Maths- Gym for Brainiacs

spanky489 wrote:weve got ourselves a genius here

it's just basic algebra :[
please don't embarrass me lol

More like physics with Analysis Good job nonthless

Immortal Babun wrote:

topic: analysis
difficulty: easy
requirements: knowledge of partial derivation and maximum/ minimum


Prove

x + y + z = 1 => xy + yz + xz < 1/2

Additional question: is it true for all x, y, z ?[/b][/size]

The winner will get the best Asian boobslip video ever

Y U NO LIKE DEM BOOBIES?

Immortal Babun wrote:More like physics with Analysis Good job nothless

Immortal Babun wrote:

topic: analysis
difficulty: easy
requirements: knowledge of partial derivation and maximum/ minimum


Prove

x + y + z = 1 => xy + yz + xz < 1/2

Additional question: is it true for all x, y, z ?[/b][/size]

The winner will get the best Asian boobslip video ever

Y U NO LIKE DEM BOOBIES?

assuming i understand the question being asked, are x, y and z all equal to 1/3

because 1/3+1/3+1/3=1
and 1/3*1/3+1/3*1/3+1/3*1/3=0.27 which is less than 0.5

i think im wrong though because that was too easy

fatman123 wrote:assuming i understand the question being asked, are x, y and z all equal to 1/3

because 1/3+1/3+1/3=1
and 1/3*1/3+1/3*1/3+1/3*1/3=0.27 which is less than 0.5

i think im wrong though because that was too easy

.
It doesn't say x=y=z .

I haven't done partial differentiation ):

beatrixasdfghjk. wrote:

fatman123 wrote:assuming i understand the question being asked, are x, y and z all equal to 1/3

because 1/3+1/3+1/3=1
and 1/3*1/3+1/3*1/3+1/3*1/3=0.27 which is less than 0.5

i think im wrong though because that was too easy

.
It doesn't say x=y=z .

I haven't done partial differentiation ):

it's taking derivative with respect to 1 independent variable, while keeping the other 2 as a constant

You should google the del operator, or gradient
super easy though, although chain rule can be confusing at times.

.__.
Can I have an example?

I know chain rule ... I think .

beatrixasdfghjk. wrote:.__.
Can I have an example?

I know chain rule ... I think .

Chain rule is kinda hard to explain :/
it's a function within a function, you might be able to youtube it.
However, partial derivative ex goes like this

d(xy)/dx = y. keeping y as a constant, dx/dx =1, so we have y as the answer.
likewise, d(xz)/dt = 0. both are constants, x &z, so they are 0 after taking the derivative.
It's around 2am atm, and i have class at 9 tmr, but i think to solve that problem, you need to draw the picture

the result shall be a plane that intersects at (1,0,0), (0,1,0), (0,0,1)

Looking at it and those triangles a bit might help.

you might notice that x*y or any couple is having a constraint with a rectangular area under the triangle. You can form another set of equations this way and that would be enough to solve this problem....or i believe. As long as you can max out the area under the curve of the triangle, it will be the same for the other 2 i think, y*z and x*z...based on the symmetry.
It's been a long time since my last vector calculus course....maybe the Lagrangian would help. Doubt that it would be harder than that since it's rated easy....


correct me if im wrong

dafaq?

he said the difficulty was easy, none of this function within function stuff is easy

Yeah, I can do chain rule if that's all it is, I was just checking there wasn't something I didn't know...

I've done partial differentiation along with implicit. Not that hard but gets confusing with trig functions

fatman123 wrote:

Immortal Babun wrote:More like physics with Analysis Good job nothless

Immortal Babun wrote:

topic: analysis
difficulty: easy
requirements: knowledge of partial derivation and maximum/ minimum


Prove

x + y + z = 1 => xy + yz + xz < 1/2

Additional question: is it true for all x, y, z ?[/b][/size]

The winner will get the best Asian boobslip video ever

Y U NO LIKE DEM BOOBIES?

assuming i understand the question being asked, are x, y and z all equal to 1/3

because 1/3+1/3+1/3=1
and 1/3*1/3+1/3*1/3+1/3*1/3=0.27 which is less than 0.5

i think im wrong though because that was too easy

You're on to something but I never said x=y=z Work with extreme values like minimum or maximum.

beatrixasdfghjk. wrote:Yeah, I can do chain rule if that's all it is, I was just checking there wasn't something I didn't know...

Partial derivation is easy:

f(x,y)= x²+y³

You need one variable value and others fixed as a constant number. Example:

df(x,y)/dx = 2x , x is variable, y is a fixed number
df(x,y)/dy = 3y² , the other way around...

Immortal Babun wrote:

fatman123 wrote:assuming i understand the question being asked, are x, y and z all equal to 1/3

because 1/3+1/3+1/3=1
and 1/3*1/3+1/3*1/3+1/3*1/3=0.27 which is less than 0.5

i think im wrong though because that was too easy

You're on to something but I never said x=y=z Work with extreme values like minimum or maximum.

He's not, really, I don't think he's even done Year 9 trigonometry .

fatman123 wrote:dafaq?

he said the difficulty was easy, none of this function within function stuff is easy

(x+1)^2

that is an example of function within a function if you let u = x+1, you'll have u^2. However, for this example, you can also write it as x^2+2x+1. No need to take the chain rule if u don't know how

I just said that I doubt he's done trig, there's no way he's done differentiation .

vizkosity wrote:

fatman123 wrote:dafaq?

he said the difficulty was easy, none of this function within function stuff is easy

(x+1)^2

that is an example of function within a function if you let u = x+1, you'll have u^2. However, for this example, you can also write it as x^2+2x+1. No need to take the chain rule if u don't know how

Y U NO SOLVE THE QUESTION?

That Asian video is legendary Ask Mole or Lex, they saw it at some point The girl in your sig isn't even close to her by a mile

beatrixasdfghjk. wrote:

Immortal Babun wrote:

fatman123 wrote:assuming i understand the question being asked, are x, y and z all equal to 1/3

because 1/3+1/3+1/3=1
and 1/3*1/3+1/3*1/3+1/3*1/3=0.27 which is less than 0.5

i think im wrong though because that was too easy

You're on to something but I never said x=y=z Work with extreme values like minimum or maximum.

He's not, really, I don't think he's even done Year 9 trigonometry .

jog on, i know sine cos and tan and the sine and cos rule

differentiation on the other hand......

Can't you just square x+y+z = 1 on both sides?

Then you get xy + yz + zx = (1/2) - ((x^2 + y^2 + z^2)/2)

Hence it is lesser than 1/2.

Can't do like this?

Immortal Babun wrote:

vizkosity wrote:

fatman123 wrote:dafaq?

he said the difficulty was easy, none of this function within function stuff is easy

(x+1)^2

that is an example of function within a function if you let u = x+1, you'll have u^2. However, for this example, you can also write it as x^2+2x+1. No need to take the chain rule if u don't know how

Y U NO SOLVE THE QUESTION?

That Asian video is legendary Ask Mole or Lex, they saw it at some point The girl in your sig isn't even close to her by a mile

I would rather aiding others to solve it If i can do so correctly....

I prefer classy looking ladies rather than slutty ones
more of a traditional person :[ ....

kiranr wrote:
Can't you just square x+y+z = 1 on both sides?

Then you get xy + yz + zx = (1/2) - ((x^2 + y^2 + z^2)/2)

Hence it is lesser than 1/2.

Can't do like this?

square polynomial doesn't work that way...
it's (x+y+z)*(x+y+z)....either do a coefficient expand or pascal triangle


It's a pain to ask highschoolers for lagrange multipliers....however, if i did it correctly, this problem is very simple. Lambda is 2/3 as the answer, that's what i got....which, will give x,y,z each has a maximum value of 1/3 to maximize the area. However, I will let the kids do it


This would be a great resource for everyone
https://www.youtube.com/watch?v=HyqBcD_e_Uw&feature=related

Langrange multiplier is definitely most useful in Lagrangian physics, as well as financial math, where you have to maximize resources in a certain area to yield maximum profit

Correct me if my lambda is wrong, or maximum areas beneath each triangle.

vizkosity wrote:

kiranr wrote:
Can't you just square x+y+z = 1 on both sides?

Then you get xy + yz + zx = (1/2) - ((x^2 + y^2 + z^2)/2)

Hence it is lesser than 1/2.

Can't do like this?

square polynomial doesn't work that way...
it's (x+y+z)*(x+y+z)....either do a coefficient expand or pascal triangle


It's a pain to ask highschoolers for lagrange multipliers....however, if i did it correctly, this problem is very simple. Lambda is 2/3 as the answer, that's what i got....which, will give x,y,z each has a maximum value of 1/3 to maximize the area. However, I will let the kids do it


This would be a great resource for everyone
https://www.youtube.com/watch?v=HyqBcD_e_Uw&feature=related

Langrange multiplier is definitely most useful in Lagrangian physics, as well as financial math, where you have to maximize resources in a certain area to yield maximum profit

Correct me if my lambda is wrong, or maximum areas beneath each triangle.

I expanded it and that is what i got. Am i wrong in the expansion?

(x+y+z)*(x+y+z) =
x^2 +xy+xz+yx+y^2+yz+zx+yz+z^2
assuming i did the math correctly
as you see, simplifying it will give x^2+y^2+z^2+2xy+2xz+2yz
there are middle terms missing

vizkosity wrote:(x+y+z)*(x+y+z) =
x^2 +xy+xz+yx+y^2+yz+zx+yz+z^2
assuming i did the math correctly
as you see, simplifying it will give x^2+y^2+z^2+2xy+2xz+2yz
there are middle terms missing

Yeah, that is what i got. I skipped a few steps. So now if you equate that to 1 which remains the same after squaring, you get the what i posted.

xy + yz + zx = (1/2) - ((x^2 + y^2 + z^2)/2)

Bring the squared terms to the other side and divide both sides by 2 again.

kiranr wrote:

vizkosity wrote:(x+y+z)*(x+y+z) =
x^2 +xy+xz+yx+y^2+yz+zx+yz+z^2
assuming i did the math correctly
as you see, simplifying it will give x^2+y^2+z^2+2xy+2xz+2yz
there are middle terms missing

Yeah, that is what i got. I skipped a few steps. So now if you equate that to 1 which remains the same after squaring, you get the what i posted.

xy + yz + zx = (1/2) - ((x^2 + y^2 + z^2)/2)

Bring the squared terms to the other side and divide both sides by 2 again.

you assumed that xy+yz+zx = 1/2, when it reality, it can be any combination with those products less than 1/2

it asks you to prove that they all are less than 1/2, so you shouldn't be using 1/2 in this problem like that i believe.
Watch the video i linked, you will be able to solve it in no time

x + y + z = 1

square both sides

x^2 + y^2 + z^2 + 2(xy + yz + zx) = 1

2(xy + yz + zx) = 1 - (x^2 + y^2 + z^2)

xy + yz + zx = (1/2) - ((x^2 + y^2 + z^2)/2)

while we wait for the answer, or confirmation from you guys, I have an interesting question (if you really like science, you will find this fascinating).

topic: Special Relavity
difficulty: easy
requirements: Know pythagorean theorem, basic algebra, and the fact that speed of light c, is the same for every reference frame.

Prove:
Using the light-clock old fashion lecture, prove that
t' = gamma* t, where t is time clock in the rest frame, and t' is time in the moving frame.

Please explain why is this important to our lives, name the most frequently used electronic that applies special relativity and why would one appreciate it so much

High school math required, no need for derivatives/integration/calculus of any kind. Transformations aren't needed either oh and distance = speed of light * time

Good luck

Winner will get....ummhh...some hot kpop girls D:?

I don't know much about boobslips, ect...
Hint: gamma is always bigger than 1,

kiranr wrote:x + y + z = 1

square both sides

x^2 + y^2 + z^2 + 2(xy + yz + zx) = 1

2(xy + yz + zx) = 1 - (x^2 + y^2 + z^2)

xy + yz + zx = (1/2) - ((x^2 + y^2 + z^2)/2)

you are trying to prove that xy+yz+zx is less than 1/2. You can't assume that it's equal to 1/2 and substitute it in