olha o macacu
#help-28
glossy valveBOT
runic bloom
yea that's a way to represent it too
woeful haven
man that sucks
runic bloom
yeahh it's a bit odd at first lol
but you get the hang of it
another way to think about it is
runic bloom
$(a+b)(a+b) = aa + ab + ba + bb$
glossy valveBOT
Kihei
runic bloom
I dunno how better to explain it
glossy valveBOT
olha o macacu
runic bloom
yup
woeful haven
x² + 4x + 4
man me and my friends where arguing about this for like 30 minutes and came down that everyone was wrong
runic bloom
oh..
woeful haven
lemme check
runic bloom
well that's incorrect if so lol
woeful haven
if 2²x²=4x² then she is teaching wrong
no but its right
here i found an example:
$(-xy²)^4 = x^4y^8$
glossy valveBOT
olha o macacu
woeful haven
is that correct?
runic bloom
if 2²x²=4x² then she is teaching wrong
yes
runic bloom
**olha o macacu**
also true
runic bloom
**olha o macacu**
well here, you are squaring 2 multiplying terms
so the exponent rules are different and you simply square both terms
this one's a binomial (a + b)
so they work differently when squaring
woeful haven
**olha o macacu**
so if it was $(-xy)^4$ it would be diferent?
glossy valveBOT
olha o macacu
oak basin
If you still truly believe that (x+2)^2=x^2+4 then start subtituting in some x values and see
woeful haven
i think i got it
oak basin
For example, take x=-2
oak basin
The reason exponents distribute for products is because of it's property
Yes, that's partially the reason
For example, you claim (xy)^2=x^2y^2, this is because of how exponentiation is defined
note that $(xy)^2=xy\cdot xy=x\cdot x \cdot y\cdot y =x^2 \cdot y^2$
Eek
woeful haven
hard words but i think i got it
glossy valveBOT
waler
woeful haven
our teacher definetly did not teached us this
oak basin
Code bars dont work on phones, excuse that a bit
oak basin
**waler**
And this was the same way you derived the expansion of (x+y)^2
They probably didnt teach you this because it probably wasnt needed yet for you to understand, or some other personal reason
I cant judge that
woeful haven
well
oak basin
But yes, some of these 'rules' didnt just appear out of nowhere, they still came from definitions that were made of
woeful haven
teacher sent us extra points questions that had this included
so it could be just that
woeful haven
ok thx, i think our work here is done
solemn obsidian
ok so I'm having a lot of trouble with problems like this can anyone help v⋅(j+y)=61y+82
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ok so I'm having a lot of trouble with problems like this can anyone help v⋅(j+y...
@solemn obsidian Has your question been resolved?
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void jay
question: Write down a bijection from (X × Y ) × Z to X × (Y × Z). Prove that it is one-to-one and onto.
so i know what bijective means, it means a function that is both surjective and injective, but i just have no clue what it means by “write down a bijection.” i wrote f: (X × Y ) × Z -> X × (Y × Z), but i have no idea if that’s right or anything. that’s the only work i have to show because i’m just so completely lost. please help!
rare dock
question: Write down a bijection from (X × Y ) × Z to X × (Y × Z). Prove that it...
hiii so f: (X × Y ) × Z -> X × (Y × Z) says f sends things in the set (X × Y ) × Z to things in the set X × (Y × Z), but we also need the description of what it sends to what to define it
void jay
okay that makes sense
rare dock
the elements in (X × Y ) × Z look like ((x,y),z) for each x in X, y in Y, and z in Z, so to define f, you can write something like f(((x,y),z)) = ...
and whatever f sends to ((x,y),z) to, it should like an element of X × (Y × Z)
void jay
but how do i know what to actually make f(((x,y),z)) equal to?
rare dock
any guesses?
void jay
well i know the elements in X × (Y × Z) will look like (x,(y,z)). but i just don’t really know what it all means so i can’t think of a function that would turn the first set into the other
rare dock
hmm a bijection from a set A to a set B is kinda a way of pairing each element in A to exactly one element in B
and having every element in B paired with something in A
so ummm
if you have some element in (X × Y ) × Z
say ((x,y),z)
is there something in X × (Y × Z) that you'd naturally pair it with?
void jay
(x,(y,z))?
rare dock
great idea!
void jay
but then how do i make a function that does that?
rare dock
just say f(((x,y),z)) = (x,(y,z))
void jay
oh okay i see
rare dock
or with it's full description, f is a function from (X × Y ) × Z to X × (Y × Z) defined by f(((x,y),z)) = (x,(y,z))
void jay
right okay that makes sense. then how do i prove it’s a bijection?
void jay
yes!
rare dock
yay ok, which one do you want to do first?
void jay
injective is normally proven by showing that if f(x1)=f(x2) then x1=x2 right?
rare dock
yep
the elements here look more complicated, so we might want to start with something like let $$((x_1,y_1),z_1),((x_2,y_2),z_2)\in(X\times Y)\times Z$$ and suppose $$f(((x_1,y_1),z_1))=f(((x_2,y_2),z_2))$$
glossy valveBOT
layla💜
void jay
okay i understand that. and then i have to prove x1 = x2, y1 = y2, z1 = z2?
rare dock
yep, that'll work
void jay
but how do i do that 😬
rare dock
remember that ordered pairs are equal if and only if their first components are equal and their second components are equal
you can write $$f(((x_1,y_1),z_1))=f(((x_2,y_2),z_2))$$ in another way
glossy valveBOT
layla💜
rare dock
you know what f(something) looks like
I guess "move the parentheses" yea lol
remember how f is defined?
void jay
remember that ordered pairs are equal if and only if their first components are ...
so by this definition then (x1,y1) and (x2,y2) must be equal and x1=x2 and y1=y2?
or is that not right
rare dock
missing a step it sounds like
void jay
man i hate proofs lol
rare dock
what does $f(((x_1,y_1),z_1))$ equal?
glossy valveBOT
layla💜
rare dock
by the way we defined f
void jay
(x1,(y1,z1))?
glossy valveBOT
layla💜
void jay
and then the same for f(((x2,y2),z2)?
rare dock
yesss
void jay
okay i get all that now. so then (y1,z1) has to equal (y2,z2) yeah?
rare dock
yep ✨
rare dock
yep it is
void jay
okay got it :) then what about surjective?
rare dock
so you want that for any element (x,(y,z)) of X × (Y × Z), there is something in (X × Y ) × Z that gets sent to it
can you think of something?
void jay
well ((x,y),z)) is in (X × Y) × Z
rare dock
it sure is!
void jay
but isn’t that just the definition of the function?
f(((x,y),z)) = (x,(y,z))? is that all i say?
rare dock
if you want more detail you could say that if (x,(y,z)) is in X × (Y × Z), then x is in X, y is in Y, and z is in Z, so ((x,y),z) is in (X × Y ) × Z
and f(((x,y),z)) = (x,(y,z))
void jay
okay got it! thank you so much for your help, you explained everything so well
rare dock
glad you figured it out!
void jay
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primal moth
hi, can I ask for help on how to read this using mathematical terms? it's for truth tables
plush egret
hi, can I ask for help on how to read this using mathematical terms? it's for tr...
? they are mathematical terms
primal moth
oh sorry i mean how are they read
hazy dagger
aye yo, im back. This time it is a similar problem but with an abelian group. Here we have H={x in G: x^n= e}. G is our abelian group and n is a fixed integer. I need to prove that this is a subgroup and I don't really know where to start.
rare dock
aye yo, im back. This time it is a similar problem but with an abelian group. He...
what subgroup criterion have you have learned?
hazy dagger
- needs to be non-empty
2)closed with respect to the opperation - closed with respect to the inverse
hazy dagger
well im pretty sure its not empty
rare dock
why?
hazy dagger
because there has to be a value n that satesfies the given equation thing
rare dock
well you don't have any control over n
rare dock
no matter what n is, can you think of an element x in G such that x^n = e?
hazy dagger
i feel like i need more information to figure that out
i dont know what e is and i dont know what n is, only that it is a fixed value
I also don't know anything about G besides that it is abelian.
rare dock
well you know G is a group so it has an identity
e
is e in H?
in other words, is e^n = e?
hazy dagger
well, maybe
for an identity value, does nothing effect it?
like for this case, would n change the value?
rare dock
you know e*e = e, right?
hazy dagger
yes
hazy dagger
yes, so since e* e * e * =e, e^n=e
rare dock
yep
hazy dagger
how does one know if something is closed?
rare dock
that would mean if we take any two elements a and b in H, ab is also in H
hazy dagger
how do you prove that?
hazy dagger
they are in H, and in this case..um...thats sort of it
because we are only given infomration about x
rare dock
well x is just a dummy variable
rare dock
it says in english: H consists of all the elements of G which, when raised to the nth power, are equal to the identity
so all the elements in H have that property
hazy dagger
okay so all elements in H when raised to the nth power are equal to e
rare dock
that would mean if we take any two elements a and b in H, ab is also in H
yep, so what can you say about a and b?
hazy dagger
so a and b also have this quality
rare dock
what does that look like in symbols?
rare dock
a^n=e and b^n=e is right
hazy dagger
oh okay
rare dock
and we want to show (ab)^n=e
that shows ab has the property needed to be an element of H
hazy dagger
since G is abelian, does it work?
rare dock
yep that's the key thing to use
hazy dagger
what else should I say besides its abelian, i know that that makes it communative
hazy dagger
a^nb^n=(ab)^n
rare dock
haha yes but not yetttt
hazy dagger
rare dock
so you know a^n=e and b^n=e
just from here what can you say?
hazy dagger
we can say that since this is true, a and b are also in G
hazy dagger
omg!!! 💡
rare dock
we can say that since this is true, a and b are also in G
well we already knew that
and actually that's not even helpful, we let a and b be elements of H
rare dock
what did we want (ab)^n to be equal to?
hazy dagger
e
rare dock
so is it?
hazy dagger
yes
rare dock
how can we start this one?
hazy dagger
we need to have the inverse in both
rare dock
what do you mean?
rare dock
ahhh no we only need to worry about H
rare dock
a little but more precisely, we need: if a is in h, then a^-1 is also in H
hazy dagger
yes
rare dock
how to start?
rare dock
haha back up
rare dock
a little but more precisely, we need: if a is in h, then a^-1 is also in H
do you know how we should start this?
hazy dagger
no, i was rly trying to figure it out tho...
rare dock
something like let $a\in H$
glossy valveBOT
layla💜
hazy dagger
well thats def a start
rare dock
what do you know about a?
rare dock
we don't have to worry about G 
hazy dagger
i know, i was just trying to think of everything
rare dock
okok
hazy dagger
but yeah the only real things is that a^n=e because its in H
rare dock
what do we want to end up with?
rare dock
we need $(a^{-1})^n=e$
glossy valveBOT
layla💜
rare dock
im trying to think and i just cant figure it out
it's ok you're doing great 😁
rare dock
lolll
hazy dagger
it's ok you're doing great 😁
thank you 🥺
okay so we need to make that happen
okay hear me out
since a^n is like a * a * a * a....* a
a^-1 is like a-1 * a-1 * a-1 *... *a-1
and if all those a's are equal to e
then all the a^-1's are equal to e^-1 which is just e...?
rare dock
the individual a's don't need to be equal to e
hazy dagger
well yeah
i think i worded that incorectly
a^-1 * a^-1 * a^-1 ....=e^-1?
and e^-1 =e?
rare dock
I'd look at it like this
a^n = e
and we can multiply each side by (a^-1)^n
everything cancels on the left
down to the identity
and (a^-1)^n is left on the right
hazy dagger
wait hold on
okay
so its kinda like
(a^-1)^n * a^n-1 = (a^-1)^n * e
and then e= (a^-1)^n *e
rare dock
(a^-1)^n * a^n = (a^-1)^n * e maybe?
rare dock
yep
hazy dagger
and that proves that we have closure with respect to inverses
and now we have proved that H is a sub group of G
rare dock
yasss
hazy dagger
im done for the night
i cant take anymore, ill be back again tomorrow night
DX i should gift you nitro
rare dock
aww don't worry 🥺
hazy dagger
ill see you later layla ❤️
rare dock
have a good night 💜
hazy dagger
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broken rain
Is this correct?
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Is this correct?
broken rain
unborn quarry
Hello, yes it's correct
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haughty loom
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@haughty loom Has your question been resolved?
bold grotto
It wont be 90
Since
We are rotating it in counterclockwise rather than clockwise
If the question would have been for clockwise then 90 would have been correct
bold grotto
If you are unable to visualize then you can draw the diagram for each 90 degrees your rotate in the counterclockwise direction
Do that and then count the number of turns
Then your answer would be 90*the number of turns
haughty loom
mhm
bold grotto
Did you understand or want me to give the solution?
haughty loom
?
bold grotto
Np
haughty loom
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mortal thorn
can you help me solve this
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can you help me solve this
deft zodiac
um
simplify each fraction
eg
a/(1-a) = (a - (1-a))/(1-a)
so then u can take out that 1-a on top to get -1
repeat for all 3 fractions and move the -3 over
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@mortal thorn Has your question been resolved?
timber ledge
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timber ledge
I don’t understand part b
Isnt the answer already in the table
Nvm
Close.
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teal mantle
$\frac{x}{y} + \frac{y}{x} = \frac{x^2 + y^2}{xy}$ does this work ?
glossy valveBOT
DikRatownik
vast fossil
Yeah, as long as x and y are non-zero
teal mantle
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abstract rain
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sonic raptor
Can somebody help me with this?
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Can somebody help me with this?
sonic raptor
I cant really comprehend the problem and how to solve it
strange fern
- use a variable e.g. "x"
strange fern
Can somebody help me with this?
so your diagram looks like
<--- 10m ---> <---------- x ---------->
and another variable for the height, like y
- xy
sonic raptor
Thanks!
light sonnet
You shouldn't be doing the work for people
strange fern
You shouldn't be doing the work for people
I'm pretty bored tbh
sonic raptor
You shouldn't be doing the work for people
I couldn't comprehend the problem even though I watched a lot of tutorials 😢
sorry
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winged spire
winged spire
how do i do this
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crude karma
how do i solve this
ln(x^2)- (1/x^2)
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how do i solve this
ln(x^2)- (1/x^2)
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prisma rampart
Hi, Its me again
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Hi, Its me again
prisma rampart
Can anyone give me the example for arcsin or arccos for example what is arcsin from (3-2x)/5 (or any other similar example)
prisma rampart
Hmmm
I have an example y=root from 3-x + arcsin (3-2x)/5
I need to write domain
onyx glen
sqrt(3-x) + arcsin( (3-2x)/5) you mean?
prisma rampart
Yes
onyx glen
the domain is the set ${x : 3-x \ge 0} \cap {x : (3-2x)/5 \in [-1,1]}$
glossy valveBOT
Ann
onyx glen
this is unsimplified, grossly so even
prisma rampart
How can I simplify the 2nd part 😦
onyx glen
(3-2x)/5 in [-1,1]
<=> 3-2x in [-5, 5]
<=> 2x-3 in [-5,5]
<=> 2x in [-2, 8]
last step is on you
prisma rampart
(3-2x)/5 in [-1,1]
<=> 3-2x in [-5, 5]
Thanks
I still don't understand how you got this but thanks for help
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agile hawk
old channel got deleted by the bot
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old channel got deleted by the bot
agile hawk
glossy valveBOT
agile hawk
(not to scale figure) I need help with this question
spice orchid
Why so urgent?
native flicker
alright so what do you understand about y here
agile hawk
we just gotta find it
native flicker
and a cyclical quadrilateral
agile hawk
the topic is circle theorem
native flicker
ik . its 1 step solution
agile hawk
your trying to say 180-142=y?
native flicker
yeah
native flicker
o fr
agile hawk
the teacher said its wrong
my other method now is 360-142
218
218/2
109
109=y
but im uncertain if its correct
<@&286206848099549185> bot closed my old ticket because i deleted something, sent it at 6:24
i need help please
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agile hawk
<@&286206848099549185>
agile hawk
<@&286206848099549185>
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torn jolt
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torn jolt
everytime i attempt this i just get stuck at x^3/2 =3
and not knowing what to do fron there
nova basin
sqrt(x) = x^1/2
Using the power law it's a linear equation in log x
torn jolt
sqrt(x) = x^1/2
Using the power law it's a linear equation in log x
could you explain further?
i started with x^2 / x^1/2 to get x^3/2 = 3
nova basin
log(x^a) = a log x for any x and a (and log basis)
Visibly you're trying to put it all into 1 log, I'd make it all into log x
Although putting it all into 1 log also works
nova basin
i started with x^2 / x^1/2 to get x^3/2 = 3
It's x^3/2 = 2^3, not 3
torn jolt
yeah thats what ive done i think
torn jolt
ohh ok i think i see my mistaje
should i have kept it as 2^3 = x^3/2
instead of doing 8= x^3/2
nova basin
Visibly you're trying to put it all into 1 log, I'd make it all into log x
Both ways work
Then you solve x^3 = 64
Not impossible
But knowing the factorization gives you extra knowledge
Mainly that cube rooting it is easy
nova basin
should i have kept it as 2^3 = x^3/2
Although here, you can also put it to the 2/3's power directly to get x = 4 if you can manage that in one go
torn jolt
how tf is the cube root of 64 4?
nova basin
4^3 = 4*4*4 = 16*4 = 64
torn jolt
cube root is square rt and square rtagain i thought
nova basin
cube root is square rt and square rtagain i thought
No
Get that out of your head immediately
torn jolt
yea lol
so what is it?
square rt then divide by 2?
or is it different for everything
nova basin
cube root is square rt and square rtagain i thought
Cbrt is cancelled by cubing. Double sqrt is cancelled by double squaring, which is power 2*2 = 4. 3 != 4
nova basin
square rt then divide by 2?
What do you take as your starting point when saying this ?
torn jolt
What do you take as your starting point when saying this ?
square root of 64 = 8
nova basin
Yes
nova basin
Also yes, though I don't see where this leads
nova basin
i see now its just 4\*4\*4
\ prevents special characters from doing their thing btw
So you can write \*
torn jolt
ty
limpid marten
Hey there! I’m really confused by g(x)- this table doesn’t have an actual equation/pattern to go with it. When it asks “if x=2, what is y” I have no idea how to plug in this into g(x) since there is no equation to the table. Please help!! If more clarification needed I can help too ❤️
rugged harbor
deft zodiac
i think
u should use the points given and the line given
to deduce its a straight line
rugged harbor
The line is h(x)
deft zodiac
and u can thus find the equ
rugged harbor
g(x) is already the table, no need to find equations
rugged harbor
@limpid marten Is the hard part understanding what f(__) means or how to read that table?
deft zodiac
do be
confused sometimes
but its ok
the
other beings can help u clear my mess
:c
keen jacinth
Sorry for the confusion, I was going to help but looks like you got that covered 👍
limpid marten
<@538844604699770902> Is the hard part understanding what f(\_\_) means or how t...
Mostly reading the table! As far as I can tell, the equation doesn’t match with the table :((
But I can plug the points into a calculator and see what I get ❤️
rugged harbor
What equation?
limpid marten
Oh my bad!
rugged harbor
Do you mean this one? It's name is cut from the photo, are you sure it's g(x)?
limpid marten
Do you mean this one? It's name is cut from the photo, are you sure it's g(x)?
My bad! I misunderstood- lol I thought you were talking about this one!
This one being the 3x-5 equation
rugged harbor
This is the table of the function g(x)
Basically the left side has the x value, the right side has the output of the function (that's g(x), or y, you can call it however you want)
So if I want to find g(-3), then it's 7
rugged harbor
Nice
limpid marten
Thank you so much for your help! I didn’t even notice that- it’s brain fart day lol
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dusk pasture
need help solving this differential equation
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need help solving this differential equation
dusk pasture
im not sure if this is supposed to be separable bc if i move the y variables over, i cannot multiply to the other side the dt since it is added
im also not sure who i would go about this using the integral factor method
dim dragon
dusk pasture
not sure if that does anything for me, but i could be wrong
appreciate the help tho
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hot herald
show work
you are told that the triangle is obtuse
so you would need a way to determine which value results in an obtuse triangle.
it would actually be better to use the sine law here yes
well it's not immediately clear whether the obtuse angle would be at K or M
I mean you could start with cos law, but you'll be fine as long as youre able to find a way to find the values that make your triangle obtuse
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noble plinth
(Not sure if this be the right place to ask for this)
how can i (if even) calculate 10^(-4.15) without a calculator
torn jolt
I need help😥
noble plinth
don't kill my msg lol
bitter orbit
@torn jolt Look for the MATH HELP (AVAILABLE)
twilit leaf
you cant really calculate that without a calculator
twilit leaf
the closest think is like 1/((10)^4*(10)^0.15)=1/10000(10)^0.15
noble plinth
I've seen people raise powers like 25^(1/4) can be broken into 5^2×1/4 or something
bitter orbit
@torn jolt Get this one https://discord.com/channels/268882317391429632/903430335474331698
Let's see
humble steppe
Rewrite $10^{-4.15}$ as $e^{-4.15\ln 10}$
glossy valveBOT
jimmy1234
humble steppe
Then apply series expansion.
bitter orbit
I'm sure the thing above is overkill
noble plinth
Ig calculator is good
twilit leaf
do you know series exapansion
noble plinth
nope sorry
twilit leaf
fair enough
bitter orbit
10^(-4 - 0.15)
noble plinth
that looks scary
twilit leaf
the best i know of is exponent rules for the 4 part, but the 0.15 is basically impossible without a calculator
bitter orbit
$10^{-4} \cdot 10^{-0.15}$
glossy valveBOT
Max Hetfield
twilit leaf
also youd still need to know ln10 for the series expansion part which requires a calculator lol
noble plinth
10^-(0.15) how do i solve that
bitter orbit
10^-(0.15) how do i solve that
Thinking
twilit leaf
you cant really do it without a calculator
bitter orbit
10^-(0.15) how do i solve that
Does the exercise say that you need to solve it WITHOUT a calculator?
noble plinth
nope it has more complex problems that require antilogs so i guess yeah
Imma leave it
glossy valveBOT
Max Hetfield
bitter orbit
Mathematically, I don't mean the context
noble plinth
(that requires antilogs)
noble plinth
Mathematically, I don't mean the context
ah yes then
glossy valveBOT
Max Hetfield
bitter orbit
$-4.15 = \log_{10} x$
glossy valveBOT
Max Hetfield
bitter orbit
And I think pH is a logarithmic scale
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dense edge
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dense edge
How would I solve for x?
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hot herald
start with some log laws
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misty kite
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misty kite
How can the transformation here be done?
smoky wing
What can you tell about the maximum value of the function
misty kite
I think I'm having trouble because I'm unsure how to shift square root x and x^2 functions but I tried playing around with it in desmos but I can't get it to look like the bottom curve
misty kite
What can you tell about the maximum value of the function
I'm not really sure
smoky wing
So do you agree that it goes up from 1 to 2?
misty kite
is it multiplication related
smoky wing
Yeah
steel cove
misty kite
okay
but how do i move forward from there
i found that if i change 2x to 8x then the curve ends at 8
but idk how to get it to start at 6
misty kite
yea
smoky wing
What about the second one
misty kite
6,0 and 8,0
smoky wing
So it’s Still the same distance
misty kite
yea
smoky wing
So what kind of transformation is that?
misty kite
its a shift to the right
misty kite
y=f(x-h)
misty kite
im not sure how to type it with the square root and all that
but would it be f(x)=2sqrt(2x-x^2)-6
smoky wing
$$ y = 2\sqrt{2(x-6) - (x-6)^2}$$
misty kite
something popped up but went away
glossy valveBOT
Pure
smoky wing
Like that and you can expand it
misty kite
whats that
smoky wing
Kind of like language for typing/coding mathematics
misty kite
ohh
that sounds cool
also how does the function itself change so much
was it factored?
misty kite
how do i know when i need to do that
smoky wing
When you see that a function is sifted
So it’s the same shape
But not in the same place
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solar wedge
$a(b^{2}+c^{2})+b(a^{2}+c^{2})+c(a^{2}+b^{2}) \ge 6abc$
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$a(b^{2}+c^{2})+b(a^{2}+c^{2})+c(a^{2}+b^{2}) \ge 6abc$
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PryingOpenMy3rdEye
solar wedge
$a, b, c \in \mathbb{R}^{+}$
glossy valveBOT
PryingOpenMy3rdEye
solar wedge
**PryingOpenMy3rdEye**
I have to prove this
fallow widget
whats the furthers you went?
solar wedge
after simplifying it, I got $ab^{2}+bc^{2}+ac^{2} \ge 3abc$
glossy valveBOT
PryingOpenMy3rdEye
solar wedge
but I don't know where to go from here
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topaz valley
by am gm
topaz valley
so close
solar wedge
yeah
i'll keep an eye out for those things
i have one more
$(1+a_1)(1+a_2)...(1+a_n) \ge 2^{n}$
glossy valveBOT
PryingOpenMy3rdEye
solar wedge
**PryingOpenMy3rdEye**
$a_1, a_2,...,a_n \in \mathbb{R}^{+}$ and their product is 1
glossy valveBOT
PryingOpenMy3rdEye
solar wedge
idk what that is
topaz valley
holders inequality isnt the most straight forward thing to prove 
maybe theres a better way
log everything and jensens?
solar wedge
considering the fact that it's in my 9th grade book first lesson
there is a better way
topaz valley
oh wait
im overthinking this lol
just expand it out
you get 1 + product + cross terms
🤦♂️
topaz valley
what is the expansion
solar wedge
you want me to expand as in multiply those parantheses together?
solar wedge
ofc
topaz valley
and the as
glossy valveBOT
PryingOpenMy3rdEye
solar wedge
there we go
idk if I did it right
if this is what you mean
$a_1a_2$ etc should be equal to 1, right?
glossy valveBOT
PryingOpenMy3rdEye
topaz valley
**PryingOpenMy3rdEye**
yeah
and then like
somehow you use am gm on all the cross terms
i think you get a binomial kind of thing
solar wedge
hm
solar wedge
just wanted to know
how are you the only one that answers my questions? lol
i have seen only you around here
and other two people
but most of the time, it's you
topaz valley
theres a lot of people around
theres circle
theres Ann
i think Denascite is around maybe a bit later? i cant recall exactly
and Ramonov
other people i know ive seen
topaz valley
oh gosh
solar wedge
back to the problem
topaz valley
lets not even get into that
solar wedge
lol alright
topaz valley
essentially what im thinking you can do is
there will be a subset of the cross terms
that take k a_i terms
and n-k 1s
and theres (n choose k) of them
if you apply am gm
you get (sum of terms)/(n choose k) >= (product of terms)^(a number)
but because theres an equal number of each a_i appearing in the product
that becomes 1
so the (sum of terms) >= (n choose k)
then thats true for every k
so the expanded product >= sum (n choose k) = 2^n
solar wedge
okay
i'm trying to understand what you just said
sorry, what do you mean by n choose k?
english isn't my first language
topaz valley
the binomial coefficient
glossy valveBOT
topaz valley
rip
topaz valley
kind of a big question for 9th grade
solar wedge
only new things we've learned are these inequalities (am gm hm, cauchy schwartz, minkowski)
and quadratic equation stuff
topaz valley
maybe cauchy schwarz then
topaz valley
you just collapse it in
glossy valveBOT
topaz valley
is the first step for example
solar wedge
lol you really like the rainbow
topaz valley
🤔
solar wedge
yeah
glossy valveBOT
topaz valley
this gets kinda yuck
solar wedge
nope
i'm gonna do this tommorow
too much work for now
already had to go through 4 pretty hard inequalities (for me)
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vernal ruin
so im working on a quesiton
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so im working on a quesiton
vernal ruin
im trying to solve a probability question. If there are two 6 sided dice, what is the probability of a 1 not appearing on either dice
i concluded that the probabilty is 35/36, since there could be only one possible event wher both are 1's
but my friend is saying that it is 25/36
how is it 25/36?
nevermind
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sacred fog
#help-17 message what does the $\delta$ notation mean here
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illuminator3
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nova basin
You'd probably have more luck asking him directly
nova island
For 2, part b. How would I go about that?? I know induction you show P(1) is true, assume P(n) is true, then show P(n+1) is true if P(n) is true. But how would I go about that process?
nova island
Would I work from pointing out r in the Euclidean algorithm that r=a-bq
<@&286206848099549185>
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fleet cedar
For 2, part b. How would I go about that?? I know induction you show P(1) is tr...
if u still need help lmk
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if u still need help lmk
fleet cedar
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nova island
.reopen
nova island
if u still need help lmk
Hi sorry yes I do still need help, I just got pulled away for a few minutes!
nova island
Did I do that? Sorry I’m pretty new to discord, I legit thought this wasn’t anyone else’s channel yet
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minor topaz
Hello. I have gotten the right substitution value yet after making the substitution I am getting the wrong answer. The part at the end is sinh(t). Is the answer 256sinh^4(t)?
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solar wedge
$a^{2}+b^{2}+c^{2} \ge ab+ac+bc$
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$a^{2}+b^{2}+c^{2} \ge ab+ac+bc$
glossy valveBOT
PryingOpenMy3rdEye
solar wedge
$\forall a, b, c \in \mathbb{R}^{+}$
glossy valveBOT
PryingOpenMy3rdEye
solar wedge
i'm gonna have nightmares with am gm at this point
glossy valveBOT
topaz valley
the rest you can probably figure out
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open quail
So for rolling a 12 with 2 dice the probability is 1/36 but the answers say that it will occur once in 50 times, what does that mean
open quail
I understand how you get the 1/36 but have no clue why it would be expected to roll a 12 once every 50 times
I just tried 1 divided by 36
and got 0.02
and then 1/0.02
which gave me 50
but I've never heard of this before
is this how it works?
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lapis marsh
how to solve this with significant figure
why is 0.030 m^2 wrong?
spice orchid
what are the exact instructions
ebon shadow
You could try to put it in scientific notation
lapis marsh
this is the anwser but idk how to solve that
spice orchid
what are the exact instructions
.
lapis marsh
what do you mean with that
spice orchid
when given a problem, there are instructions that come with it, what are they?
lapis marsh
there are no instructions
spice orchid
well great then you dont have to do anything
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