because anything times 0 is 0 ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy . | how high can the exponent be ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy . | why do we need the exponent 0 ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | ( so let me write this down in the appropriate colors . ) so 2 to the 3rd power . ( 2^3 . ) | what is 0 to the 0 power ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | ( 2^3 . ) so you might be tempted to say , `` hey , maybe this is 2 × 3 , which would be 6 . '' but remember , i just said this is repeated multiplication . | if a number has no exponent would it be equivalent to a zero or would that not be possible ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | well 5 × 5 is 25 . ( 5 × 5 = 25 . ) 25 × 5 is 125 . | we multipy 25 times 5 then 5 again ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy . | is it possible to have a fraction as a exponent ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | what is , say , 5 to the – let 's say – 5 to the 4th power ( 5^4 ) ? and what you 'll see here is this number is going to get large very , very , very fast . so 5 to the 4th power ( 5^4 ) is going to be equal to multiplying 4 5 's together . | when teachers see an exponent do they get it confused to ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . | what is that noisy sound ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy . | what happens if the exponent is infinity ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' and it sounds very fancy . | 0 to the exponent of zero ? |
you already know that we can view multiplication as repeated addition . so , if we had 2 times 3 ( 2 × 3 ) , we could literally view this as 3 2 's being added together . so it could be 2 + 2 + 2 . notice this is [ counting : 1 , 2 ] 3 2 's . and when you add those 2 's together , you get 6 . what we 're going to intro... | and when you add those 2 's together , you get 6 . what we 're going to introduce you to in this video is the idea of repeated multiplication – a new operation that really can be viewed as repeated multiplication . and that 's the operation of taking an 'exponent . ' | what if i does n't show a multiplication sign ? |
a pool table is 1 meter by 2 meters . so this is 1 meter -- let me label that -- so this distance right over here is 1 meter . this distance right over here is 2 meters . that 's 2 meters right over there . there are 6 pockets total , 1 , 2 , 3 , 4 , 5 , 6 , 4 in the corners and 2 at the midpoints of each of the 2-mete... | so if they 're mirror images , this angle is going to be congruent to that angle . if those two angles are congruent , then this angle , which is complementary to that black angle , must be equal to this angle . each of these are going to be 90 degrees minus that black angle right over there . | is n't there one angle formed between the two rays that mark the ball 's travel ? |
a pool table is 1 meter by 2 meters . so this is 1 meter -- let me label that -- so this distance right over here is 1 meter . this distance right over here is 2 meters . that 's 2 meters right over there . there are 6 pockets total , 1 , 2 , 3 , 4 , 5 , 6 , 4 in the corners and 2 at the midpoints of each of the 2-mete... | if two corresponding angles of two different triangles are congruent , then the triangles are going to be similar . so this top triangle is similar to this bottom triangle . and what that helps us is that means that the ratio of the lengths of corresponding parts of those triangles are going to be the same . | what if the side of the smaller mirrored triangle was not an integer but a fraction ? |
a pool table is 1 meter by 2 meters . so this is 1 meter -- let me label that -- so this distance right over here is 1 meter . this distance right over here is 2 meters . that 's 2 meters right over there . there are 6 pockets total , 1 , 2 , 3 , 4 , 5 , 6 , 4 in the corners and 2 at the midpoints of each of the 2-mete... | so if they 're mirror images , this angle is going to be congruent to that angle . if those two angles are congruent , then this angle , which is complementary to that black angle , must be equal to this angle . each of these are going to be 90 degrees minus that black angle right over there . | how do we know that they are complementary to the black angle ? |
a pool table is 1 meter by 2 meters . so this is 1 meter -- let me label that -- so this distance right over here is 1 meter . this distance right over here is 2 meters . that 's 2 meters right over there . there are 6 pockets total , 1 , 2 , 3 , 4 , 5 , 6 , 4 in the corners and 2 at the midpoints of each of the 2-mete... | well , we definitely know the length of this segment right over here . we know that the pockets are 1 meter apart , so that is 1 meter . and we also know the length of this segment right over here . | how are the angles complementary to each other ? |
a pool table is 1 meter by 2 meters . so this is 1 meter -- let me label that -- so this distance right over here is 1 meter . this distance right over here is 2 meters . that 's 2 meters right over there . there are 6 pockets total , 1 , 2 , 3 , 4 , 5 , 6 , 4 in the corners and 2 at the midpoints of each of the 2-mete... | well , if you have two angles , they both have a 90 degree angle , and they both have this green angle , so that means that the third angle must also be the same . if you know two angles , you know what the third angle has to be . if two corresponding angles of two different triangles are congruent , then the triangles... | how do you know that mirror line is perpendicular to the rectangle ? |
a pool table is 1 meter by 2 meters . so this is 1 meter -- let me label that -- so this distance right over here is 1 meter . this distance right over here is 2 meters . that 's 2 meters right over there . there are 6 pockets total , 1 , 2 , 3 , 4 , 5 , 6 , 4 in the corners and 2 at the midpoints of each of the 2-mete... | well , if you have two angles , they both have a 90 degree angle , and they both have this green angle , so that means that the third angle must also be the same . if you know two angles , you know what the third angle has to be . if two corresponding angles of two different triangles are congruent , then the triangles... | how do we know that the mirror line 6 forms a right angle with side e ? |
so we have two different substances here and just for the sake of an argument , let 's assume that they are in their liquid state . well you probably already recognize this substance right here , each molecule has one oxygen atom and two hydrogen atoms , this is water and we have drawn all neat hydrogen bonds right ov... | and so you can imagine that water has a higher temperature at which it starts to boil than ethanol and that is indeed the case . water 's boiling point is exactly 100° celsius , in fact , water 's boiling point was an important data point for even establishing the celsius scale , so by definition , it 's 100° celsius ,... | what is the difference between heat of vaporisation and boiling point ? |
so we have two different substances here and just for the sake of an argument , let 's assume that they are in their liquid state . well you probably already recognize this substance right here , each molecule has one oxygen atom and two hydrogen atoms , this is water and we have drawn all neat hydrogen bonds right ov... | i found slightly different numbers , depending on which resource i looked at but what i found for water , the heat of vaporization is 2260 joules per gram or instead of using joules , remember joules is a unit of energy it could be a unit of heat , instead of joules if you wan na think of it in terms of calories , that... | would n't ethanol catch on fire when exposed to high level of heat , since it is used very often as a fire starter ? |
so we have two different substances here and just for the sake of an argument , let 's assume that they are in their liquid state . well you probably already recognize this substance right here , each molecule has one oxygen atom and two hydrogen atoms , this is water and we have drawn all neat hydrogen bonds right ov... | when we talk about the temperature of a system , we 're really just talking about the average kinetic energy . each molecule , remember they 're all bouncing around in all different ways , this one might have , for example , a much higher kinetic energy than this one . they 're all moving in different directions , this... | so is it also the amount needed to raise one gram of water one thousand degrees celsius ? |
so we have two different substances here and just for the sake of an argument , let 's assume that they are in their liquid state . well you probably already recognize this substance right here , each molecule has one oxygen atom and two hydrogen atoms , this is water and we have drawn all neat hydrogen bonds right ov... | when we talk about the temperature of a system , we 're really just talking about the average kinetic energy . each molecule , remember they 're all bouncing around in all different ways , this one might have , for example , a much higher kinetic energy than this one . they 're all moving in different directions , this... | or the amount needed to raise one thousand grams of water by one degree celsius ? |
so we have two different substances here and just for the sake of an argument , let 's assume that they are in their liquid state . well you probably already recognize this substance right here , each molecule has one oxygen atom and two hydrogen atoms , this is water and we have drawn all neat hydrogen bonds right ov... | because there 's more hydrogen bonds here to break , than here , you can imagine it would take , on average , more heat to vaporize this thing than to vaporize this thing and that is indeed the case . the term for how much heat do you need to vaporize a certain mass of a substance , you can imagine , is called the heat... | how does the heat of vaporization impact the effectiveness of evaporative cooling ? |
so we have two different substances here and just for the sake of an argument , let 's assume that they are in their liquid state . well you probably already recognize this substance right here , each molecule has one oxygen atom and two hydrogen atoms , this is water and we have drawn all neat hydrogen bonds right ov... | which one is going to be easier to vaporize or which one is going to have more of it 's molecules turning into vapor , or i guess you could say turning into vapor more easily ? well you immediately see that they both have hydrogen bonds , you have this hydrogen bond between the partially negative end and the partial po... | on ethanol , why would n't the carbon change have a partial positive charge in comparison to the oxygen ? |
so we have two different substances here and just for the sake of an argument , let 's assume that they are in their liquid state . well you probably already recognize this substance right here , each molecule has one oxygen atom and two hydrogen atoms , this is water and we have drawn all neat hydrogen bonds right ov... | in that case , it is going to turn into its gaseous state . the hydrogen bonds are gon na break apart , and it 's gon na be so far from any of its sibling molecules , i guess you could say , from the other ethanol molecules that it wo n't be able to form new hydrogen bonds . same thing with this one , once it vaporizes... | why is hardest to vaporize molecules with hidrogen bonds ? |
so we have two different substances here and just for the sake of an argument , let 's assume that they are in their liquid state . well you probably already recognize this substance right here , each molecule has one oxygen atom and two hydrogen atoms , this is water and we have drawn all neat hydrogen bonds right ov... | you can put a heat lamp on top of them or you could just put them outside where they 're experiencing the same atmospheric conditions , the same sun 's rays and see what 's the difference -- how much more energy , how much more time does it take for the water to evaporate than the ethanol . there 's a similar idea here... | as the atmospheric pressure changes , do the heat of vaporization and boiling point as well ? |
so we have two different substances here and just for the sake of an argument , let 's assume that they are in their liquid state . well you probably already recognize this substance right here , each molecule has one oxygen atom and two hydrogen atoms , this is water and we have drawn all neat hydrogen bonds right ov... | because there 's more hydrogen bonds here to break , than here , you can imagine it would take , on average , more heat to vaporize this thing than to vaporize this thing and that is indeed the case . the term for how much heat do you need to vaporize a certain mass of a substance , you can imagine , is called the heat... | what is heat of vaporization ? |
so we have two different substances here and just for the sake of an argument , let 's assume that they are in their liquid state . well you probably already recognize this substance right here , each molecule has one oxygen atom and two hydrogen atoms , this is water and we have drawn all neat hydrogen bonds right ov... | there 's a similar idea here which is boiling point . we 've all boiled things , boiling point is the point at which the vapor pressure from the substance has become equal to and starts to overcome the pressure from just a regular atmospheric pressure . and so you can imagine that water has a higher temperature at whic... | what is `` vapor pressure '' ? |
so we have two different substances here and just for the sake of an argument , let 's assume that they are in their liquid state . well you probably already recognize this substance right here , each molecule has one oxygen atom and two hydrogen atoms , this is water and we have drawn all neat hydrogen bonds right ov... | and so you can imagine that water has a higher temperature at which it starts to boil than ethanol and that is indeed the case . water 's boiling point is exactly 100° celsius , in fact , water 's boiling point was an important data point for even establishing the celsius scale , so by definition , it 's 100° celsius ,... | why is water 's boiling point a key point for creating the measurement celcious ? |
so we have two different substances here and just for the sake of an argument , let 's assume that they are in their liquid state . well you probably already recognize this substance right here , each molecule has one oxygen atom and two hydrogen atoms , this is water and we have drawn all neat hydrogen bonds right ov... | in that case , it is going to turn into its gaseous state . the hydrogen bonds are gon na break apart , and it 's gon na be so far from any of its sibling molecules , i guess you could say , from the other ethanol molecules that it wo n't be able to form new hydrogen bonds . same thing with this one , once it vaporizes... | can ions form hydrogen bonds ? |
so we have two different substances here and just for the sake of an argument , let 's assume that they are in their liquid state . well you probably already recognize this substance right here , each molecule has one oxygen atom and two hydrogen atoms , this is water and we have drawn all neat hydrogen bonds right ov... | the same thing for ethanol . the heat of vaporization for ethanol is , based on what i looked up , is 841 joules per gram or if we wan na write them as calories , 201 calories per gram which means it would require , roughly , 201 calories to evaporate , to fully vaporize a gram of ethanol at standard temperature , keep... | how does that end up being 541 calories to arrive at vaporization ? |
so we have two different substances here and just for the sake of an argument , let 's assume that they are in their liquid state . well you probably already recognize this substance right here , each molecule has one oxygen atom and two hydrogen atoms , this is water and we have drawn all neat hydrogen bonds right ov... | i found slightly different numbers , depending on which resource i looked at but what i found for water , the heat of vaporization is 2260 joules per gram or instead of using joules , remember joules is a unit of energy it could be a unit of heat , instead of joules if you wan na think of it in terms of calories , that... | so when we boil the water is that the reason why hot air comes out of the boiler ? |
so we have two different substances here and just for the sake of an argument , let 's assume that they are in their liquid state . well you probably already recognize this substance right here , each molecule has one oxygen atom and two hydrogen atoms , this is water and we have drawn all neat hydrogen bonds right ov... | in that case , it is going to turn into its gaseous state . the hydrogen bonds are gon na break apart , and it 's gon na be so far from any of its sibling molecules , i guess you could say , from the other ethanol molecules that it wo n't be able to form new hydrogen bonds . same thing with this one , once it vaporizes... | can a vaporized molecule form hydrogen bonds in the air ? |
so we have two different substances here and just for the sake of an argument , let 's assume that they are in their liquid state . well you probably already recognize this substance right here , each molecule has one oxygen atom and two hydrogen atoms , this is water and we have drawn all neat hydrogen bonds right ov... | so we have two different substances here and just for the sake of an argument , let 's assume that they are in their liquid state . well you probably already recognize this substance right here , each molecule has one oxygen atom and two hydrogen atoms , this is water and we have drawn all neat hydrogen bonds right ov... | for example , if water evaporates , can it interact with the water vapor already present in air and form hydrogen bonds ? |
so we have two different substances here and just for the sake of an argument , let 's assume that they are in their liquid state . well you probably already recognize this substance right here , each molecule has one oxygen atom and two hydrogen atoms , this is water and we have drawn all neat hydrogen bonds right ov... | in that case , it is going to turn into its gaseous state . the hydrogen bonds are gon na break apart , and it 's gon na be so far from any of its sibling molecules , i guess you could say , from the other ethanol molecules that it wo n't be able to form new hydrogen bonds . same thing with this one , once it vaporizes... | in a mixture of ethanol and water , would the two types of molecules remain separate from each other like they are in the picture or ( since they both use hydrogen bonds ) would water molecules and ethanol molecules be bonded together ? |
so we have two different substances here and just for the sake of an argument , let 's assume that they are in their liquid state . well you probably already recognize this substance right here , each molecule has one oxygen atom and two hydrogen atoms , this is water and we have drawn all neat hydrogen bonds right ov... | and so you can imagine that water has a higher temperature at which it starts to boil than ethanol and that is indeed the case . water 's boiling point is exactly 100° celsius , in fact , water 's boiling point was an important data point for even establishing the celsius scale , so by definition , it 's 100° celsius ,... | so if i heat up an alchoholic drink to 80 celsius for a while , it will no longer be alchoholic ? |
so we have two different substances here and just for the sake of an argument , let 's assume that they are in their liquid state . well you probably already recognize this substance right here , each molecule has one oxygen atom and two hydrogen atoms , this is water and we have drawn all neat hydrogen bonds right ov... | this is ethanol , which is the primary constituent in the alcohol that people drink , it 's also an additive into car fuel , but what i wan na think about here , is if we assume that both of these are in their liquid state and let 's say they 're hanging out in a cup and we 're just at sea level so it 's just a standar... | did sal say 0 which one is easier to vaporize ? |
so we have two different substances here and just for the sake of an argument , let 's assume that they are in their liquid state . well you probably already recognize this substance right here , each molecule has one oxygen atom and two hydrogen atoms , this is water and we have drawn all neat hydrogen bonds right ov... | so you have this imbalance here and then on top of that , this carbon , you have a lot more atoms here in which to distribute a partial charge . there could be a very weak partial charge distributed here amongst the carbons but you have a stronger partial charge on the hydrogen but it 's not gon na be strong as what yo... | why are c2h5 molecules weak partial charge ? |
so we have two different substances here and just for the sake of an argument , let 's assume that they are in their liquid state . well you probably already recognize this substance right here , each molecule has one oxygen atom and two hydrogen atoms , this is water and we have drawn all neat hydrogen bonds right ov... | in that case , it is going to turn into its gaseous state . the hydrogen bonds are gon na break apart , and it 's gon na be so far from any of its sibling molecules , i guess you could say , from the other ethanol molecules that it wo n't be able to form new hydrogen bonds . same thing with this one , once it vaporizes... | and what do c2h5 contribute to the charges of the ethnol molecules ? |
so we have two different substances here and just for the sake of an argument , let 's assume that they are in their liquid state . well you probably already recognize this substance right here , each molecule has one oxygen atom and two hydrogen atoms , this is water and we have drawn all neat hydrogen bonds right ov... | i found slightly different numbers , depending on which resource i looked at but what i found for water , the heat of vaporization is 2260 joules per gram or instead of using joules , remember joules is a unit of energy it could be a unit of heat , instead of joules if you wan na think of it in terms of calories , that... | but why are there more water molecules than ethanol ? |
so we have two different substances here and just for the sake of an argument , let 's assume that they are in their liquid state . well you probably already recognize this substance right here , each molecule has one oxygen atom and two hydrogen atoms , this is water and we have drawn all neat hydrogen bonds right ov... | before i even talk about breaking things free and these molecules turning into vapors entering their gas state , let 's just think about how that happens . when we talk about the temperature of a system , we 're really just talking about the average kinetic energy . each molecule , remember they 're all bouncing around... | how does the water loose kinetic energy ? |
so we have two different substances here and just for the sake of an argument , let 's assume that they are in their liquid state . well you probably already recognize this substance right here , each molecule has one oxygen atom and two hydrogen atoms , this is water and we have drawn all neat hydrogen bonds right ov... | i found slightly different numbers , depending on which resource i looked at but what i found for water , the heat of vaporization is 2260 joules per gram or instead of using joules , remember joules is a unit of energy it could be a unit of heat , instead of joules if you wan na think of it in terms of calories , that... | why does everything need to be confusing for figuring out for heat of vaporization of water and ethanal ? |
so we have two different substances here and just for the sake of an argument , let 's assume that they are in their liquid state . well you probably already recognize this substance right here , each molecule has one oxygen atom and two hydrogen atoms , this is water and we have drawn all neat hydrogen bonds right ov... | i found slightly different numbers , depending on which resource i looked at but what i found for water , the heat of vaporization is 2260 joules per gram or instead of using joules , remember joules is a unit of energy it could be a unit of heat , instead of joules if you wan na think of it in terms of calories , that... | i have a question in my mind , why the water evaporate , why does not it just move faster in every direction ? |
so we have two different substances here and just for the sake of an argument , let 's assume that they are in their liquid state . well you probably already recognize this substance right here , each molecule has one oxygen atom and two hydrogen atoms , this is water and we have drawn all neat hydrogen bonds right ov... | the heat of vaporization for ethanol -- let me make this clear this right over here is water , that 's for water . the same thing for ethanol . the heat of vaporization for ethanol is , based on what i looked up , is 841 joules per gram or if we wan na write them as calories , 201 calories per gram which means it would... | is ethanol a liquid or a solid ? |
so we have two different substances here and just for the sake of an argument , let 's assume that they are in their liquid state . well you probably already recognize this substance right here , each molecule has one oxygen atom and two hydrogen atoms , this is water and we have drawn all neat hydrogen bonds right ov... | in that case , it is going to turn into its gaseous state . the hydrogen bonds are gon na break apart , and it 's gon na be so far from any of its sibling molecules , i guess you could say , from the other ethanol molecules that it wo n't be able to form new hydrogen bonds . same thing with this one , once it vaporizes... | if we had a universe with only two molecules of water in it , and then we changed molecules positions to the others position , we would have a universe different from the original universe ? |
all right , we 're told that the arithmetic sequence a-sub-i is defined by the formula where the ith term in the sequence is going to be 4 plus 3 times i minus 1 . what is a-sub-20 ? and so a-sub-20 is the 20th term in the sequence and i encourage you to pause the video and figure out what is the 20th term ? well , we... | all right , we 're told that the arithmetic sequence a-sub-i is defined by the formula where the ith term in the sequence is going to be 4 plus 3 times i minus 1 . what is a-sub-20 ? | how do we transform from a recursive sequence to explicit ones and vice versa ? |
all right , we 're told that the arithmetic sequence a-sub-i is defined by the formula where the ith term in the sequence is going to be 4 plus 3 times i minus 1 . what is a-sub-20 ? and so a-sub-20 is the 20th term in the sequence and i encourage you to pause the video and figure out what is the 20th term ? well , we... | what is a-sub-20 ? and so a-sub-20 is the 20th term in the sequence and i encourage you to pause the video and figure out what is the 20th term ? well , we can just think about it like this . | is there a quicker way to find the nth term in the sequence ? |
all right , we 're told that the arithmetic sequence a-sub-i is defined by the formula where the ith term in the sequence is going to be 4 plus 3 times i minus 1 . what is a-sub-20 ? and so a-sub-20 is the 20th term in the sequence and i encourage you to pause the video and figure out what is the 20th term ? well , we... | well , we do n't know what a-sub-4 is just yet , so let 's try to figure that out . so we could say that a-sub-4 is equal to , well if we use the second line again , it 's going to be a-sub-3 , minus 2 . we still do n't know what a-sub-3 is . | for what purpose a recursive formula could be useful ? |
all right , we 're told that the arithmetic sequence a-sub-i is defined by the formula where the ith term in the sequence is going to be 4 plus 3 times i minus 1 . what is a-sub-20 ? and so a-sub-20 is the 20th term in the sequence and i encourage you to pause the video and figure out what is the 20th term ? well , we... | all right , we 're told that the arithmetic sequence a-sub-i is defined by the formula where the ith term in the sequence is going to be 4 plus 3 times i minus 1 . what is a-sub-20 ? | so what part of life does a sequence problem come into play ? |
all right , we 're told that the arithmetic sequence a-sub-i is defined by the formula where the ith term in the sequence is going to be 4 plus 3 times i minus 1 . what is a-sub-20 ? and so a-sub-20 is the 20th term in the sequence and i encourage you to pause the video and figure out what is the 20th term ? well , we... | i 'll keep switching colors 'cause it looks nice . a-sub-3 is going to be equal to a-sub-3 minus 1 , so a-sub-2 minus 2 . we still do n't know what a-sub-2 is , and so , we could write , a-sub-2 is equal to a-sub-2 minus 1 , so that 's a-sub-1 minus 2 . | what does `` sub i '' mean ? |
all right , we 're told that the arithmetic sequence a-sub-i is defined by the formula where the ith term in the sequence is going to be 4 plus 3 times i minus 1 . what is a-sub-20 ? and so a-sub-20 is the 20th term in the sequence and i encourage you to pause the video and figure out what is the 20th term ? well , we... | well , we can just think about it like this . a-sub-20 , we just use this definition of the ith term . everywhere we see an i , we would put a 20 in , so it 's going to be 4 plus 3 times 20 minus 1 , so once again , just to be clear , a-sub-20 , where instead of a-sub-i , wherever we saw an i , we put a 20 , and now we... | can you also replace the letters or do u always have to use ai ? |
all right , we 're told that the arithmetic sequence a-sub-i is defined by the formula where the ith term in the sequence is going to be 4 plus 3 times i minus 1 . what is a-sub-20 ? and so a-sub-20 is the 20th term in the sequence and i encourage you to pause the video and figure out what is the 20th term ? well , we... | a-sub-3 is going to be equal to a-sub-3 minus 1 , so a-sub-2 minus 2 . we still do n't know what a-sub-2 is , and so , we could write , a-sub-2 is equal to a-sub-2 minus 1 , so that 's a-sub-1 minus 2 . now , luckily we know what a-sub-1 is . | for a1= -7 a5= a4 - 2 could n't you just do -2 * 4 and then put in the equation a5 = a1 - 8 or does that just happen to be a coincidence in this problem ? |
all right , we 're told that the arithmetic sequence a-sub-i is defined by the formula where the ith term in the sequence is going to be 4 plus 3 times i minus 1 . what is a-sub-20 ? and so a-sub-20 is the 20th term in the sequence and i encourage you to pause the video and figure out what is the 20th term ? well , we... | let 's do another one of these . and here , they 've told us the arithmetic sequence a-sub-i is defined by the formula a-sub-1 , they gave us the first term , and they say , every other term , so a-sub-i , they 're defining it in terms of the previous terms , so a-sub-i is going to be a-sub-i minus 1 minus 2 , so this ... | does the sub always have to be an i , in arithmetic sequence symbol ? |
all right , we 're told that the arithmetic sequence a-sub-i is defined by the formula where the ith term in the sequence is going to be 4 plus 3 times i minus 1 . what is a-sub-20 ? and so a-sub-20 is the 20th term in the sequence and i encourage you to pause the video and figure out what is the 20th term ? well , we... | we still do n't know what a-sub-2 is , and so , we could write , a-sub-2 is equal to a-sub-2 minus 1 , so that 's a-sub-1 minus 2 . now , luckily we know what a-sub-1 is . a-sub-1 is negative 7 . a-sub-1 is negative 7 , so if this is negative 7 , then a-sub-2 is negative 7 minus 2 , which is equal to negative 9 . | in math , should the sequences start from 1 or from 0 like in programming , or there is no difference and i can use always 1 or 0 ? |
all right , we 're told that the arithmetic sequence a-sub-i is defined by the formula where the ith term in the sequence is going to be 4 plus 3 times i minus 1 . what is a-sub-20 ? and so a-sub-20 is the 20th term in the sequence and i encourage you to pause the video and figure out what is the 20th term ? well , we... | we still do n't know what a-sub-2 is , and so , we could write , a-sub-2 is equal to a-sub-2 minus 1 , so that 's a-sub-1 minus 2 . now , luckily we know what a-sub-1 is . a-sub-1 is negative 7 . | how do you know if the sequence is a recursive or explicit ? |
all right , we 're told that the arithmetic sequence a-sub-i is defined by the formula where the ith term in the sequence is going to be 4 plus 3 times i minus 1 . what is a-sub-20 ? and so a-sub-20 is the 20th term in the sequence and i encourage you to pause the video and figure out what is the 20th term ? well , we... | a-sub-1 is negative 7 . a-sub-1 is negative 7 , so if this is negative 7 , then a-sub-2 is negative 7 minus 2 , which is equal to negative 9 . well that starts helping us out because if a-sub-2 is negative 9 , if this is negative 9 , then a-sub-3 is negative 9 minus 2 , which is equal to negative 11 . | 7 , ca n't you just use the formula a1= -7 to find what a4 is ? |
all right , we 're told that the arithmetic sequence a-sub-i is defined by the formula where the ith term in the sequence is going to be 4 plus 3 times i minus 1 . what is a-sub-20 ? and so a-sub-20 is the 20th term in the sequence and i encourage you to pause the video and figure out what is the 20th term ? well , we... | i 'll keep switching colors 'cause it looks nice . a-sub-3 is going to be equal to a-sub-3 minus 1 , so a-sub-2 minus 2 . we still do n't know what a-sub-2 is , and so , we could write , a-sub-2 is equal to a-sub-2 minus 1 , so that 's a-sub-1 minus 2 . | what does `` a '' sub `` i '' mean ? |
i 'm going to draw for you two of the most important organs in our body . and actually , on the left and right side of our body , they pretty much look like that , like little kidney beans . and in fact , that 's what they are . they 're kidneys . and so we have some arteries , the renal arteries that flow into them . ... | and in fact , that 's what they are . they 're kidneys . and so we have some arteries , the renal arteries that flow into them . | i suppose that the waste removal is not the focus here , but a byproduct of the kidneys main focus which would be fluid balance in the body ? |
i 'm going to draw for you two of the most important organs in our body . and actually , on the left and right side of our body , they pretty much look like that , like little kidney beans . and in fact , that 's what they are . they 're kidneys . and so we have some arteries , the renal arteries that flow into them . ... | they 're kidneys . and so we have some arteries , the renal arteries that flow into them . and renal is just another word referring to kidneys , and we 've got renal veins with blood flowing back out of them . so once the blood is headed back to the heart , we call it a renal vein . and there are two of them . | are renal arteries carrying oxygenated blood ? |
i 'm going to draw for you two of the most important organs in our body . and actually , on the left and right side of our body , they pretty much look like that , like little kidney beans . and in fact , that 's what they are . they 're kidneys . and so we have some arteries , the renal arteries that flow into them . ... | and then it gets into kind of a long deep loop , long loop like that . and this loop is called the loop of henle . so you 're seeing now part three is loop of henle . | at 5min - the loop of henle - is there anything specific about the `` thick part '' of the loop of henle ? |
i 'm going to draw for you two of the most important organs in our body . and actually , on the left and right side of our body , they pretty much look like that , like little kidney beans . and in fact , that 's what they are . they 're kidneys . and so we have some arteries , the renal arteries that flow into them . ... | and that 's with all of the blood coming together . so this little network is considered -- this little network of capillaries , then , is considered , right here , the peritubular , going around the tubule , tubular capillaries . and that makes sense . | the capillaries in the nephron - are these `` fenestration '' capillaries ? |
i 'm going to draw for you two of the most important organs in our body . and actually , on the left and right side of our body , they pretty much look like that , like little kidney beans . and in fact , that 's what they are . they 're kidneys . and so we have some arteries , the renal arteries that flow into them . ... | i 'm going to draw for you two of the most important organs in our body . and actually , on the left and right side of our body , they pretty much look like that , like little kidney beans . and in fact , that 's what they are . | what do the tubules actually look like ? |
i 'm going to draw for you two of the most important organs in our body . and actually , on the left and right side of our body , they pretty much look like that , like little kidney beans . and in fact , that 's what they are . they 're kidneys . and so we have some arteries , the renal arteries that flow into them . ... | so that 's bowman 's capsule , and that 's the first part of the nephron . i 'll actually show you all the parts of the nephron . so the next part of the nephron -- and nephron just means kind of the unit of the kidney that we care about . the next part is looking really squiggly , very convoluted . | how much fluid can a nephron process in a minute ? |
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