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so here i want to talk about the gradient and the context of a contour map . so let 's say we have a multivariable function . a two-variable function f of x , y . and this one is just gon na equal x times y . so we can visualize this with a contour map just on the xy plane . so what i 'm gon na do is i 'm gon na go ov... | so it 's a good one to keep in the back of your mind . gradient is always perpendicular to contour lines . great . | why , then , do some of the vectors point towards contour lines that are closer together ( which makes sense because close contour lines indicate high steepness ) , yet in another section of the field the vectors are pointing toward contour lines that are farther apart ? |
so here i want to talk about the gradient and the context of a contour map . so let 's say we have a multivariable function . a two-variable function f of x , y . and this one is just gon na equal x times y . so we can visualize this with a contour map just on the xy plane . so what i 'm gon na do is i 'm gon na go ov... | something like that . but it 's probably gon na be scaled down because of the way we usually draw vector fields . and the entire field looks like this . | how to plot vector fields in microsoft mathematics ? |
so here i want to talk about the gradient and the context of a contour map . so let 's say we have a multivariable function . a two-variable function f of x , y . and this one is just gon na equal x times y . so we can visualize this with a contour map just on the xy plane . so what i 'm gon na do is i 'm gon na go ov... | and then kind of the reverse for when you take the partial derivative with respect to y. y looks like a variable . x looks like a constant . and the derivative is just that constant , x . and this can be visualized as a vector field in the xy plane as well . | using the power rule i thought the derivative of a constant was 0 why does he say it 's one ? |
let 's see if we can now give ourselves a more tangible understanding of what 's on the new sat and how it might be different than sats of the past . so right over here i have a bullet point list of kind of the major features , the defining features of the new sat , and starting up here are relevant words in context .... | so looking at what 's happening , and analyzing where kind of the conclusions are coming from and we can go into more depth in future videos on that . now the math portion , this is a big deal that the new sat -- classically the sat had been associated with , hey , maybe it 's a little bit trickier or things like that ... | do you have to take the psat test before the sat ? |
let 's see if we can now give ourselves a more tangible understanding of what 's on the new sat and how it might be different than sats of the past . so right over here i have a bullet point list of kind of the major features , the defining features of the new sat , and starting up here are relevant words in context .... | so looking at what 's happening , and analyzing where kind of the conclusions are coming from and we can go into more depth in future videos on that . now the math portion , this is a big deal that the new sat -- classically the sat had been associated with , hey , maybe it 's a little bit trickier or things like that ... | does the new sat include pre-calculus math problems ? |
let 's see if we can now give ourselves a more tangible understanding of what 's on the new sat and how it might be different than sats of the past . so right over here i have a bullet point list of kind of the major features , the defining features of the new sat , and starting up here are relevant words in context .... | then you 're gon na see the passport to advanced math , and these are the skills that allow you to have the knowledge to get higher level math that you will take in college . so you 're ready to take those pre-calculus , calculus , statistics courses that you might see in college , and then there 's problem solving and... | would taking pre-calculus in junior year benefit a student taking the sat at the end of 11th grade ( vs taking algebra 2 during junior year ) ? |
let 's see if we can now give ourselves a more tangible understanding of what 's on the new sat and how it might be different than sats of the past . so right over here i have a bullet point list of kind of the major features , the defining features of the new sat , and starting up here are relevant words in context .... | so looking at what 's happening , and analyzing where kind of the conclusions are coming from and we can go into more depth in future videos on that . now the math portion , this is a big deal that the new sat -- classically the sat had been associated with , hey , maybe it 's a little bit trickier or things like that ... | what age do you have to be to take the sat ? |
let 's see if we can now give ourselves a more tangible understanding of what 's on the new sat and how it might be different than sats of the past . so right over here i have a bullet point list of kind of the major features , the defining features of the new sat , and starting up here are relevant words in context .... | so looking at what 's happening , and analyzing where kind of the conclusions are coming from and we can go into more depth in future videos on that . now the math portion , this is a big deal that the new sat -- classically the sat had been associated with , hey , maybe it 's a little bit trickier or things like that ... | what 's the difference between sat i & sat ii ? |
let 's see if we can now give ourselves a more tangible understanding of what 's on the new sat and how it might be different than sats of the past . so right over here i have a bullet point list of kind of the major features , the defining features of the new sat , and starting up here are relevant words in context .... | so looking at what 's happening , and analyzing where kind of the conclusions are coming from and we can go into more depth in future videos on that . now the math portion , this is a big deal that the new sat -- classically the sat had been associated with , hey , maybe it 's a little bit trickier or things like that ... | will i be needing to take an sat anytime soon ? |
let 's see if we can now give ourselves a more tangible understanding of what 's on the new sat and how it might be different than sats of the past . so right over here i have a bullet point list of kind of the major features , the defining features of the new sat , and starting up here are relevant words in context .... | so looking at what 's happening , and analyzing where kind of the conclusions are coming from and we can go into more depth in future videos on that . now the math portion , this is a big deal that the new sat -- classically the sat had been associated with , hey , maybe it 's a little bit trickier or things like that ... | for the new sat , should i spend time studying a load of sat vocab like i did for the last sat ? |
let 's see if we can now give ourselves a more tangible understanding of what 's on the new sat and how it might be different than sats of the past . so right over here i have a bullet point list of kind of the major features , the defining features of the new sat , and starting up here are relevant words in context .... | so the sections or the types of problems you 'll see are the heart of algebra . this is really the core of algebra that really matters . then you 're gon na see the passport to advanced math , and these are the skills that allow you to have the knowledge to get higher level math that you will take in college . | what do i do if i took algebra 1 in grade 9 , geometry in grade 10 , algebra 2 in 11th grade , and going to take pre calc in 12th grade ? |
let 's see if we can now give ourselves a more tangible understanding of what 's on the new sat and how it might be different than sats of the past . so right over here i have a bullet point list of kind of the major features , the defining features of the new sat , and starting up here are relevant words in context .... | so i would have gone with that . but anyway , this is n't about doing the questions , but more seeing how these questions -- what they actually look like . these are n't crazy words that you would only just memorize for a test , these are useful words to know in life , and once again we have a context of when we would ... | how will i be fully prepared for the sat if i do n't know some of the math that will be on the test ? |
let 's see if we can now give ourselves a more tangible understanding of what 's on the new sat and how it might be different than sats of the past . so right over here i have a bullet point list of kind of the major features , the defining features of the new sat , and starting up here are relevant words in context .... | what 's different about the new sat , is that they 're going to be relevant words , and not just relevant words in a vacuum , they 're going to be in a context , in a situation where you might be editing a passage or reading something , so it 's going to matter to understand what those words are , and once again , they... | should i take the writing section of the sat and , if so , why is it better to do the optional writing part ? |
let 's see if we can now give ourselves a more tangible understanding of what 's on the new sat and how it might be different than sats of the past . so right over here i have a bullet point list of kind of the major features , the defining features of the new sat , and starting up here are relevant words in context .... | all of these things happen together in the real world , and it might not just be data evidence , it could be looking at evidence , an author 's argument , so it could be written evidence of some sort as well . the essay , the optional essay on the new sat is going to be about analyzing a source . so looking at what 's ... | is there going be formula 's on the new sat ? |
let 's see if we can now give ourselves a more tangible understanding of what 's on the new sat and how it might be different than sats of the past . so right over here i have a bullet point list of kind of the major features , the defining features of the new sat , and starting up here are relevant words in context .... | and this is an example of that , i have a passage of relevant words in context , and this is going to be from the new sat writing section . and the new sat writing section , as you see , we 're in context here , and this little four with the circle around it , this shows that , hey , this part of the passage is referri... | the writing part , is there any way to take an sat and still take the writing part ? |
let 's see if we can now give ourselves a more tangible understanding of what 's on the new sat and how it might be different than sats of the past . so right over here i have a bullet point list of kind of the major features , the defining features of the new sat , and starting up here are relevant words in context .... | i know i keep repeating that , but you see that theme that they 're not just kind of brain teaser type things , these are things that you will see as you go through your college career . analysis in science and social studies . so even though the sections are formerly reading and math and writing , they 're going to us... | is the history section mandatory for people who want to take science ? |
let 's see if we can now give ourselves a more tangible understanding of what 's on the new sat and how it might be different than sats of the past . so right over here i have a bullet point list of kind of the major features , the defining features of the new sat , and starting up here are relevant words in context .... | so looking at what 's happening , and analyzing where kind of the conclusions are coming from and we can go into more depth in future videos on that . now the math portion , this is a big deal that the new sat -- classically the sat had been associated with , hey , maybe it 's a little bit trickier or things like that ... | what 's the difference between the act and the sat ? |
let 's see if we can now give ourselves a more tangible understanding of what 's on the new sat and how it might be different than sats of the past . so right over here i have a bullet point list of kind of the major features , the defining features of the new sat , and starting up here are relevant words in context .... | so looking at what 's happening , and analyzing where kind of the conclusions are coming from and we can go into more depth in future videos on that . now the math portion , this is a big deal that the new sat -- classically the sat had been associated with , hey , maybe it 's a little bit trickier or things like that ... | what types of math should i do to take the sat ? |
let 's see if we can now give ourselves a more tangible understanding of what 's on the new sat and how it might be different than sats of the past . so right over here i have a bullet point list of kind of the major features , the defining features of the new sat , and starting up here are relevant words in context .... | so looking at what 's happening , and analyzing where kind of the conclusions are coming from and we can go into more depth in future videos on that . now the math portion , this is a big deal that the new sat -- classically the sat had been associated with , hey , maybe it 's a little bit trickier or things like that ... | what is the sat equivalent in the uk ? |
let 's see if we can now give ourselves a more tangible understanding of what 's on the new sat and how it might be different than sats of the past . so right over here i have a bullet point list of kind of the major features , the defining features of the new sat , and starting up here are relevant words in context .... | so looking at what 's happening , and analyzing where kind of the conclusions are coming from and we can go into more depth in future videos on that . now the math portion , this is a big deal that the new sat -- classically the sat had been associated with , hey , maybe it 's a little bit trickier or things like that ... | can i take two sat tests ? |
let 's see if we can now give ourselves a more tangible understanding of what 's on the new sat and how it might be different than sats of the past . so right over here i have a bullet point list of kind of the major features , the defining features of the new sat , and starting up here are relevant words in context .... | but anyway , this is n't about doing the questions , but more seeing how these questions -- what they actually look like . these are n't crazy words that you would only just memorize for a test , these are useful words to know in life , and once again we have a context of when we would use it . we would use it maybe to... | i know it is suggested that one should not sit down and just memorize numerous vocabulary words for the new sat , but what should i do about this issue of mine ? |
let 's see if we can now give ourselves a more tangible understanding of what 's on the new sat and how it might be different than sats of the past . so right over here i have a bullet point list of kind of the major features , the defining features of the new sat , and starting up here are relevant words in context .... | all of these things happen together in the real world , and it might not just be data evidence , it could be looking at evidence , an author 's argument , so it could be written evidence of some sort as well . the essay , the optional essay on the new sat is going to be about analyzing a source . so looking at what 's ... | is the optional essay one that is highly recommended for college applications ? |
let 's see if we can now give ourselves a more tangible understanding of what 's on the new sat and how it might be different than sats of the past . so right over here i have a bullet point list of kind of the major features , the defining features of the new sat , and starting up here are relevant words in context .... | so looking at what 's happening , and analyzing where kind of the conclusions are coming from and we can go into more depth in future videos on that . now the math portion , this is a big deal that the new sat -- classically the sat had been associated with , hey , maybe it 's a little bit trickier or things like that ... | is there the part of `` sentence completion '' in the new sat ? |
let 's see if we can now give ourselves a more tangible understanding of what 's on the new sat and how it might be different than sats of the past . so right over here i have a bullet point list of kind of the major features , the defining features of the new sat , and starting up here are relevant words in context .... | so learn in school , and it 's even a subset of that . it 's kind of the most important subset especially for being college and life ready . so the sections or the types of problems you 'll see are the heart of algebra . | why is the sat so important to get into a college ? |
let 's see if we can now give ourselves a more tangible understanding of what 's on the new sat and how it might be different than sats of the past . so right over here i have a bullet point list of kind of the major features , the defining features of the new sat , and starting up here are relevant words in context .... | and the reason why that 's important , is because you will see this throughout life . it 's not like reading or writing is somehow separated from data . all of these things happen together in the real world , and it might not just be data evidence , it could be looking at evidence , an author 's argument , so it could ... | is it monitory to do the writing portion on the test as a avid student ? |
let 's see if we can now give ourselves a more tangible understanding of what 's on the new sat and how it might be different than sats of the past . so right over here i have a bullet point list of kind of the major features , the defining features of the new sat , and starting up here are relevant words in context .... | so i would have gone with that . but anyway , this is n't about doing the questions , but more seeing how these questions -- what they actually look like . these are n't crazy words that you would only just memorize for a test , these are useful words to know in life , and once again we have a context of when we would ... | will we always have access to all the questions and practices ? |
let 's see if we can now give ourselves a more tangible understanding of what 's on the new sat and how it might be different than sats of the past . so right over here i have a bullet point list of kind of the major features , the defining features of the new sat , and starting up here are relevant words in context .... | this is really the core of algebra that really matters . then you 're gon na see the passport to advanced math , and these are the skills that allow you to have the knowledge to get higher level math that you will take in college . so you 're ready to take those pre-calculus , calculus , statistics courses that you mig... | do you have to take both the sat and the act to get into a college ? |
let 's see if we can now give ourselves a more tangible understanding of what 's on the new sat and how it might be different than sats of the past . so right over here i have a bullet point list of kind of the major features , the defining features of the new sat , and starting up here are relevant words in context .... | so looking at what 's happening , and analyzing where kind of the conclusions are coming from and we can go into more depth in future videos on that . now the math portion , this is a big deal that the new sat -- classically the sat had been associated with , hey , maybe it 's a little bit trickier or things like that ... | should a student that is a junior in high school ( who takes algebra 2 full year ) taking the new sat this year be worried about the calculus questions on the math sections ? |
let 's see if we can now give ourselves a more tangible understanding of what 's on the new sat and how it might be different than sats of the past . so right over here i have a bullet point list of kind of the major features , the defining features of the new sat , and starting up here are relevant words in context .... | so it 's a really , i would say , good incentive to get familiar with things like to get familiar with things like the gandhi 's quit india speech , or the declaration of independence , or the federalist papers . you 're going to see this type of thing in the new sat in a reading passage or to kind of make some judgeme... | when i take the sat test , can i write/underline/make marks on it ? |
let 's see if we can now give ourselves a more tangible understanding of what 's on the new sat and how it might be different than sats of the past . so right over here i have a bullet point list of kind of the major features , the defining features of the new sat , and starting up here are relevant words in context .... | so looking at what 's happening , and analyzing where kind of the conclusions are coming from and we can go into more depth in future videos on that . now the math portion , this is a big deal that the new sat -- classically the sat had been associated with , hey , maybe it 's a little bit trickier or things like that ... | what does sat stand for ? |
let 's see if we can now give ourselves a more tangible understanding of what 's on the new sat and how it might be different than sats of the past . so right over here i have a bullet point list of kind of the major features , the defining features of the new sat , and starting up here are relevant words in context .... | and then , the last bullet point here , this is just kind of a high level point , and this emphasizes that this new sat really is about what do you know , not having to think about , hey do i guess , do i not guess ? there 's no penalty for wrong answers . in the past , there was a penalty for wrong answers , but now t... | in the psat does the new rule about `` no penalties for wrong answers '' still apply ? |
let 's see if we can now give ourselves a more tangible understanding of what 's on the new sat and how it might be different than sats of the past . so right over here i have a bullet point list of kind of the major features , the defining features of the new sat , and starting up here are relevant words in context .... | so looking at what 's happening , and analyzing where kind of the conclusions are coming from and we can go into more depth in future videos on that . now the math portion , this is a big deal that the new sat -- classically the sat had been associated with , hey , maybe it 's a little bit trickier or things like that ... | why did the sat change ? |
let 's see if we can now give ourselves a more tangible understanding of what 's on the new sat and how it might be different than sats of the past . so right over here i have a bullet point list of kind of the major features , the defining features of the new sat , and starting up here are relevant words in context .... | so looking at what 's happening , and analyzing where kind of the conclusions are coming from and we can go into more depth in future videos on that . now the math portion , this is a big deal that the new sat -- classically the sat had been associated with , hey , maybe it 's a little bit trickier or things like that ... | do you have to take the sat in 10th grade ? |
let 's see if we can now give ourselves a more tangible understanding of what 's on the new sat and how it might be different than sats of the past . so right over here i have a bullet point list of kind of the major features , the defining features of the new sat , and starting up here are relevant words in context .... | and you look at the choices here , evacuated , departed , retired , once again , all words that you will see in college , and you will see in life , at least for this one , and my job here is n't to answer the sat questions , but hey , this feels like he departed from the traditions . so i would have gone with that . b... | would sat ii increase my chances of getting into a good college ? |
let 's see if we can now give ourselves a more tangible understanding of what 's on the new sat and how it might be different than sats of the past . so right over here i have a bullet point list of kind of the major features , the defining features of the new sat , and starting up here are relevant words in context .... | all of these things happen together in the real world , and it might not just be data evidence , it could be looking at evidence , an author 's argument , so it could be written evidence of some sort as well . the essay , the optional essay on the new sat is going to be about analyzing a source . so looking at what 's ... | what is a narrative essay ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | well , for this , it will probably be useful to use a calculator . and the way that we 'd use a calculator is we would use the inverse tan function . so we could rewrite this as we 're going to take the inverse tangent -- and sometimes it 's written as tangent with this negative 1 superscript . | could someone explain again what is the difference between tan and tan-1 ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | well , for this , it will probably be useful to use a calculator . and the way that we 'd use a calculator is we would use the inverse tan function . so we could rewrite this as we 're going to take the inverse tangent -- and sometimes it 's written as tangent with this negative 1 superscript . | why did sal use tan-1 instead of tan ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | i was about to say maybe it should be a man in black . a men in black agent is standing at ground level , 54 meters across the eiffel square . so 54 meters from , i guess you could say the center of the base of the eiffel tower , aiming his laser gun at the alien . | is n't tan-1 the same as when we divide a square root ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | so we could rewrite this as we 're going to take the inverse tangent -- and sometimes it 's written as tangent with this negative 1 superscript . so the inverse tangent of tan of theta is going to be equal to the inverse tangent of 324/54 . and just to be clear , what is this inverse tangent ? | is n't cot is the inverse of tan ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | well , i 'm just going to assume that they want our answers in degrees . so let me make sure my calculator is actually in degree mode . so i 'll go to the 2nd mode right over here . | would the alien died if the mib man shot with rounded degree and not actual supposed degree ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | this width right over here is 54 meters . it is a right triangle . what they 're really asking us is what is this angle right over here . | what is the difference between a right and a left triangle ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | and these are really by definition . so you just have to know this , and soh cah toa helps us . sine is opposite over hypotenuse . | does the majority of the answers in solving mathematical problems for trigonometry while using soh cah toa have to be in degrees ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | and the way that we 'd use a calculator is we would use the inverse tan function . so we could rewrite this as we 're going to take the inverse tangent -- and sometimes it 's written as tangent with this negative 1 superscript . so the inverse tangent of tan of theta is going to be equal to the inverse tangent of 324/5... | can anyone explain exactly what the inverse tangent is ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | what they 're really asking us is what is this angle right over here . and they 've given us two pieces of information . they gave us the side that is opposite the angle . | can you solve a triangle if all 3 angles are given when its area is also given ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | and the way that we 'd use a calculator is we would use the inverse tan function . so we could rewrite this as we 're going to take the inverse tangent -- and sometimes it 's written as tangent with this negative 1 superscript . so the inverse tangent of tan of theta is going to be equal to the inverse tangent of 324/5... | so what was the point then of him writing tangent inverse of tangent of theta ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | so the height of this right triangle is 324 meters . this width right over here is 54 meters . it is a right triangle . what they 're really asking us is what is this angle right over here . | a tangent is a function , right ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . | if a=3 what is sin a ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | so we could rewrite this as we 're going to take the inverse tangent -- and sometimes it 's written as tangent with this negative 1 superscript . so the inverse tangent of tan of theta is going to be equal to the inverse tangent of 324/54 . and just to be clear , what is this inverse tangent ? | inverse of tan theta is 1/tan theta ... ... so , 1/tan theta is 1/ ( opposite / adjacent ) now , this will get reciprocal ... ... .. now it 's called adjacent / opposite or cot theta so now , inverse of tan theta is adjacent / opposite now , ca n't inverse of tan theta be simply called as cot theta ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | and the way that we 'd use a calculator is we would use the inverse tan function . so we could rewrite this as we 're going to take the inverse tangent -- and sometimes it 's written as tangent with this negative 1 superscript . so the inverse tangent of tan of theta is going to be equal to the inverse tangent of 324/5... | could someone explain again what is the difference between sin-1 and tan-1 ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | what angle , when i take its tangent , gives me 324/54 ? well , for this , it will probably be useful to use a calculator . and the way that we 'd use a calculator is we would use the inverse tan function . so we could rewrite this as we 're going to take the inverse tangent -- and sometimes it 's written as tangent wi... | could sal use sin-1 instead of sin ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | so you just have to know this , and soh cah toa helps us . sine is opposite over hypotenuse . cosine is adjacent over hypotenuse . | if you know the degree of 1 angle , and the length of the opposite angle , can you find the hypotenuse ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | it 's how we will solve for theta . so let 's get our calculator out . and let 's say that we want our answer in degrees . | this may just be my calculator but when i take the tan^-1 of 6 i get his answer but if i input it as ( 324/54 ) i get .10510 ... .. any ideas/suggestions ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | well , for this , it will probably be useful to use a calculator . and the way that we 'd use a calculator is we would use the inverse tan function . so we could rewrite this as we 're going to take the inverse tangent -- and sometimes it 's written as tangent with this negative 1 superscript . | when should you use inverse or regular trig ratios ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . | is the difference for when you are finding the sides or the angles ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | and these are really by definition . so you just have to know this , and soh cah toa helps us . sine is opposite over hypotenuse . | when do we have to use soh cah toa ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | and they 've given us two pieces of information . they gave us the side that is opposite the angle . and they 've given us the side that is adjacent to the angle . | could you solve the problem above with one side and one angle ( 90 degrees ) ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | well , i 'm just going to assume that they want our answers in degrees . so let me make sure my calculator is actually in degree mode . so i 'll go to the 2nd mode right over here . | for cc geometry , should you keep the calculator at degree mode ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | well , for this , it will probably be useful to use a calculator . and the way that we 'd use a calculator is we would use the inverse tan function . so we could rewrite this as we 're going to take the inverse tangent -- and sometimes it 's written as tangent with this negative 1 superscript . | what is the difference b/w tan ^-1 and cot ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | well , for this , it will probably be useful to use a calculator . and the way that we 'd use a calculator is we would use the inverse tan function . so we could rewrite this as we 're going to take the inverse tangent -- and sometimes it 's written as tangent with this negative 1 superscript . | how do you use inverse of sine and cosine ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | so we could rewrite this as we 're going to take the inverse tangent -- and sometimes it 's written as tangent with this negative 1 superscript . so the inverse tangent of tan of theta is going to be equal to the inverse tangent of 324/54 . and just to be clear , what is this inverse tangent ? | why was the inverse of tan calculated instead of tan ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | and the way that we 'd use a calculator is we would use the inverse tan function . so we could rewrite this as we 're going to take the inverse tangent -- and sometimes it 's written as tangent with this negative 1 superscript . so the inverse tangent of tan of theta is going to be equal to the inverse tangent of 324/5... | is n't the inverse of tangent called cotangent ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | this width right over here is 54 meters . it is a right triangle . what they 're really asking us is what is this angle right over here . | why do we assume that it is a right angled triangle ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | so what trig function deals with opposite and adjacent ? and to remind ourselves , we can write , like i always like to do , soh , cah , toa . and these are really by definition . | does sal multiply both sides by tan^-1 like we do in linear equations ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | well , for this , it will probably be useful to use a calculator . and the way that we 'd use a calculator is we would use the inverse tan function . so we could rewrite this as we 're going to take the inverse tangent -- and sometimes it 's written as tangent with this negative 1 superscript . | why does sal use the inverse tan function ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | and these are really by definition . so you just have to know this , and soh cah toa helps us . sine is opposite over hypotenuse . | for the question , instead of using soh cah toa , could you not just use the cosine rule that states : 324 squared + 54 squared - ( 2ab ) cos 90 ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | and the way that we 'd use a calculator is we would use the inverse tan function . so we could rewrite this as we 're going to take the inverse tangent -- and sometimes it 's written as tangent with this negative 1 superscript . so the inverse tangent of tan of theta is going to be equal to the inverse tangent of 324/5... | what is an inverse tangent ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | now you might say , well , ok , that 's fine . what angle , when i take its tangent , gives me 324/54 ? well , for this , it will probably be useful to use a calculator . and the way that we 'd use a calculator is we would use the inverse tan function . so we could rewrite this as we 're going to take the inverse tange... | how do i input inverse tangent in calculator ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | they gave us the side that is opposite the angle . and they 've given us the side that is adjacent to the angle . so what trig function deals with opposite and adjacent ? | how would you find a length given one side ( not hypotenuse ) and three other angles ? |
a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | a tiny but horrible alien is standing at the top of the eiffel tower -- so this is where the tiny but horrible alien is -- which is 324 meters tall -- and they label that , the height of the eiffel tower -- and threatening to destroy the city of paris . a men in black -- or a men in black agent . i was about to say may... | what is a men in black agent ? |
you do n't need numbers or fancy equations to prove the pythagorean theorem , all you need is a piece of paper . there is a ton of ways to prove it , and people are inventing new ones all the time , but i am going to show you my favorite . only instead of looking at diagrams , we 're gon na fold it . first , you need a... | so be sure to not believe me when i tell you things like : this is a square . think of a few ways you could convince yourself that no matter what the triangles on the outside look like , this will always be a square , and not some kind of a rombus or parallelogram or dolphin or something . or , you know , maybe it is a... | or more clearly , why would you have to describe the attributes of a dolphin , if in your perspective , it could be anything ? |
you do n't need numbers or fancy equations to prove the pythagorean theorem , all you need is a piece of paper . there is a ton of ways to prove it , and people are inventing new ones all the time , but i am going to show you my favorite . only instead of looking at diagrams , we 're gon na fold it . first , you need a... | if you called the sides of your triangle something more abstract , like : a , b , and c , you 'd of course have a squared plus b squared equals c squared so quick review : step 0 : aquire a paper square . ok , step one : fold it in half three times . step 2 : fold parallel to the edges anywhere you choose and extend th... | how does step `` 0 '' exist ? |
you do n't need numbers or fancy equations to prove the pythagorean theorem , all you need is a piece of paper . there is a ton of ways to prove it , and people are inventing new ones all the time , but i am going to show you my favorite . only instead of looking at diagrams , we 're gon na fold it . first , you need a... | you do n't need numbers or fancy equations to prove the pythagorean theorem , all you need is a piece of paper . there is a ton of ways to prove it , and people are inventing new ones all the time , but i am going to show you my favorite . | how come when someone akes a question vi doesent aculay answer it someelse does how come ? |
you do n't need numbers or fancy equations to prove the pythagorean theorem , all you need is a piece of paper . there is a ton of ways to prove it , and people are inventing new ones all the time , but i am going to show you my favorite . only instead of looking at diagrams , we 're gon na fold it . first , you need a... | you do n't need numbers or fancy equations to prove the pythagorean theorem , all you need is a piece of paper . there is a ton of ways to prove it , and people are inventing new ones all the time , but i am going to show you my favorite . | how mathematically pythagorean theorem can be proofed ? |
you do n't need numbers or fancy equations to prove the pythagorean theorem , all you need is a piece of paper . there is a ton of ways to prove it , and people are inventing new ones all the time , but i am going to show you my favorite . only instead of looking at diagrams , we 're gon na fold it . first , you need a... | think of a few ways you could convince yourself that no matter what the triangles on the outside look like , this will always be a square , and not some kind of a rombus or parallelogram or dolphin or something . or , you know , maybe it is a dolphin , in which case you should define what a dolphin is and then show tha... | how can we define s.a.s ? |
you do n't need numbers or fancy equations to prove the pythagorean theorem , all you need is a piece of paper . there is a ton of ways to prove it , and people are inventing new ones all the time , but i am going to show you my favorite . only instead of looking at diagrams , we 're gon na fold it . first , you need a... | this is where you are choosing how long and pointy , or short and fat , your right triangle is going to be , because this is a general proof . now when you unwrap it , you 'll have a square centered in your square . extend those creases and make them sharp , and now we 've got we 've got four lines all the same distanc... | hi vi , how can you fold a square into 3 equal parts ? |
you do n't need numbers or fancy equations to prove the pythagorean theorem , all you need is a piece of paper . there is a ton of ways to prove it , and people are inventing new ones all the time , but i am going to show you my favorite . only instead of looking at diagrams , we 're gon na fold it . first , you need a... | which has to be equal to this area , which is hypotenus squared . if you called the sides of your triangle something more abstract , like : a , b , and c , you 'd of course have a squared plus b squared equals c squared so quick review : step 0 : aquire a paper square . ok , step one : fold it in half three times . | i know to figure this out is a2+b2=c2 , but how are you suppose to know which side is a , b , or c ? |
you do n't need numbers or fancy equations to prove the pythagorean theorem , all you need is a piece of paper . there is a ton of ways to prove it , and people are inventing new ones all the time , but i am going to show you my favorite . only instead of looking at diagrams , we 're gon na fold it . first , you need a... | step 2 : make a crease along this triangle , parallel to the side of the triangle that has the edges of the paper . you can make it anywhere you want . this is where you are choosing how long and pointy , or short and fat , your right triangle is going to be , because this is a general proof . | how long did it take vi hart to make this video ? |
you do n't need numbers or fancy equations to prove the pythagorean theorem , all you need is a piece of paper . there is a ton of ways to prove it , and people are inventing new ones all the time , but i am going to show you my favorite . only instead of looking at diagrams , we 're gon na fold it . first , you need a... | if you called the sides of your triangle something more abstract , like : a , b , and c , you 'd of course have a squared plus b squared equals c squared so quick review : step 0 : aquire a paper square . ok , step one : fold it in half three times . step 2 : fold parallel to the edges anywhere you choose and extend th... | how do you fold a paper 12 times ? |
you do n't need numbers or fancy equations to prove the pythagorean theorem , all you need is a piece of paper . there is a ton of ways to prove it , and people are inventing new ones all the time , but i am going to show you my favorite . only instead of looking at diagrams , we 're gon na fold it . first , you need a... | repeat on the following two sides . the original paper minus those four triangles , gives us a lovely square . how much paper is this ? well , the length of a side is the hypotenus of one of these triangles . | hey vi how did your paper suddenly split or did it just trick my eyes ? |
i 've got a transformation t. when you apply the transformation t to some x in your domain , it is equivalent to multiplying that x in your domain , or that vector . by the matrix a . and let 's say we know the linear transformation t can be -- that 's transformation matrix when you put it in reduced row echelon form -... | so this equation simplifies to the in t-inverse applied to c times some vector a , is equal to this thing , c times t-inverse times some vector a . and just like that , we 've met our second condition for being a linear transformation . the first condition was met up here . so now we know . | if the first condition for linearity is satisfied , wo n't the second condition be satisfied too ? |
i 've got a transformation t. when you apply the transformation t to some x in your domain , it is equivalent to multiplying that x in your domain , or that vector . by the matrix a . and let 's say we know the linear transformation t can be -- that 's transformation matrix when you put it in reduced row echelon form -... | or we can take it the other way . t applied to two separate vectors -- so we call this one vector right here , and this vector right here . so in this case i have a t applied to one vector , and i 'm summing it to a t applied to another vector . | if we know that the transformation of two added vectors is the same as their transformations added , then multiplying one vector by c could be seen as adding another vector to it also , right ? |
i 've got a transformation t. when you apply the transformation t to some x in your domain , it is equivalent to multiplying that x in your domain , or that vector . by the matrix a . and let 's say we know the linear transformation t can be -- that 's transformation matrix when you put it in reduced row echelon form -... | well the best way to get rid of those t 's is to take the composition with t-inverse on both sides . or take the t-inverse transformation of both sides of this equation . so let 's do that . | is it simply to find the perpendicular line to our equation , or rather the equation of the original equation flipped over the y=x axis ? |
i 've got a transformation t. when you apply the transformation t to some x in your domain , it is equivalent to multiplying that x in your domain , or that vector . by the matrix a . and let 's say we know the linear transformation t can be -- that 's transformation matrix when you put it in reduced row echelon form -... | now we know what a transformation -- what it means to be invertible . we know what the conditions are for invertibility . so this begs the next question . | or does invertibility imply linearity ? |
i 've got a transformation t. when you apply the transformation t to some x in your domain , it is equivalent to multiplying that x in your domain , or that vector . by the matrix a . and let 's say we know the linear transformation t can be -- that 's transformation matrix when you put it in reduced row echelon form -... | so we can rewrite this thing right here as being equal to the sum of these two things . in fact we do n't even have to rewrite it . we can just write it 's equal to -- this transformation is equal to this . | to add on to fares comment : do n't we only need the fact that t is injective to show that t ( a ) = t ( b ) implies a = b ? |
i 've got a transformation t. when you apply the transformation t to some x in your domain , it is equivalent to multiplying that x in your domain , or that vector . by the matrix a . and let 's say we know the linear transformation t can be -- that 's transformation matrix when you put it in reduced row echelon form -... | that 's what this left hand side is . this part right here , t-inverse of t of this , these first two steps i 'm just writing as a composition of t-inverse with t applied to this right here . that right there is the same thing as that right there . | does associativity only apply to linear transformations ? |
i 've got a transformation t. when you apply the transformation t to some x in your domain , it is equivalent to multiplying that x in your domain , or that vector . by the matrix a . and let 's say we know the linear transformation t can be -- that 's transformation matrix when you put it in reduced row echelon form -... | we know that t , if we take -- let me put it this way . we know that t of x is equal to ax . so if we write t-inverse , the composition of t-inverse with t applied to some vector x is going to be equal to first , a being applied to x is going to be equal to ax , this a right here , ax . and then you 're going to apply ... | regarding syntax , t^-1 ( b ) , b , should have a vector arrow above it , and at 1 ax , should also have a vector arrow above the x ? |
i 've got a transformation t. when you apply the transformation t to some x in your domain , it is equivalent to multiplying that x in your domain , or that vector . by the matrix a . and let 's say we know the linear transformation t can be -- that 's transformation matrix when you put it in reduced row echelon form -... | but what 's interesting here is , this composition is equal to that , but it 's also equal to the identity transformation on rn applied to that vector x , which is equal to the identity matrix applied to x . right ? that is the n by n matrix , so when you multiply by anything , you get that anything again . | but we do n't know for sure that a and b are members of the domain of t-1 right ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | but 36 factorial would go all the way down to 27 , 26 , 25 . it would just keep going . but we stopped only nine away from 36 . | would we multiply the final result shown by 4 ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | that is 36 factorial . now what is 36 minus 9 factorial , that 's 27 factorial . so if you divide by 27 factorial , 27 factorial is 27 times 26 , all the way down to 1 . | would you be able to simplify the factorial expression by dividing by 9 ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | but 36 factorial would go all the way down to 27 , 26 , 25 . it would just keep going . but we stopped only nine away from 36 . | how would you compute the number of distinct permutations you can get from the word architecture ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . | always resulting in an integer ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | and this right here is called 36 choose 9 . and sometimes you 'll see this formula written like this , n choose k. and they 'll write the formula as equal to n factorial over n minus k factorial , and also in the denominator , k factorial . and this is a general formula that if you have n things , and you want to find ... | how would the formula for combination and permutation change if k > n ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | so 27 factorial -- so let 's think about this -- 36 factorial , it 'd be 36 times 35 , you keep going all the way , times 28 times 27 , going all the way down to 1 . that is 36 factorial . now what is 36 minus 9 factorial , that 's 27 factorial . so if you divide by 27 factorial , 27 factorial is 27 times 26 , all the ... | what if the denominator became 0 factorial ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | i can put a parentheses -- divided by parentheses , 9 times 8 , times 7 , times 6 , times 5 , times 4 , times 3 , times 2 , times 1 . now , hopefully the calculator can handle this . and it gave us this number , 94,143,280 . | why does sal put the denominator in parenthesis when he 's using the calculator ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | fair enough . how many 9 card hands are possible ? so let 's think about it . | how many 6-card hands are possible ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | fair enough . how many 9 card hands are possible ? so let 's think about it . | how many fewer 5-card hands are available than 6-card hands ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | well , i can do it this way . i can put a parentheses -- divided by parentheses , 9 times 8 , times 7 , times 6 , times 5 , times 4 , times 3 , times 2 , times 1 . now , hopefully the calculator can handle this . | so i wondered : when taking 8 random questions from a pool of 20 possible questions , what are the odds of having 2 or more times the same question ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | right ? i 'm going to pick nine cards for my hand . and so for the very first card , how many possible cards can i pick from ? well , there 's 36 unique cards , so for that first slot , there 's 36 . but then that 's now part of my hand . | a card is drown at random from a well suffel packs of cards.what is the probability that it is a heart or a quine ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | so we have to divide this by the way nine cards can be rearranged . so how many ways can nine cards be rearranged ? if i have nine cards and i 'm going to pick one of nine to be in the first slot , well , that means i have 9 ways to put something in the first slot . | how many unique ways are there to arrange the letters in the word that ? |
a card game using 36 unique cards , four suits , diamonds , hearts , clubs and spades -- this should be spades , not spaces -- with cards numbered from 1 to 9 in each suit . a hand is chosen . a hand is a collection of 9 cards , which can be sorted however the player chooses . fair enough . how many 9 card hands are po... | so this is 36 factorial , so this part right here , that part right there , is not just 36 factorial . it 's 36 factorial divided by 36 , minus 9 factorial . what is 36 minus 9 ? | would n't it be 36 factorial over nine factorial instead of 36*35*34 ... 30*29*28 ? |
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