Parametric equations 1 | Parametric equations and polar coordinates | Precalculus | Khan Academy
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- Опубликовано: 1 окт 2024
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Introduction to parametric equations
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Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!
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I have my Calc 2 final tomorrow morning at 7 am and I would absolutely love to be in that car driving off of the cliff
@@Ryan50Ryan I ended up getting a 95%, which was a MASSIVE surprise
Well
That's a world with no air, you would have died without driving off
@@ScrawnyCFB congratulations ❤️❤️❤️❤️❤️
@@ScrawnyCFB yayy nice job
❤❤❤❤❤😂😂😂😂
Why am I being taught this at the very end of Calc 2?
Same here. I'm confused as to why this video is categorized as precalc.
Same
@@Lucky10279 this topic is involved in precalculus textbooks
@@rayyfire5738 Clearly, it varies by curriculum, as a lot of other people said they're learning it a lot later.
@@Lucky10279 the curriculum is not the textbook, of course it would vary by curriculum
as a mechanical engineering student, relating this to physics helped immensely. thank you.
Same
It's been 8 years. How has ur life changed?
@@bychen5011 i wanna know too
How has your life changed?
when i saw projectile motions i got so triggered :( ptsd got me
"And this car is not just sitting on the cliff, its driving off of it."
I love Sal that much more now.
I love this dude .. lol thanks Sal
Why is this video more helpful than my pre-cal teacher?
Pa-RAMETER. Parameter. ...pa-rameter.
This man has literally saved my life in high school. And will still be there in college...haha I wish every teacher of mine taught like him, learning is SO EASY.
me too man. 3 weeks till final and I'm stuck on this shit.
lol its been 9 years, do you still use maths often in ur career? Thx just asking :)
parameter. parameter. parammmmeterrrr. hahaha
can someone explain at 4:24 from where t^2÷2 came?
I believe it's in his projectile motion videos www.khanacademy.org/science/physics/one-dimensional-motion/old-projectile-motion/v/projectile-motion-part-1
Generally speaking, if you integrate acceleration twice with respect to time, you should get an equation with (t^2)/2 as one of the terms.
Here's a helpful crash course video on Integrals (kinematic equations) if you're interested in finding out why: ruclips.net/video/jLJLXka2wEM/видео.html
Why does he use t^2/2 (4:25) ?
Ah yes, the very practical "driving off a cliff problem" ; my favorite.
as a Brit this guys voice and positive attitude is a welcome break honestly lmao
I came here because of my Cal 3 textbook yet this video says precal... Uh, what?
+Tyler Yates I came here from my Advanced Algebra Honors class...
I came here from my Theoretical Physics class...
People, people.... math is like the crying baby on an airplane...its EVERYWHERE, no matter where you go!
^Well said.
I came here from my phd in mathamatics honors super duper high level secret school of big boys
I have the worst calculus teacher ever!!! Thumbs up:)
So that parameter 't' is like a third variable or a third axis? If you used a three-dimensional graph it would be the same thing, right? (if you look at it from the plane of the x and y dimensions only, of course)
ratio
Thanks, this was really helpful in understanding WHY we're learning parametrics!
Your comment is new
Anyone else got a test they aren't ready for? lol
you lost me at car
can someone please link the video that explain the t^2/2 for the y(t) equation??
usually the equation of the curve of an accelerating object is x=1/2a.t^2+Vi.t+Xi , where you can substitute x with any dimension and i is the initial point. This is a physics equation related to a(acceleration), v(velocity) and position(x,y,z,...)
@@monahusseini6876 u think he waited 5 years for an answer lol
Nicely explained. Thanks to You tube and Khan Academy.
Hey!...Sal...More power!...(is it ok to say then that the Projectile Motion videos are mathematical analyses of one-dimensional variables (h or delta D)...the 2-Dimensional Projectile Motion...of two-dimensional variables (delta D & Ave. Velocity)...the Prametric Equation...of three-dimensional variables (x, y, & t) or are they...Alll...3D analyses???)...tnx! :D
This is a very good video on the concept of parametric equations. I've known about them for some time now but couldn't link them to everyday life until I came across this video. Now I won't forget about parametric equations, because i now grasped the concept fully, thanks to this video.
Y is acceleration due to gravity negative (-10m/s²)
Based on equations of motion, for any body moving downwards (g) is positive, and if it's projected upwards it's magnitude becomes negative cause it's acting in an opposite direction to (g)
So sir explain why 10m/s² is negative
Cause am confused at that point 😕
are parametric equations calculous or precalculous? Cause its in my pre calculous text book O_O
No, mass has nothing to do with acceleration of gravity. A ping pong ball and a golf ball would have the same path if there was no air resistance.
He must have gone to college like 20x with different majors each time to be this damn smart D: That's a lot of money T_T
brilliant! I'm a math major and a Trig tutor and this lecture has given me a new method of teaching parameters.
Thank God Khan doesn't use imperial like my Calc book. I'll never understand smh
Exactly what I needed thanks!
If you want to know when the car exactly hit the ground.
Solve for t using y=0
and find value of t
8:24 - Sal's visual scaling accuracy needs to improve in order to make this channel even better :)
@Naruto0519 All he does is not fill his videos with fucking mathematical jargon! Ace!
why isn't it y = 50 - 10t
I feel like I learned nothing in physics now T___T
Parametric = multi DGN per IGN? For example polar coords
@restituted
Because, he set the equation equal to zero(the y axis being the height(when would the car be at zero height, or hit the ground)), and the equation was then 0 = 50 - 5t^2. So, he had to figure out what t would have to be for 50 - 5t^2 to equal 0. If t = the square root of 10, then the square root of 10 squared = 10. 50-5(10) = 0. So at the square root of 10 seconds, the car hits the ground.
I love your teaching style, very good job!
watch video 2 if u didnt understand where he got t = sqrt (10) :P
Tomorrow - year 12 extension maths.
Fucking hate parametrics.
@Lamboragon if you don't like the video, find another one that takes your fancy out of the 396 other videos on parametric equations.
I'm even more confused now
well your dumb aren't u
Ethan Palinkas you’re*
DAS COS U DUMB
can you please replace my boring Precal teacher????? PLEASE!
I'm taking Calculus right now but I'm having a lot of trouble because m teacher isn't very helpful.. She is mostly a verbal teacher and it's really hard. To be honest this video didn't really help me either )':
Who writes those subtitles? "And I encourage you to watch the [UNINTELLIGIBLE]" I guess it's not Khanacademy, as he probably would have understood his own words? :P
The mass would be used in calculating the force on the car (or the ground), or some other information. If the car had no mass, gravity would not affect its motion. In a vacuum, all masses would behave in exactly the same way, so the equation covers objects of any mass.
lol i have the same problem my teacher goes WAY TOO FAST but honestly the best tutorial for calculus is patrickJMT (his username on youtube) so you just type in the topic or chapter you're in and his name at the end and search, if he has a video on it his name comes up HONESTLY he has absolutely every topic explained with RLLY good examples that he clearly explains, he is the only reason i have an 87 in calc. just try looking him up he rlly helped me
@ForeverWiked acceleration : ax=0, ay= -g (gravitational acceleration on earth)
You integrate the acceleration to get the velocity -> velocity : vx= 5, vy = -gt (don't forget the initial conditions, here the velocity at t=0)
Then you inegrate the whole thing again to get the position -> position : x=5t+10, y= -gt²/2 + 50 with g~10m/s²
Again, initial conditions. Position at t=0.
Unless it's, uh...Unless it's, uh...Unless it's, uh...
im 11 and i can understand this and my friend is a ginesous (and i misspelled that sorry for my compertance ) and he diden't understAND IT ;)
Hey this was made on my birthday
all right so i have some questions and any help is appreciated!
*I'm just learning this and so far I've really only seen the conventional f(x)= x + a (or trig/rational functions etc.) basically where y or f(x) is on one side and the equation is on the other and that suffices to describe the function. But I've never seen two equations describe a single function and i want to know why this is suddenly happening (i get that the two equations show where the object with respect to time) it's just a function has never been described with two equations for me and i feel like I'm missing something here why is this extra description needed (I know it's a weird question)
*Also what is a parameter exactly, is it the same thing as a variable, like for an equation F(x)=cos2x is x the parameter?????
*Finally, under what conditions/or what type of function do we need something like this where we need a pair of equations to describe the function?
I haven't gotten my textbook yet and all I have to go off of are my notes so i would really appreciate the help THANKS AGAIN!
Sal can you please make a basic gemonetry video? I was going to start practicing but I have no idea what to do.
"Parameter....."
Mahogany...
@2454014 not everyone is as fast as you my friend
I really like these clearer high-def videos ! It'd be great if you could redo the projectile motion videos in HD. In my opinion there's nothing better for the beginning/struggling physics student than clear, easy-to-follow AND read fundamental videos. :)
thanks Sal, you've done an awesome job !
Greetings from Finland !
3:20
Purrramitterrr
Let's make a table here... let's make a TABLE.
I loved putting this in my HP prime using the parametric app, thanks and I have just been studying kinematics beautiful thank you.
I didn't know that there was a specific name for this. This would have been kind of useful to know before working with Rates of Change differentials.
For God so loved the world, he gave us Mr. Khan. Sal is the next savior!! Thumbs up if you agree.
at 4:21 why over 2?
Where did it come from?
Does the mass of the car have any influence on the downward motion? Or is it taken in by the projectile curve formula?
I made my RUclips account to listen to free music.... I never thought I would subscribe to a math teacher! haha
wtf? ifoud this of a skrillex song wtf?
I really wonder thathow to know salman khan all of things . really thanks.
i was wondering..do you use the mouse to draw these things or is it like a smart board?
ah yes, an 11 year old khan academy video
The car off the cliff problem always makes me think of Toonces the driving cat.
When you lose money on Wall Street Bets
why are you using t^2/2?
Im gonna take Cal 3 next semester, need to study ahead bcuz of crappy teacher
@HoorayforOranges True true! It's not confusing like teachers always make it seem!
How come on my graphing calculator the length of the line ends depending on t?
Ex: x(t)=2t
The line will only go 2 to the +x direction. But what if t=2? Then x would be 4, but my calculator will only go a certain specified distance.
superrr...
if the planet has no air there would the car wouldnt be able to drive
Get to the point faster dude.
nice videos!
How is this precalc when it's part of my last sections in Calculus 2?
BEEKEEPER.
this is the wrath of khan
@obsidianfinger haha 420
do you want to be my TA?
PARAMETER.....PARAMETER
i am not gay. bad video hard to read. 1*
i want the reason why y = 50-10 t sqaure comes plz help me
+Vedant Kulkarni This is because of some "simple" physical properties expressed in so-called "suvat" equations.
This is basically mechanics in physics if you have ever done that, if not, I'll try to be brief: acceleration is defined as the change of velocity, so a =(v-u)/t v is final velocity and u is the initial velocity. We can use this equation to arrive at some other equations, as long as acceleration is constant, and in the video it is (gravitational acceleration). Average velocity is defined as displacement (s) divided by time (t), but is also defined as (u+v)/2. From these equations we know that s/t = (u+v)/2, and from here, it is just a matter of rearranging: the first equation: a = (v-u)/t can be rearranged to isolate for v: v = at + u.
Substituting this into s/t = (u+v)/2 for v gives us s/t = (u+(at+u))/2 which, isolating for s (displacement or our "y"): s = ut +0.5at^2. The gravitational acceleration is pulling downwards and is also denoted the value 10, so s = ut - 5t^2, where we know that initial velocity is 5 ms^-1. It is very important to remember that our x axis accounts for time and that Hall denoted this starting point before the car began falling from the cliff t = 10, this means that y =50 - 5t^2.
I hope this helps.
Oh :) thanx
I learnt it during precalc. But naturally it applies in calculus too.
wow.. you seem to be enjoying this. a lot. and pretty colors :)
Well I think I may ditch my textbook. He’s such a great teacher !
does anyone know the program he uses to draw the diagrams?
I'm in 9th grade o.o
Oh God. Thank you. Finally I see why. Why is this not the first thing we get taught?
@bamfan151 We did, but then we looked at this video :)
what is this app
thank you
@mechwarreir2
its in calc too, (calc bc to be exact)
2:06 Assuming that we are in a planet and there is no air and no forces like friction etc ,we are in vaccum
4:15 how gravity comes?
Please could you please explain the topic , I can't understand clearly.
did you resolve it, i dont get it too
Lol so I have been working with parametric equations all along.