#help-28
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stiff musk
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wet quiver
ok
misty fractal
but can u hep pls
what's the issue?
just use the regular algorithms to find mean, median, and range lol
misty fractal
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misty fractal
If you want to do it quick then at least cooperate
sum all these stuffs: 4.7, 8.9, 3.5, 3.2, 9.2
then divide the result by 5
wet quiver
thats the aswer
marsh cloak
Can i also ask for physics help here ?
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Can i also ask for physics help here ?
vapid scarab
Np!
marsh cloak
what about chem ?
vapid scarab
clear root
there is one for that too but it's dead
vapid scarab
there is one for that too but it's dead
Oiii
marsh cloak
thanks 🙂
vapid scarab
Hey there again
clear root
hello
marsh cloak
there is one for that too but it's dead
yeahh it is dead 😭
vapid scarab
Ive been studying organic since the day u meet me
Ive just been fairly decent at it now
marsh cloak
i havent tried the physics one
vapid scarab
physics one is quite ok
marsh cloak
Ive been studying organic since the day u meet me
COuld you help me pls ?
clear root
i havent tried the physics one
the physics server has help forums which is decent, they do check it occasionally
vapid scarab
u can close the channel now if ur done
clear root
Ive just been fairly decent at it now
you'll get it!
marsh cloak
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distant silo
This is probably a stupid question, but what is the power set of an empty set? Is it {Ø} because 2^0 = 1, or is it just Ø on its own because the empty set does not contain anything and it can't contain itself? Been thinking on this for 2 hours ever since my lecture ended and my head hurts at this point 🥲
torn jolt
This is probably a stupid question, but what is the power set of an empty set? I...
The former
And it’s not a stupid question
Note that the cardinality of the empty set is 0
And the cardinality of a set A’s power set is 2^|A|
So 2^0 is indeed 1
You can also think of it this way
distant silo
Okay, so the empty set can be a subset of itself, then? Because it's practically nothing I can't really wrap my mind around it containing nothing when it doesnt contain anything
torn jolt
The power set of A is the set of all subsets of A
Since the empty set is a subset of every set, and A is the empty set, by definition P(A) must contain only the empty set
torn jolt
Okay, so the empty set can be a subset of itself, then? Because it's practically...
Yes
The empty set is a subset of every set
Look at the definition of what it means for something to be a subset
distant silo
I see. I got it now, sort of, it's somewhat similar to infinity, though 💀 if that makes any sense
distant silo
Nothing actually, just wasnt sure if the empty set can contain itself, so I got it now
Thx a lot
torn jolt
The empty set doesn’t contain itself. The POWER SET of the empty set contains the empty set
I hope that’s clear
The empty set doesn’t contain anything
distant silo
Ooh I see that makes sense
torn jolt
That’s why, for any set A, the power set of A will contain the empty set.
inland hill
I Need helpppp
distant silo
Well thx once again, have a nice day and a ride on your taxi 🙂
inland hill
are word problems good
distant silo
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scarlet parrot
hi
sacred yarrow
why do we put [pi] / [2pi] / [2pi) in front of arg (z) = x
wdym
scarlet parrot
like this
whats the pi in the brackets for?
or this
other times its 2pi instead of pi
and sometimes the right bracket is open like this: [2pi)
help lol
vivid thunder
Brackets is modulo
Basically what this means is x = y [a] if there exists an integer k such that y + k×a = x
Essentially by adding or substracting whats in brackets a certain amount of times you get whats on the other side of the equality @scarlet parrot
Is that understandable ?
For example here an angle or that same + 2pi is the same thing
scarlet parrot
hmm
scarlet parrot
For example is 5 = 17 [4] ?
no?
vivid thunder
Why would that be ?
scarlet parrot
because 17 + (a real number) x 4 doesnt equal 5?
vivid thunder
First of all it is not any real number
It is an integer
Secondly, what about -3 ?
vivid thunder
Look
17 + 4 × (-3) = 5
And with modulo you can add or substract
Whats in modulo times an INTEGER
That is a very important condition
So here if you substract 4 three times
You get 5
scarlet parrot
okay this i understand
what about the one with pi
arg(z) is the value of the angle
let's say z is an imaginary number
scarlet parrot
let's do arg(z) = pi/2
if the modulo is [pi]
it means that if i add 2pi to pi/2 i'll still get pi/2
bc its 360°
so is arg(z) = pi/2 [pi] correct?
since if we add pi to pi/2 = 3pi/2
vivid thunder
No
The = is misleading
Because it is not an equality
It is a relation between the two numbers
Which tells you one is equal to the other plus a certain number pf times whats in brackets
So arg(z) = pi/2 is not the same as arg (z) = pi/2 [pi]
One implies rhe other
vivid thunder
it means that if i add 2pi to pi/2 i'll still get pi/2
In a sense yes. But thats because you define arguments mod 2 pi
Basically you dont care if its angle or angle + 2pi
vivid thunder
so is arg(z) = pi/2 [pi] correct?
Yes that final statement is correct but only if you have arg (z) = pi/2 [pi]
Im not sure if you wanted to statz that i the first place
But then you havent proven much
Could you rewrite what you know about arg (z) and what you wnat to prove please ?
scarlet parrot
all i know is that arg(z) is the angle of a point from its vector to the X axis. i've been tought that if z is a real number, then arg(z) = 0[pi]
vivid thunder
Yes
scarlet parrot
because if we add or substract k*pi from 0 we'll still get the same value
vivid thunder
No
scarlet parrot
okay then i must've understood that wrong
scarlet parrot
sorry wait
vivid thunder
But you only consider angles mod 2 pi
So you can say either its 0 mod 2pi or pi mod 2pi
(Because of the parity of k)
Do you follow me ?
scarlet parrot
So you can say either its 0 mod 2pi or pi mod 2pi
0 mod 2pi means that it will stay in the same position?
same thing with pi mod 2pi?
scarlet parrot
yes that's what i'm trying to base it on
vivid thunder
Do you see where the angle pi is ?
scarlet parrot
yes on the negative side of the x axis
vivid thunder
So it wont stay on the same side right ?
scarlet parrot
if we add pi to it then no it wont
vivid thunder
But you are not allowed
Because angles are defined mod pi
If i give you -1
And you give back 1
Thats not the same thing
scarlet parrot
hmm
are u free for a call?
it would be easier for u to see what i'm trying to work with
vivid thunder
Great ill call you
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wet quiver
guys i need help for a+dje + 2
wet quiver
ok
hollow grove
Show the original question.
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coarse flame
crude rapids
So, I have a problem in trigo- I got to a point where the variable is being divided by
so for example:
tan30 = 32/b
instead of tan30 = b/32
How do I handle this? Usually I'd just bring the number to the other side and change it (In case of trigo, Change from division into multiplication)
viral jasper
So, I have a problem in trigo- I got to a point where the variable is being divi...
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So, I have a problem in trigo- I got to a point where the variable is being divi...
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
glossy valveBOT
dqvidutzul
crude rapids
yes
south island
and you want to calculate for b
crude rapids
There:
Basically- In the third question- it says: in another train station ther's another staircase with the same angle of 30 degrees, and to the length of the track. also- see the lanterns here? It basically says that there are 25 lanterns along THIS (The original) track, and that the space between 2 lanterns is 4 meters
south island
my question is what are you solving for
crude rapids
In the third question it also states that the the lanterns are set in the same manner as the original one. and it asks how many lanterns are on the new one
errant mesa
sorry but i didnt understand it
crude rapids
sorry but i didnt understand it
The question basically asks how many lanterns are on the second track
It states that the lanterns on the second track are placed and put in the same manner as the first one
ant also states that the height(Or depth) or the second track is 32
oh, I think I got it
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long tangle
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sharp fable
What two numbers can get you 9?
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rugged pecan
This is a math problem I swear,,,,
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This is a math problem I swear,,,,
rugged pecan
How should i answer this?
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rugged pecan
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odd wolf
i’m watching video solution of this problem in a language i don’t understand. why is m(BAD) equals to 2B here?
granite torrent
i’m watching video solution of this problem in a language i don’t understand. wh...
,
we are given ABC = DAB
we also define ABD = DBC = B; hence, ABD + DBC = ABC = DAB = 2B
odd wolf
wait i didn’t read ABC = DAB initially
i assumed it just tells about DBA = DBC
thank you
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polar salmon
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polar salmon
K is an unknown constant
would my solution be a function in terms of k?
since its a geometric series I applied the a(1-r^n)/1-r
and got 4(1-1/2^k)
granite torrent
thing is this is not geometric series
granite torrent
would my solution be a function in terms of k?
yes
polar salmon
thing is this is not geometric series
i see
so then this work dosen't count?
OH
this is power series right?
wait
nvm im lost
languid junco
could try letting u = sin^2(x) since then cos^2(x) = 1 - u
granite torrent
this looks suspiciously like a differentiation under the integral sign problem
languid junco
alternatively weierstrass substitution can be really useful for these kinds of problems
granite torrent
there we go
you may know it as "tangent half-angle substitution"
though idt that is intended approach (well i have not tried solving yet. just looked at problem)
hallow walrus
you may know it as "tangent half-angle substitution"
Seems unnecessary
granite torrent
y reply ping i did not suggest that
languid junco
was my idea, it would work
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granite torrent
assuming what you have is right, partial fraction decomposition
though i think t = tanx would be better used on one of the first-order differentiated integrals you had
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modest rain
is it best to use ratio test here?
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is it best to use ratio test here?
modest rain
and what test should i apply here?
languid junco
is it best to use ratio test here?
this is alternating, so use the alternating series test
languid junco
and what test should i apply here?
same here
stiff musk
is it best to use ratio test here?
this isn't going to be absolutely convergent, so the ratio test will not help
modest rain
same here
how is this alternating?
oh
obvisously cos ranges from -1 and 1 each pi cycle
languid junco
yep, cos(pi n) = (-1)^n
modest rain
this isn't going to be absolutely convergent, so the ratio test will not help
then what test is the most efficient way
stiff musk
obvisously cos ranges from -1 and 1 each pi cycle
not gonna do you much good when it's squared...
modest rain
cus i thought ratio test would
languid junco
oh I misread, that's squared yep
stiff musk
cos^2(pi n) has a much simpler name 😁
languid junco
so alternating won't work, I'd use comparison test
modest rain
so alternating won't work, I'd use comparison test
is a 1/n^3 a good comparison?
no i think 1.n
1/n
modest rain
so alternating won't work, I'd use comparison test
do you mean the limit comparison test?
languid junco
do you mean the limit comparison test?
just regular
modest rain
Would this suffice?
in the solutions they did the limit comparison test but idk if my way works aswell
languid junco
looks good to me, nice
oh wait
I looked at the solution lol 1 sec
your solution isn't rigorous enough unfortunately
that's very hand wavy even if it is true
modest rain
oh
languid junco
do you know how the regular comparison test works?
languid junco
it doesn't have to be one of those, you can compare any series to anything
those are commonly used tho I guess
modest rain
so how would i do the comparison test?
languid junco
Would this suffice?
if the sum of a_n diverges and b_n is larger than a_n, then b_n diverges as well
looks like you said the opposite
the LHS is larger than the RHS
modest rain
the LHS is larger than the RHS
so then i cant compare it to 1/n
languid junco
so then i cant compare it to 1/n
you can. the sum of 1/n diverges, and the series you're looking at is bigger, so it also diverges
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charred escarp
Can someone help me understand how to use the cofunction identities?
charred escarp
sin(x+90) = cos(x)
cos(x+90) = -sin(x)
Say I had sin(135)
Would it be cos(45?)
charred escarp
sin(x+90) = cos(x)
Using this
placid vale
shouldn't it be sin(90-x) = cos(x) ?
charred escarp
I've seen both ones be used
placid vale
😵💫
charred escarp
So using sin(x+90) = cos(x)
sin(135) = sin(135-90) = cos(45)
Correct?
Is the middle step valid?
It is
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spring mist
Can some one help with this question?
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Can some one help with this question?
spring mist
I expanded and collected like terms, then I got a 4th degree polynomial
spring mist
I noticed a f(f(x)) = x pattern but I do not know how to use it
spring mist
notice the trinomial are the same
yes
charred escarp
Is it not a hidden quadratic?
If you let: t = (x^2-3x+1)
t^2-3t+1=x
Oh wait nvm
Oh wait
You can expand then factorise by grouping
spring mist
can we factor out the polynomial? (x^4-6x^3+8x^2+2x-1=0)
idk, but I think not using that precious f(f(x)) would be a pity
charred escarp
can we factor out the polynomial? (x^4-6x^3+8x^2+2x-1=0)
Yes
charred escarp
idk, but I think not using that precious f(f(x)) would be a pity
You could solve by factorising first then use that method to check your answer?
spring mist
the problem is that a. I can't factor b. I don't know how to use that f(f(x)) characteristic
charred escarp
I can show you how to factor it
spring mist
I can show you how to factor it
sure
charred escarp
I'll write it on paper then send a pic
spring mist
I'll write it on paper then send a pic
ok
So far I figured out that it could be (x^2+ax+1)(x^2+bx-1), where a, b could be any integer
spring mist
oh yes, it works
charred escarp
Step 2 can be difficult to understand if you've not seen how to factorise by grouping before
I can link a video if you wnat
spring mist
So far I figured out that it could be (x^2+ax+1)(x^2+bx-1), where a, b could be ...
Can I brute force a, b? Or are there some clues for finding a, b?
charred escarp
From this we can see a is -4 and b is -2
spring mist
I can link a video if you wnat
I would like this video, please
charred escarp
spring mist
nice
Here is the solution. I did not get it, especially the 3rd sentence.
How can the x^2-4x+1 be a factor of the polynomial?
charred escarp
So we know that f(f(x)) = x
And we know that f(x) = x is also x^2-3x+1=x
Which can be written as f(x) = x^2-4x+1
Do you understand so far?
We can say that a function g(x) x f(x) will give us our original quortic
spring mist
Do you understand so far?
yep
charred escarp
So we use polynomial division to divide the quortic by f(x) which we said was x^2-4x+1
spring mist
hold on, that's where confusion comes from
I do not understand why is x^2-4x+1 a factor, I know this polynomial is valid
charred escarp
Ohh okay
spring mist
Is that because we have got x^2-4x+1=0, so we can go to "zeros"?
charred escarp
I think so
charred escarp
Tbh I think this method is better
spring mist
Oh I got it, since this little polynomial is 0, and the big polynomial is 0, so the remainder is 0, and then the polynomial is the factor?
charred escarp
Yes
spring mist
for the polynomial division, I know how to do it
spring mist
Tbh I think this method is better
That's easier to understand
Thanks bro for the help today
charred escarp
No problem
spring mist
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granite torrent
what progress have you made so far? or do you have any ideas?
it helps greatly that the only dice that can show 5 are the 6-sided ones
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minor needle
How do i find the exact value for this series?
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How do i find the exact value for this series?
quaint prawn
How do i find the exact value for this series?
maybe you can somehow write it as a geometric series
plush egret
theres a n on the numerator
how could you introduce an n?
minor needle
wdym
buoyant pewter
How do i find the exact value for this series?
you must use the theorem on the differentiation of power series to the appropriate geometric series
minor needle
so i tried doing it your way but i got 4 as the answer 🤔
buoyant pewter
yes
but now
you ought to
multiply
by
1/4
correct?
4 = 2^2
and expoent of yours is n - 1
tomake it n + 1
minor needle
oh right
minor needle
wow thx again
buoyant pewter
yw
minor needle
but like
how did you recognize that it was a differentiation of power series lol
cuz i would never think of that
minor needle
oh wow are you a mathematician
buoyant pewter
yes i give you a hint:
when n or sth liek n in numerator
then you need to use diffeerentaion
and
if n is in denomiantor
then you need to use integration
in both cases to the geometric series
ok?
buoyant pewter
)
minor needle
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jolly girder
im stuck on this atm can someone help?
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im stuck on this atm can someone help?
polar apex
whats the problem
peak elk
whats the problem
solve for x?
polar apex
2025/81 ^ 2 ?
peak elk
2025/81 ^ 2 ?
yeah
polar apex
yeh first divide both sides by 81
then use power of 2 to get rid of that sqrt
tacit siren
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jolly girder
yeh first divide both sides by 81
then use power of 2 to get rid of that sqrt
so bassicly square root method?
for the last one
jolly girder
idk what to do on that part
polar apex
sqrt(x) ^ 2 = x
polar apex
x = a => x^2 = a^2
peak elk
x = a => x^2 = a^2
yes
jolly girder
what does a mean
peak elk
what does a mean
any value
jolly girder
so sqrt(21) and i get the answer?
peak elk
so sqrt(21) and i get the answer?
no
jolly girder
is it like this
step 1
81/2025 =sqrt(x) 81/81
21 = sqrt (x)
step 2
sqrt (21) = sqrt (x)
is it right
peak elk
also step 2 is wrong
peak elk
then a can remove the sqrt of x now right/
by squaring both sides
in step 2
$(25)^2 = (\sqrt x)^2$
glossy valveBOT
Wither
peak elk
then 25^2?
yes
jolly girder
and i can remvoe the sqrt and ^2
peak elk
that's the answer
peak elk
and i can remvoe the sqrt and ^2
yes
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torn bane
I don’t get the T of T prime =Iw part..
oh sht
thats not how you draw it
you cant do that
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tacit siren
!da2a
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tacit siren
R u taking an exam rn
well ask ur question
So r u gonna eat lunch first
ok srry im dipping out 
Gl
U can ping Helpers when ur done eating lunch
Or open uo a new channel with the actual questions :p
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dapper lantern
$$\frac{x}{x+1}+\frac{x+1}{x}=\frac{13}{2}$$
glossy valveBOT
Tree
dapper lantern
$$\frac{(x+1)^{2}+x^{2}}{x(x+1)}=\frac{13}{2}$$
glossy valveBOT
Tree
dapper lantern
latex is so annoying to write in without a backslash lol ima just write it on a whiteboard rq
thats how i wouldve done it
expanding, cross multiply and then just put it in the quadratic formula
though theres probably an easier way
heady breach
why were you pinging while you had a helper??
dapper lantern
no worries :))
you have any other questions
?
ask away then
alrighty
ooooo okay
this one seems quite long so gimme a bit
it seems like a question that definitely has some sort of trick to it
but im not sure what it would be tbh
but just putting sqrt(3) - sqrt(2) should simplify down enough
thats the sustitution, gimme a bit to actually work it out now 😭
expanded brackets
basically after that, rationalise all the denominators, expand brackets, simplify down
its really just a lot of steps
im assuming you know how to do each individual step?
if not i can walk you through them
thats all the steps there
if you need me to walk through any individual one then i can help
but it goes in order of equation, define x, substitute in x, exponents, rationalise denominators, simplify down x 2
anything else?
alrighty then, have a nice day lol
use .close to open the channel to the next person whenever youre ready :))
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winter yacht
I've been stuck on a question since last night,
I have to show that R^N is a vector space which is not of finite dimension
winter yacht
I proceed with the absurd, that R^N is of finite dimension
SO
Let n € N
dim R^N = n
But I don't see what more to do,
I must show a sequence which is not expressible as a linear combination of n sequences?
<@&286206848099549185>
rugged void
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winter yacht
mb
rugged void
all good bro
fast peak
have you thought more about the hint I gave you last time?
fast peak
I gave you that argument aswell
winter yacht
I construct a free family of n vectors and I show that there is a sequence which is not expressible from the n vectors?
winter yacht
I'm sorry but I don't see, what authorizes me to consider an infinity of free vectors?
fast peak
what do you mean, "authorizes"
winter yacht
I assume from the start that dim R^n = n
fast peak
if you have infinitely many vectors, then in particular you at least have n+1 vectors
winter yacht
Okay and my vectors are free
fast peak
free is the wrong word
winter yacht
I'm sorry I'm French and we use that. You mean linearly independent? I'll use that know
fast peak
yes linearly independent
winter yacht
All right,
Now I have n+1 linearly independent vectors under the assumption that the dimension of my vector space is n.
I need to show that my n+1 vectors form a base of R^N?
winter yacht
Base extracted?
fast peak
"in a vector space of dimension n, n+1 vectors are not linearly independent"
winter yacht
I will see that
In a vector space generated by n vectors (n ∈ N), any family of n+1 vectors is linked.
fast peak
yes
so if you have n+1 vectors which are linearly independent, then your vector space cant be n dimensional
winter yacht
yes
ok I see
Just a question what allows us basic
To take n+1 lineary independant vectors
fast peak
why shouldnt we
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urban jetty
A triangle is inscribed in a circle, the difference between its longest and shortest side is 4 cm, and the third side is distant from the center of the circle by 2 cm. Find the sides of the triangle if the radius of the circle is 4 cm.
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clear juniper
How did they got 1/2
thorn fjord
Having trouble solving this system. Anyone can point me in the right direction
dull citrus
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patent sierra
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patent sierra
Uh i hvae not done these types before
I heard some tree diagr is used or smthg
but couldnt do it
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lyric quail
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jaunty fox
Yes, but you're double counting numbers that are multiples of both 11 and 17 for example
Also, your fractions are upside down, but that's not a serious issue since the results are correct
lyric quail
Yes, but you're double counting numbers that are multiples of both 11 and 17 for...
oh so to account for that, i should subtract multiples of LCMs of each pair of prime factors?
i.e
jaunty fox
Correct. Since they're prime, the LCM is also the product
jaunty fox
Sure thing
jaunty fox
That looks good-- I didn't check the exact math, but that should be correct in terms of methodology
lyric quail
Appreciate the help Jeff, have yourself a wonderful day bro
jaunty fox
You too
north pumice
How do you do these types of questions?
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How do you do these types of questions?
languid junco
these all look like separable Differential Equations
north pumice
how are these different from from first order linear equations?
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restive hawk
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restive hawk
can someone help me find some bounds for this
got a graph but still feeling a little difficult
i think bounds for x will be most inwards, as I only have x=0 and x=y/4 (y=4x) to define it
im initially thinking something like thisZ?
(all of the 0s come from the fact that i am in exclusively the first octant)
graphically x going from 0 to y/4 looks correct
however im not certain on y
but feel good about z
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low root
For the question, "If fx = 2x^3 -6x, at what point on the interval 0<=x<=sqrt3, if any, if the tangent to the curve parallel to the secant line on that interval." Instead of finding the secant slope first, could you set the secant and tangent equal to each other to solve? (teachers work is shown)
low root
<@&286206848099549185>
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low root
i asked in the other channel 15 min ago
robust slate
could you set the secant and tangent equal to each other to solve?
if you mean setting this equal to f'
then yeah
it's all the same thing in the end
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robust slate
srry I didn't see this
robust slate
is it possible to do it without distributing the ^3 here?
not rlly
you kinda need to simplify that in one way or another
low root
Then would it be wrong to take a gcf of sqrt3 in here to get, sqrt3 (2sqrt3^2 - 6)
robust slate
that's fine too
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minor needle
Hello, I don't understand intuitively how to do this
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Hello, I don't understand intuitively how to do this
Show your work, and if possible, explain where you are stuck.
minor needle
There's no work cuz idk where to start 💀
boreal marlin
Do you know how to calculate the ways to choose k items out of n?
boreal marlin
Right, so you choose 4 out of 13, and for each you choose 2 out of 13
The card left need only to be a diamond or spade, so 26 possibilities for that
minor needle
wdym i choose 4/13 and for each 2/13?
boreal marlin
It just means you multiply the results
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wispy axle
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wispy axle
I need help in this problem Z is a standard normal and X is a chi square random variable it asks me to find the probability listed above
So I divided everything by 1 and 16 (the degrees of freedom for my chi square random variables)
Which means I had to multiply the whole equation by 16
Which makes my probability the area of the F curve between 64 and 400 right ?
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hexed spruce
Being a, b, c, d four odd natural numbers, justify if there's a solution for:
1/a + 1/b + 1/c + 1/d = 1
hexed spruce
Idk how to start with this
timid prawn
What about indirect proofs
hexed spruce
wdym
timid prawn
Start by saying it's not equal to one
Then end up with something that makes no sense
And use that to say it must equal one
empty topaz
big brain
timid prawn
Being a, b, c, d four odd natural numbers, justify if there's a solution for:
1/a + 1/b + 1/c + 1/d ≠ 1
hexed spruce
but how do I know the value of each letter
timid prawn
You don't need to
solemn gate
I just replace the 1 with whatever I need?
i dont think you can
timid prawn
You should pick a number that leaves you with one of the variables equalling another one
And since they said they are all different
Use that to say it's 1
Also I just realized you can't pick any number
TheSnake was right
solemn gate
if you want to prove by contradiction you need to prove for every number that isnt 1
timid prawn
Yeah
solemn gate
if you stated 1/a+..=/=1
if youd pick for example 2 you just prove that it isnt equal to 2
timid prawn
Yeah because it can still be 3
solemn gate
but can be for 3 or any other
hexed spruce
yeah Ik that
timid prawn
Yeah
hexed spruce
but wyd then
solemn gate
maybe id try to add the fractions?
hexed spruce
Ok i'll try with that
timid prawn
a + b + c + d ≠ 1
timid prawn
Thats a great idea
hexed spruce
And I'm just overthinking
timid prawn
a + b + c + d ≠ 1
solemn gate
and check if sides if they are odd or even
timid prawn
I think that's it
solemn gate
a + b + c + d ≠ 1
how did you get that?
timid prawn
Multiplying by a,b,c,d cancels out the fractions
solemn gate
Multiplying by a,b,c,d cancels out the fractions
you multiplied both sides?
solemn gate
XD
solemn gate
yeah that was wrong
timid prawn
It's a + b + c + d ≠ 4
solemn gate
wait ill try to do it myself
timid prawn
Okay
a+b+c+d(1/a + 1/b + 1/c + 1/d) ≠ 1(a+b+c+d)
Since you distribute to the respective fractions, they cancel out to only be the numerators, and they numerators are all 1, and they are being added up so you add up the 1's
solemn gate
ok i got it
timid prawn
Yeah
solemn gate
left side is even and right side is odd
solemn gate
ok ill write it then sorry
timid prawn
Like I can sort of
solemn gate
1/a+1/b+1/c+1/d=1 (multiply both sides by abcd)
bcd+acd+abd+abc=abcd
a,b,c and d are odd
odd times odd gives you odd
solemn gate
so bcd,acd,abd and abc are odd
solemn gate
Did we need to do FOIL
dont know what FOIL is im not native
timid prawn
Hmmmmm
solemn gate
1/a+1/b+1/c+1/d=1 (multiply both sides by abcd)
bcd+acd+abd+abc=abcd
is this step wrong?
hexed spruce
if you multiply 3 odd numbers it gives you and odd number?
solemn gate
if you multiply 3 odd numbers it gives you and odd number?
yes
timid prawn
Yeah
hexed spruce
and if you divide that number by another odd number it's still an odd number?
timid prawn
But how did you get bcd,acd,abd and abc
solemn gate
so bcd,acd,abd and abc are odd
four odds added together is even
hexed spruce
like odd/odd = odd?
timid prawn
Yes
solemn gate
But how did you get bcd,acd,abd and abc
(1/a+1/b+1/c+1/d)*abcd=abcd/a+abcd/b+abcd/c+abcd/d
timid prawn
Oops I thought decimals counted as still odd
hexed spruce
then it can't be
timid prawn
Well multiply odd on the other side
hexed spruce
i got in the denominator a×b×c×d
solemn gate
Oops I thought decimals counted as still odd
no, odds are integeres
timid prawn
Is odd^2 = odd
hexed spruce
i got in the denominator a×b×c×d
so that does give an odd number?
timid prawn
So odd/odd = odd
solemn gate
1/a+1/b+1/c+1/d=1 (multiply both sides by abcd)
bcd+acd+abd+abc=abcd
here
look
@hexed spruce
timid prawn
That way you cancel out all the fraction
solemn gate
yes
timid prawn
So what if we try that
solemn gate
and as i was saying
odd* odd * odd=odd
so bcd,acd,abd,abc are odd
4 odds added together is even
and right side is odd
since odd* odd* odd* odd=odd
timid prawn
Yeah
hexed spruce
Yeah I do but why does that prove all equals 1
solemn gate
are you on the other planet 😭
timid prawn
Because it disproves any other number
solemn gate
its equivalent
solemn gate
1/a+1/b+1/c+1/d=1 (multiply both sides by abcd)
bcd+acd+abd+abc=abcd
if this is impossible
hexed spruce
are you on the other planet 😭
Sorry I'm not native english and I might be a lil bit lost sometimes
solemn gate
then original is also
solemn gate
Sorry I'm not native english and I might be a lil bit lost sometimes
me neither
dont worry
solemn gate
So let's straighten things up
yeah
timid prawn
We are multiplying by a*b *c * d
solemn gate
both sides yes
timid prawn
Okay
solemn gate
so its equivalent to the original
timid prawn
Yeah
And we place it in the numerator of each fraction
Okay
And that cancels out some of the variables
solemn gate
yes
timid prawn
so we get bcd,acd,abd and abc
solemn gate
ok
hexed spruce
oh ok
solemn gate
@hexed spruce do you follow thru?
solemn gate
so you get bcd+acd+abd+abc=abcd
and if this is impossible to get the original also is impossible to get
solemn gate
so you get bcd+acd+abd+abc=abcd
if this is wrong yes
hexed spruce
but how do I prove that is wrong
hexed spruce
yeah
hexed spruce
yeah
solemn gate
if odd* odd=odd then also odd* odd* odd=odd and odd* odd* odd* odd=odd
hexed spruce
ok
solemn gate
also if odd+odd=even then odd+odd+odd+odd=even
solemn gate
so are bcd,acd,abd,abc even or odd?
hexed spruce
odd
hexed spruce
even
hexed spruce
yea
solemn gate
is abcd even or odd?
hexed spruce
odd
solemn gate
yes so right side is odd
hexed spruce
even =/=odd
solemn gate
1/a + 1/b + 1/c + 1/d = 1 is equivalent to bcd+acd+abd+abc=abcd
hexed spruce
Im sorry for being this lost I haven't done this kind of problems in a while now
hexed spruce
1/a + 1/b + 1/c + 1/d = 1 is equivalent to bcd+acd+abd+abc=abcd
yea
solemn gate
if bcd+acd+abd+abc=abcd is impossible for reason even=/=odd that mean 1/a + 1/b + 1/c + 1/d = 1 is impossible but the reason is that bcd+acd+abd+abc=abcd is impossible bcs its equivalent