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what is an algorithm ? one definition might be a set of steps to accomplish a task . you might have an algorithm for getting from home to school , for making a grilled cheese sandwich , or for finding what you 're looking for in a grocery store . in computer science , an algorithm is a set of steps for a computer prog... | what is an algorithm ? one definition might be a set of steps to accomplish a task . | can an algorithm be termed incorrect ? |
what is an algorithm ? one definition might be a set of steps to accomplish a task . you might have an algorithm for getting from home to school , for making a grilled cheese sandwich , or for finding what you 're looking for in a grocery store . in computer science , an algorithm is a set of steps for a computer prog... | what is an algorithm ? one definition might be a set of steps to accomplish a task . | is an algorithm like a routine ? |
what is an algorithm ? one definition might be a set of steps to accomplish a task . you might have an algorithm for getting from home to school , for making a grilled cheese sandwich , or for finding what you 're looking for in a grocery store . in computer science , an algorithm is a set of steps for a computer prog... | how do you measure the efficiency of an algorithm ? we could time how long it takes to run the code , but that would only tell us about that particular implementation in a certain programming language on a particular computer and just for the input it was given . instead , computer scientists use a technique called asy... | what is the difference between container and panel in java programming ? |
what is an algorithm ? one definition might be a set of steps to accomplish a task . you might have an algorithm for getting from home to school , for making a grilled cheese sandwich , or for finding what you 're looking for in a grocery store . in computer science , an algorithm is a set of steps for a computer prog... | what is an algorithm ? one definition might be a set of steps to accomplish a task . | how long does it usually take until a person knows how to write complex algorithm ? |
what is an algorithm ? one definition might be a set of steps to accomplish a task . you might have an algorithm for getting from home to school , for making a grilled cheese sandwich , or for finding what you 're looking for in a grocery store . in computer science , an algorithm is a set of steps for a computer prog... | instead , computer scientists use a technique called asymptotic analysis , which allows algorithms to be compared independently of a particular programming language or hardware so that we can conclusively say that yes , some algorithms are more efficient than others . now you can learn about algorithms and asymptotic a... | is there a specific area of mathematics ( preferably on khan academy ) that i can go through to help me learn the proper math to fully understand how to reduce an algorithm down to asymptotic notation ? |
what is an algorithm ? one definition might be a set of steps to accomplish a task . you might have an algorithm for getting from home to school , for making a grilled cheese sandwich , or for finding what you 're looking for in a grocery store . in computer science , an algorithm is a set of steps for a computer prog... | he built the world 's first origami folding robot . tom and devin will teach you many of the algorithms that you would learn in apcs or cs 101 , like searching algorithms , sorting algorithms , recursive algorithms and my personal favorite , graph algorithms . there will be tons of interactive visualizations , quizzes ... | is there any source to find such fundamental algorithms ? |
what is an algorithm ? one definition might be a set of steps to accomplish a task . you might have an algorithm for getting from home to school , for making a grilled cheese sandwich , or for finding what you 're looking for in a grocery store . in computer science , an algorithm is a set of steps for a computer prog... | what is an algorithm ? one definition might be a set of steps to accomplish a task . | how to figure out algorithm to solve a problem in dynamic situation ? |
what is an algorithm ? one definition might be a set of steps to accomplish a task . you might have an algorithm for getting from home to school , for making a grilled cheese sandwich , or for finding what you 're looking for in a grocery store . in computer science , an algorithm is a set of steps for a computer prog... | he built the world 's first origami folding robot . tom and devin will teach you many of the algorithms that you would learn in apcs or cs 101 , like searching algorithms , sorting algorithms , recursive algorithms and my personal favorite , graph algorithms . there will be tons of interactive visualizations , quizzes ... | what kind of algorithms are being used on the job of a computer engineer ? |
what is an algorithm ? one definition might be a set of steps to accomplish a task . you might have an algorithm for getting from home to school , for making a grilled cheese sandwich , or for finding what you 're looking for in a grocery store . in computer science , an algorithm is a set of steps for a computer prog... | let 's talk about a few famous algorithms . how does google hangouts transmit live video across the internet so quickly ? they use audio and video compression algorithms . | how does the internet gather so much info about someone ? |
what is an algorithm ? one definition might be a set of steps to accomplish a task . you might have an algorithm for getting from home to school , for making a grilled cheese sandwich , or for finding what you 're looking for in a grocery store . in computer science , an algorithm is a set of steps for a computer prog... | how does google hangouts transmit live video across the internet so quickly ? they use audio and video compression algorithms . how does google maps figure out how to get from dallas , texas to orlando , florida so that you can get to disney world ? | what sort of algorithms does khan academy use ? |
- [ voicover ] prejudice is made up of several different components . the first component that we have is a fundamental underlying thought overgeneralized belief , otherwise known as a cognition . we often refer to these as stereotypes . the second aspect to prejudice is that it carries with it an emotional component ,... | in line with the frustration aggression hypothesis , i want to tell you about another hypothesis . and this is called the hypothesis of relative deprivation . now , what the hypothesis of relative deprivation suggests is that people become very frustrated and you get upsurge in prejudice and discrimination when people ... | would conservatives ' negative reaction to obama 's immigration reform be considered a form of the hypothesis of relative deprivation because we 're all immigrants ? |
- [ voicover ] prejudice is made up of several different components . the first component that we have is a fundamental underlying thought overgeneralized belief , otherwise known as a cognition . we often refer to these as stereotypes . the second aspect to prejudice is that it carries with it an emotional component ,... | so as you can see , living standards actually do n't increase with time , actually these tend to drop off , maybe because of some economic problem . we 're left with a difference . and it 's this difference that is the relative deprivation . | i wonder what the difference is between the scapegoating mentioned in the video and the psychoanalytic idea of displacement ? |
- [ voicover ] prejudice is made up of several different components . the first component that we have is a fundamental underlying thought overgeneralized belief , otherwise known as a cognition . we often refer to these as stereotypes . the second aspect to prejudice is that it carries with it an emotional component ,... | in line with the frustration aggression hypothesis , i want to tell you about another hypothesis . and this is called the hypothesis of relative deprivation . now , what the hypothesis of relative deprivation suggests is that people become very frustrated and you get upsurge in prejudice and discrimination when people ... | why is there upsurge of prejudice in the hypothesis of relative deprivation ? |
stacy wants to find the derivative of f of x equals x squared plus one at the point x equals two . her table below shows the average rate of change of f over the intervals from x to two or from two to x , and these are closed intervals , for x-values that get increasingly closer to two . so they get -- so we 're talki... | stacy wants to find the derivative of f of x equals x squared plus one at the point x equals two . her table below shows the average rate of change of f over the intervals from x to two or from two to x , and these are closed intervals , for x-values that get increasingly closer to two . so they get -- so we 're talki... | why do the order of those intervals change ? |
stacy wants to find the derivative of f of x equals x squared plus one at the point x equals two . her table below shows the average rate of change of f over the intervals from x to two or from two to x , and these are closed intervals , for x-values that get increasingly closer to two . so they get -- so we 're talki... | she gets even closer to two and the average rate of change gets even closer to four , and then she goes on the other side of two , you could view it as this is approaching , this is -- this is approaching -- this is x approaching two from the left hand side , and this is x approaching two from the right hand side . whe... | and in the table , why do the interval switch side when going from 1.999 to 2.001 ? |
stacy wants to find the derivative of f of x equals x squared plus one at the point x equals two . her table below shows the average rate of change of f over the intervals from x to two or from two to x , and these are closed intervals , for x-values that get increasingly closer to two . so they get -- so we 're talki... | stacy wants to find the derivative of f of x equals x squared plus one at the point x equals two . her table below shows the average rate of change of f over the intervals from x to two or from two to x , and these are closed intervals , for x-values that get increasingly closer to two . | this might be a stupid question , but i have not been able to understand what the relation between d ( x ) and f ' ( x ) is , are they the same ? |
stacy wants to find the derivative of f of x equals x squared plus one at the point x equals two . her table below shows the average rate of change of f over the intervals from x to two or from two to x , and these are closed intervals , for x-values that get increasingly closer to two . so they get -- so we 're talki... | you might recognize , this is one of the definitions of a derivative . this is one of the definitions of a derivative . this right over here would be f prime of two , the derivative at x equals two is equal to the limit as x approaches two of all of this business . | how are definitions of derivative and limit same ? |
let 's look at our gentleman in the middle . he is lying down and he is dreaming . that raises the question , do our dreams have a meaning ? so if he 's thinking about money , relationships , even weird and wonderful things like monsters chasing him down the road , what does that mean ? where are all these dreams comi... | on one side , freud feels that dreams indeed have a meaning and important to helping us to resolve hidden conflicts and understand unconcious feelings , desires , impulses , and that 's his theory of dreams . on the other hand , we have this activation synthesis hypothesis . that suggest that dreams are simply a part o... | in regards to the `` activation synthesis hypothesis '' dream theory , where do the electrical impulses come from , i would assume that since a person is asleep they are unable to perceive anything so what activity creates the electrical impulses ? |
i 'm going to quickly sketch out the human heart . we 're also going to label some vessels coming off of it . so the big vessel , of course , is the aorta . this is the giant aortic arch . and the aortic arch has a couple of key branches that go , for example , up to the head and neck . it has other branches as well th... | and the aortic arch has a couple of key branches that go , for example , up to the head and neck . it has other branches as well that go out to the arms . but these branches that are going up are the ones i 'm going to focus on . | how does this go with lungs ? |
i 'm going to quickly sketch out the human heart . we 're also going to label some vessels coming off of it . so the big vessel , of course , is the aorta . this is the giant aortic arch . and the aortic arch has a couple of key branches that go , for example , up to the head and neck . it has other branches as well th... | and really , the same thing is going on on the aorta side . so on the aorta side , you 've got little branches coming off of the aorta , of course . and these branches are going to branch again , and again , and again , and again . | why does it appear that the aorta is coming from the right ventricle ? |
i 'm going to quickly sketch out the human heart . we 're also going to label some vessels coming off of it . so the big vessel , of course , is the aorta . this is the giant aortic arch . and the aortic arch has a couple of key branches that go , for example , up to the head and neck . it has other branches as well th... | and these oxygen molecules -- these are oxygen molecules over here -- are going to diffuse down into the tissue and get into our glomus cell . it 's going to look something like that . and if you have a lot of oxygen in the blood , of course , a lot of molecules are going to diffuse in . | why do we draw hearts like that when they dont look like that ? |
i 'm going to quickly sketch out the human heart . we 're also going to label some vessels coming off of it . so the big vessel , of course , is the aorta . this is the giant aortic arch . and the aortic arch has a couple of key branches that go , for example , up to the head and neck . it has other branches as well th... | this is really interesting . our cell is depolarizing . it can depolarize . | at 05 , the causes of the depolarization of the glomus cell are low pressure of oxygen , high pressure of carbon dioxide , and low ph , but is n't chemoreceptor detect chemical/concentration ? |
i 'm going to quickly sketch out the human heart . we 're also going to label some vessels coming off of it . so the big vessel , of course , is the aorta . this is the giant aortic arch . and the aortic arch has a couple of key branches that go , for example , up to the head and neck . it has other branches as well th... | and if the oxygen levels fall really low , let 's say they get dangerously low , where the cell is very unhappy , then you 're going to get much more neurotransmitter getting dumped out , and you 're going to get many more action potentials . so this is how the glomus cell helps to detect oxygen . and in fact , it also... | why is it pressure of oxygen / carbon dioxides are the causes ? |
i 'm going to quickly sketch out the human heart . we 're also going to label some vessels coming off of it . so the big vessel , of course , is the aorta . this is the giant aortic arch . and the aortic arch has a couple of key branches that go , for example , up to the head and neck . it has other branches as well th... | this is really interesting . our cell is depolarizing . it can depolarize . | so , what would be the name of the actual neurotransmitter that is released as a response to the glomus cell depolarizing ? |
i 'm going to quickly sketch out the human heart . we 're also going to label some vessels coming off of it . so the big vessel , of course , is the aorta . this is the giant aortic arch . and the aortic arch has a couple of key branches that go , for example , up to the head and neck . it has other branches as well th... | and now i want to remind you that there 's this little formula . there 's this formula where carbon dioxide binds with water , and it forms h2co3 . and that 's going to break down into bicarbonate and a proton . | in h2co3 what does the 3 stand for ? |
i 'm going to quickly sketch out the human heart . we 're also going to label some vessels coming off of it . so the big vessel , of course , is the aorta . this is the giant aortic arch . and the aortic arch has a couple of key branches that go , for example , up to the head and neck . it has other branches as well th... | so this is how the glomus cell helps to detect oxygen . and in fact , it also detects carbon dioxide . because , remember , this cell is going to be making carbon dioxide . | if someone had carbon monoxide poisoning , would this affect the interpretation of the chemoreceptors ? |
i 'm going to quickly sketch out the human heart . we 're also going to label some vessels coming off of it . so the big vessel , of course , is the aorta . this is the giant aortic arch . and the aortic arch has a couple of key branches that go , for example , up to the head and neck . it has other branches as well th... | and if you could do this in one minute , if you could pour out this bottle in one minute , imagine how wet this tomato 's going to get , how much profusion , in a sense , this tomato is going to get . that is how much profusion your carotid body gets . so it really puts it in perspective how much blood flow 's going in... | for instance , if there was higher amount of circulating 02 ( not bound to hbg because the co is.. ) would the receptors incorrectly perceive this as the body having too much o2 and then communicate to the cns that our o2 level is high ? |
i 'm going to quickly sketch out the human heart . we 're also going to label some vessels coming off of it . so the big vessel , of course , is the aorta . this is the giant aortic arch . and the aortic arch has a couple of key branches that go , for example , up to the head and neck . it has other branches as well th... | these things are called glomus cells . i had initially misstated it as a globus cell . but actually it 's an m -- glomus . | does the globus cell die when it depolarizes and releases its neurotransmitters ? |
i 'm going to quickly sketch out the human heart . we 're also going to label some vessels coming off of it . so the big vessel , of course , is the aorta . this is the giant aortic arch . and the aortic arch has a couple of key branches that go , for example , up to the head and neck . it has other branches as well th... | and my red blood cell , of course , has some hemoglobin in it , which is a protein . and this protein has got some oxygen bound to it . i 'm going to draw little blue oxygen molecules . and of course , there 's some oxygen out here in the plasma itself as well . | the cell lets the neurotransmitter know there is too little oxygen , so what happens on the cellular level when there is too much oxygen ? |
i 'm going to quickly sketch out the human heart . we 're also going to label some vessels coming off of it . so the big vessel , of course , is the aorta . this is the giant aortic arch . and the aortic arch has a couple of key branches that go , for example , up to the head and neck . it has other branches as well th... | so this is how the glomus cell helps to detect oxygen . and in fact , it also detects carbon dioxide . because , remember , this cell is going to be making carbon dioxide . | also are there any problems when there is very low amounts of carbon dioxide ? |
i 'm going to quickly sketch out the human heart . we 're also going to label some vessels coming off of it . so the big vessel , of course , is the aorta . this is the giant aortic arch . and the aortic arch has a couple of key branches that go , for example , up to the head and neck . it has other branches as well th... | because what our cell is going to be able to do is start to detect low oxygen levels . low oxygen levels in the glomus cell tells this cell that , actually , there are probably low levels in the blood . and when the levels are low , this cell is going to depolarize . | would the heart be considered the organ that measures the oxygen levels in our blood or would that be the kidney ? |
i 'm going to quickly sketch out the human heart . we 're also going to label some vessels coming off of it . so the big vessel , of course , is the aorta . this is the giant aortic arch . and the aortic arch has a couple of key branches that go , for example , up to the head and neck . it has other branches as well th... | and specifically they have a name . these things are called glomus cells . i had initially misstated it as a globus cell . | do glomus cells only detect plasma o2 or also the amount that is carried in the rbc ? |
i 'm going to quickly sketch out the human heart . we 're also going to label some vessels coming off of it . so the big vessel , of course , is the aorta . this is the giant aortic arch . and the aortic arch has a couple of key branches that go , for example , up to the head and neck . it has other branches as well th... | and that 's going to help regulate our blood pressure . now , in this video , we 're actually going to focus on chemoreceptors . chemoreceptors are also important in giving us information , but they 're going to give us information about things like oxygen levels , carbon dioxide levels , ph of the blood , things like ... | do you have a video explaining clearly then what happens during the hypoxic drive of a patient with copd ? |
i 'm going to quickly sketch out the human heart . we 're also going to label some vessels coming off of it . so the big vessel , of course , is the aorta . this is the giant aortic arch . and the aortic arch has a couple of key branches that go , for example , up to the head and neck . it has other branches as well th... | and as a result , carbon dioxide starts building up . the tissue starts gathering more and more co2 , because it ca n't go anywhere . and this glomus cell is going to say , hey , wait a second . | at 8 ; 10 , i ca n't understand how high pco2 & low po2 cause the same thing ? |
i 'm going to quickly sketch out the human heart . we 're also going to label some vessels coming off of it . so the big vessel , of course , is the aorta . this is the giant aortic arch . and the aortic arch has a couple of key branches that go , for example , up to the head and neck . it has other branches as well th... | and if the oxygen levels fall really low , let 's say they get dangerously low , where the cell is very unhappy , then you 're going to get much more neurotransmitter getting dumped out , and you 're going to get many more action potentials . so this is how the glomus cell helps to detect oxygen . and in fact , it also... | what neurotransmiter does the glomus cell secrete ? |
i 'm going to quickly sketch out the human heart . we 're also going to label some vessels coming off of it . so the big vessel , of course , is the aorta . this is the giant aortic arch . and the aortic arch has a couple of key branches that go , for example , up to the head and neck . it has other branches as well th... | and really , the same thing is going on on the aorta side . so on the aorta side , you 've got little branches coming off of the aorta , of course . and these branches are going to branch again , and again , and again , and again . | baroreceptors , i 've been taught that they are located in internal carotis , not only in the aorta arch ? |
i 'm going to quickly sketch out the human heart . we 're also going to label some vessels coming off of it . so the big vessel , of course , is the aorta . this is the giant aortic arch . and the aortic arch has a couple of key branches that go , for example , up to the head and neck . it has other branches as well th... | so a high proton concentration -- i 'm going to put it in brackets , to indicate concentration . or another way of saying that would be a low ph . so these are the things that are going to make our glomus cell send off more action potentials . | why does many protons make for a low ph ? |
macdonald had a farm with a certain number of orange trees . he had to cut down 5 trees to control the insects . each of the remaining trees produced 210 oranges , producing a total harvest of 41,790 oranges . how many trees did macdonald 's farm have initially ? let 's let t equal what they 're asking is for . so this... | now we know where this is going to go . i could do the long division again . t is going to be equal to 42,840 divided 210 , which is equal to 204 . | how does sal do that complex division using mental math ? |
macdonald had a farm with a certain number of orange trees . he had to cut down 5 trees to control the insects . each of the remaining trees produced 210 oranges , producing a total harvest of 41,790 oranges . how many trees did macdonald 's farm have initially ? let 's let t equal what they 're asking is for . so this... | macdonald had a farm with a certain number of orange trees . he had to cut down 5 trees to control the insects . | if a house 's property taxes are 3 % , what is the distance of that house from the school ? |
macdonald had a farm with a certain number of orange trees . he had to cut down 5 trees to control the insects . each of the remaining trees produced 210 oranges , producing a total harvest of 41,790 oranges . how many trees did macdonald 's farm have initially ? let 's let t equal what they 're asking is for . so this... | and now you can divide both sides by 210 . now we know where this is going to go . i could do the long division again . | so in a different context of a question how do we know we are supposed to use parenthesis ? |
macdonald had a farm with a certain number of orange trees . he had to cut down 5 trees to control the insects . each of the remaining trees produced 210 oranges , producing a total harvest of 41,790 oranges . how many trees did macdonald 's farm have initially ? let 's let t equal what they 're asking is for . so this... | each of the remaining trees produced 210 oranges , producing a total harvest of 41,790 oranges . how many trees did macdonald 's farm have initially ? let 's let t equal what they 're asking is for . | the problem asks how many trees did mcdonald initially start with ... should n't the answer be 204 + 5 = 209 ? |
macdonald had a farm with a certain number of orange trees . he had to cut down 5 trees to control the insects . each of the remaining trees produced 210 oranges , producing a total harvest of 41,790 oranges . how many trees did macdonald 's farm have initially ? let 's let t equal what they 're asking is for . so this... | so this is equal to 41,790 . so we 've set up our equation . now we just have to solve for t , the number of trees that macdonald initially had . | is there some sort of pattern that you can use when comes to different variations of the same linear equation problems ? |
macdonald had a farm with a certain number of orange trees . he had to cut down 5 trees to control the insects . each of the remaining trees produced 210 oranges , producing a total harvest of 41,790 oranges . how many trees did macdonald 's farm have initially ? let 's let t equal what they 're asking is for . so this... | 9 times 1 is 9 . 9 times 2 is 18 . and then we subtract again . | determine whether the ordered pairs given are solutions of the following linear inequality in two ( 5,2 ) ( 4 , 2 ) x+4y < 4 yes or no is the ordered pair 5 , 2 a solution of the linear inequality ? |
macdonald had a farm with a certain number of orange trees . he had to cut down 5 trees to control the insects . each of the remaining trees produced 210 oranges , producing a total harvest of 41,790 oranges . how many trees did macdonald 's farm have initially ? let 's let t equal what they 're asking is for . so this... | remember , whatever we have to do to one side , we have to do the other . otherwise , the equality would n't be equal anymore . they were equal before adding 5 , so if you want them to still be equal , you have to do the same thing to both sides . | how would you do this : when a number n is increased by 25 % and 11 is added , the result is 51 ? |
macdonald had a farm with a certain number of orange trees . he had to cut down 5 trees to control the insects . each of the remaining trees produced 210 oranges , producing a total harvest of 41,790 oranges . how many trees did macdonald 's farm have initially ? let 's let t equal what they 're asking is for . so this... | and then you would have ended up with -- let me do another alternate way of doing it . 210 times t minus 5 times 210 . actually , let me just multiply it out so we save some space . | why did n't you just take 210 away from 5 then you would of got 204 ? |
macdonald had a farm with a certain number of orange trees . he had to cut down 5 trees to control the insects . each of the remaining trees produced 210 oranges , producing a total harvest of 41,790 oranges . how many trees did macdonald 's farm have initially ? let 's let t equal what they 're asking is for . so this... | he had to cut down 5 trees to control the insects . each of the remaining trees produced 210 oranges , producing a total harvest of 41,790 oranges . how many trees did macdonald 's farm have initially ? | maria 20 apples and oranges.apples cost .40 $ and oranges cost .35 $ how many of each fruit did maria bought ? |
macdonald had a farm with a certain number of orange trees . he had to cut down 5 trees to control the insects . each of the remaining trees produced 210 oranges , producing a total harvest of 41,790 oranges . how many trees did macdonald 's farm have initially ? let 's let t equal what they 're asking is for . so this... | so this is equal to 41,790 . so we 've set up our equation . now we just have to solve for t , the number of trees that macdonald initially had . | what is the linear equation ? |
macdonald had a farm with a certain number of orange trees . he had to cut down 5 trees to control the insects . each of the remaining trees produced 210 oranges , producing a total harvest of 41,790 oranges . how many trees did macdonald 's farm have initially ? let 's let t equal what they 're asking is for . so this... | and then you would have ended up with -- let me do another alternate way of doing it . 210 times t minus 5 times 210 . actually , let me just multiply it out so we save some space . | 9 sal says that number of trees ( t-5 ) times number of oranges per trees ( 210 ) , so when in math we divide instead of multiplying and why not it is 210/ ( t-5 ) ? |
macdonald had a farm with a certain number of orange trees . he had to cut down 5 trees to control the insects . each of the remaining trees produced 210 oranges , producing a total harvest of 41,790 oranges . how many trees did macdonald 's farm have initially ? let 's let t equal what they 're asking is for . so this... | actually , i will do it both ways just to show that you could do it both ways . so the first way , i 'm going to divide both sides by 210 . the left-hand side simplifies to t minus 5 . | it is able to block the sun because it is way father and the sun might be smaller than the sun , but how much light does the moon receive and how bright it is ? |
macdonald had a farm with a certain number of orange trees . he had to cut down 5 trees to control the insects . each of the remaining trees produced 210 oranges , producing a total harvest of 41,790 oranges . how many trees did macdonald 's farm have initially ? let 's let t equal what they 're asking is for . so this... | each of the remaining trees produced 210 oranges , producing a total harvest of 41,790 oranges . how many trees did macdonald 's farm have initially ? let 's let t equal what they 're asking is for . | now we will come up with a function telling us how many units a factory can produce depending on how many skilled workers and how many unskilled workers there are ? |
macdonald had a farm with a certain number of orange trees . he had to cut down 5 trees to control the insects . each of the remaining trees produced 210 oranges , producing a total harvest of 41,790 oranges . how many trees did macdonald 's farm have initially ? let 's let t equal what they 're asking is for . so this... | and then you would have ended up with -- let me do another alternate way of doing it . 210 times t minus 5 times 210 . actually , let me just multiply it out so we save some space . | i do n't understand why you put 210 outside of the ( t-5 ) ? |
macdonald had a farm with a certain number of orange trees . he had to cut down 5 trees to control the insects . each of the remaining trees produced 210 oranges , producing a total harvest of 41,790 oranges . how many trees did macdonald 's farm have initially ? let 's let t equal what they 're asking is for . so this... | it does not going into 41 . it goes into 417 one time , because two times would be 420 -- one time . 1 times 210 is 210 . | how do you distinguish between two in the word problem ? |
macdonald had a farm with a certain number of orange trees . he had to cut down 5 trees to control the insects . each of the remaining trees produced 210 oranges , producing a total harvest of 41,790 oranges . how many trees did macdonald 's farm have initially ? let 's let t equal what they 're asking is for . so this... | macdonald had a farm with a certain number of orange trees . he had to cut down 5 trees to control the insects . | what was the maximum height , in feet , of the ball above the ground after it was kicked ? |
macdonald had a farm with a certain number of orange trees . he had to cut down 5 trees to control the insects . each of the remaining trees produced 210 oranges , producing a total harvest of 41,790 oranges . how many trees did macdonald 's farm have initially ? let 's let t equal what they 're asking is for . so this... | let 's let t equal what they 're asking is for . so this is the number of trees initially . so he starts off with t trees , but then they tell us that he has to cut down 5 trees to control the insects . | the product of 8 and a number increase by 6 is 104 what is the number ? |
macdonald had a farm with a certain number of orange trees . he had to cut down 5 trees to control the insects . each of the remaining trees produced 210 oranges , producing a total harvest of 41,790 oranges . how many trees did macdonald 's farm have initially ? let 's let t equal what they 're asking is for . so this... | macdonald had a farm with a certain number of orange trees . he had to cut down 5 trees to control the insects . | is there something online to help people form equations from word problems ? |
macdonald had a farm with a certain number of orange trees . he had to cut down 5 trees to control the insects . each of the remaining trees produced 210 oranges , producing a total harvest of 41,790 oranges . how many trees did macdonald 's farm have initially ? let 's let t equal what they 're asking is for . so this... | now we know where this is going to go . i could do the long division again . t is going to be equal to 42,840 divided 210 , which is equal to 204 . | why did sal have to use his own division ? |
macdonald had a farm with a certain number of orange trees . he had to cut down 5 trees to control the insects . each of the remaining trees produced 210 oranges , producing a total harvest of 41,790 oranges . how many trees did macdonald 's farm have initially ? let 's let t equal what they 're asking is for . so this... | so the left-hand side becomes t. i 'll do the t in that purple color . and the right-hand side becomes 204 . so he started off with 204 trees . | the current sum of ages of anjli and aarti is 49.how old is aarti right now ? |
macdonald had a farm with a certain number of orange trees . he had to cut down 5 trees to control the insects . each of the remaining trees produced 210 oranges , producing a total harvest of 41,790 oranges . how many trees did macdonald 's farm have initially ? let 's let t equal what they 're asking is for . so this... | he had to cut down 5 trees to control the insects . each of the remaining trees produced 210 oranges , producing a total harvest of 41,790 oranges . how many trees did macdonald 's farm have initially ? | why did mcdonald need so many oranges ? |
macdonald had a farm with a certain number of orange trees . he had to cut down 5 trees to control the insects . each of the remaining trees produced 210 oranges , producing a total harvest of 41,790 oranges . how many trees did macdonald 's farm have initially ? let 's let t equal what they 're asking is for . so this... | each of the remaining trees produced 210 oranges , producing a total harvest of 41,790 oranges . how many trees did macdonald 's farm have initially ? let 's let t equal what they 're asking is for . | how many solutions does this system of equations have ? |
we 're in the very crowded and not very large room called the stanza della segnatura that is not only dense with people , but it 's dense with imagery . we 're looking at frescoes by raphael . painted during the high renaissance at the same time that michelangelo was painting the sistine chapel ceiling just a few doo... | plato was , in fact , aristotle 's teacher , but also because he holds one of his own books , the timaeus . and aristotle holds his book , the ethics . both of those books represent the contrasting philosophies of these two men . | who is the figure sprawled on the steps by himself in front of aristotle and plata , and what does he signify ? |
we 're in the very crowded and not very large room called the stanza della segnatura that is not only dense with people , but it 's dense with imagery . we 're looking at frescoes by raphael . painted during the high renaissance at the same time that michelangelo was painting the sistine chapel ceiling just a few doo... | plato was , in fact , aristotle 's teacher , but also because he holds one of his own books , the timaeus . and aristotle holds his book , the ethics . both of those books represent the contrasting philosophies of these two men . | with so many of this cast being portraits of renaissance superstars , do we know is aristotle was a portrait ? |
we 're in the very crowded and not very large room called the stanza della segnatura that is not only dense with people , but it 's dense with imagery . we 're looking at frescoes by raphael . painted during the high renaissance at the same time that michelangelo was painting the sistine chapel ceiling just a few doo... | and in fact , appropriate to his reincarnation here as euclid , bramante 's design for saint peter 's was based on a perfect geometry of circles and squares . and is really visible in the architecture that raphael constructed for the school of athens . here we see an architecture that is very bramantian , but also ve... | when raphael transferred his drawing of the school of athens to the wall for painting , what substance did he force through perforations in the paper ? |
we 're in the very crowded and not very large room called the stanza della segnatura that is not only dense with people , but it 's dense with imagery . we 're looking at frescoes by raphael . painted during the high renaissance at the same time that michelangelo was painting the sistine chapel ceiling just a few doo... | and in fact , appropriate to his reincarnation here as euclid , bramante 's design for saint peter 's was based on a perfect geometry of circles and squares . and is really visible in the architecture that raphael constructed for the school of athens . here we see an architecture that is very bramantian , but also ve... | when raphael transferred his drawing of the school of athens to the wall for painting , what substance did he force through perforations in the paper ? |
we 're in the very crowded and not very large room called the stanza della segnatura that is not only dense with people , but it 's dense with imagery . we 're looking at frescoes by raphael . painted during the high renaissance at the same time that michelangelo was painting the sistine chapel ceiling just a few doo... | we 're in the very crowded and not very large room called the stanza della segnatura that is not only dense with people , but it 's dense with imagery . we 're looking at frescoes by raphael . | how is reform shown throughout this piece ? |
we 're in the very crowded and not very large room called the stanza della segnatura that is not only dense with people , but it 's dense with imagery . we 're looking at frescoes by raphael . painted during the high renaissance at the same time that michelangelo was painting the sistine chapel ceiling just a few doo... | and we can see representations of classical sculpture in the niches on the left , that is on the platonic side . we see apollo , the god of the sun , the god of music , the god of poetry , things that would be appropriate to the platonic . in turn on the right , we see athena , the god of war and wisdom , who presumab... | does her shield have the likeness of the nature god pan on it ? |
we 're in the very crowded and not very large room called the stanza della segnatura that is not only dense with people , but it 's dense with imagery . we 're looking at frescoes by raphael . painted during the high renaissance at the same time that michelangelo was painting the sistine chapel ceiling just a few doo... | euclid is modeled actually on a friend of raphael 's and that 's bramante the great architect asked by pope julius ii to provide a new model for a new saint peter 's . and in fact , appropriate to his reincarnation here as euclid , bramante 's design for saint peter 's was based on a perfect geometry of circles and s... | at 9.13 , how do we know that it is , in fact , john the baptist and not some other prophet or saint ? |
we 're in the very crowded and not very large room called the stanza della segnatura that is not only dense with people , but it 's dense with imagery . we 're looking at frescoes by raphael . painted during the high renaissance at the same time that michelangelo was painting the sistine chapel ceiling just a few doo... | but here , on the walls of the papal apartments , we get this image of sharing knowledge and the history of the accumulation of knowledge all with figures who move beautifully who in their bodies represent a gracefulness that is a reflection of their inner wisdom and knowledge . you 'll notice that raphael has not pla... | there is a story that raphael put himself in the painting , but where is he ? |
we 're in the very crowded and not very large room called the stanza della segnatura that is not only dense with people , but it 's dense with imagery . we 're looking at frescoes by raphael . painted during the high renaissance at the same time that michelangelo was painting the sistine chapel ceiling just a few doo... | and also imagine quiet which is hard to do here , and an environment of learning where you could look up at what raphael painted here on the four walls which are the four branches of human knowledge , philosophy , having to do with things of this world . the philosophy at this time also meant what we know call the sc... | the speaker throws out a lot of art terms i do n't know , could someone explain ? |
we 're in the very crowded and not very large room called the stanza della segnatura that is not only dense with people , but it 's dense with imagery . we 're looking at frescoes by raphael . painted during the high renaissance at the same time that michelangelo was painting the sistine chapel ceiling just a few doo... | virtually , every known great figure , but let 's start with the two in the center . we can tell plato from aristotle because plato is older . plato was , in fact , aristotle 's teacher , but also because he holds one of his own books , the timaeus . | why did raphael place him on team plato ? |
we 're in the very crowded and not very large room called the stanza della segnatura that is not only dense with people , but it 's dense with imagery . we 're looking at frescoes by raphael . painted during the high renaissance at the same time that michelangelo was painting the sistine chapel ceiling just a few doo... | what a moment in the high renaissance all commissioned thanks to pope julius ii . and think about what it means for theology to be presented equally with human knowledge . it is this extraordinarily liberal moment in church history . | quick question- did all the later popes like this equality of the human knowledge and theology or did some oppose it ? |
we 're in the very crowded and not very large room called the stanza della segnatura that is not only dense with people , but it 's dense with imagery . we 're looking at frescoes by raphael . painted during the high renaissance at the same time that michelangelo was painting the sistine chapel ceiling just a few doo... | so we have dozens of figures here without any sense of stiffness or repetition . raphael , like leonardo , in the last supper divides the figures into groups . each figure overlaps and moves easily between and amongst the others . | when was the site last updated ? |
we 're in the very crowded and not very large room called the stanza della segnatura that is not only dense with people , but it 's dense with imagery . we 're looking at frescoes by raphael . painted during the high renaissance at the same time that michelangelo was painting the sistine chapel ceiling just a few doo... | and in fact , appropriate to his reincarnation here as euclid , bramante 's design for saint peter 's was based on a perfect geometry of circles and squares . and is really visible in the architecture that raphael constructed for the school of athens . here we see an architecture that is very bramantian , but also ve... | why is it entitle `` the school of athens '' ? |
we 're in the very crowded and not very large room called the stanza della segnatura that is not only dense with people , but it 's dense with imagery . we 're looking at frescoes by raphael . painted during the high renaissance at the same time that michelangelo was painting the sistine chapel ceiling just a few doo... | and so it 's so interesting that raphael is paying homage to michelangelo the great artist here personifying heraclitus , the philosopher who believed that all things were always in flux . that figure of heraclitus was actually added later . raphael finished the frescoe , added some wet plaster , and added in that fi... | who does the figure sprawled on the steps represent ? |
we 're in the very crowded and not very large room called the stanza della segnatura that is not only dense with people , but it 's dense with imagery . we 're looking at frescoes by raphael . painted during the high renaissance at the same time that michelangelo was painting the sistine chapel ceiling just a few doo... | this idea that there is a reality that transcends the reality that we see . compare that to the lower right where we see euclid , the figure we associate with geometry . in fact , he seems to be drawing a geometric diagram for some very eager students . | who is the figure with a beard on the right in red ? |
let 's talk about arteriolosclerosis . i 'm going to first point out a couple of important big picture ideas . why it is arteriolosclerosis matter ? well , we know that it 's basically soft , flexible kind of vessels like this that are very elastic and can expand , becoming very rigid , firm like pipes . and this is ba... | so you 've got protein hanging out in the blood vessel . and these are serum proteins . serum , s-e-r-u-m , proteins . | what do serum proteins do when they 're not causing arteriolosclerosis ? |
let 's talk about arteriolosclerosis . i 'm going to first point out a couple of important big picture ideas . why it is arteriolosclerosis matter ? well , we know that it 's basically soft , flexible kind of vessels like this that are very elastic and can expand , becoming very rigid , firm like pipes . and this is ba... | and you 'll learn as i go through it step by step a couple of interesting facts . so fact number one , we know that there 's a lot of glucose in the blood vessels . so lots of glucose in the blood vessels of someone with diabetes . so let 's draw in some glucose . | how does your body reflect the cells back into the body once being rotated through the blood vessels ? |
let 's talk about arteriolosclerosis . i 'm going to first point out a couple of important big picture ideas . why it is arteriolosclerosis matter ? well , we know that it 's basically soft , flexible kind of vessels like this that are very elastic and can expand , becoming very rigid , firm like pipes . and this is ba... | and one of their jobs is to make sure that that basement membrane is doing a good job of forming a barrier . and that basement membrane becomes very leaky . so the basement membrane actually becomes thicker -- which is counterintuitive , right -- becomes thicker . | how can the basement membrane becomes leaky ? |
let 's talk about arteriolosclerosis . i 'm going to first point out a couple of important big picture ideas . why it is arteriolosclerosis matter ? well , we know that it 's basically soft , flexible kind of vessels like this that are very elastic and can expand , becoming very rigid , firm like pipes . and this is ba... | and here is kind of fact number one , and that is that glucose can get into the endothelial cells without the help of insulin . so endothelial cells take in glucose without -- there 's the big catch -- without insulin . so they do n't need insulin to take in the glucose . there have other ways of getting the glucose in... | are there any other cells other than endothelial cells that do n't need insulin to take in glucose ? |
let 's talk about arteriolosclerosis . i 'm going to first point out a couple of important big picture ideas . why it is arteriolosclerosis matter ? well , we know that it 's basically soft , flexible kind of vessels like this that are very elastic and can expand , becoming very rigid , firm like pipes . and this is ba... | so you 've got protein hanging out in the blood vessel . and these are serum proteins . serum , s-e-r-u-m , proteins . | do the serum proteins themselves physically do anything when in the t. media ? |
for the past 12 weeks , we 've been investigating our living planet together , learning how it works on many levels , how populations of organisms interact , how communities thrive and ecosystems change , and how humans are wrecking the nice , perfectly functioning systems earth has been using for hundreds of thousands... | sometimes we get things wrong . for example , when you bring an invasive species into a place to eradicate another invasive species . sometimes you just end up with two invasive species on your hands , which collapses the ecosystem even more rapidly . the introduction of cane toads to australia in the 1930s to control ... | are there any examples of good invasive species which have benefited an ecosystem ? |
for the past 12 weeks , we 've been investigating our living planet together , learning how it works on many levels , how populations of organisms interact , how communities thrive and ecosystems change , and how humans are wrecking the nice , perfectly functioning systems earth has been using for hundreds of thousands... | but if there were a population of 100 bears , the population would likely be able to survive for 200 years . something to note , ecology involves a lot of math . so if you 're interested in this , that 's just the way it is . | and , on an unrelated side note , is there a bacteria/archae/protist that is capable of turning co2 into oxygen and organic carbon ? |
for the past 12 weeks , we 've been investigating our living planet together , learning how it works on many levels , how populations of organisms interact , how communities thrive and ecosystems change , and how humans are wrecking the nice , perfectly functioning systems earth has been using for hundreds of thousands... | now this stretch of the clark fork river runs unimpeded for the first time in over a century , and the restored area where the dam used to be is being turned into a state park . efforts like this show us conservation biology and restoration ecology in action . conservation biology involves measuring the biodiversity of... | can someone please explain the difference between conservation and restoration ecology along with some examples ? |
for the past 12 weeks , we 've been investigating our living planet together , learning how it works on many levels , how populations of organisms interact , how communities thrive and ecosystems change , and how humans are wrecking the nice , perfectly functioning systems earth has been using for hundreds of thousands... | now this stretch of the clark fork river runs unimpeded for the first time in over a century , and the restored area where the dam used to be is being turned into a state park . efforts like this show us conservation biology and restoration ecology in action . conservation biology involves measuring the biodiversity of... | which country is devoting , or spending the most on conservation as well as restoration ecology ? |
for the past 12 weeks , we 've been investigating our living planet together , learning how it works on many levels , how populations of organisms interact , how communities thrive and ecosystems change , and how humans are wrecking the nice , perfectly functioning systems earth has been using for hundreds of thousands... | and most of it washed into the reservoir created by the milltown dam . i mean , actually it was lucky that the dam was there -- it had only been completed six months before -- or the whole river system all the way to the pacific ocean would have been a toxic mess . as it happened , though , only about 160 kilometers of... | 0 would n't getting the dam out of the way release the rest of the toxic copper sediments ? |
for the past 12 weeks , we 've been investigating our living planet together , learning how it works on many levels , how populations of organisms interact , how communities thrive and ecosystems change , and how humans are wrecking the nice , perfectly functioning systems earth has been using for hundreds of thousands... | yet another , somewhat more invasive , restoration method is biological augmentation . rather than removing harmful substances , this involves adding organisms to the ecosystem to restore materials that are gone . plants that help fix nitrogen , like beans , acacia trees , and lupine , are often used to replenish nitro... | how long does it take to restore an ecosystem ? |
for the past 12 weeks , we 've been investigating our living planet together , learning how it works on many levels , how populations of organisms interact , how communities thrive and ecosystems change , and how humans are wrecking the nice , perfectly functioning systems earth has been using for hundreds of thousands... | yet another , somewhat more invasive , restoration method is biological augmentation . rather than removing harmful substances , this involves adding organisms to the ecosystem to restore materials that are gone . plants that help fix nitrogen , like beans , acacia trees , and lupine , are often used to replenish nitro... | what is an adaptation that organisms in the aphotic zone might have ? |
for the past 12 weeks , we 've been investigating our living planet together , learning how it works on many levels , how populations of organisms interact , how communities thrive and ecosystems change , and how humans are wrecking the nice , perfectly functioning systems earth has been using for hundreds of thousands... | sometimes you just end up with two invasive species on your hands , which collapses the ecosystem even more rapidly . the introduction of cane toads to australia in the 1930s to control beetles is a particularly infamous example . not only are they everywhere now , but because they 're toxic , they 're poisoning native... | kill off all the cane toad eating dingoes ? |
for the past 12 weeks , we 've been investigating our living planet together , learning how it works on many levels , how populations of organisms interact , how communities thrive and ecosystems change , and how humans are wrecking the nice , perfectly functioning systems earth has been using for hundreds of thousands... | sometimes we get things wrong . for example , when you bring an invasive species into a place to eradicate another invasive species . sometimes you just end up with two invasive species on your hands , which collapses the ecosystem even more rapidly . the introduction of cane toads to australia in the 1930s to control ... | are there any examples of good invasive species which have benefited an ecosystem ? |
for the past 12 weeks , we 've been investigating our living planet together , learning how it works on many levels , how populations of organisms interact , how communities thrive and ecosystems change , and how humans are wrecking the nice , perfectly functioning systems earth has been using for hundreds of thousands... | but if there were a population of 100 bears , the population would likely be able to survive for 200 years . something to note , ecology involves a lot of math . so if you 're interested in this , that 's just the way it is . | and , on an unrelated side note , is there a bacteria/archae/protist that is capable of turning co2 into oxygen and organic carbon ? |
for the past 12 weeks , we 've been investigating our living planet together , learning how it works on many levels , how populations of organisms interact , how communities thrive and ecosystems change , and how humans are wrecking the nice , perfectly functioning systems earth has been using for hundreds of thousands... | and finally , you have to get at what 's causing the decline and figure out how to address it . milltown dam actually gives us a good example of this process . in the winter of 1996 , authorities had to release some of the water behind the dam as an emergency measure because of a big ice floe in the river that was thre... | 0 wouldnt the ice break the dam anyway so it looked to me either way the fish would die ? |
for the past 12 weeks , we 've been investigating our living planet together , learning how it works on many levels , how populations of organisms interact , how communities thrive and ecosystems change , and how humans are wrecking the nice , perfectly functioning systems earth has been using for hundreds of thousands... | as it happened , though , only about 160 kilometers of the river was all toxic , messed up . a lot of it recuperated over time . but all that nasty hazardous waste was still sitting behind milltown dam . | why did the toads that they talked about at the time of why did it poison every thing in its path ? |
( lively piano music ) : we 're on the 4th floor of the museum of modern art in new york , and we 're looking at robert rauschenberg 's , `` bed . '' this is a combine , not quite a sculpture , not quite a painting , from 1955 . : so , combine means a combination of painting and sculpture ? : well , johns and rausch... | this is a combine , not quite a sculpture , not quite a painting , from 1955 . : so , combine means a combination of painting and sculpture ? : well , johns and rauschenberg were actually thinking about their art as between art and life , and what is that narrow space between the two ? | so a combine is always something that 's more of a painting and less of a sculpture , as is the case here , or could it be a work that more readily resembles a sculpture , but also has elements of painting ? |
( lively piano music ) : we 're on the 4th floor of the museum of modern art in new york , and we 're looking at robert rauschenberg 's , `` bed . '' this is a combine , not quite a sculpture , not quite a painting , from 1955 . : so , combine means a combination of painting and sculpture ? : well , johns and rausch... | : so , combine means a combination of painting and sculpture ? : well , johns and rauschenberg were actually thinking about their art as between art and life , and what is that narrow space between the two ? : instead of thinking about it between painting and sculpture between these two things that symbolize fine ar... | what challenges to conserving of art are presented when the art is made from things like pillows , quilts , sheets and housepaint ? |
( lively piano music ) : we 're on the 4th floor of the museum of modern art in new york , and we 're looking at robert rauschenberg 's , `` bed . '' this is a combine , not quite a sculpture , not quite a painting , from 1955 . : so , combine means a combination of painting and sculpture ? : well , johns and rausch... | what we 're looking at is , in fact , the stuff of a real bed . we 're looking at a real pillow . we 're looking at a real pillowcase , and a handmade quilted blanket , sheets , but if you look closely , you 're also seeing pencil and paint . | to use artifacts from the real world in their work ? |
we 've already seen scenarios where we start with a differential equation and then we generate a slope field that describes the solutions to the differential equation and then we use that to visualize those solutions . what i want to do in this video is do an exercise that takes us the other way , start with a slope f... | so , i 'm feeling pretty good about this , especially if we can knock this one out here , if we can knock that one out . so , dy/dx is equal to x over y . well , then when x equals one and y equals one , dy/dx would be equal to one , and this slope looks larger than one . | dy/dx = x+y -y dy = x dx 1/2 y^2 = 1/2x^2 + c1 then use an initial value to solve for the constant , which i did for 1 , -3 and ended up with y^2 = -x^2 + 10 am i even remotely on the right track here ? |
we 've already seen scenarios where we start with a differential equation and then we generate a slope field that describes the solutions to the differential equation and then we use that to visualize those solutions . what i want to do in this video is do an exercise that takes us the other way , start with a slope f... | our derivative here looks negative . it looks like negative two , which is consistent with this yellow differential equation . the slope here is definitely not a positive one , so we could rule this one out as well . | how do you solve the differential equation if we ca n't separate the variables ? |
we 've already seen scenarios where we start with a differential equation and then we generate a slope field that describes the solutions to the differential equation and then we use that to visualize those solutions . what i want to do in this video is do an exercise that takes us the other way , start with a slope f... | and it looks like if the solution contained , say , this point right over here , that would actually be a solution to the differential equation y is equal to negative x minus one and you can verify that . if y is equal to negative x minus one , then the x and negative x cancel out and you are just left with dy/dx is eq... | could n't you have just observed that the slop field vectors are level at ( 0,0 ) , ( 1 , -1 ) , ( 2 , -2 ) , which means y ' = 0 at those points thus y ' = x + y ? |
we 've already seen scenarios where we start with a differential equation and then we generate a slope field that describes the solutions to the differential equation and then we use that to visualize those solutions . what i want to do in this video is do an exercise that takes us the other way , start with a slope f... | and now that we 've done it , we can actually think about well , okay , what are the solutions for this differential equation going to look like . well , it depends where they start or what points they contain . if you have a solution that contains that point , it looks like it might do something like this . | what does sal mean when he said the solution depends on the points it contains ? |
we 've already seen scenarios where we start with a differential equation and then we generate a slope field that describes the solutions to the differential equation and then we use that to visualize those solutions . what i want to do in this video is do an exercise that takes us the other way , start with a slope f... | if you have a solution that contains that point , it looks like it might do something like this . if you had a solution that contained this point , it might do something like that . and , of course , it keeps going . | the shape of the graph is depended on the starting point and anything else ? |
we 've already seen scenarios where we start with a differential equation and then we generate a slope field that describes the solutions to the differential equation and then we use that to visualize those solutions . what i want to do in this video is do an exercise that takes us the other way , start with a slope f... | and you can also see what is happening here . when dy/dx is equal to x plus y , you would expect that as x increases for a given y your slope would increase and as y increases for a given x your slope increases . and we see that . | a man and his dog are runninng on a straight beach.at a given point in time the dog is 12m from his owner who strats running in a direction perpendicular to the beach with a certain constant speed.the dog runs twice as fast and always towards his owner.where do the man and and his dog meet ? |
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