wolframalpha
#help-27
frozen aurora
willow hare
winter torrent
bot is ded
frozen aurora
so sed
real whale
Hey, since the bot is dead, I will ask my question here ^^
I have to find a and b knowing the fact that a-b= 21 and ppmc(a,b) = 280
I find no solution because a = 21 -b = 3(7) -b and 280 = 2^3 (5)(7) so a can't be written as 3*smth
Am I wrong somewhere?
fossil locust
I have to find a and b knowing the fact that a-b= 21 and ppmc(a,b) = 280
that's wrong
cause a = 56 and b = 35 works
essentially the strategy is to assume a and b are both multiples of 7
so if a = 7m and b = 7n
we have m - n = 3 and lcm(m, n) = 40
we can easily find m, n that work
m = 8 and n = 5
(7 because it's a factor of both 21 and 280)
frozen aurora
I have to find a and b knowing the fact that a-b= 21 and ppmc(a,b) = 280
ppmc?
fossil locust
I'm assuming lcm
real whale
it's lcm sorry
@fossil locust Okay I see and then I can use an integer factorization to find all the solutions
fossil locust
<@1151031274413228043> Okay I see and then I can use an integer factorization to...
yeah lcm(m, n) = 40 doesn't have many candidates
you can't factorise this
real whale
yes
fossil locust
if you want to write the proof down, it's cause if a is not a multiple of 7, then b also can't be a multiple of 7
the LCM would thus not be a multiple of 7 - contradiction
kind flicker
Is this still being used?
real whale
@fossil locust so I find that the unique solution is 8 and 5
as you said
thank you for the help!!
real whale
Is this still being used?
No it's not
fossil locust
no worries!
kind flicker
This question is solved using a Poisson Distribution with PDF. But isn't the premise of a PDF that it can't be an exact value, but a range of them?
fossil locust
This question is solved using a Poisson Distribution with PDF. But isn't the pre...
I see Revision Village lol
kind flicker
I see Revision Village lol
LOL
frozen aurora
I see Revision Village lol
trauma 
kind flicker
Oh damn you know Day as well
fossil locust
this is a discrete probability distribution
kind flicker
Damn two IB students?
fossil locust
oh right yeah I know day
kind flicker
oh right yeah I know day
Damn small world
kind flicker
this is a discrete probability distribution
Now I'm even more confused.
PDF are continous?
Aren't PMF's discrete?
kind flicker
So why call it PoissonPDF and not PoissonPMF
That just makes everything more confusing
fossil locust
So why call it PoissonPDF and not PoissonPMF
they did not use a PDF at all
fossil locust
So why call it PoissonPDF and not PoissonPMF
where do you see that?
kind flicker
Look at the answer
frozen aurora
i think it's a calculator thing
frozen aurora
i think it's a calculator thing
i don't recall mine having PMFs
kind flicker
I mean is PDF and PMF interchangable in IB?
Alright so all Poisson Distributions are Discrete, even though the calculator says PoissonPDF wherein PDF is continous?
frozen aurora
i guess so
fossil locust
oh jesus
fossil locust
Alright so all Poisson Distributions are Discrete, even though the calculator sa...
yep
frozen aurora
checked it online too xd
frozen aurora
Alright so all Poisson Distributions are Discrete, even though the calculator sa...
does your calculator say that?
kind flicker
does your calculator say that?
It says PDF
frozen aurora
it just might be a typo on RV's end, i have seen typos in their texts before
kind flicker
Do your calculators say PDF and PMF?
gleaming hill
Hi
odd linden
Can someone explain why case two, epsilon is root L epsilon. Like, how are we supposed to interpret the question to get it like that
devout snowBOT
Can someone explain why case two, epsilon is root L epsilon. Like, how are we su...
sand dove
Can someone explain why case two, epsilon is root L epsilon. Like, how are we su...
if you're trying it out on your own, you're supposed to reach this first
odd linden
I managed to get the conjugate part
sand dove
and then say $|\sqrt{a_n}-\sqrt{L}| < \frac{|a_n-L|}{\sqrt{L}}$
woven radishBOT
rafilou is not not born in 2003
odd linden
but after that, it didnt really make sense what to do afterwards
sand dove
**rafilou is not not born in 2003**
does this still make sense
odd linden
what does the root an go?
odd linden
ohh
ok
that makes sense
but how is epsilon root L epislon. That just doesn't make sense to me
sand dove
but how is epsilon root L epislon. That just doesn't make sense to me
your objective is to show $|\sqrt{a_n}-\sqrt{L}| < \varepsilon$ for any $\varepsilon > 0$
woven radishBOT
rafilou is not not born in 2003
sand dove
so fix some $\varepsilon > 0$
woven radishBOT
rafilou is not not born in 2003
sand dove
you know there exists $N$ such that for $n > N$, $|a_n-L| < \varepsilon'$, with $\varepsilon' > 0$ some arbitrary value that we'll determine next
woven radishBOT
rafilou is not not born in 2003
sand dove
**rafilou is not not born in 2003**
so now because of this
$|\sqrt{a_n}-\sqrt{L}| < \frac{\varepsilon'}{\sqrt{L}}$
woven radishBOT
rafilou is not not born in 2003
sand dove
now the question is, which value of $\varepsilon'$ makes us get the result we desire?
woven radishBOT
rafilou is not not born in 2003
odd linden
oohhhh
ok
that makes a lot of sense
now
that acutalyl cleared up a lot of confusion
ty
.close
devout snowBOT
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Available help channel!
hexed berry
devout snowBOT
small jackal
We gotta find the value when ak = a7
so find the 7th term?
hexed berry
-6*7
small jackal
Ah, fuck I forgot.
Yeah I think you know what is next?
hexed berry
the exercise has q different formula for that
Yeah
N*(n+1)/2
So basically 7*(7+1)/2
small jackal
the exercise has q different formula for that
Hmm?
I mean subtract the sum of the first 6 terms from the sum of the first 7 terms to get the seventh term.
Or are you looking for $\sum _{k=7} ^n a_k?$
woven radishBOT
David
hexed berry
Hmm?
I mean subtract the sum of the first 6 terms from the sum of the first 7 te...
But I suppose they're asking me to get the 7th term using that damn formula
small jackal
$\sum _{k=1} ^7 a_k - \sum _{k=1} ^6 a_k$
woven radishBOT
David
hexed berry
N^2 - 6n
hexed berry
$\sum _{k=1} ^7 a_k - \sum _{k=1} ^6 a_k$
Yes, this makes sense but
what about using that formula the book gave me
Maybe doing the exact same thing
except now
devout snowBOT
Maybe doing the exact same thing
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.
small jackal
No
hexed berry
Alright.
small jackal
Send it.
hexed berry
small jackal
Okay determine the value of a_7 given that...
hexed berry
Yes.
hexed berry
Okay. I do not need to use the formula, then?
small jackal
Be sure to replace the sums
With the formula n²-6n
And
small jackal
Okay. I do not need to use the formula, then?
You do
hexed berry
Ah so
small jackal
Replace the sum with the formula n²-6n
And put in the values of n
Then simplify
hexed berry
Pretty much 7^2-6*7 - 6^2-6X6?
small jackal
Pretty much 7^2-6*7 - 6^2-6X6?
Yes
hexed berry
Thank you, thank you.
small jackal
Pretty much 7^2-6*7 - 6^2-6X6?
Wait it's "+6×6" not -6×6
small jackal
-(n²-6n)
hexed berry
Yes
small jackal
Distribute the minus
small jackal
No problem 😃
hexed berry
So, I think I have it.
Lemme do the formula, then.
So, when I wanna look up for the value of a term
I just gotta do sigma of my term - n-1
small jackal
So, I think I have it.
What is your answer 
hexed berry
right?
small jackal
I just gotta do sigma of my term - n-1
Yup
hexed berry
Well, I gotta do the calculation yet!
small jackal
😅
hexed berry
First, I wanna get my breakfast.
small jackal
Okay
hexed berry
Buddy
small jackal
!done
devout snowBOT
If you are done with this channel, please mark your problem as solved by typing .close
hexed berry
Be honest my friend.
small jackal
Be honest my friend.
Yes
small jackal
can I pass it?
If you study, you can!
hexed berry
.close
zenith cairn
can someone help with latex pls
devout snowBOT
can someone help with latex pls
zenith cairn
can someone write the bottom right (circled blue) in latex plsss
hexed berry
can someone write the bottom right (circled blue) in latex plsss
wdym in latex?
Also Ka is a pretty funny topic. You will get a lot of fun
woven radishBOT
s a g e
zenith cairn
..
zenith cairn
Also Ka is a pretty funny topic. You will get a lot of fun
yeahh it’s quite interesting
hexed berry
My tip: do not waste time with x^2+x+n equations.
You can always omit the -x on the bottom side.
Since realistically, if ka is so low, x will be so low it won't affect the initial concentración of reactive
thin basin
${frac/1/2}$
i think frac should be outside the {}
zenith cairn
My tip: do not waste time with x^2+x+n equations.
You can always omit the -x on...
ohh im not learning quadratic equations with Ka the content doesn’t go that much in depth
i need the bottom right
boreal lion
oops
zenith cairn
where it’s sqrt
boreal lion
$[H^{+}] = \sqrt{K_a[HA]_{\text{init}}}$
woven radishBOT
w
zenith cairn
tysmm
boreal lion
👍
gleaming magnet
Could anyone example this:
devout snowBOT
Could anyone example this:
gleaming magnet
How can the i be simply absorbed by B, when it is clearly stated that it is a real constant
If we wanted only the real part, would it not be A 2 cos(x)?
If B is real, than we have changed to equality, because sin(x) is meant to be imaginary
I have seen some videos now and in most there is no mention of B having to be a real constant, maybe this page is just wrong?
<@&286206848099549185>
devout snowBOT
@gleaming magnet Has your question been resolved?
devout snowBOT
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Available help channel!
frail osprey
how could i solve this diophantine
devout snowBOT
how could i solve this diophantine
devout snowBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
ripe grove
distribute the 4 and solve for m in terms of n
frail osprey
m = 4
ripe grove
okay what about 1
frail osprey
m = -2
ripe grove
i want where m is negative
frail osprey
why?
ripe grove
because you are solving for where $m<0$
woven radishBOT
Nyxzore
frail osprey
im solving for the opposite
ripe grove
my bad
frail osprey
im solving for m > 0
frail osprey
alright, so we wnt where m is positive
how do i get an ordered pair of solutions tho
ripe grove
it helps to draw a number line
so if i plug in any of of n less than zero i get a positive value for m right?
frail osprey
yes
ripe grove
no m>0 where n is ...
devout snowBOT
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Available help channel!
restive river
Can someone explain me what is the question and how we can get the idea of solution
devout snowBOT
Can someone explain me what is the question and how we can get the idea of solut...
queen hearth
Can someone explain me what is the question and how we can get the idea of solut...
Check the properties for each function
sturdy yew
devout snowBOT
sturdy yew
why does f(f(f(x))) have the point (1,1) included in it
isn't x= 1 not part of f(x)'s domain
glacial wyvern
why does f(f(f(x))) have the point (1,1) included in it
it doesn't
sturdy yew
it doesn't
but desmos shows otherwise
glacial wyvern
maybe you haven't zoomed in enough
sturdy yew
no i did
glacial wyvern
if you click on it it should say (1, undefined)
glacial wyvern
alright I saw the same thing
so I guess that's probably just some kind of numerical error on Desmos' part
sturdy yew
so it 1,1 should be a removable discontinuity right
glacial wyvern
yes indeed
thin basin
you have to understand that f(x) and f(f(x)) may have different domains
they are different functions
thin basin
do you know about log?
sturdy yew
and composition of f on f
thin basin
lets say f(x) = 2x
and lets define x as logt
so f(x) = 2x and also 2 logt
now f(x) and f(t) are the same function
but will have different domains
t > 0 and not 1
while x can be any number
get it?
sturdy yew
yea
glacial wyvern
And I don't think it's standard that f°g would not have the domain of g as the domain
if you need to restrict the domain of g then you'd restrict it explicitly
thin basin
hmm
glacial wyvern
f°g does not exist if the image of g is not a subset of the domain of f
thin basin
f(x) = 1 /1-x
f(f(x)) = 1 - 1/x
(used wa)
so x=1 is valid for f(f(x))
,w simplify 1 /(1 - 1 /(1-x))
woven radishBOT
glacial wyvern
yeah in this case you have to restrict the domain of f a fair bit
sturdy yew
but for 1 to be taken by f(f(x)), 1 should first be taken by f(x)
next bane
f(x) = 1 /1-x
f(f(x)) = 1 - 1/x
(used wa)
doesn't work this way.
f(x) = (x^2 - 1)/(x-1) is also equal to x + 1, but its still undefined for x=1
sturdy yew
yeah in this case you have to restrict the domain of f a fair bit
u have to remove 1 and 0 from f(x) for f(f(f(x))) to be defined
right?
thin basin
doesn't work this way.
f(x) = (x^2 - 1)/(x-1) is also equal to x + 1, but its st...
makes sense
glacial wyvern
f(0)=1 (and x=0 is the only such input) so if we disallow 0 and 1 then the image of f is a subset of the domain of f and then the composition is well-defined
thin basin
maybe desmos made the same error
glacial wyvern
u have to remove 1 and 0 from f(x) for f(f(f(x))) to be defined
yes exactly
sturdy yew
f(0)=1 (and x=0 is the only such input) so if we disallow 0 and 1 then the image...
thanks
.close
devout snowBOT
glacial wyvern
np ^^
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Available help channel!
gusty pier
does this make any sense?
devout snowBOT
does this make any sense?
ripe grove
Yes but why write it like that
ripe grove
And not $c \cdot dt = d \tau$
woven radishBOT
Nyxzore
gusty pier
And not $c \cdot dt = d \tau$
cuz this makes no sense to me
gusty pier
why would you even do that
for an assignment, question wants it in a different form
ripe grove
And not $c = \frac{d \tau}{dt}$
woven radishBOT
Nyxzore
ripe grove
Is that better for understanding?
gusty pier
Is that better for understanding?
so $\tau$ is a function of t?
woven radishBOT
Hemesfere
gusty pier
but its x(t) im guessing
woven radishBOT
Nyxzore
crude wasp
does this make any sense?
this is with regards to proper spacetime right?
or whatever it's called
crude wasp
does this make any sense?
basically it just tells you how to convert speed into better units for when you factor relativity
oh wait sorry it's not proper time, u're just converting units
crude wasp
does this make any sense?
yeah so this basically just tells u how speed changes when we convert units
crude wasp
Yes but why write it like that
? what's wrong with it?
ripe grove
I was just taught to always work with relations in their simplist form
crude wasp
I was just taught to always work with relations in their simplist form
yeah but if i gave you speed with normal units
and you needed to convert it into units t' = ct instead
crude wasp
does this make any sense?
then it's just that
devout snowBOT
@gusty pier Has your question been resolved?
gusty pier
oh wait sorry it's not proper time, u're just converting units
Ya no, this is new to me
Fir maths modelling
Thx anyway
tame bough
how do i solve this
devout snowBOT
how do i solve this
glacial wyvern
draw the sign diagram for each of the factors
tame bough
wdym
glacial wyvern
Do you have a textbook?
this is a very standard problem
but it's difficult to communicate via text
tame bough
Do you have a textbook?
kinda not rlly
like it only has the problems not the way to solve thm 💀💀
ripe grove
Way simpler let's try $f(x) = (2x+3)(3x)$
Solve for where f(x) >0
You'd work out the zeros and then put them on a number line
Or sign diagram
tame bough
Way simpler let's try $f(x) = (2x+3)(3x)$
whats the dollar symbol
woven radishBOT
Nyxzore
ripe grove
That
tame bough
ofc
tame bough
.close
devout snowBOT
devout snowBOT
Available help channel!
tame bough
grrrr
thin basin
feel you bro
tame bough
😭😭😭😭
devout snowBOT
@tame bough Has your question been resolved?
strong remnant
Help, where did I go wrong?
devout snowBOT
Help, where did I go wrong?
eternal dune
Is the formula Int(A U B) = Int(A) U Int(B) correct? How can I prove it?
eternal dune
question from topology
acoustic leaf
consider a simple case, like intervals of the real number line
eternal dune
Well, [a,b] and [b,c] is a counter example
Could the formula be fixed using an inclusion?
acoustic leaf
it would be correct if you replaced the = with a subset sign
devout snowBOT
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Available help channel!
oblique rock
devout snowBOT
oblique rock
Double integral, need explanation why the result is that value?
Explain to me me the last step.
oblique rock
It is a typo for sure.
oblique rock
Looks like a u-sub
What do you mean?
faint gorge
you can substitute x²+2y²=u
oblique rock
xy will be an obsticle after you do so.
faint gorge
xy will be an obsticle after you do so.
no
oblique rock
Do it and you will see.
devout snowBOT
@oblique rock Has your question been resolved?
bronze olive
can somebody help me?
devout snowBOT
can somebody help me?
eager nova
What did u tried?
bronze olive
i simplified everything correctly and results as something like 3^x=-4/3 x 7^x
@eager nova r u still here
bronze olive
base 21 of 10/3
bronze olive
Does it say log in base 24 of 20/3?
Sorry for my writing im dysgraphic
eager nova
,w is ln(10/3)/ln(21)=log(21, 10/3)?
bronze olive
Yeah that should be correct
ok thanks
woven radishBOT
eager nova
Yeah good
bronze olive
thanks mate
eager nova
!done
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@bronze olive Has your question been resolved?
devout snowBOT
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Available help channel!
outer merlin
Hello, I have this question and barely even know where to begin
devout snowBOT
Hello, I have this question and barely even know where to begin
woven radishBOT
vrsth
faint gorge
but the j + 1 is whats giving me a hard time
write a few first terms
outer merlin
of the sum?
faint gorge
ya
woven radishBOT
vrsth
faint gorge
,, S = \ \sin^2(1) + \cos^2(0) + \sin^2(2) + \cos^2(1) + \sin^2(3) + \cos^2(2) + ... + \sin^2(99) + \sin^2(100) + \cos^2(99)
too long
woven radishBOT
bacc (unhelpful)
outer merlin
oh i see
faint gorge
you can use the identity multiple times
outer merlin
so 99+cos^2(0)+sin^2(100)?
faint gorge
ya
devout snowBOT
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Available help channel!
velvet thunder
I don't know how to start this question
devout snowBOT
I don't know how to start this question
dense jay
theres a missing word
velvet thunder
There is? What would it be?
dense jay
rate at which the distance from the ship to the lighthouse (...) when it is 12 miles away
velvet thunder
Ohh, there is no hour for me to calculate?
dense jay
no hour?
if the ship isnt accelerating either then this just seems like unit conversion
(am i missing something)
velvet thunder
Yeah, because I believe I've got to find the slope of miles over hours. Which is with unit conversion? I think?
velvet thunder
What was it? :0
dense jay
i was thinking of the ship going on a straight line to the lighthouse
you might want to draw your diagram from an above pov than the side view
velvet thunder
I guess you're right. I drew that drawing because I thought it'd help me but it's probably not accurate XP
velvet thunder
you might want to draw your diagram from an above pov than the side view
Like this?
velvet thunder
Ohh
dense jay
since we know the rate the bottom side of that triangle changes at
we can try find the rate the hypotenuse changes
may need to change to mph first though
if you havent
dense jay
seems right
can you find an equation for the distance, D
in terms of the length of the undrawn base, B?
velvet thunder
5^2+b^2=12^2
25+b^2=144
b^2=119
b=√(119)
dense jay
bit like this
thats its B in this snapshot sure, but we didnt need to know that
replace 12 with D
velvet thunder
a^2+b^2=12 ??
dense jay
not quite
velvet thunder
What exactly am I trying to find again?
dense jay
equation for the distance between the ship and lighthouse
hypotenuse is D at some time t
velvet thunder
12 = 17.2617/t ??
devout snowBOT
@velvet thunder Has your question been resolved?
devout snowBOT
@velvet thunder Has your question been resolved?
velvet thunder
I don't know how to start this question
<@&286206848099549185> Can I get some help on this :0
full cloak
Can you post the question down here again?
velvet thunder
velvet thunder
I was told that was nautical miles per hour
velvet thunder
I don't think so? Based on the question, I assumed that I'd have to do something with 5 miles and 15 knots to get the rate for 12 miles?
full cloak
Ok ima google what a knot is real quick
distant perch
passes by
I think it means the light house is directly across the ship
so like "your x distance is 5 miles away"
distant perch
use relative rates + pythogorean thm
full cloak
I can answer that
distant perch
to solve this q
full cloak
Ok this question has so many problems
First of all, are we assuming the speed is constant
Second, does the rate mean the time?
velvet thunder
?? I can ask the person who made this question but I likely won't get an answer until tomorrow-
full cloak
Third, if first and second is not true, then the rate is not calculable
distant perch
?? I can ask the person who made this question but I likely won't get an answer ...
no
the assumptions are obvious
speed is constant
distant perch
because we are measuring it from the lightouse
not the gorund
how is the distance from the light house changing w/ respect to time
that's what they mean by rate
velvet thunder
the rate of change of the hypotenuse
5^2 + 12^2 = c^2
25 + 144 = c^2
169 = c^2
13 = c
Like this??
distant perch
5^2 + 12^2 = c^2
25 + 144 = c^2
169 = c^2
13 = c
Like this??
dyk implicit differentiation
velvet thunder
It's for find y' right?
distant perch
mhm
distant perch
thats ur answer
velvet thunder
Just 13? But what about y' ?
velvet thunder
find y'
Like this? Because 13 is the rate of change, I made the slope equation with 15 because it's a number we haven't used yet
devout snowBOT
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Available help channel!
smoky gyro
Stuck on here, not sure what to do
devout snowBOT
Stuck on here, not sure what to do
devout snowBOT
devout snowBOT
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candid bison
How do I find the supremum and the infumum of this set. I need to justify my answer with a proof.
devout snowBOT
How do I find the supremum and the infumum of this set. I need to justify my ans...
topaz beacon
it would help to simplify the fraction
candid bison
So I would rewrite it by doing:
3 + 2/n^2
topaz beacon
it would also be good to prove monotonicity
candid bison
how so
alpine tapir
could you start by multiplying the top and bottom by 1/n^2?
$\frac{3+\frac{2}{n^2}}{1}}$
woven radishBOT
Joshii
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
topaz beacon
first is it monotone increasing or decreasing?
topaz beacon
monotone increasing or monotone decreasing
candid bison
monotone increasing
alpine tapir
if its monotone increasing then its first term must be the smallest term correct?
topaz beacon
so youre saying that the terms get bigger?
candid bison
Im gonna be honest im kinda lost haha
With sets, is it always a different approach or when you know the steps you can just apply it every time
alpine tapir
if something is monotone increasing that means the set looks like this $p_1<p_2<p_3<...<p_n$
woven radishBOT
Joshii
alpine tapir
i feel like the better term is monotone non-decreasing cuz that includes the case where they're all equal
topaz beacon
basically if you compare two terms, the one that comes later in the sequence is bigger
monotone decreasing, on the other hand, can you guess what it is?
alpine tapir
With sets, is it always a different approach or when you know the steps you can ...
basically if we can show the set is always incresing or always decresing, if we can find a "first term" that term must be the smallest term in the set
candid bison
opposite of that
topaz beacon
can you be more specific
alpine tapir
which is half of what you gotta do lol
alpine tapir
the first term is the biggest
its better to think of it as every element is smaller than the element before
topaz beacon
show that one term is bigger than the next term after it
alpine tapir
sorry this is probably hard with 2 people 😭
i'm trying to see if i can explain it or not
topaz beacon
if you show this, then if you pick any two terms in the sequence, you can follow the chain the first term is bigger than the next, which is bigger than the next, which is the bigger than the next and so on until you get to the other term
topaz beacon
what you want to try to show is this: E_n > E_(n+1)
candid bison
Yes
topaz beacon
do you know where to start?
candid bison
well what I would do is since n is appart of N*
I would start with putting 1
the smallest number of N*
but again that doesnt prove anything, its just putting a value to n
candid bison
If we put n it stays the same: (3n^2 + 2)/n^2
If we put n+1 it becomes: (3n^2+6n+5)/(n^2+2n+1)
topaz beacon
good
candid bison
we can simplify n+1
topaz beacon
now we have to use that to show the inequality is true
oh you forgot the +2 in the numerator
candid bison
yea haha
candid bison
then after I show n and n+1, how do I show the inequality
candid bison
oh okay so when you look at it for the first time youre like this set defenetly gets smaller
and you prove that by showing that E_n > E_(n+1)
topaz beacon
yup
candid bison
alright hold on ill write that on a piece of paper
alright
but im not getting where I can find the supremum and the infumum
topaz beacon
once you prove monotone decreasing, the supremum is the first term since its the biggest and the infimum is the limit since the sequence keeps getting smaller
candid bison
can we assume the infimum is 0
topaz beacon
no
candid bison
Im just so confused becuase my teacher gives us how to do stuff and what I see on internet (which is what you say) is different
candid bison
Oh okay
Do you have any good youtube videos you could send me so I could learn that
I dont want you spending like an hour since I have problems with that loll
topaz beacon
i dont know if i have any
candid bison
Oh okay
ill check the rest on youtube by my own, im sure there are videos that explain it
thanks
topaz beacon
youre welcome
devout snowBOT
@candid bison Has your question been resolved?
lunar kiln
devout snowBOT
lunar kiln
,rotate
woven radishBOT
young spade
since im bad at vectorial algebra but somewhat good at geometry, ill try to check it
young spade
now im in doubt, fuck
lunar kiln
i mean u can use the working ifi it helps
but i got it wrong
so its probs the wrong working
devout snowBOT
@lunar kiln Has your question been resolved?
young spade
yeah, i found a geometric way to prove
this is kinda iffy and probably comes from my "imagination" with trig, so i may not be explaining myself in the most appropiate manner
with any given rhombus you can create two isosceles triangles from it, if you draw out this imaginary "90 degree lines from the corners A and C, which is kinda what the problems asks, you form a rectangle and two rectangular triangles.
since two of these rectangles are created, and they all share the same lengths, their lines must be lined up with the bigger diagonal of the rhombus
this also is related to the orthocenter of any triangle
and since the two sides line up with 90 degrees each + with the diagonal, the original idea is true
lunar kiln
huh
i see
but it has to be with vector geo bro
thanks a lot for hits but like ineed vector geo practice
young spade
based on that, it surely has to be something related to the sum of vectors forming a rhombus or a triangle if divided by two
young spade
if you can prove it as a general thing, yeah
lunar kiln
thats what i need help with
i tried doing that
and like there was too many vriables in the enda
young spade
ill try to make myself do vectorial algebra for once
young spade
first of all, to make things easier, consider D = 0;0 and C = a; 0
like if they were on the x axis
like so, vector (v) = DC will have length a
lunar kiln
first of all, to make things easier, consider D = 0;0 and C = a; 0
right
yeah i just pu tit as a
therfroe ab is also a
tame bough
<@1267793492680245340> Has your question been resolved?
no
young spade
while trying to do vectors i found an even easier geometric proof, lol
im not into vectors, my minds cant wrap itself around them
devout snowBOT
@lunar kiln Has your question been resolved?
solid osprey
by contradiction, prove that a quadratic with all odd coefficients has no rational root
devout snowBOT
by contradiction, prove that a quadratic with all odd coefficients has no ration...
sand dove
they aren't necessarily
solid osprey
wdym
sand dove
b/a and c/a aren't necessarily integers
solid osprey
yeah but theres an added restriction thst the roots are all integers
sand dove
yeah but theres an added restriction thst the roots are all integers
where?
solid osprey
i deduced it
sand dove
did you prove it?
feral agate
In fact, the roots cannot be integers, since you would just have odd+odd+odd=0 or even+even+odd=0, which is impossible
solid osprey
for finding the roots, sqrt(D) must be rational, so sqrt(b^2-4ac) must be rational, since a,b,c are integers then D must also be an integer, so sqrt(D) must also be an integer, since the formula for the roots are (-b±sqrt(D))/2a then uhh
ok i found a slight flaw
solid osprey
In fact, the roots cannot be integers, since you would just have odd+odd+odd=0 o...
i mean like if it were to exist it had to be an integer
hm fuck ok ig back to the drawing board
sand dove
just let p/q be a supposed rational root (p,q coprime)
and work it out from here
(hint : parity)
feral agate
for finding the roots, sqrt(D) must be rational, so sqrt(b^2-4ac) must be ration...
this would work if a=1
solid osprey
this would work if a=1
yeah thats what i realized
feral agate
(to prove that the roots must be integers)
solid osprey
er technichally wouldnt it still not work if a=1 cause like sqrt(D) could aswell be odd
sand dove
this would work if a=1
even so, how is -b +- sqrtD even?
feral agate
(hint : parity)
yeah it just becomes the same thing as I said above, odd+odd+odd or even+even+odd
sand dove
yes ok
feral agate
infact b and sqrtD always have the same parity
like if sqrtD is an integer
i.e a monic polynomial can't have rational roots that are not integers
sand dove
yes because algebraic integer + rational = integer
solid osprey
hm
sand dove
i.e a monic polynomial can't have rational roots that are not integers
with integer coeffs
solid osprey
well if one of the roots is a rational one then both are rational right
sand dove
yes bc of vieta law
sand dove
how would you use parity here :(
what are the possible parities of p,q
solid osprey
odd odd, even odd, odd even?
sand dove
one of them doesn't add up
solid osprey
:p
solid osprey
uhh sorry brb
ok i did some tbinking
im guessing odd/odd=odd and even/odd=even
so uf its (o,o) that means its odd+odd+odd=0 which isnt possivle
if its (e,o) then its even+even+odd=0 which isnt possivle
for (o,e) idk
sand dove
im guessing odd/odd=odd and even/odd=even
what does odd/odd = odd mean
and even/odd = even
is 4/3 even?
solid osprey
yeah i have no ckue what you meant ngl
oh wait
ap^2/q^2+bp/q+c=0
is this what you meant lol?
sand dove
yes
solid osprey
oh lmao
devout snowBOT
@solid osprey Has your question been resolved?
solid osprey
aa how :(
hold on i just have a lightbulb
(ap^2+qbp)/q^2+c=0
(odd+even)/even+c=0
odd+even is odd, odd/even wont be an integer thus (o,e) doesent work
well that enliminates one of them
sand dove
hold on i just have a lightbulb
(ap^2+qbp)/q^2+c=0
(odd+even)/even+c=0
odd+even ...
you know you can just put everything in the same denominator
solid osprey
(ap^2+bpq+cq^2)/q^2=0
sand dove
ap^2+bpq+cq^2 = 0
devout snowBOT
devout snowBOT
Available help channel!
next tinsel
Hey
next tinsel
I have recently found out by myself that
π = -iln(-1)
(exact value)
However now I'm trying to find a way to write the exact value of e
weak drift
Can someone help for this limits and thx
next tinsel
not using sigma, but a literal way to write it
next tinsel
Can someone help for this limits and thx
I'm already using this channel
so anyways
Does anyone know if there's already been an expression which is exactly equals to e
apart from euler's and bernoulli's definitions of e
dry geyser
π = -iln(-1)
By the same equation you could get e = (-1)^(-i/pi)
next tinsel
not π
neat solstice
Oh oops
next tinsel
By the same equation you could get e = (-1)^(-i/pi)
im trying to find a way to express e without π tho
sorry for not precising
neat solstice
There is a limit definition
twilit comet
π = -iln(-1)
no
next tinsel
but thats not what i need
next tinsel
that's not true
tell me how
neat solstice
dry geyser
that's not true
It is according to wolfram alpha
twilit comet
in what way is -i ln 1 = pi
next tinsel
tell me how π ≠ -iln(-1)
next tinsel
bruh
twilit comet
mb, ur correct then
twilit comet
as in?
twilit comet
i found that on my own
how so
and wdym you're trying to find e
like a representation?
next tinsel
the exact value of e written as a literal expression
dry geyser
Well it’ll be harder to do without pi, limits or sums
woven radishBOT
ren
twilit comet
tell me how π ≠ -iln(-1)
and using this, e is the number such that e^i pi = -1
which is precisely what is mentioned in the famous euler's identity "e^i pi + 1 = 0"
e has a lot of representations, frankly
e is the constant such that (log_e x)' = 1/x, the constant such that (e^x)' = e^x, etc
those are two from basic calc
well three, including the limit
dry geyser
Would $e = (\cos(1) + i \sin(1))^{-i}$ be fine with you?
woven radishBOT
FirstNameLastName
next tinsel
which is precisely what is mentioned in the famous euler's identity "e^i pi + 1 ...
yh exactly
thats how I found it
dry geyser
it doesnt work
dry geyser
Degrees wouldn’t make sense here
next tinsel
H SHIT
MY MISTAKE
i did ^-1
yh works
but its ugly lmaoooo
but it does work
and thanks
dry geyser
Np
dry geyser
Gonna be very difficult without pi…
next tinsel
ye
ik
but i found π without e
so I should be able to find e without π
(okay maybe not)
dry geyser
but i found π without e
Well unless you count ln as using e
next tinsel
true
dry geyser
But using Eulers formula I think the two solutions so far are the prettiest solutions there are
(If you don’t wanna use pi directly, that is)
dry geyser
That’s nice
dry geyser
Just inserted your solution for pi?
next tinsel
By the same equation you could get e = (-1)^(-i/pi)
this
i changed π with my definition of it
which is
-iln(-1)
and I simplified
dry geyser
Though i must say
next tinsel
to get
dry geyser
Using ln to define e may look nice
next tinsel
e = (-1)^1/ln(-1)
next tinsel
Using ln to define e may look nice
mhm
dry geyser
But it’s kinda recursive isn’t it
next tinsel
wel
yes
but
its the best i can do till now
till i find a new way
or else
wait no that wont work
dry geyser
You can just write 2^(1/ln(2))
dry geyser
Any n^(1/ln(n)) should work as long as n is different from 1 and larger than 0
dry geyser
yh but what does it change
ln doesn’t have to be extended to the negative numbers
next tinsel
yh
but then
π equals
-2iln(i)
that works too
but i see you
WAIT THATS INSANE
i mean
idk
but its cool that e equals this
next tinsel
Any n^(1/ln(n)) should work as long as n is different from 1 and larger than 0
.
its cool
dry geyser
It’s follows directly from e^ln(n) = n
Which is why it’s recursive
ln is defined through this property (which used e)
next tinsel
yh
dry geyser
You’re defining e by inverting the definition of ln (which is defined through e)
dry geyser
Absolutely, it’s good to discover such things
next tinsel
next objective: find the exact value of π+e without using anything related to π or e
dry geyser
Without limits or infinite sums
next tinsel
phi equals 1+sqrt5/2
next tinsel
Without limits or infinite sums
yep
and i wont bother finding the exact value of i
its already done lmao
dry geyser
phi equals 1+sqrt5/2
pi and e are transcendental, meaning they can’t be expressed using roots and rationals
next tinsel
Ye ik
dry geyser
So i suppose you need either limits or something already transcendental
next tinsel
Only time will tell