Why does the area under a graph represents probability of something happening. Extending from discrete variables, their probability was not the area under the graph but rather just the corresponding value on the y-axis, why is it different here?
Think about it like this. Look at it backwards. -(3x-1)^2 = -(3x-1)(3x-1) And use distributive property. = (-3x+1)(3x-1) = -9x^2+3x+3x-1 = -9x^2+6x-1 I hope it helps to look at it backwards.
You can do it like this -9x² + 6x - 1 = -1(9x² - 6x + 1) Now you need 2 factors, say (ax + b)(cx + d) to get 9x² - 6x + 1 Multiplying gives (ac)x² + (ad)x + (bc)x + (bd) = (ac)x² + (ad + bc)x + (bd) We need ac to be 9, ad + bc to be -6, and bd to be 1 For ac: 9 = 1 x 9 or 3 x 3 or -1 x -9 or -3 x -3 For bd: 1 = 1 x 1 or -1 x -1 From here it's basically just trial and error, but i'll skip it and go straight to the correct combination, which is: a = 3 c = 3 b = -1 d = -1 The check: ac = 9 (true) ad + bc = -3 - 3 = -6 (true) bd = 1 (true) So (ax + b)(cx + d) = (3x - 1)(3x - 1) = (3x - 1)² And don't forget that -1 you factored in the beginning The complete factorization is -(3x - 1)² as required This is only for explaining 'why it works' tho, if you're doing this in exam or for homeworks, there's a lot of ways to do it faster like tic tac toe factoring and others, doing it like what i did would be time consuming
Brow, pick the 2 term, devide by 2, pick the 2 numbers, eg: 6x/2= 3x, + or - them, square the hole things and compare the results. This is the better way
oh my gosh where do you teach? Probably on some kinds of wonderland where fairies live... Is teacher who teaches so great like this normal? How come I've never seen one? T_T
I like your passion in teaching. Share the passion as a math teacher! Good job explaining Eddie!
Watched one video about a year ago, it was great. First time I've seen you since. You make me feel like I could go to MIT.
Your passion is fantastic
I think Eddie took his profile pic right after this video lol
Some people don't age for decades, and then all at once over like.. 5 minutes ..
Deserves all the accolades he has been awarded.
Sir, it would be great for we students, if u could group your videos into Playlists. And Thank You for Teaching in interesting way sir.
got trials tmr this helped lots thanks !
"Can we count on your discretion?"
".. I mean.. I can be continuous..."
Why does the area under a graph represents probability of something happening. Extending from discrete variables, their probability was not the area under the graph but rather just the corresponding value on the y-axis, why is it different here?
I can't understand my teacher, but I understand this guy.
Why is that?
@@matemaatika-math Idk
@@gameboycharanyt6723 What's different?
@@matemaatika-math The teacher can't explain that well
as him
@@gameboycharanyt6723 Can it be that for somebody your teacher's explanations are clearer than his or is it unidirectional?
Such a good teacher
please can anyone explain to me about the graph concerning condition one?
thaaaaaaaank you. you are amazing teacher very nice explain.very useful.
Im somali african peape firts thank you teacher
Command please zoom the less to see very well🙏
I really can’t get my head around factorisation.
Why, for example, does -9x^2+6x-1 result in -(3x-1)^2?
Think about it like this.
Look at it backwards.
-(3x-1)^2
= -(3x-1)(3x-1)
And use distributive property.
= (-3x+1)(3x-1)
= -9x^2+3x+3x-1
= -9x^2+6x-1
I hope it helps to look at it backwards.
You can do it like this
-9x² + 6x - 1
= -1(9x² - 6x + 1)
Now you need 2 factors, say (ax + b)(cx + d) to get 9x² - 6x + 1
Multiplying gives (ac)x² + (ad)x + (bc)x + (bd)
= (ac)x² + (ad + bc)x + (bd)
We need ac to be 9, ad + bc to be -6, and bd to be 1
For ac:
9 = 1 x 9 or 3 x 3 or -1 x -9 or -3 x -3
For bd:
1 = 1 x 1 or -1 x -1
From here it's basically just trial and error, but i'll skip it and go straight to the correct combination, which is:
a = 3
c = 3
b = -1
d = -1
The check:
ac = 9 (true)
ad + bc = -3 - 3 = -6 (true)
bd = 1 (true)
So (ax + b)(cx + d) = (3x - 1)(3x - 1)
= (3x - 1)²
And don't forget that -1 you factored in the beginning
The complete factorization is -(3x - 1)² as required
This is only for explaining 'why it works' tho, if you're doing this in exam or for homeworks, there's a lot of ways to do it faster like tic tac toe factoring and others, doing it like what i did would be time consuming
Brow, pick the 2 term, devide by 2, pick the 2 numbers, eg: 6x/2= 3x, + or - them, square the hole things and compare the results. This is the better way
@@joaoroberto689 What?
Let's go Eddie!!!!
Are Australian schools open?
They've been open since June I think lmao I am Aussie by the way
Thank you
4k loved it
Upper boundary should qbrt(7/4). Then you’d get 1.
If your lower boundary is a, your upper boundary should be qbrt(3/4 +a^3)
As there is no such function as "qbrt" unless defined by you and you use the roof notation anyway, the clearer solution is (7 / 4) ^ (1 / 3).
@@matemaatika-math Thank you, I’ll keep it in mind for the next time!
your electric cord is dtawing binomial curve
Good job 👍👍👍👍
oh my gosh where do you teach? Probably on some kinds of wonderland where fairies live... Is teacher who teaches so great like this normal? How come I've never seen one? T_T
Ok, I cannot understand this issue in significant figures . I very hope that I can understand it 3.489 • (5.65-2.3)
What issue? What's your expression?
pretty nice !!!!
Pt 2?
Please communicate to resolve the issue💔
hi I am fiza Khan from pakistan seriously i dont like maths but i want to be a maths champion like u but i cant kindly clear my concepts by reply me
If you are work hard you will are success. My sister im from somalia🇸🇴