Thanks. Haven’t done math for many decades. I was an ace then. I love your videos as I totally follow what you are explaining. I know I still have it. Too bad my life is almost done. Hoping for math after death.
I usually, if x^2 without the "-" represent a parabola with branches up, the roots are an intersection with the "x" axis. in this case, it is a parabola with branches upwards, which intersects the "x" axis at points -3 and 2, therefore x = (-inf; -3] and [2; inf)
Could you please drop another one showing parallelogram properties using diagonals and their formulas in terms of perimeter, area, and the side lengths. Thank you.
This is actually a great time to go back to completing the square and stress that (x^2)^(1/2) = |x|. x^2 + x - 6 ≥ 0 x^2 + x - 6 + 6 ≥ 0 + 6 x^2 + x ≥ 6 4(x^2 + x) ≥ 4(6) 4x^2 + 4x ≥ 24 4x^2 + 4x + 1 ≥ 24 + 1 (2x + 1)^2 ≥ 25 (2x + 1)^2 ≥ 5^2 [(2x + 1)^2]^(1/2) ≥ (5^2)^(1/2) |2x + 1| ≥ |5| At this point, using the nature of absolute value, we can redefine this as two simple inequalities. 2x + 1 ≥ 5 2x + 1 - 1 ≥ 5 - 1 2x ≥ 4 2x/2 ≥ 4/2 x ≥ 2 2x + 1 ≤ -5 2x + 1 - 1 ≤ -5 - 1 2x ≤ -6 2x/2 ≤ -6/2 x ≤ -3 Put them together and we have our domain without the need to check the groups that crop up around the x values. We _should_ check, but we have our notation without that step. (-∞, -3] ∪ [2, ∞)
All numbers are greater than or equal to 0. Numbers aren't assumed with a negative sign. So all numbers 0 through 9 are equal to or greater than 0. You don't need math to figure that one out. He just is creating more confusion. I'm pretty sure that's what the purpose of all this is anyway. What I mean by all of this is the confusion that were debating nonsense over and over and over again. So from the hierarchy perspective it's working we're fighting amongst ourselves debating amongst ourselves arguing amongst ourselves while they're digging for gold
@@nodistraction5857 Every school and every class within the school, has a completely different syllabus. The general public a thousand miles away, will know nothing about your class's specific syllabus.
Extremely thorough and clear, as always! Thank you, Mr. H!
Thanks. Haven’t done math for many decades. I was an ace then. I love your videos as I totally follow what you are explaining. I know I still have it. Too bad my life is almost done. Hoping for math after death.
I like your method - makes a lot sense
I am reviewing pre calc, this is very clear and well explained. Thanks, Professor.
You're most welcome ~
Thank you, thank you! ❤
which chalk do you use? It marks so nicely!
Thank you so much ❤
I like it so much and it's very good.
To make it easier, you can just find yes or no on one side then it will be either "yes-no-yes" or "no-yes-no"
Prof has reminded me of my 1st degree mathematics
Thank you!!❤
thank you
i like your explain
i had thought of this method too!
weird method, easier to just sketch the parabola through -3 and 2 and mark the positive and negative areas
Of course, it is the fastest method
Sometimes it doesn't work trust me
선생님! 유튭에서 보다니 너무 반가워요😊
오랜만이다!
Will you ever do a real or complex analysis series? or any advanced topics?
goated
I usually, if x^2 without the "-" represent a parabola with branches up, the roots are an intersection with the "x" axis. in this case, it is a parabola with branches upwards, which intersects the "x" axis at points -3 and 2, therefore x = (-inf; -3] and [2; inf)
Sir in some trignometric equations of simplification we multiply by minus 1 in denominator.what kind of operation is it?
Could you please drop another one showing parallelogram properties using diagonals and their formulas in terms of perimeter, area, and the side lengths. Thank you.
👍🙏
Very good. I would have used s rough parabola
Any class 10th student here ?
👇
me
Also we can write the solution as :
R \ (-3,2)
Real numbers except numbers inside the period (-3.2)
According to Hörner method I found (x+2)(x-3) thanks
It's not (x+2)(x-3)
Noted
I normally see alternate value between greater and less than zero for the sections.
Easy peasy
X is greater than or equal to -2 or less than or equal to 3
This is actually a great time to go back to completing the square and stress that (x^2)^(1/2) = |x|.
x^2 + x - 6 ≥ 0
x^2 + x - 6 + 6 ≥ 0 + 6
x^2 + x ≥ 6
4(x^2 + x) ≥ 4(6)
4x^2 + 4x ≥ 24
4x^2 + 4x + 1 ≥ 24 + 1
(2x + 1)^2 ≥ 25
(2x + 1)^2 ≥ 5^2
[(2x + 1)^2]^(1/2) ≥ (5^2)^(1/2)
|2x + 1| ≥ |5|
At this point, using the nature of absolute value, we can redefine this as two simple inequalities.
2x + 1 ≥ 5
2x + 1 - 1 ≥ 5 - 1
2x ≥ 4
2x/2 ≥ 4/2
x ≥ 2
2x + 1 ≤ -5
2x + 1 - 1 ≤ -5 - 1
2x ≤ -6
2x/2 ≤ -6/2
x ≤ -3
Put them together and we have our domain without the need to check the groups that crop up around the x values. We _should_ check, but we have our notation without that step.
(-∞, -3] ∪ [2, ∞)
That's seems like wavy curved method
Mengapa gambar mininya menampilkan
x²+x-6[>=]0
(x+3)(x-2)[>=]0
x+3=0
x=-3
x-2=0
x=2
When x=-4
(-4)²+(-4)-6[>=]0
16-4-6[>=]0
6[>=]0 true
When x=0
0²+0-6[>=]0
-6[>=]0 false
When x=3
3²+3-6[>=]0
9+3-6[>=]0
6[>=]0 true
Therefore
x[=]2 ❤
654×7=4578😢
All numbers are greater than or equal to 0. Numbers aren't assumed with a negative sign. So all numbers 0 through 9 are equal to or greater than 0. You don't need math to figure that one out. He just is creating more confusion. I'm pretty sure that's what the purpose of all this is anyway. What I mean by all of this is the confusion that were debating nonsense over and over and over again. So from the hierarchy perspective it's working we're fighting amongst ourselves debating amongst ourselves arguing amongst ourselves while they're digging for gold
Bro he's just showing the proof of why the answer is as it is... Sometimes you just can't understand math problems at first glance
Can anyone send me the syllabus of Grade12 mathematics
That is determined by the school district or possibly the state.
@@jamesharmon4994 do you have the syllabus??? Or only school can give,, is there any website so that I can download from it.
Thank you for telling me
@nodistraction5857 the school has it. Ask them for it.
@@nodistraction5857 Every school and every class within the school, has a completely different syllabus. The general public a thousand miles away, will know nothing about your class's specific syllabus.
Easier just sketching a gragh
wrong
ok bud