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i want to figure out how blood gets from my heart , which i 'm going to draw here , all the way to my toe . and i 'm going to draw my foot over here and show you which toe i 'm talking about . let 's say this toe right here . now , to start the journey , it 's going to have to go out of the left ventricle and into the ... | there 's also another one over here called the superior vena cava , and this is bringing back blood from the arms and head . so these two veins , the superior vena cava and the inferior vena cava , are dragging the blood back to the heart . and generally speaking , these are all considered , of course , veins . | is the superior vena cava called as it is because it 's above the inferior vena cava , or is there any relevance to the size of the veins ? |
i want to figure out how blood gets from my heart , which i 'm going to draw here , all the way to my toe . and i 'm going to draw my foot over here and show you which toe i 'm talking about . let 's say this toe right here . now , to start the journey , it 's going to have to go out of the left ventricle and into the ... | so the arterial system we know is a high-pressure system . so this makes perfect sense that the first few arteries , those large arteries and even those medium-sized arteries , are going to be able to deal with the pressure really well . now , let me draw a little line here just to keep it straight . | so the arterioles are the branches arteries spread out to the other parts ? |
i want to figure out how blood gets from my heart , which i 'm going to draw here , all the way to my toe . and i 'm going to draw my foot over here and show you which toe i 'm talking about . let 's say this toe right here . now , to start the journey , it 's going to have to go out of the left ventricle and into the ... | so unlike the arterial side where it was all about large pressure , down here with the vein side , we have to think about large volumes . remember about 2/3 of your blood at any point in time is sitting in some vein or venule somewhere . | there are 3 pump of blood flow throughout the body 1.heart 2 ? |
i want to figure out how blood gets from my heart , which i 'm going to draw here , all the way to my toe . and i 'm going to draw my foot over here and show you which toe i 'm talking about . let 's say this toe right here . now , to start the journey , it 's going to have to go out of the left ventricle and into the ... | so unlike the arterial side where it was all about large pressure , down here with the vein side , we have to think about large volumes . remember about 2/3 of your blood at any point in time is sitting in some vein or venule somewhere . | 3. vein - valves dude to skeletal muscle contraction 2. i know it has due with the elastic arteries , due the systole , and diastole will please explain how that function works ? |
i want to figure out how blood gets from my heart , which i 'm going to draw here , all the way to my toe . and i 'm going to draw my foot over here and show you which toe i 'm talking about . let 's say this toe right here . now , to start the journey , it 's going to have to go out of the left ventricle and into the ... | they 're tightly wound , so you 're going to create like a little straw . and this process is called vasoconstriction . vaso just means blood vessel . | why would arterioles want to perform vasoconstriction ? |
i want to figure out how blood gets from my heart , which i 'm going to draw here , all the way to my toe . and i 'm going to draw my foot over here and show you which toe i 'm talking about . let 's say this toe right here . now , to start the journey , it 's going to have to go out of the left ventricle and into the ... | they 're tightly wound , so you 're going to create like a little straw . and this process is called vasoconstriction . vaso just means blood vessel . and constriction is kind of tightening down . | so vasoconstriction means bloodflow to that part is reduced ? |
i want to figure out how blood gets from my heart , which i 'm going to draw here , all the way to my toe . and i 'm going to draw my foot over here and show you which toe i 'm talking about . let 's say this toe right here . now , to start the journey , it 's going to have to go out of the left ventricle and into the ... | and that 's probably the easiest way to think about it . if you have a blood vessel , one of these large arteries , for example , and let 's say blood is under a lot of pressure because the heart is squeezing out a lot of high pressure blood , this artery is literally going to balloon out . and if you actually looked a... | if your blood is traveling at 120 unit of pressure and it gets to the arteriole would the arteriole contracting causing vasoconstriction increase that pressure even more and therefore increase how fast that blood is getting to there destination ? |
i want to figure out how blood gets from my heart , which i 'm going to draw here , all the way to my toe . and i 'm going to draw my foot over here and show you which toe i 'm talking about . let 's say this toe right here . now , to start the journey , it 's going to have to go out of the left ventricle and into the ... | i want to figure out how blood gets from my heart , which i 'm going to draw here , all the way to my toe . and i 'm going to draw my foot over here and show you which toe i 'm talking about . | what is the difference between arteriovenous anastomoses and venous anastomoses ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | well the amplitude is 2 you can view it as the absolute value of 2 well it 's common sense the amplitude here was 1 but now you 're swaying from that middle position twice as far because you 're multiplying by 2 now let 's go back to sin ( x ) and let 's change it in a different way let 's graph sin ( -x ) so now let m... | what is the difference between -2sin ( x ) and 2sin ( -x ) ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | but remember this negative is not completely ignored . it does n't change the period but it does change how the graph looks when you start getting increased x 's instead of sin being positive as it would be in the case of a traditional sine function here as x grows you 're taking the sine of -x you 're taking the sine ... | hi , i was just wondering if you are given what would generally appear to be a vertical shift but it is in parentheses what do you do ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | well the difference between the minimum value and the maximum value just increased by a factor of 2 the total difference is 4 , half of that difference is 2 so what is the amplitude here ? well the amplitude is 2 you can view it as the absolute value of 2 well it 's common sense the amplitude here was 1 but now you 're... | sin ( -x ) would also be flipping over the x axis as well , right ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | but remember this negative is not completely ignored . it does n't change the period but it does change how the graph looks when you start getting increased x 's instead of sin being positive as it would be in the case of a traditional sine function here as x grows you 're taking the sine of -x you 're taking the sine ... | does the period of a sine function change ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | who invented the unit circle definition ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | when sine is zero oh sorry , when x is zero , sin ( 0 ) is 0 ok , i 'll draw a little unit circle here for reference this is what i like to do in my head as i like to figure out the value of the trigonometric functions so this is x this is y draw unit circle and remember over here x is refering to the angle so that 's ... | use a vertical shift to graph one period of the function.y = 2 cos1/2x +1 ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | well we vary between 1 and -1 the total difference between the minimum and maximum is 2 half of that is 1 or another way of thinking about it is we vary 1 from our middle point so that was pretty straight forward let 's change it up a little bit now let 's graph y=2sin ( x ) so let me draw let me put my little axis the... | does having negative pi over 2 plus .25 times sine affect my vertical and if so how do i show that on a table ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | well the difference between the minimum value and the maximum value just increased by a factor of 2 the total difference is 4 , half of that difference is 2 so what is the amplitude here ? well the amplitude is 2 you can view it as the absolute value of 2 well it 's common sense the amplitude here was 1 but now you 're... | how come the peaks are flipped ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | well the difference between the minimum value and the maximum value just increased by a factor of 2 the total difference is 4 , half of that difference is 2 so what is the amplitude here ? well the amplitude is 2 you can view it as the absolute value of 2 well it 's common sense the amplitude here was 1 but now you 're... | i understand the unit circle and how you graphed the original y=sin ( x ) but what makes them flip ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | do the cosine and sin of all values on the unit circle flip when going in the negative direction ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | well the difference between the minimum value and the maximum value just increased by a factor of 2 the total difference is 4 , half of that difference is 2 so what is the amplitude here ? well the amplitude is 2 you can view it as the absolute value of 2 well it 's common sense the amplitude here was 1 but now you 're... | which is the co-ordinate for the midline and which is for minimum point and how to use x=0 ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | well we just have twice the amplitude we 're multiplying this one by 2 and so you get twice the amplitude and so the last thought or question i have for you is how does the period of 2sin ( -x ) how does that relate to the period of sin ( x ) well there 's 2 ways of thinking about it we could actually i 'll you think a... | what does period actual means ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | well the difference between the minimum value and the maximum value just increased by a factor of 2 the total difference is 4 , half of that difference is 2 so what is the amplitude here ? well the amplitude is 2 you can view it as the absolute value of 2 well it 's common sense the amplitude here was 1 but now you 're... | what will be y=sin ( 2x ) ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | well the amplitude is 2 you can view it as the absolute value of 2 well it 's common sense the amplitude here was 1 but now you 're swaying from that middle position twice as far because you 're multiplying by 2 now let 's go back to sin ( x ) and let 's change it in a different way let 's graph sin ( -x ) so now let m... | what is the period of 2sin ( x ) ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | well the difference between the minimum value and the maximum value just increased by a factor of 2 the total difference is 4 , half of that difference is 2 so what is the amplitude here ? well the amplitude is 2 you can view it as the absolute value of 2 well it 's common sense the amplitude here was 1 but now you 're... | : y = a sin bx : what is the formula to find b ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | well the difference between the minimum value and the maximum value just increased by a factor of 2 the total difference is 4 , half of that difference is 2 so what is the amplitude here ? well the amplitude is 2 you can view it as the absolute value of 2 well it 's common sense the amplitude here was 1 but now you 're... | so now i get how to graph the sin of x ... but how do i graph the cos of x ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | well we vary between 1 and -1 the total difference between the minimum and maximum is 2 half of that is 1 or another way of thinking about it is we vary 1 from our middle point so that was pretty straight forward let 's change it up a little bit now let 's graph y=2sin ( x ) so let me draw let me put my little axis the... | are the altitudes always located at the special values of x , such as pi , pi/2 , 2pi.. ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | well the difference between the minimum value and the maximum value just increased by a factor of 2 the total difference is 4 , half of that difference is 2 so what is the amplitude here ? well the amplitude is 2 you can view it as the absolute value of 2 well it 's common sense the amplitude here was 1 but now you 're... | like you would n't find the altitude at x=3.7 right ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | well the difference between the minimum value and the maximum value just increased by a factor of 2 the total difference is 4 , half of that difference is 2 so what is the amplitude here ? well the amplitude is 2 you can view it as the absolute value of 2 well it 's common sense the amplitude here was 1 but now you 're... | how do you determine the vertical and horizontal stretch or shrink of the sin function just by looking at the equation ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | well we vary between 1 and -1 the total difference between the minimum and maximum is 2 half of that is 1 or another way of thinking about it is we vary 1 from our middle point so that was pretty straight forward let 's change it up a little bit now let 's graph y=2sin ( x ) so let me draw let me put my little axis the... | how do you know the vertex is ( 0,0 ) ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | well the difference between the minimum value and the maximum value just increased by a factor of 2 the total difference is 4 , half of that difference is 2 so what is the amplitude here ? well the amplitude is 2 you can view it as the absolute value of 2 well it 's common sense the amplitude here was 1 but now you 're... | should n't we really think about it as sin ( -x ) being reflected about the origin since sin ( x ) is an odd function ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | well the difference between the minimum value and the maximum value just increased by a factor of 2 the total difference is 4 , half of that difference is 2 so what is the amplitude here ? well the amplitude is 2 you can view it as the absolute value of 2 well it 's common sense the amplitude here was 1 but now you 're... | what is the difference between sin ( x ) and sin ( theta ) ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | well the difference between the minimum value and the maximum value just increased by a factor of 2 the total difference is 4 , half of that difference is 2 so what is the amplitude here ? well the amplitude is 2 you can view it as the absolute value of 2 well it 's common sense the amplitude here was 1 but now you 're... | could n't it also have been reflected about the x-axis ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | well the difference between the minimum value and the maximum value just increased by a factor of 2 the total difference is 4 , half of that difference is 2 so what is the amplitude here ? well the amplitude is 2 you can view it as the absolute value of 2 well it 's common sense the amplitude here was 1 but now you 're... | do these graphs have any special name or are they just the conventional cartesian plane with the x-axis expressed in radians ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | well the difference between the minimum value and the maximum value just increased by a factor of 2 the total difference is 4 , half of that difference is 2 so what is the amplitude here ? well the amplitude is 2 you can view it as the absolute value of 2 well it 's common sense the amplitude here was 1 but now you 're... | what is the meaning of reflected vertically and reflected horizontally actually ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | well the difference between the minimum value and the maximum value just increased by a factor of 2 the total difference is 4 , half of that difference is 2 so what is the amplitude here ? well the amplitude is 2 you can view it as the absolute value of 2 well it 's common sense the amplitude here was 1 but now you 're... | ... when sal was finding the period of 2 sin ( -x ) , why did he add a -11 to the denominator of the equation ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | well the difference between the minimum value and the maximum value just increased by a factor of 2 the total difference is 4 , half of that difference is 2 so what is the amplitude here ? well the amplitude is 2 you can view it as the absolute value of 2 well it 's common sense the amplitude here was 1 but now you 're... | i thought the negative graphs were reflected over the x axis and not the y axis ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | well the difference between the minimum value and the maximum value just increased by a factor of 2 the total difference is 4 , half of that difference is 2 so what is the amplitude here ? well the amplitude is 2 you can view it as the absolute value of 2 well it 's common sense the amplitude here was 1 but now you 're... | when you translate sinx pi/2 to the left ( y = sin ( x+pi/2 ) ) , it equals cosx , and seems to be even ( it should be even , right , because it has the same x and y values as cosx , so it 's the same function ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | well we just have twice the amplitude we 're multiplying this one by 2 and so you get twice the amplitude and so the last thought or question i have for you is how does the period of 2sin ( -x ) how does that relate to the period of sin ( x ) well there 's 2 ways of thinking about it we could actually i 'll you think a... | is each `` half-period '' ( such as from zero to pi ) a semicircle ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | well the difference between the minimum value and the maximum value just increased by a factor of 2 the total difference is 4 , half of that difference is 2 so what is the amplitude here ? well the amplitude is 2 you can view it as the absolute value of 2 well it 's common sense the amplitude here was 1 but now you 're... | 0 , would n't flipping the graph over the x-axis work as well ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | well we vary between 1 and -1 the total difference between the minimum and maximum is 2 half of that is 1 or another way of thinking about it is we vary 1 from our middle point so that was pretty straight forward let 's change it up a little bit now let 's graph y=2sin ( x ) so let me draw let me put my little axis the... | here , in this video , how the sinx is graphed between 2 and -2 as we know that sin ( x ) lies between 1 and -1 ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | is horizontal shift and phase shift the same thing ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | what app did sal use to explain all of these maths ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | well the difference between the minimum value and the maximum value just increased by a factor of 2 the total difference is 4 , half of that difference is 2 so what is the amplitude here ? well the amplitude is 2 you can view it as the absolute value of 2 well it 's common sense the amplitude here was 1 but now you 're... | just asking , could you have used the identity sin ( -x ) = -sin ( x ) to not have to use the unit circle ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | well we vary between 1 and -1 the total difference between the minimum and maximum is 2 half of that is 1 or another way of thinking about it is we vary 1 from our middle point so that was pretty straight forward let 's change it up a little bit now let 's graph y=2sin ( x ) so let me draw let me put my little axis the... | in why is sine of pi , one ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | well we just have twice the amplitude we 're multiplying this one by 2 and so you get twice the amplitude and so the last thought or question i have for you is how does the period of 2sin ( -x ) how does that relate to the period of sin ( x ) well there 's 2 ways of thinking about it we could actually i 'll you think a... | how do i graph these as well as a unit circle on a ti89 ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | well the difference between the minimum value and the maximum value just increased by a factor of 2 the total difference is 4 , half of that difference is 2 so what is the amplitude here ? well the amplitude is 2 you can view it as the absolute value of 2 well it 's common sense the amplitude here was 1 but now you 're... | why does the graph get flipped over the y-axis when x is changed ? |
we 're asked to graph the function y = 2sin ( -x ) on the interval the closed interval so it includes the endpoints -2π to 2π so to do this i 'm going to graph the function y = sin ( x ) and then think about how it 's changed by the 2 and the negative in front of the x over here so let 's look at the sine of x first so... | well the period 's the same . but remember this negative is not completely ignored . it does n't change the period but it does change how the graph looks when you start getting increased x 's instead of sin being positive as it would be in the case of a traditional sine function here as x grows you 're taking the sine ... | why on adding horizontal shifts are towards negative axis ? |
- let 's see we have a zero order reaction where a turns into our products and when time is equal to zero we 're starting with our initial concentration of a and after some time period t , we would have the concentration of a at that time . so we could express the rate of our reaction , one way to do it would be to say... | so let me draw in some ammonia molecules in blue here in contact with our platinum surface . remember this is a zero order reaction . so the rate is equal to the rate constant times the concentration of ammonia to the zero power . | how do you know this equation is zero-order ? |
- let 's see we have a zero order reaction where a turns into our products and when time is equal to zero we 're starting with our initial concentration of a and after some time period t , we would have the concentration of a at that time . so we could express the rate of our reaction , one way to do it would be to say... | so let me draw in some ammonia molecules in blue here in contact with our platinum surface . remember this is a zero order reaction . so the rate is equal to the rate constant times the concentration of ammonia to the zero power . | how can a reaction have a zero order while the molecularity can never be zero ? |
- let 's see we have a zero order reaction where a turns into our products and when time is equal to zero we 're starting with our initial concentration of a and after some time period t , we would have the concentration of a at that time . so we could express the rate of our reaction , one way to do it would be to say... | they 're directly proportional . so if you increase the initial concentration of a , the half life should increase . so the half life should increase . | hello everyone i have a doubt ... in this video we 're told that the increase in concentration of a does n't affect the rate ... but wo n't it be false if the reaction occurs in a closed container as it would lead to a greater pressure and thus the compression of the gas and thus increase in it 's density ... .which wi... |
- let 's see we have a zero order reaction where a turns into our products and when time is equal to zero we 're starting with our initial concentration of a and after some time period t , we would have the concentration of a at that time . so we could express the rate of our reaction , one way to do it would be to say... | so let me draw in some ammonia molecules in blue here in contact with our platinum surface . remember this is a zero order reaction . so the rate is equal to the rate constant times the concentration of ammonia to the zero power . | please can you give some other examples for zero order ? |
- let 's see we have a zero order reaction where a turns into our products and when time is equal to zero we 're starting with our initial concentration of a and after some time period t , we would have the concentration of a at that time . so we could express the rate of our reaction , one way to do it would be to say... | and any number to the zero power is equal to one . therefore , the rate of the reaction would be equal to k times one or the rate is just equal to the rate constant k. so the rate of a zero order reaction is a constant . it 's independent of the concentration of a . | if k is always the same regardless of concentration , and rate = k , is k still the same over time as the reaction continues ? |
- let 's see we have a zero order reaction where a turns into our products and when time is equal to zero we 're starting with our initial concentration of a and after some time period t , we would have the concentration of a at that time . so we could express the rate of our reaction , one way to do it would be to say... | and this picture helps us understand that a little bit better . if you increase the concentration of ammonia , right , i 'm adding some more ammonia molecules in here . you 're not affecting the overall rate of the reaction because the ammonia molecules i just added are not in contact with our platinum surface . so onl... | we added more ammonia molecules but it did not affect the rate of reaction as the added molecules were not on ammonia surface.what if we added the extra molecules on the ammonia surface ? |
- let 's see we have a zero order reaction where a turns into our products and when time is equal to zero we 're starting with our initial concentration of a and after some time period t , we would have the concentration of a at that time . so we could express the rate of our reaction , one way to do it would be to say... | and so this is just another way to write our integrated rate law . so here 's the integrated rate law for a zero order reaction . and if we look at the form of that , it 's y is equal to mx plus b. y is equal is to mx plus b . | is the integrated rate law used always the same for zero order reactions ? |
- let 's see we have a zero order reaction where a turns into our products and when time is equal to zero we 're starting with our initial concentration of a and after some time period t , we would have the concentration of a at that time . so we could express the rate of our reaction , one way to do it would be to say... | so let me draw in some ammonia molecules in blue here in contact with our platinum surface . remember this is a zero order reaction . so the rate is equal to the rate constant times the concentration of ammonia to the zero power . | what is the half live of a zero order reaction ? |
let 's say that f of x is equal to x plus 7 to the third power , minus one . and let 's say that g of x g of x is equal to the cube root of x plus one the cube root of x plus one , minus seven . now , what i wan na do now is evaluate f of g of x i wan na evaluate f of g of x and i also wan na evaluate g of f of x g of... | so , g of f of x is going to be equal to , i 'll do it right over here , this is going to be equal to the cube root of actually , let me write it out , wherever i see an x , i can write f of x instead , i did n't do it that last time , i went directly and replaced with the definition of f of x but just to make it clear... | can someone explain to me why the cube root and 3 exponent got erased ? |
let 's say that f of x is equal to x plus 7 to the third power , minus one . and let 's say that g of x g of x is equal to the cube root of x plus one the cube root of x plus one , minus seven . now , what i wan na do now is evaluate f of g of x i wan na evaluate f of g of x and i also wan na evaluate g of f of x g of... | and the same thing is happening over here . if i put x into f of x ... i 'm sorry , if i put x into the function f , and i get f of x , the output is f of x , and then i input that into g , into the function g into the function g , once again i do this round-trip and i get back to x . | also , if , say you 're given f ( x ) and h ( x ) , and f ( h ( x ) ) simplifies to x , is it reasonably safe to assume that h ( f ( x ) ) will equal x too ? |
let 's say that f of x is equal to x plus 7 to the third power , minus one . and let 's say that g of x g of x is equal to the cube root of x plus one the cube root of x plus one , minus seven . now , what i wan na do now is evaluate f of g of x i wan na evaluate f of g of x and i also wan na evaluate g of f of x g of... | so , we see something very interesting . f of g of x is just x and g of f of x is x . so , in this case , if we start with an x if we start with an x , we input it into the function g and we get g of x we get g of x and then we input that into the function f , then we input that into the function f , f of g of x gets u... | if there is a function f where f ( x ) =2/ ( x-1 ) , and the inverse is function g where g ( x ) = ( 2+x ) /x , then a restriction on the domain in the function f would be that x can not equal 1 , and in the function g , x can not equal zero but function f can equal zero , and function g can equal 1 , so for the two fu... |
let 's say that f of x is equal to x plus 7 to the third power , minus one . and let 's say that g of x g of x is equal to the cube root of x plus one the cube root of x plus one , minus seven . now , what i wan na do now is evaluate f of g of x i wan na evaluate f of g of x and i also wan na evaluate g of f of x g of... | so , we see something very interesting . f of g of x is just x and g of f of x is x . so , in this case , if we start with an x if we start with an x , we input it into the function g and we get g of x we get g of x and then we input that into the function f , then we input that into the function f , f of g of x gets u... | 8 when sal replaces x with g ( x ) , how come g ( x ) does n't have to be in brackets ? |
let 's say that f of x is equal to x plus 7 to the third power , minus one . and let 's say that g of x g of x is equal to the cube root of x plus one the cube root of x plus one , minus seven . now , what i wan na do now is evaluate f of g of x i wan na evaluate f of g of x and i also wan na evaluate g of f of x g of... | so we kind of did a round-trip . and the same thing is happening over here . if i put x into f of x ... i 'm sorry , if i put x into the function f , and i get f of x , the output is f of x , and then i input that into g , into the function g into the function g , once again i do this round-trip and i get back to x . | i guess i thought things always have to go in brackets when substituting into x because you are substituting the whole thing into x and then performing operations on the whole thing ? |
in this video i want to talk about the system of jim crow segregation , which was common in the united states from about 1877 to approximately 1954 ; although , it goes a little bit further than that . now , you 're probably familiar with some of the aspects of jim crow segregation from the civil rights movement . jim... | a stock character is kind of a basic well-known character , in usually a comedy , and we still have stock characters in comedy today , in lots of different forms of entertainment ; think of , the absent-minded professor , or more recently , the manic-pixie-dream girl , the girl who is going to change your whole life by... | if one was a confederate , would not one be able to make the point that a proclamation of spain would not be binding in italy , for example ? |
in this video i want to talk about the system of jim crow segregation , which was common in the united states from about 1877 to approximately 1954 ; although , it goes a little bit further than that . now , you 're probably familiar with some of the aspects of jim crow segregation from the civil rights movement . jim... | alright , so that 's the origin of the name , but where did they system come from ? and for that we 're gon na have to do fairly deep dive into american history , and i wo n't be able to go into everything here but let 's kind of look at this from the thousand-foot view and get a sense of the overall pattern of slavery... | does anyone see the 2nd picture poster under the colored waiting line sign ? |
in this video i want to talk about the system of jim crow segregation , which was common in the united states from about 1877 to approximately 1954 ; although , it goes a little bit further than that . now , you 're probably familiar with some of the aspects of jim crow segregation from the civil rights movement . jim... | eventually it tore the country apart into the civil war . in 1863 , abraham lincoln , the president of the united states issued the emancipation proclamation , saying that all enslaved people , and the states which were currently in rebellion were now free . but it was n't until the end of the civil war that slavery 's... | why is it 1877 , would n't it start immediately after the states were readmitted ? |
in this video i want to talk about the system of jim crow segregation , which was common in the united states from about 1877 to approximately 1954 ; although , it goes a little bit further than that . now , you 're probably familiar with some of the aspects of jim crow segregation from the civil rights movement . jim... | and so the name , jim crow , became kind of synonymous with african american 's and with enslaved people in the early 19th century , the way that say patty became synonymous with an irish person . so , the term jim crow law , or the jim crow system means laws that were specifically aimed at african americans . alright ... | how much further does the jim crow segregation go ? |
in this video i want to talk about the system of jim crow segregation , which was common in the united states from about 1877 to approximately 1954 ; although , it goes a little bit further than that . now , you 're probably familiar with some of the aspects of jim crow segregation from the civil rights movement . jim... | so , this might be transportation , separate areas in trains and buses , or hotels , bathrooms , swimming pools , water fountains . so , these places in public life , where african americans were put in the place of a second-class citizenship . where they could not the full range of movement , job benefits , protection... | it says hitler 's love life revealed.when was this picture taken after or before the world wars ? |
in this video i want to talk about the system of jim crow segregation , which was common in the united states from about 1877 to approximately 1954 ; although , it goes a little bit further than that . now , you 're probably familiar with some of the aspects of jim crow segregation from the civil rights movement . jim... | eventually it tore the country apart into the civil war . in 1863 , abraham lincoln , the president of the united states issued the emancipation proclamation , saying that all enslaved people , and the states which were currently in rebellion were now free . but it was n't until the end of the civil war that slavery 's... | who was freed by the emancipation proclamation ? |
in this video i want to talk about the system of jim crow segregation , which was common in the united states from about 1877 to approximately 1954 ; although , it goes a little bit further than that . now , you 're probably familiar with some of the aspects of jim crow segregation from the civil rights movement . jim... | and during this period of jim crow this kind of segregation was legal , this was not just in practice , but encoded in the law . so , where did this system of jim crow come from ? well , let 's start with the name jim crow . jim crow was not the name of a specific person . | why not just let an african american be jim crow ? |
in this video i want to talk about the system of jim crow segregation , which was common in the united states from about 1877 to approximately 1954 ; although , it goes a little bit further than that . now , you 're probably familiar with some of the aspects of jim crow segregation from the civil rights movement . jim... | so , this character of jim crow was supposed to be kind of the stupid slave who lived on the plantation , and this character of jim crow was almost always played by a white man wearing black makeup on his face . so , it was not an actual african american person , but rather a caricature of an african american person by... | why not have a real african american play the `` character `` ? |
in this video i want to talk about the system of jim crow segregation , which was common in the united states from about 1877 to approximately 1954 ; although , it goes a little bit further than that . now , you 're probably familiar with some of the aspects of jim crow segregation from the civil rights movement . jim... | so , where did this system of jim crow come from ? well , let 's start with the name jim crow . jim crow was not the name of a specific person . | when did slavery start and how did it start ? |
in this video i want to talk about the system of jim crow segregation , which was common in the united states from about 1877 to approximately 1954 ; although , it goes a little bit further than that . now , you 're probably familiar with some of the aspects of jim crow segregation from the civil rights movement . jim... | and so the name , jim crow , became kind of synonymous with african american 's and with enslaved people in the early 19th century , the way that say patty became synonymous with an irish person . so , the term jim crow law , or the jim crow system means laws that were specifically aimed at african americans . alright ... | in the video when they were explaining jim crow , was the information about all the things they were naming what was all of the about ? |
in this video i want to talk about the system of jim crow segregation , which was common in the united states from about 1877 to approximately 1954 ; although , it goes a little bit further than that . now , you 're probably familiar with some of the aspects of jim crow segregation from the civil rights movement . jim... | but it was n't until the end of the civil war that slavery 's end was official everywhere in the united states . and the end of slavery really posed a problem for the states of the south . now obviously this was a wonderful thing for people who had been enslaved , now they had full freedom to move , and work , and marr... | why did the end of slavery pose a problem for the states of the south ? |
in this video i want to talk about the system of jim crow segregation , which was common in the united states from about 1877 to approximately 1954 ; although , it goes a little bit further than that . now , you 're probably familiar with some of the aspects of jim crow segregation from the civil rights movement . jim... | so , it was not an actual african american person , but rather a caricature of an african american person by a white man who was part of a minstrel troupe . and so the name , jim crow , became kind of synonymous with african american 's and with enslaved people in the early 19th century , the way that say patty became ... | when did segregation became illegal ? |
in this video i want to talk about the system of jim crow segregation , which was common in the united states from about 1877 to approximately 1954 ; although , it goes a little bit further than that . now , you 're probably familiar with some of the aspects of jim crow segregation from the civil rights movement . jim... | the first thing we have on here is the end of the civil war . now , before the civil war in the southern part of the united states , which i have outlined in red here , most of these states had legal slavery . and in these states , or the colonies that preceded them , starting about 1620 , they imported african slaves ... | in the map why are all the slave states in red but missouri red ? |
in this video i want to talk about the system of jim crow segregation , which was common in the united states from about 1877 to approximately 1954 ; although , it goes a little bit further than that . now , you 're probably familiar with some of the aspects of jim crow segregation from the civil rights movement . jim... | so , this character of jim crow was supposed to be kind of the stupid slave who lived on the plantation , and this character of jim crow was almost always played by a white man wearing black makeup on his face . so , it was not an actual african american person , but rather a caricature of an african american person by... | why did the african american community witness segregation after they were freed ? |
in this video i want to talk about the system of jim crow segregation , which was common in the united states from about 1877 to approximately 1954 ; although , it goes a little bit further than that . now , you 're probably familiar with some of the aspects of jim crow segregation from the civil rights movement . jim... | so , where did this system of jim crow come from ? well , let 's start with the name jim crow . jim crow was not the name of a specific person . actually , jim crow was the name of a stock character . a stock character is kind of a basic well-known character , in usually a comedy , and we still have stock characters in... | did the producers get the name `` crow '' from the bird because it is `` black '' ? |
in this video i want to talk about the system of jim crow segregation , which was common in the united states from about 1877 to approximately 1954 ; although , it goes a little bit further than that . now , you 're probably familiar with some of the aspects of jim crow segregation from the civil rights movement . jim... | in 1863 , abraham lincoln , the president of the united states issued the emancipation proclamation , saying that all enslaved people , and the states which were currently in rebellion were now free . but it was n't until the end of the civil war that slavery 's end was official everywhere in the united states . and th... | how did slavery rise up again if it was outlawed at the end of the civil war ? |
in this video i want to talk about the system of jim crow segregation , which was common in the united states from about 1877 to approximately 1954 ; although , it goes a little bit further than that . now , you 're probably familiar with some of the aspects of jim crow segregation from the civil rights movement . jim... | and so the name , jim crow , became kind of synonymous with african american 's and with enslaved people in the early 19th century , the way that say patty became synonymous with an irish person . so , the term jim crow law , or the jim crow system means laws that were specifically aimed at african americans . alright ... | furgeson a big part of jim crow ? |
in this video i want to talk about the system of jim crow segregation , which was common in the united states from about 1877 to approximately 1954 ; although , it goes a little bit further than that . now , you 're probably familiar with some of the aspects of jim crow segregation from the civil rights movement . jim... | a stock character is kind of a basic well-known character , in usually a comedy , and we still have stock characters in comedy today , in lots of different forms of entertainment ; think of , the absent-minded professor , or more recently , the manic-pixie-dream girl , the girl who is going to change your whole life by... | who were the characters in the minstrel show ? |
in this video i want to talk about the system of jim crow segregation , which was common in the united states from about 1877 to approximately 1954 ; although , it goes a little bit further than that . now , you 're probably familiar with some of the aspects of jim crow segregation from the civil rights movement . jim... | and so the name , jim crow , became kind of synonymous with african american 's and with enslaved people in the early 19th century , the way that say patty became synonymous with an irish person . so , the term jim crow law , or the jim crow system means laws that were specifically aimed at african americans . alright ... | what is the reason for only making the jim crow laws in the south ? |
in this video i want to talk about the system of jim crow segregation , which was common in the united states from about 1877 to approximately 1954 ; although , it goes a little bit further than that . now , you 're probably familiar with some of the aspects of jim crow segregation from the civil rights movement . jim... | in 1863 , abraham lincoln , the president of the united states issued the emancipation proclamation , saying that all enslaved people , and the states which were currently in rebellion were now free . but it was n't until the end of the civil war that slavery 's end was official everywhere in the united states . and th... | why did the end of slavery cause a problem for the southern states ? |
in this video i want to talk about the system of jim crow segregation , which was common in the united states from about 1877 to approximately 1954 ; although , it goes a little bit further than that . now , you 're probably familiar with some of the aspects of jim crow segregation from the civil rights movement . jim... | in this video i want to talk about the system of jim crow segregation , which was common in the united states from about 1877 to approximately 1954 ; although , it goes a little bit further than that . now , you 're probably familiar with some of the aspects of jim crow segregation from the civil rights movement . jim... | how long did it take segregation to completely stop ? |
in this video i want to talk about the system of jim crow segregation , which was common in the united states from about 1877 to approximately 1954 ; although , it goes a little bit further than that . now , you 're probably familiar with some of the aspects of jim crow segregation from the civil rights movement . jim... | eventually it tore the country apart into the civil war . in 1863 , abraham lincoln , the president of the united states issued the emancipation proclamation , saying that all enslaved people , and the states which were currently in rebellion were now free . but it was n't until the end of the civil war that slavery 's... | in what year did abraham lincoln issued the emancipation proclamation ? |
in this video i want to talk about the system of jim crow segregation , which was common in the united states from about 1877 to approximately 1954 ; although , it goes a little bit further than that . now , you 're probably familiar with some of the aspects of jim crow segregation from the civil rights movement . jim... | in this video i want to talk about the system of jim crow segregation , which was common in the united states from about 1877 to approximately 1954 ; although , it goes a little bit further than that . now , you 're probably familiar with some of the aspects of jim crow segregation from the civil rights movement . jim... | how long did it take segregation to completely stop ? |
so we have some tables here that give us what the functions f and g are when you give it certain inputs . so , when you input negative four , f of negative four is 29 . that 's going to be the output of that function . so we have that for both f and g , and what i want to do is evaluate two composite functions . i wan... | so this is going to be equal , this is equal to eight , and we 're done . and notice these are different values , because these are different composite functions . f of g of zero is 11 , and g of f of zero is eight . | what would the composition of functions apply to in the real world ? |
so we have some tables here that give us what the functions f and g are when you give it certain inputs . so , when you input negative four , f of negative four is 29 . that 's going to be the output of that function . so we have that for both f and g , and what i want to do is evaluate two composite functions . i wan... | so we 're now going to input five into our function f. we 're essentially going to evaluate f of five . so when you input five into our function . i 'm gon na do it in this brown color . | so , what is the process to complete the function with the criteria of `` 3 units up '' ? |
so we have some tables here that give us what the functions f and g are when you give it certain inputs . so , when you input negative four , f of negative four is 29 . that 's going to be the output of that function . so we have that for both f and g , and what i want to do is evaluate two composite functions . i wan... | when you input x equals five into f , you get the function f of five is equal to 11 . so this is going to be 11 . so , f of g of zero is equal to 11 . | what high school grade level ( grade 10/11/12 ? |
so we have some tables here that give us what the functions f and g are when you give it certain inputs . so , when you input negative four , f of negative four is 29 . that 's going to be the output of that function . so we have that for both f and g , and what i want to do is evaluate two composite functions . i wan... | i 'm gon na do it in this brown color . when you input x equals five into f , you get the function f of five is equal to 11 . so this is going to be 11 . | my question : when you speak of functions such as f ( x ) or g ( x ) and then define them as you do on the videos as , for example f ( x ) =9+x2 or g ( x ) +5x2 + 2x +1 , where do these equations come from ? |
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 . | so , if x^0 is 1 , then is 0^0 also 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... | ( so let me write this down in the appropriate colors . ) so 2 to the 3rd power . ( 2^3 . ) | i 'm very confused , considering the fact that 0*0 is 0 , thus 0 to the 0th power would be 0 , right ? |
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 far can the exponent go ? |
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 . | do you do anything different if an exponent is negitive ? |
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 . | will it be a ^ ( b ^ c ) or ( a ^ b ) ^ c ? |
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 . | could zero be 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... | 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 . ' | does the symbol * mean multiplication ? |
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 . | can you have 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 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 do you calculate 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 . | um ... can an exponent be placed after a number that goes on forever ? |
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 powers be used with 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 2 to the 3rd power . ( 2^3 . ) so you might be tempted to say , `` hey , maybe this is 2 × 3 , which would be 6 . '' | okay so , n^2 is square , n^3 is cube , n^4 is hypercube ? |
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 . | i do n't understand how to find the area of the hypercube ... what's the correct intuition ? |
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 . | can an exponent be a number with an exponent ? |
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