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( jazzy piano music ) : we 're just north of the center of rome looking at zaha hadid 's relatively new building , the maxxi museum , devoted to 21st century art . as we approached the museum we walked by military barracks and we just begin to spot the concrete facade of the museum resting gently on the older building... | : what does it mean to design a museum in the 21st century ? if you think about the history of museums , they 're generally palaces that have been re-purposed . for example , the leuven , paris which was the royal residence of the king fo france or here in rome , the vatican museum is the papal palace . | i do n't think we have museums in the us that are in converted palaces do we ? |
( jazzy piano music ) : we 're just north of the center of rome looking at zaha hadid 's relatively new building , the maxxi museum , devoted to 21st century art . as we approached the museum we walked by military barracks and we just begin to spot the concrete facade of the museum resting gently on the older building... | of course , a delta is a river that forks and flows into the sea . : what does it mean to design a museum in the 21st century ? if you think about the history of museums , they 're generally palaces that have been re-purposed . | ok , goofy question : so does `` xxi century arts '' mean `` 21st century arts '' or `` 21 century arts '' ? |
( jazzy piano music ) : we 're just north of the center of rome looking at zaha hadid 's relatively new building , the maxxi museum , devoted to 21st century art . as we approached the museum we walked by military barracks and we just begin to spot the concrete facade of the museum resting gently on the older building... | : the fact that it feels like it 's landed suggest weightlessness despite the fact that it is an almost unbroken slab of concrete and that 's in part because of the shadow created by the overhang of that concrete reminiscent of the international style and the work of people like le corbusier or mies van der rohe . : ... | is there an implied `` st '' when using roman numerals ? |
( jazzy piano music ) : we 're just north of the center of rome looking at zaha hadid 's relatively new building , the maxxi museum , devoted to 21st century art . as we approached the museum we walked by military barracks and we just begin to spot the concrete facade of the museum resting gently on the older building... | ( jazzy piano music ) : we 're just north of the center of rome looking at zaha hadid 's relatively new building , the maxxi museum , devoted to 21st century art . as we approached the museum we walked by military barracks and we just begin to spot the concrete facade of the museum resting gently on the older building... | do any urban planners and architects pay any attention to popular public opinion and their concerns ? |
( jazzy piano music ) : we 're just north of the center of rome looking at zaha hadid 's relatively new building , the maxxi museum , devoted to 21st century art . as we approached the museum we walked by military barracks and we just begin to spot the concrete facade of the museum resting gently on the older building... | this was one of the most inventive and theoretically important architectural firms in the 1970s and 1980s . : hadid is clearly drawing inspiration from modernism , from constructivism , from the work of the great russian painters of the early 20th century like malevich , embodying early 20th century utopianism about t... | why does authors of this video decided that malevich was russian artist ? |
what i 'd like to do in this video is talk about the notion of a frame of reference and this is an introductory video . in future videos , we 'll go into a lot more depth , but a frame of reference is really the idea it 's a point of view from which you are measuring things and as we 'll see , many of the quantities t... | you can view it for this introductory video as a point of view from which you 're making your measurements . now , it 's tempting for a lot of folks to say well there must be one correct frame of reference and a lot of times in our everyday world you might say well this , maybe this is the correct frame of reference an... | sal says that all these frames of reference are equally valid , but the ground has got to be stationary , right ? |
what i 'd like to do in this video is talk about the notion of a frame of reference and this is an introductory video . in future videos , we 'll go into a lot more depth , but a frame of reference is really the idea it 's a point of view from which you are measuring things and as we 'll see , many of the quantities t... | there 's the first one , this is the second one , and this is the third one . so in this first frame of reference , this first scenario , we 're gon na talk about the frame of reference of the ground . so if you are a stationary observer on the ground , so you could imagine this is you here and you 're the person doing... | can one particular frame of reference contain the same information as any other frame of reference ? |
what i 'd like to do in this video is talk about the notion of a frame of reference and this is an introductory video . in future videos , we 'll go into a lot more depth , but a frame of reference is really the idea it 's a point of view from which you are measuring things and as we 'll see , many of the quantities t... | so this gives you an appreciation for what frames of references are . you can view it for this introductory video as a point of view from which you 're making your measurements . now , it 's tempting for a lot of folks to say well there must be one correct frame of reference and a lot of times in our everyday world you... | so i notice sal says we are taking the view point of this big giant thing called earth when really the earth is spinning on a axis but we never see it , how does that work ? |
what i 'd like to do in this video is talk about the notion of a frame of reference and this is an introductory video . in future videos , we 'll go into a lot more depth , but a frame of reference is really the idea it 's a point of view from which you are measuring things and as we 'll see , many of the quantities t... | well , the plane not only would it look like it 's moving to the right at 250 meters per second , not only would it be just that 250 meters per second , but relative to you it 'd look like it 's going even faster 'cause you 're going past it , you are going to the left from the stationary , from the ground 's point of ... | the earth itself as a whole spins around 1042 miles per hours so why does the ground not take on an additional 250 or 50 ? |
what i 'd like to do in this video is talk about the notion of a frame of reference and this is an introductory video . in future videos , we 'll go into a lot more depth , but a frame of reference is really the idea it 's a point of view from which you are measuring things and as we 'll see , many of the quantities t... | well in this frame of reference , let 's say you 're sitting in this car and i do n't recommend you doing this while driving , let 's say someone else is driving or it 's an autonomous vehicle of some kind and you take out your physics instruments with the stopwatch and you see what the displacement is of the ground an... | if there is a strong wind blowing , and the leaves and branches of the tree are moving but the trunk of the tree is still , so the tree would be in the state of rest or in the state of motion ? |
what i 'd like to do in this video is talk about the notion of a frame of reference and this is an introductory video . in future videos , we 'll go into a lot more depth , but a frame of reference is really the idea it 's a point of view from which you are measuring things and as we 'll see , many of the quantities t... | you can view it for this introductory video as a point of view from which you 're making your measurements . now , it 's tempting for a lot of folks to say well there must be one correct frame of reference and a lot of times in our everyday world you might say well this , maybe this is the correct frame of reference an... | can someone please explain to me in depth about what are inertial and non inertial reference frames ? |
what i 'd like to do in this video is talk about the notion of a frame of reference and this is an introductory video . in future videos , we 'll go into a lot more depth , but a frame of reference is really the idea it 's a point of view from which you are measuring things and as we 'll see , many of the quantities t... | it would look like it 's moving behind you or in this case , the way we 're looking at it , to the right at 50 meters per second . now , what would the plane look like ? well , the plane not only would it look like it 's moving to the right at 250 meters per second , not only would it be just that 250 meters per second... | if so , what would be my velocity with respect to jupiter or the supermassive black hole at the center of our galaxy or what would be my velocity with respect to andromeda galaxy ? |
what i 'd like to do in this video is talk about the notion of a frame of reference and this is an introductory video . in future videos , we 'll go into a lot more depth , but a frame of reference is really the idea it 's a point of view from which you are measuring things and as we 'll see , many of the quantities t... | so this should be 1/5 of that length . so let me draw a little bit . so let 's say this is moving to the left at 50 meters per second . | did sal draw the arrow wrongly ? |
what i 'd like to do in this video is talk about the notion of a frame of reference and this is an introductory video . in future videos , we 'll go into a lot more depth , but a frame of reference is really the idea it 's a point of view from which you are measuring things and as we 'll see , many of the quantities t... | there 's the first one , this is the second one , and this is the third one . so in this first frame of reference , this first scenario , we 're gon na talk about the frame of reference of the ground . so if you are a stationary observer on the ground , so you could imagine this is you here and you 're the person doing... | is a reference force the same as a reference point ? |
what i 'd like to do in this video is talk about the notion of a frame of reference and this is an introductory video . in future videos , we 'll go into a lot more depth , but a frame of reference is really the idea it 's a point of view from which you are measuring things and as we 'll see , many of the quantities t... | so if you are a stationary observer on the ground , so you could imagine this is you here and you 're the person doing the measuring of let 's say we want to measure velocities . so from your point of view , since you 're stationary relative to the ground , what does the ground 's velocity look like ? well , you and th... | 2 , how is the car stationary , but the ground is moving ? |
what i 'd like to do in this video is talk about the notion of a frame of reference and this is an introductory video . in future videos , we 'll go into a lot more depth , but a frame of reference is really the idea it 's a point of view from which you are measuring things and as we 'll see , many of the quantities t... | so if you are a stationary observer on the ground , so you could imagine this is you here and you 're the person doing the measuring of let 's say we want to measure velocities . so from your point of view , since you 're stationary relative to the ground , what does the ground 's velocity look like ? well , you and th... | in the 3 case.. why would the car move at a velocity of 300 and ground move at a velocity of 250 ? |
what i 'd like to do in this video is talk about the notion of a frame of reference and this is an introductory video . in future videos , we 'll go into a lot more depth , but a frame of reference is really the idea it 's a point of view from which you are measuring things and as we 'll see , many of the quantities t... | what if we 're talking about the plane 's frame of reference ? why do n't you pause this video and think about what the velocities would be of the plane , the car , and the ground from the plane 's point of view . all right , now let 's work through this together . | the velocities are assuming that there is no diplacement from the earth to the plane , or car , correct ? |
what i 'd like to do in this video is talk about the notion of a frame of reference and this is an introductory video . in future videos , we 'll go into a lot more depth , but a frame of reference is really the idea it 's a point of view from which you are measuring things and as we 'll see , many of the quantities t... | now , what about from the point of view of the plane ? what if we 're talking about the plane 's frame of reference ? why do n't you pause this video and think about what the velocities would be of the plane , the car , and the ground from the plane 's point of view . | when we take the plane to be a frame of reference , the earth is already moving on its own at 460 m/s along the equator region , so is it not necessary to add up the same along with the 300 m/s towards left considering that the earth is rotating from right to left ? |
what i 'd like to do in this video is talk about the notion of a frame of reference and this is an introductory video . in future videos , we 'll go into a lot more depth , but a frame of reference is really the idea it 's a point of view from which you are measuring things and as we 'll see , many of the quantities t... | so the plane , to you , is gon na look like it 's going 250 plus 50 meters per second . so the vector would look like this and so it would look like it 's going to the right at 300 , let me write that in that orange color , at 300 meters per second . now , what about from the point of view of the plane ? | why does vector have no location information ? |
what i 'd like to do in this video is talk about the notion of a frame of reference and this is an introductory video . in future videos , we 'll go into a lot more depth , but a frame of reference is really the idea it 's a point of view from which you are measuring things and as we 'll see , many of the quantities t... | there 's the first one , this is the second one , and this is the third one . so in this first frame of reference , this first scenario , we 're gon na talk about the frame of reference of the ground . so if you are a stationary observer on the ground , so you could imagine this is you here and you 're the person doing... | can anyone tell me the definition of a reference frame ? |
what i 'd like to do in this video is talk about the notion of a frame of reference and this is an introductory video . in future videos , we 'll go into a lot more depth , but a frame of reference is really the idea it 's a point of view from which you are measuring things and as we 'll see , many of the quantities t... | so if you are a stationary observer on the ground , so you could imagine this is you here and you 're the person doing the measuring of let 's say we want to measure velocities . so from your point of view , since you 're stationary relative to the ground , what does the ground 's velocity look like ? well , you and th... | so if all points of views are valid why do we mostly go with the ground point of view ? |
what i 'd like to do in this video is talk about the notion of a frame of reference and this is an introductory video . in future videos , we 'll go into a lot more depth , but a frame of reference is really the idea it 's a point of view from which you are measuring things and as we 'll see , many of the quantities t... | you might be able to go outside next to the highway and see , well 50 meters per second would be quite fast , but anyway , you could observe this type of thing happening and it seems completely reasonably . but what if we were to change our frame of reference , change the point of view from which we are measuring thing... | how many coordinates change during linear motion ? |
what i 'd like to do in this video is talk about the notion of a frame of reference and this is an introductory video . in future videos , we 'll go into a lot more depth , but a frame of reference is really the idea it 's a point of view from which you are measuring things and as we 'll see , many of the quantities t... | it 's going to be moving to the left 50 meters per second faster than the ground is . so the car is gon na look not like it 's just going 50 meters per second , it 's gon na look like it 's going 50 meters plus another 250 meters per second for a total of 300 meters per second to the left . so this gives you an appreci... | however , i was just wondering what would happen if you had an object move at 299,792,457 meters/second ( 1 meter/second less than the speed of light ) , and you moved passed that object in the opposite direction at 2 meters/second ? |
what i 'd like to do in this video is talk about the notion of a frame of reference and this is an introductory video . in future videos , we 'll go into a lot more depth , but a frame of reference is really the idea it 's a point of view from which you are measuring things and as we 'll see , many of the quantities t... | so if you are a stationary observer on the ground , so you could imagine this is you here and you 're the person doing the measuring of let 's say we want to measure velocities . so from your point of view , since you 're stationary relative to the ground , what does the ground 's velocity look like ? well , you and th... | from your point of reference , would the object be traveling ftl ( faster than light ) , and relative to you , does that mean it is traveling ftl ? |
what i 'd like to do in this video is talk about the notion of a frame of reference and this is an introductory video . in future videos , we 'll go into a lot more depth , but a frame of reference is really the idea it 's a point of view from which you are measuring things and as we 'll see , many of the quantities t... | so , at 250 meters per second to the left . and the car , well it 's moving to the left even faster . it 's going to be moving to the left 50 meters per second faster than the ground is . | how is the street moving when the car is stationary ? |
what i 'd like to do in this video is talk about the notion of a frame of reference and this is an introductory video . in future videos , we 'll go into a lot more depth , but a frame of reference is really the idea it 's a point of view from which you are measuring things and as we 'll see , many of the quantities t... | well in this frame of reference , let 's say you 're sitting in this car and i do n't recommend you doing this while driving , let 's say someone else is driving or it 's an autonomous vehicle of some kind and you take out your physics instruments with the stopwatch and you see what the displacement is of the ground an... | does the earth move too slow to be measured in sal 's example ? |
what i 'd like to do in this video is talk about the notion of a frame of reference and this is an introductory video . in future videos , we 'll go into a lot more depth , but a frame of reference is really the idea it 's a point of view from which you are measuring things and as we 'll see , many of the quantities t... | well , the plane not only would it look like it 's moving to the right at 250 meters per second , not only would it be just that 250 meters per second , but relative to you it 'd look like it 's going even faster 'cause you 're going past it , you are going to the left from the stationary , from the ground 's point of ... | why did sal add the 50 m/s onto the 250 m/s instead of another order of operations ? |
what i 'd like to do in this video is talk about the notion of a frame of reference and this is an introductory video . in future videos , we 'll go into a lot more depth , but a frame of reference is really the idea it 's a point of view from which you are measuring things and as we 'll see , many of the quantities t... | so if you are a stationary observer on the ground , so you could imagine this is you here and you 're the person doing the measuring of let 's say we want to measure velocities . so from your point of view , since you 're stationary relative to the ground , what does the ground 's velocity look like ? well , you and th... | how is a vector related to velocity ? |
what i 'd like to do in this video is talk about the notion of a frame of reference and this is an introductory video . in future videos , we 'll go into a lot more depth , but a frame of reference is really the idea it 's a point of view from which you are measuring things and as we 'll see , many of the quantities t... | so if you are a stationary observer on the ground , so you could imagine this is you here and you 're the person doing the measuring of let 's say we want to measure velocities . so from your point of view , since you 're stationary relative to the ground , what does the ground 's velocity look like ? well , you and th... | how do i calculate the velocity of the approaching rain ( at an angle ) while i observe the motion of the rain from the window ? |
what i 'd like to do in this video is talk about the notion of a frame of reference and this is an introductory video . in future videos , we 'll go into a lot more depth , but a frame of reference is really the idea it 's a point of view from which you are measuring things and as we 'll see , many of the quantities t... | and the car , well it 's moving to the left even faster . it 's going to be moving to the left 50 meters per second faster than the ground is . so the car is gon na look not like it 's just going 50 meters per second , it 's gon na look like it 's going 50 meters plus another 250 meters per second for a total of 300 me... | how could you add the meters per second the car is moving to the meters per second that you think the ground is moving , when the car is moving on the ground ? |
what i 'd like to do in this video is talk about the notion of a frame of reference and this is an introductory video . in future videos , we 'll go into a lot more depth , but a frame of reference is really the idea it 's a point of view from which you are measuring things and as we 'll see , many of the quantities t... | so in this first frame of reference , this first scenario , we 're gon na talk about the frame of reference of the ground . so if you are a stationary observer on the ground , so you could imagine this is you here and you 're the person doing the measuring of let 's say we want to measure velocities . so from your poin... | can the magnitude of a person 's displacement be equal to the distance be traveled ? |
what i 'd like to do in this video is talk about the notion of a frame of reference and this is an introductory video . in future videos , we 'll go into a lot more depth , but a frame of reference is really the idea it 's a point of view from which you are measuring things and as we 'll see , many of the quantities t... | so if you are a stationary observer on the ground , so you could imagine this is you here and you 're the person doing the measuring of let 's say we want to measure velocities . so from your point of view , since you 're stationary relative to the ground , what does the ground 's velocity look like ? well , you and th... | is the velocity more useful than the speed ? |
what i 'd like to do in this video is talk about the notion of a frame of reference and this is an introductory video . in future videos , we 'll go into a lot more depth , but a frame of reference is really the idea it 's a point of view from which you are measuring things and as we 'll see , many of the quantities t... | so from the plane 's point of view , you feel like , or from your point of view in the plane , it feels like the plane is stationary . now the ground , however , looks like it 's moving quite quickly . it 'll look like it 's moving past you at 250 meters per second . | sal says you would feel like the ground is moving although the car is stationary ? |
male : you might be wondering why the exchange would be willing to take on the counter party risk for people trained , exchanging these kinds of standardized futures contract . the first reason is that the exchange actually stands to make a lot of money . what he can do is tell these people who wan na buy apples in th... | male : you might be wondering why the exchange would be willing to take on the counter party risk for people trained , exchanging these kinds of standardized futures contract . the first reason is that the exchange actually stands to make a lot of money . | so the exchange dude is basically ripping off the buyers of his futures contract ? |
male : you might be wondering why the exchange would be willing to take on the counter party risk for people trained , exchanging these kinds of standardized futures contract . the first reason is that the exchange actually stands to make a lot of money . what he can do is tell these people who wan na buy apples in th... | the first reason is that the exchange actually stands to make a lot of money . what he can do is tell these people who wan na buy apples in the future , he could say for example , `` hey , you can enter into a futures contract `` with a settlement price of 22 cents per pound . '' so that 's what they 're going to have ... | okay why would any farmer not directly enter into a contract with the customer so as to get a higher price ? |
male : you might be wondering why the exchange would be willing to take on the counter party risk for people trained , exchanging these kinds of standardized futures contract . the first reason is that the exchange actually stands to make a lot of money . what he can do is tell these people who wan na buy apples in th... | male : you might be wondering why the exchange would be willing to take on the counter party risk for people trained , exchanging these kinds of standardized futures contract . the first reason is that the exchange actually stands to make a lot of money . what he can do is tell these people who wan na buy apples in th... | why would anyone go to the exchange if they know that they can get a higher price on otc 's ? |
male : you might be wondering why the exchange would be willing to take on the counter party risk for people trained , exchanging these kinds of standardized futures contract . the first reason is that the exchange actually stands to make a lot of money . what he can do is tell these people who wan na buy apples in th... | the first reason is that the exchange actually stands to make a lot of money . what he can do is tell these people who wan na buy apples in the future , he could say for example , `` hey , you can enter into a futures contract `` with a settlement price of 22 cents per pound . '' so that 's what they 're going to have ... | does the exchange sell future 's contract to the apple farmers and tell them the settlement price is $ 0.20/lb and tells the people who want to buy the apples that the settlement price will be $ 0.22/lb ? |
male : you might be wondering why the exchange would be willing to take on the counter party risk for people trained , exchanging these kinds of standardized futures contract . the first reason is that the exchange actually stands to make a lot of money . what he can do is tell these people who wan na buy apples in th... | if these guys are going to pay 22 cents for the apples and then as the exchange , this guy only has to give 20 cents to the farmers , he 's going to make 2 cents profit . on futures contracts , on 1,000 pounds of apples that 's going to be $ 20 for each of those contracts . that 's going to be $ 20 per contract and he ... | standardized contracts are created to protect farmers and chains from future unpredictability , while margins are created to protect the third party from losses , am i making sense ? |
male : you might be wondering why the exchange would be willing to take on the counter party risk for people trained , exchanging these kinds of standardized futures contract . the first reason is that the exchange actually stands to make a lot of money . what he can do is tell these people who wan na buy apples in th... | male : you might be wondering why the exchange would be willing to take on the counter party risk for people trained , exchanging these kinds of standardized futures contract . the first reason is that the exchange actually stands to make a lot of money . | how to value an option contract ? |
male : you might be wondering why the exchange would be willing to take on the counter party risk for people trained , exchanging these kinds of standardized futures contract . the first reason is that the exchange actually stands to make a lot of money . what he can do is tell these people who wan na buy apples in th... | male : you might be wondering why the exchange would be willing to take on the counter party risk for people trained , exchanging these kinds of standardized futures contract . the first reason is that the exchange actually stands to make a lot of money . what he can do is tell these people who wan na buy apples in th... | so is the exchange in change of funding any default ? |
male : you might be wondering why the exchange would be willing to take on the counter party risk for people trained , exchanging these kinds of standardized futures contract . the first reason is that the exchange actually stands to make a lot of money . what he can do is tell these people who wan na buy apples in th... | male : you might be wondering why the exchange would be willing to take on the counter party risk for people trained , exchanging these kinds of standardized futures contract . the first reason is that the exchange actually stands to make a lot of money . what he can do is tell these people who wan na buy apples in th... | did n't have the $ $ $ to fulfill his contract ) , does the exchange need to have that capital to purchase ( at the same price ) from the farmer ? |
male : you might be wondering why the exchange would be willing to take on the counter party risk for people trained , exchanging these kinds of standardized futures contract . the first reason is that the exchange actually stands to make a lot of money . what he can do is tell these people who wan na buy apples in th... | so that 's what they 're going to have to come to the table with . that is 22 cents per pound and he could tell the people who are gon na deliver the apples that when you deliver the apples , the settlement price is 20 cents per pound . essentially , when the settlement occurs , he 's going to be able to make a 2 cent ... | does the exchange then try to sell the apples to a different customer ? |
male : you might be wondering why the exchange would be willing to take on the counter party risk for people trained , exchanging these kinds of standardized futures contract . the first reason is that the exchange actually stands to make a lot of money . what he can do is tell these people who wan na buy apples in th... | so that 's what they 're going to have to come to the table with . that is 22 cents per pound and he could tell the people who are gon na deliver the apples that when you deliver the apples , the settlement price is 20 cents per pound . essentially , when the settlement occurs , he 's going to be able to make a 2 cent ... | when exactly does the customer pay the exchange the $ 0.22 per pound , and when does the farmer get his $ 0.2 per pound ? |
male : you might be wondering why the exchange would be willing to take on the counter party risk for people trained , exchanging these kinds of standardized futures contract . the first reason is that the exchange actually stands to make a lot of money . what he can do is tell these people who wan na buy apples in th... | that 's going to be $ 20 per contract and he 's going to be doing this night and day , trading with all of the different farmers and all of the different customers and even some speculators who might wan na do this . so maybe if the spread , if we kind of can maintain this 2 cents spread , he 'll keep making $ 20 every... | why the exchange keep margin equal to amount by contract move in a given day rather than extended period such a week or month ? |
male : you might be wondering why the exchange would be willing to take on the counter party risk for people trained , exchanging these kinds of standardized futures contract . the first reason is that the exchange actually stands to make a lot of money . what he can do is tell these people who wan na buy apples in th... | male : you might be wondering why the exchange would be willing to take on the counter party risk for people trained , exchanging these kinds of standardized futures contract . the first reason is that the exchange actually stands to make a lot of money . | why people would agree for two different contracts instead of a single contract between farmer & customer at a single specified price ? |
male : you might be wondering why the exchange would be willing to take on the counter party risk for people trained , exchanging these kinds of standardized futures contract . the first reason is that the exchange actually stands to make a lot of money . what he can do is tell these people who wan na buy apples in th... | if these guys are going to pay 22 cents for the apples and then as the exchange , this guy only has to give 20 cents to the farmers , he 's going to make 2 cents profit . on futures contracts , on 1,000 pounds of apples that 's going to be $ 20 for each of those contracts . that 's going to be $ 20 per contract and he ... | what is the purpose of stock market futures ? |
male : you might be wondering why the exchange would be willing to take on the counter party risk for people trained , exchanging these kinds of standardized futures contract . the first reason is that the exchange actually stands to make a lot of money . what he can do is tell these people who wan na buy apples in th... | the first reason is that the exchange actually stands to make a lot of money . what he can do is tell these people who wan na buy apples in the future , he could say for example , `` hey , you can enter into a futures contract `` with a settlement price of 22 cents per pound . '' so that 's what they 're going to have ... | is the settlement price a close concept to the option premium ? |
male : you might be wondering why the exchange would be willing to take on the counter party risk for people trained , exchanging these kinds of standardized futures contract . the first reason is that the exchange actually stands to make a lot of money . what he can do is tell these people who wan na buy apples in th... | male : you might be wondering why the exchange would be willing to take on the counter party risk for people trained , exchanging these kinds of standardized futures contract . the first reason is that the exchange actually stands to make a lot of money . what he can do is tell these people who wan na buy apples in th... | how to make forward contract in hydro-power project on power purchase agreement ? |
male : you might be wondering why the exchange would be willing to take on the counter party risk for people trained , exchanging these kinds of standardized futures contract . the first reason is that the exchange actually stands to make a lot of money . what he can do is tell these people who wan na buy apples in th... | male : you might be wondering why the exchange would be willing to take on the counter party risk for people trained , exchanging these kinds of standardized futures contract . the first reason is that the exchange actually stands to make a lot of money . what he can do is tell these people who wan na buy apples in th... | how can the exchange simply manipulate the settlement price like that ? |
male : you might be wondering why the exchange would be willing to take on the counter party risk for people trained , exchanging these kinds of standardized futures contract . the first reason is that the exchange actually stands to make a lot of money . what he can do is tell these people who wan na buy apples in th... | the first reason is that the exchange actually stands to make a lot of money . what he can do is tell these people who wan na buy apples in the future , he could say for example , `` hey , you can enter into a futures contract `` with a settlement price of 22 cents per pound . '' so that 's what they 're going to have ... | what is the difference between the future price and the asset price ? |
male : you might be wondering why the exchange would be willing to take on the counter party risk for people trained , exchanging these kinds of standardized futures contract . the first reason is that the exchange actually stands to make a lot of money . what he can do is tell these people who wan na buy apples in th... | he can actually use the margin as kind of insurance so he can make sure that on the settlement date , both parties will kind of be able to meet their obligations . i 'll go into more detail with that on the next video on exactly how margin works . | does anybody have a better understanding in how future works ? |
luiza runs a lawn-mowing business . she decides to measure the rate at which the volume of fuel she uses increases with the area of the lawn . what would be an appropriate unit for luiza 's purpose ? so let me reread this to make sure i understand it . she decides to measure . she 's gon na measure the rate at which t... | so let me reread this to make sure i understand it . she decides to measure . she 's gon na measure the rate at which the volume of fuel she uses increases with the area of the lawn . | what if you are trying to measure a 3d area ? |
luiza runs a lawn-mowing business . she decides to measure the rate at which the volume of fuel she uses increases with the area of the lawn . what would be an appropriate unit for luiza 's purpose ? so let me reread this to make sure i understand it . she decides to measure . she 's gon na measure the rate at which t... | she 's gon na measure the rate at which the volume of fuel she uses increases with the area of the lawn . so her unit should be something that says volume per area . she wants to see how her volume of fuel increases with the area of the lawn . | km2 is a unit of area , but who in the world , except a groundskeeper at a public park thinks of lawn area in km2 ? |
- gestation is a term that most people use synonymously with pregnancy . now many people use the term conception to define when a pregnancy or gestation starts . now , conception is kind of a cloudy term , and there 's not really a good definition for what it means . so , in general , it 's probably best if we just do ... | so here on the same scale i 've just given us week segments instead of monthly segments . i 'll put marks at 10 , 20 , 30 , 40 weeks . so you can see basically how these are laid out . | does embryogenesis last 10 weeks ( in which case it would fall on week 12 ) or 8 weeks ( to fall on week 10 ) ? |
- gestation is a term that most people use synonymously with pregnancy . now many people use the term conception to define when a pregnancy or gestation starts . now , conception is kind of a cloudy term , and there 's not really a good definition for what it means . so , in general , it 's probably best if we just do ... | you start counting at the last menstrual period at week zero . fertilization happens at week two . you go through embryogenesis , organogenesis , fetal development , along with a period of growth and further development , before birth at the end of pregnancy . | i 'm sure using week 2 as the point of fertilization is based off of ovulation , but is n't it individualized for each pregnancy ? |
- gestation is a term that most people use synonymously with pregnancy . now many people use the term conception to define when a pregnancy or gestation starts . now , conception is kind of a cloudy term , and there 's not really a good definition for what it means . so , in general , it 's probably best if we just do ... | so if you 're born at about 24 weeks , you have even odds of actually surviving , but after 24 weeks , your complication rate significantly declines . and here we get to the end of our 39th week , and at that point we are full term . there 's a little bit of leeway in this definition , and most people consider full ter... | why do some pregnancies go far pass the full term ? |
hey , this is kim and i 'm here with leah , khan academy 's us government and politics fellow . welcome leah . - [ leah ] how 's it going ? - [ kim ] alright , so we 're talking about the articles of confederation , which i think many people do n't realize was the first constitution of the united states before the one... | - [ kim ] right , so they 're trying to run away from the past that they 're getting away from in the revolutionary war and trying to create a separate government that does n't have any of those abuses that they are rebelling against . - [ leah ] if they 're running away from a monarchy , what they 're running towards ... | what are some examples of limited government in modern times ? |
hey , this is kim and i 'm here with leah , khan academy 's us government and politics fellow . welcome leah . - [ leah ] how 's it going ? - [ kim ] alright , so we 're talking about the articles of confederation , which i think many people do n't realize was the first constitution of the united states before the one... | it happens in massachusets , and it 's a group of farmers led by this guy named daniel shays . what 's happening is that we had just gotten out of the revolutionary war , and a lot of of the people who had fought in the revolutionary war still had n't gotten payment for their duty . they also were experiencing really h... | could someone explain how the war ended ? |
hey , this is kim and i 'm here with leah , khan academy 's us government and politics fellow . welcome leah . - [ leah ] how 's it going ? - [ kim ] alright , so we 're talking about the articles of confederation , which i think many people do n't realize was the first constitution of the united states before the one... | - [ kim ] so what led the early government of the united states to realize that they wanted to abandon these articles of confederation in favor of a different constitution ? - [ leah ] so the inciting incident is shays ' rebellion . it happens in massachusets , and it 's a group of farmers led by this guy named daniel ... | how did the rebellion stop or start ? |
hey , this is kim and i 'm here with leah , khan academy 's us government and politics fellow . welcome leah . - [ leah ] how 's it going ? - [ kim ] alright , so we 're talking about the articles of confederation , which i think many people do n't realize was the first constitution of the united states before the one... | - [ leah ] if they 're running away from a monarchy , what they 're running towards is what we would call limited government . - [ kim ] ok. - [ leah ] so their central government , which is synonymous with a federal government , the central government is actually really , really , really small . - [ kim ] ok. - [ leah... | why was the government so weak ? |
hey , this is kim and i 'm here with leah , khan academy 's us government and politics fellow . welcome leah . - [ leah ] how 's it going ? - [ kim ] alright , so we 're talking about the articles of confederation , which i think many people do n't realize was the first constitution of the united states before the one... | so on both ends , we are in a really bad situation politically . - [ kim ] wow , so , there 's this moment where you find armed rebellion against the united states for a lack of money and the us government finds that it ca n't raise money and it ca n't raise an army to put down this rebellion . - [ leah ] exactly , and... | why did n't the rebellion realize that the government needed money for the military ? |
hey , this is kim and i 'm here with leah , khan academy 's us government and politics fellow . welcome leah . - [ leah ] how 's it going ? - [ kim ] alright , so we 're talking about the articles of confederation , which i think many people do n't realize was the first constitution of the united states before the one... | - [ kim ] right , so they 're trying to run away from the past that they 're getting away from in the revolutionary war and trying to create a separate government that does n't have any of those abuses that they are rebelling against . - [ leah ] if they 're running away from a monarchy , what they 're running towards ... | what are some examples of limited government in modern times ? |
hey , this is kim and i 'm here with leah , khan academy 's us government and politics fellow . welcome leah . - [ leah ] how 's it going ? - [ kim ] alright , so we 're talking about the articles of confederation , which i think many people do n't realize was the first constitution of the united states before the one... | when the articles of confederation were first created , it was in the middle of the american revolution . they were created in 1777 , and so the question becomes , well , how can we run a government that looks as different from monarchy as possible ? - [ kim ] right , so they 're trying to run away from the past that t... | at the time frame of they vocalize that they attempt to create a solid government which looks as different as tyranny as plausible , but the `` elite '' men end up with all the power , why did this particular event occur ? |
hey , this is kim and i 'm here with leah , khan academy 's us government and politics fellow . welcome leah . - [ leah ] how 's it going ? - [ kim ] alright , so we 're talking about the articles of confederation , which i think many people do n't realize was the first constitution of the united states before the one... | when the articles of confederation were first created , it was in the middle of the american revolution . they were created in 1777 , and so the question becomes , well , how can we run a government that looks as different from monarchy as possible ? - [ kim ] right , so they 're trying to run away from the past that t... | they say that they try to create a government that looks as different as monarchy as possible , but the `` elite '' white men end up with all the power , why did this happen ? |
in the last video we saw that if we had some line that was defined as all of the scalar multiples of sum vector -- i 'll just write it like this . the scalar multiples , obviously , are any real number . we defined a transformation , and i did n't speak of it much in terms of transformations , but it was a transformati... | there 's two conditions for it to be a linear transformation . let 's see what happens if i take the projection onto l of two vectors . let 's say the vector a plus the vector v. if i take the sum of their vectors . | how do i extend this process to form a matrix that projects 3d vectors onto a plane ? |
in the last video we saw that if we had some line that was defined as all of the scalar multiples of sum vector -- i 'll just write it like this . the scalar multiples , obviously , are any real number . we defined a transformation , and i did n't speak of it much in terms of transformations , but it was a transformati... | we can always write it like this . let 's see if this is always going to be a linear transformation . there 's two conditions for it to be a linear transformation . let 's see what happens if i take the projection onto l of two vectors . | what is the significance of something being linear transformation ? |
in the last video we saw that if we had some line that was defined as all of the scalar multiples of sum vector -- i 'll just write it like this . the scalar multiples , obviously , are any real number . we defined a transformation , and i did n't speak of it much in terms of transformations , but it was a transformati... | where this is a unit vector version of your vector v up there . i just said that , look , this is a transformation from rn to rn . the one thing that we 're not sure of , is this a linear transformation . | would n't a projection be a mapping from rn to rn-1 ? |
in the last video we saw that if we had some line that was defined as all of the scalar multiples of sum vector -- i 'll just write it like this . the scalar multiples , obviously , are any real number . we defined a transformation , and i did n't speak of it much in terms of transformations , but it was a transformati... | when i drew it in the previous video , i just picked a line , like that . the line can be really defined to this vector v in the line . it can be any of the vectors that 's contained in the line . the vector v could be like that . | specifically : in your example all the output vectors are on a line , so would n't you be in r1 ? |
in the last video we saw that if we had some line that was defined as all of the scalar multiples of sum vector -- i 'll just write it like this . the scalar multiples , obviously , are any real number . we defined a transformation , and i did n't speak of it much in terms of transformations , but it was a transformati... | 2 times 1 over square root of 5 times square root of 5 . so , 2/5 . i just multiplied these two . | the determinant of the matrix sal created in this video is 0 : ( u1^2 x u2^2 ) - ( u1u2 x u2u1 ) = ( u1u2 ) ^2 - ( u1u2 ) ^2 = 0 is it another coincidence ? |
in the last video we saw that if we had some line that was defined as all of the scalar multiples of sum vector -- i 'll just write it like this . the scalar multiples , obviously , are any real number . we defined a transformation , and i did n't speak of it much in terms of transformations , but it was a transformati... | if you take this vector , let 's say a , and you multiply it times this matrix right there , you 're going to get its projection . its projection onto the line . if you could take this vector -- no , it should go through the origin . i want to draw it in standard position . | what is the formulation if the line does not go through the origin ? |
in the last video we saw that if we had some line that was defined as all of the scalar multiples of sum vector -- i 'll just write it like this . the scalar multiples , obviously , are any real number . we defined a transformation , and i did n't speak of it much in terms of transformations , but it was a transformati... | let 's go back to what i did before . let 's say we want to find any projection onto the line , onto the vector , i 'll draw it here . we 'll do the same example that we did in the last video . | and what if the vector that we want to find the projection for lies on the other side of the line than what was shown in the video ? |
in the last video we saw that if we had some line that was defined as all of the scalar multiples of sum vector -- i 'll just write it like this . the scalar multiples , obviously , are any real number . we defined a transformation , and i did n't speak of it much in terms of transformations , but it was a transformati... | let 's say the vector a plus the vector v. if i take the sum of their vectors . if this is a linear transformation , this should be equivalent to taking each of their projections individually , and then summing . let 's see if this is the case . | is there any relationship between projections and cross products ? |
in the last video we saw that if we had some line that was defined as all of the scalar multiples of sum vector -- i 'll just write it like this . the scalar multiples , obviously , are any real number . we defined a transformation , and i did n't speak of it much in terms of transformations , but it was a transformati... | you start with a unit vector there . you just create this matrix , and then we will have our transformation matrix . if this is our u , what will our matrix be equal to . | how do i go about constructing a projection matrix in r^3 ? |
in the last video we saw that if we had some line that was defined as all of the scalar multiples of sum vector -- i 'll just write it like this . the scalar multiples , obviously , are any real number . we defined a transformation , and i did n't speak of it much in terms of transformations , but it was a transformati... | let 's say we want to find any projection onto the line , onto the vector , i 'll draw it here . we 'll do the same example that we did in the last video . if i have some vector v that looks like that . | will the matrix of product of the transformations in 1 ) and 2 ) be the same with the one sal defined at 1 ? |
in the last video we saw that if we had some line that was defined as all of the scalar multiples of sum vector -- i 'll just write it like this . the scalar multiples , obviously , are any real number . we defined a transformation , and i did n't speak of it much in terms of transformations , but it was a transformati... | and then , all of that times our unit vector . we know that the dot product has a distributive property , so that this is equal to a dot u plus b dot u . these are unit vectors . all of that times the vector u . | does the angle between the vectors not come into play when calculating the dot product ? |
in the last video we saw that if we had some line that was defined as all of the scalar multiples of sum vector -- i 'll just write it like this . the scalar multiples , obviously , are any real number . we defined a transformation , and i did n't speak of it much in terms of transformations , but it was a transformati... | let me draw it with a little hat to show that it is a unit vector . times the unit vector itself , so that we actually get a vector . how can i write this as some matrix product . | again , question about syntax - should cproj_l ( a ) - should the a have a vector arrow above it ? |
in the last video we saw that if we had some line that was defined as all of the scalar multiples of sum vector -- i 'll just write it like this . the scalar multiples , obviously , are any real number . we defined a transformation , and i did n't speak of it much in terms of transformations , but it was a transformati... | what is the projection onto l of some scalar multiple of some vector a . that is equal to ca dot our unit vector u times unit vector u . this one is a little bit more straightforward . | i just feel the need to ask , is it possible to turn the equation ( vector x dot unit vector u ) dot unit vector u into vector x dot the length of the unit vector u squared ? |
in the last video we saw that if we had some line that was defined as all of the scalar multiples of sum vector -- i 'll just write it like this . the scalar multiples , obviously , are any real number . we defined a transformation , and i did n't speak of it much in terms of transformations , but it was a transformati... | if you take this vector , let 's say a , and you multiply it times this matrix right there , you 're going to get its projection . its projection onto the line . if you could take this vector -- no , it should go through the origin . | when calculating the projection of a vector onto a line , is the line treated as though it passes through the origin no matter where it actually is ? |
in the last video we saw that if we had some line that was defined as all of the scalar multiples of sum vector -- i 'll just write it like this . the scalar multiples , obviously , are any real number . we defined a transformation , and i did n't speak of it much in terms of transformations , but it was a transformati... | that was my vector v. how can we find sum transformation for the projection onto the line defined by v ? onto this line right here . the line defined by v. what we can first do is convert v into a unit vector . | and since location does n't matter in that case , projecting a vector onto a line is really more like projecting a vector onto another vector , right ? |
in the last video we saw that if we had some line that was defined as all of the scalar multiples of sum vector -- i 'll just write it like this . the scalar multiples , obviously , are any real number . we defined a transformation , and i did n't speak of it much in terms of transformations , but it was a transformati... | when i drew it in the previous video , i just picked a line , like that . the line can be really defined to this vector v in the line . it can be any of the vectors that 's contained in the line . | is the location of the line important ? |
in the last video we saw that if we had some line that was defined as all of the scalar multiples of sum vector -- i 'll just write it like this . the scalar multiples , obviously , are any real number . we defined a transformation , and i did n't speak of it much in terms of transformations , but it was a transformati... | you start with a unit vector there . you just create this matrix , and then we will have our transformation matrix . if this is our u , what will our matrix be equal to . | is there any connection between projection and the covariance matrix ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , which is a natural logarithm , and log base 10 . so you generally have to change your ... | so why do we always take log ( base 10 ) ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | so you would get c is equal to -- and i 'll stick to the color -- so it 's log base x of b , which is this , over log base x of a . and this was what c was . c was log base a of b . it 's equal to log base a of b . | why does clogx ( a ) =logx ( a^c ) ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | and if we have time , i 'll tell you why it makes a lot of sense , or how we can derive it . so the change of base formula just tells us that log -- let me do some colors here -- log base a of b is the exact same thing as log base x , where x is an arbitrary base of b , over log base , that same base , base x over a . ... | can you put any number as a base in the logarithmic base conversion formula ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | so this numerator is just equal to 2 . so it simplifies to 2 over log base 10 of 5 . and we can now use our calculator , because the log function on a calculator is log base 10 . | why did you make the base 10 3 ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | so this is also equal to c. and we 're done . we 've proven the change of base formula . log base a of b is equal to log base x of b divided by log base x of a . | why is the base change formula that ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , which is a natural logarithm , and log base 10 . so you generally have to change your ... | what is the value of log ( base 10 ) ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | log base 10 of 100 -- what power do i have to raise 10 to to get to 100 ? the second power . so this numerator is just equal to 2 . | what is the difference between power and exponent ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | we 've proven the change of base formula . log base a of b is equal to log base x of b divided by log base x of a . in this example , a was 5 , b is 100 , and the base that we switched it to is 10. x is 10 . | if we can do sin^y x = ( sin x ) ^y ( so that we do n't confuse it with sin x^y ) , then can we do log^y_b x = ( log_b x ) ^y ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | we 've proven the change of base formula . log base a of b is equal to log base x of b divided by log base x of a . in this example , a was 5 , b is 100 , and the base that we switched it to is 10. x is 10 . | is log x the same as log base x ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | we 've proven the change of base formula . log base a of b is equal to log base x of b divided by log base x of a . in this example , a was 5 , b is 100 , and the base that we switched it to is 10. x is 10 . | what is log ... exactly ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | so i 'm not putting in all of the digits . what do i get ? i get 99.94 . | how did the c get bumped out ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | so this numerator is just equal to 2 . so it simplifies to 2 over log base 10 of 5 . and we can now use our calculator , because the log function on a calculator is log base 10 . | 5 : why is x = 10 ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | so this numerator is just equal to 2 . so it simplifies to 2 over log base 10 of 5 . and we can now use our calculator , because the log function on a calculator is log base 10 . | why did you choose log base 10 ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | we 've proven the change of base formula . log base a of b is equal to log base x of b divided by log base x of a . in this example , a was 5 , b is 100 , and the base that we switched it to is 10. x is 10 . | does n't sal mean ln x =lne of x or is it log ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | and if we have time , i 'll tell you why it makes a lot of sense , or how we can derive it . so the change of base formula just tells us that log -- let me do some colors here -- log base a of b is the exact same thing as log base x , where x is an arbitrary base of b , over log base , that same base , base x over a . ... | can you use a base that is not log base 10 ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | and if we have time , i 'll tell you why it makes a lot of sense , or how we can derive it . so the change of base formula just tells us that log -- let me do some colors here -- log base a of b is the exact same thing as log base x , where x is an arbitrary base of b , over log base , that same base , base x over a . ... | for example , if you had log base 4 of 9 + log base 2 of x , could you change the base to be log 2 , not log 10 , and have it still work ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | this is a logarithmic way of writing this truth . this is equal to b . now , we can take the logarithm of any base of both sides of this . | is'nt logx ofb/logx of a=logx ( b-a ) ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | this is a logarithmic way of writing this truth . this is equal to b . now , we can take the logarithm of any base of both sides of this . | so is it equal to loga of b ? |
use the change of base formula to find log base 5 of 100 to the nearest thousandth . so the change of base formula is a useful formula , especially when you 're going to use a calculator , because most calculators do n't allow you to arbitrarily change the base of your logarithm . they have functions for log base e , w... | so if our calculator has a certain base x function , we can convert to that base . it 's usually e or base 10 . base 10 is an easy way to go . | so e , similarly to pi , is infinite ? |
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