yeah so if you draw the hyperbola x^2 - y^2 = 1, cosh x and sinh x are the x and y coordinates of the curve
#help-23
split kayak
i doubt you will ever get complex analysis unless youre majoring in some strictly math-related major
complex algebra maybe as an introduction
visual linden
yeah so if you draw the hyperbola x^2 - y^2 = 1, cosh x and sinh x are the x and...
Yeah I had that idea about hyperbolic functions, don't know much about them though
vagrant ice
yeah so if you draw the hyperbola x^2 - y^2 = 1, cosh x and sinh x are the x and...
instead of the unit circle, you have the unit hyperbola
glacial meadow
Depends on the country, usually taught in the first years of uni
vagrant ice
and then take the x- and y- coordinates yep
glacial meadow
Or, well, depending on how profound your complex analysis course is, it may be taught later, around third or fourth year
visual linden
Or, well, depending on how profound your complex analysis course is, it may be t...
In what major?
glacial meadow
In what major?
A course literally called complex analysis
glacial meadow
In what major?
Mathematics, doubt you'll be taught that in any other major
vagrant ice
complex analysis is usually offered in 3rd year if you're not in Europe/the UK
split kayak
tbh complex algebra is just basically
$$a+bi, i^2 = -1$$
$$Re^{i\theta} = R(\cos \theta + i\sin \theta)$$
glacial meadow
Maybe some bits in Physics, but not too much
flat frigateBOT
vagrant ice
but you can take it earlier if you have the right prerequisites
visual linden
So just BSc in Mathematics right?
vagrant ice
you don't need to take real analysis first, for example (depends on uni!)
glacial meadow
So just BSc in Mathematics right?
Yup
vagrant ice
but of course it's a proof-based course
visual linden
Yeah I knew that, we're taught that in 11th here
glacial meadow
you don't need to take real analysis first, for example (depends on uni!)
Haven't seen any university offer complex analysis before real analysis
vagrant ice
but of course it's a proof-based course
let me ask wai what year they take it, iirc it's similar?
split kayak
to my knowledge most of the formulas and facts about complex algebra can be strictly derived from this two facts and knowledge from real algebra.
vagrant ice
or for India
glacial meadow
Here, for example, real analysis is a first year course and complex analysis an early third year one
vagrant ice
you don't need to take real analysis first, for example (depends on uni!)
my uni lets you do this
glacial meadow
but of course it's a proof-based course
Is there such a thing as a non-proof based course in mathematics though?
visual linden
or for India
Yeah I'm from India, we're taught a decent level of complex numbers in 11th itself, I'm not sure what they teach in college though
vagrant ice
Is there such a thing as a non-proof based course in mathematics though?
yeah, so computational linear algebra for example
split kayak
im in engineering we basically dont do complex analyisis
glacial meadow
that's not how it works in Europe I know
Guess that's the thing, I'm in Europe
glacial meadow
im in engineering we basically dont do complex analyisis
Fair enough, you don't really need it for anything in engineering
visual linden
How about Astrophysics, what fields of mathematics do they cover there?
glacial meadow
How about Astrophysics, what fields of mathematics do they cover there?
Astrophysics is a branch of physics, really, but it's just a lotta calculus and differential equations
They'll skim over the proofs in physics as well, be warned
split kayak
for most people, lin algebra, (Diff, integral, vectorial and dynamical) calc and just a bit of complex algebra covers any realistic use-case of math in their career
glacial meadow
for most people, lin algebra, (Diff, integral, vectorial and dynamical) calc and...
Yeah, that's as far as most people go
visual linden
Damn gotta look into linear algebra, heard it's tough
split kayak
its a really extense topic, and it has a lot of uses for computers
glacial meadow
Really glad I chose mathematics instead, though, would've hated it else as I really don't like calculus/analysis
visual linden
They'll skim over the proofs in physics as well, be warned
Physics should be fine with me I hope, unless they bring it way too high way too fast
split kayak
Really glad I chose mathematics instead, though, would've hated it else as I _re...
i havent had much of analysis, just calc, but i swear by it, lmao
glacial meadow
Physics should be fine with me I hope, unless they bring it way too high way too...
Physics is a lotta calculus built really fast so you can apply it
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tardy crescent
i need to solve by disk method
safe radishBOT
i need to solve by disk method
tardy crescent
i have an integral, but its really weird to solve
is what my work looks like
i im trying expanding nr
visual linden
How did you get the integral, by slicing out the part of the triangle and rotating it around y-axis?
finite igloo
seems like x-axis
visual linden
I don't think that'd work
finite igloo
why not
visual linden
The width above is not the same as the width below, if you rotate it along x-axis, then it won't work because it's not symmetrical
tardy crescent
is what my work looks like
im pretty sure i got it now
tardy crescent
The width above is not the same as the width below, if you rotate it along x-axi...
no like
ill send a pic
hardy lion
The width above is not the same as the width below, if you rotate it along x-axi...
what are you on about homie
hardy lion
i need to solve by disk method
,rotate ccw
flat frigateBOT
finite igloo
hardy lion
,rotate ccw
flat frigateBOT
tardy crescent
and just draw an x axis thru it
and use that slant line as ur main thing
to solve with
visual linden
,rotate ccw
Alright then, I was trying it with this figure unaltered
safe radishBOT
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cursive tiger
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twilit spindle
cursive tiger
i tried w(m-n) = 2mn but i dont understand what to do next
and i tried dividing
but that doesnt work
twilit spindle
right because we still not n on both sides of the equation, is there a way to get all the n's on one side?
supple light
i tried w(m-n) = 2mn but i dont understand what to do next
After this first open the bracket
ember socket
in exercises like these, always start by pulling every term that contains your new subject to one side
supple light
(m+n)^2=m^2+n^2+2mn
How is this relevant here☠️
cursive tiger
yes i understand that but i just dont know how to get all the ns to one side
supple light
yes i understand that but i just dont know how to get all the ns to one side
Cross multiply first
Then say what you get
twilit spindle
yes i understand that but i just dont know how to get all the ns to one side
if a=b then a-b=0, apply this fact here
and w(m-n)=2mn is indeed the correct first step if that wasn't clear
grizzled coral
wm−wn=2mn
grizzled coral
wm=2mn+wn
ember socket
um, you're not OP...?
supple light
Now in Right side take n common
supple light
um, you're not OP...?
What's OP?
grizzled coral
wm=n(2m+w)
ember socket
I would think that OP's supposed to be the one working through the problem here
ember socket
What's OP?
original poster
supple light
wm=n(2m+w)
Now leaving n, divide both side by (2m+n)
ember socket
aka the person who asked the question
the person you're responding to is not the person asking the question
supple light
aka the person who asked the question
I did not even see that LOL
grizzled coral
original poster
no no
just my thought
ember socket
no no
just my thought
try not to spoil it for OP, I suppose
cursive tiger
i tried the distributive property
supple light
i tried the distributive property
See the process and you will get it most likely
cursive tiger
i got wm-wn = 2mn
ember socket
correct
supple light
Yeah That's correct
ember socket
and that's it
twilit spindle
just be careful to put parentheses
twilit spindle
wm/2m+w is correct but would be better to write it as wm/(2m+w) so as to be interpreted as one fraction
safe radishBOT
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versed anchor
im working on my undergrad final year project mainly about CVRP, i mainly done with like anything but the result. Anyone have a website or code that can turn matrix into graph
safe radishBOT
im working on my undergrad final year project mainly about CVRP, i mainly done w...
tranquil crane
versed anchor
yea i tried it, and it doesnt give the one that i wanted
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@versed anchor Has your question been resolved?
versed anchor
nvm
rich dune
how do i do this
safe radishBOT
how do i do this
quasi bison
can you write down what it means that
matrix A has eigenvalue λ and corresponding eigenvector e
though actually it feels very fishy that it's apparently claimed AB and BA have all eigenvalues the same just bc they share one eigenvector...
quasi bison
you didn't write out what i asked for here
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rich dune
you didn't write out what i asked for here
what shld i write down
fringe dock
for part d i dont understand how 4+3 gives 9
safe radishBOT
for part d i dont understand how 4+3 gives 9
fringe dock
what makes sense is they add A = 2 to 4 and 3 to give 9
but idk why A is needed if im not expanding it
kind seal
@fringe dock where is part d in the image, also please ellaborate your present working
honest perch
4+3=7 btw
fringe dock
<@691741830710034493> where is part d in the image, also please ellaborate your...
ive gotten to the point where i got
4 -8x + 16x^2
and
3 +3x +3x^2
when i add them up its fine, but the first value is meant to be 9 but i get 7
kind seal
also answer the first part, where is d?
kind seal
ooh ok
fringe dock
entire ms
kind seal
when i add them up its fine, but the first value is meant to be 9 but i get 7
why do you add
should it not be the product
kind seal
aah ok
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@fringe dock Has your question been resolved?
worldly fulcrum
Two vertical poles, 80 m and 20 m high, are 13 m apart on level ground. Straight wires
are attached from the top of each pole to the bottom of the other pole. Find the vertical
distance, in metres, from the ground to the intersection of the wires.
safe radishBOT
Two vertical poles, 80 m and 20 m high, are 13 m apart on level ground. Straight...
@worldly fulcrum Has your question been resolved?
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lilac epoch
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lilac epoch
How to solve que c
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steel crest
How to solve que c
do you have your drawing?
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fallen talon
in answer sheet answer is given A but mine answer is coming D is aswersheet is wrong T-T ??
muted sapphire
could you show your steps?
fallen talon
local minimum is -0.343 and endpoint min is -1.57
muted sapphire
have you not done derivatives?
muted sapphire
true
so how would you solve cos(2theta) = 1/2
when is cosine equal to 1/2?
think of the unit circle
fallen talon
in interval of -pie and pie
muted sapphire
forget that for now
fallen talon
there would be two solution
muted sapphire
when is cosine equal to 1/2
fallen talon
-pie/6 and pie/6
muted sapphire
firstly solve this: cos(x) = 1/2
yeah x = pi/6 and - pi/6
true
now we have that 2theta = pi/6 or -pi/6
so theta = pi/12 or -pi/12 right?
muted sapphire
alright first lets solve cos(x) = 1/2 without any constraint
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fallen talon
.close
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placid flower
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placid flower
this is the solution
but I want to solve this using desmos
also why does the solution make the slope of f(x) as -2
isn't the slope -4?
silk tendon
placid flower
I got -16 with desmos
and I get -8 (the solution given) if I take -2 instead of -4 as slope while regressing n(x)
I am taking n(x) as equivalent to h(g(x))
also I got the answer but I still don't properly understand the logic behind using x1 values to regress n(x)
I was using another seperate variable x2 before and didn't get the answer
but why is it neccessary to use x1 here, logically?
safe radishBOT
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@placid flower Has your question been resolved?
placid flower
<@&286206848099549185>
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@placid flower Has your question been resolved?
neat cypress
@placid flower Do you still need help?
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@placid flower Has your question been resolved?
civic laurel
what shld i write down
stfu ripico
north raven
the gradient of f(x) is definitely -4. Maybe there was a typo in the question or the solution of the question
safe radishBOT
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light slate
How to factor something like this more quickly i usually do guess and check but this is my complex
safe radishBOT
How to factor something like this more quickly i usually do guess and check but ...
flat frigateBOT
light slate
How to factor something like this more quickly i usually do guess and check but this is my complex
novel frost
The second equation isn't the same as the first. If that was your attempt to factor it, that's wrong.
I kinda forgot how to do this, but you got the right idea with the -15 and +1. The only issue is the 8
Edit: that's how you figure out when a=1. It's different when a≠1
Imma look this up real quick
Its the ac method
First, simplify the equation. So in your case, it would be 0=4x²-7x-15
Multiply a and c to get -60. What adds to -7 but multiplies to -60?
I immediately think 12 and 5 multiply to 60, which works when it's -12 and 5
So split it into 4x²-12x+5x-15=0
Group and simplify to 0= 4x(x-3)+5(x-3)
Then distribute so (4x+5)(x-3)=0
Check your work. This multiplies out to 4x²-12x+5x-15=0. Multiply that by 2 and you get the original equation, so this factoring was correct.
novel frost
How to factor something like this more quickly i usually do guess and check but ...
Does my explanation make sense?
Basically, first you simplify. Then, you multiply a and c to find a number. You then figure out numbers that multiplies to ac and adds to b. Use those numbers to split up b, and then group and simplify.
safe radishBOT
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timid token
Hello, ive tried to solve this question , ive done this g v (c\wedge b)=(g v c)\wedge(g v b)=c\wedge a=c
and g\wedge(c v b)=(g\wedge c) v (g\wedge b)=g v h = g , this means that the lattice isnt distributive right?
In the solution it says it shoudlnt be, but my teacher said during the lecture that it should, so im lost. can anyone help me figuring it out and what i do wrong?
safe radishBOT
Hello, ive tried to solve this question , ive done this g v (c\wedge b)=(g v c)\...
mortal sandal
Why would those statements make the lattice not distributive?
safe radishBOT
@timid token Has your question been resolved?
timid token
Why would those statements make the lattice not distributive?
because g\neq c?
im unsure how to solve it
safe radishBOT
timid token
.reopen
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✅ Original question: #help-23 message
@timid token Has your question been resolved?
short jewel
Hello, ive tried to solve this question , ive done this g v (c\wedge b)=(g v c)\...
That is correct the lattice is not distributive.
timid token
That is correct the lattice is not distributive.
is my solution correct? and also do anyone know how to check if its complemented? i just know a v a'=1 and a\wedge a'=0
short jewel
is my solution correct? and also do anyone know how to check if its complemented...
It should be right
timid token
do you know how to check if its complemented?
yeah the soultion to the exam says its not distributive but during a lecture he could show it
short jewel
do you know how to check if its complemented?
yeah the soultion to the exam says...
Well you could identify the bounds then define the complement afterwards
short jewel
like a v a'=a? and a\wedge a'=h
Yep
timid token
thats the bounds i suppose but idk with the complements
short jewel
Well, you could "test" the elements. You've already proven that e fails it, no?
Pick an element to test then it must meet the conditions. It Must join the biggest element and meet the smallest
Just take note that as long as one element fails, then it isn't distributive
timid token
i think i prove it not being distributive, but when looking at the lattice i cant think of two elements that doesnt join the biggest and the smallest
safe radishBOT
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✅ Original question: #help-23 message
short jewel
i think i prove it not being distributive, but when looking at the lattice i can...
Well, one element is just enough to prove it's not distributive, if that's what you mean
SLR
One element failing is enough proof it's not
Wait hold up
*complemented rather
It's not about two elements that don't join the smallest/biggest, it's more about a specific pair of elements for example x and x' that must simultaneously satisfy the conditions
timid token
It's not about two elements that don't join the smallest/biggest, it's more abou...
i dont really understand, any element b,d ,f with c,e,g in my opinion share a and h . can u give a example that shows its not complemented?
short jewel
i dont really understand, any element b,d ,f with c,e,g in my opinion share a an...
You're right that some pairs share the greatest element which in this problem is a like take for instance pair b and c. However, to be complement they should also be share h as their meet
x v x' = a
x ^ x' = h
Just assume that ^ is the "meet"
If we look at element e in the same problem and it's join with a, b, and c however the meet of e of those elements are...
e and b -> d
e and c -> g
Neither of d and g, doesn't the least element of h, no?
So, we could conclude that there's no element x' that satisfies both conditions for e
And because one element has not complement, the entire lattice is not complemented
Also the lattice non distributive in a way, it violates the distributive law
safe radishBOT
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timid token
.reopen
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✅ Original question: #help-23 message
timid token
If we look at element e in the same problem and it's join with a, b, and c howev...
how does e and b -> d?, i would understand if it was d and e -> b , like (d v e)=b
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untold marlin
x(=\frac{1}{4}+\frac{2}{16}+\frac{3}{64}+\frac{4}{256}+...)
flat frigateBOT
Boogie
untold marlin
aight yeah
untold marlin
yeah i did
lone void
can u explain why u did dat?
we are dividing by 4 because if u look at the denominators they are all powers of 4
untold marlin
i got sumn like x/4= 1/16+2/64+3/256+4/1024+...
lone void
i got sumn like x/4= 1/16+2/64+3/256+4/1024+...
yes correct
lone void
**Boogie**
now do x-(x/4)
untold marlin
we are dividing by 4 because if u look at the denominators they are all powers o...
would it be legit to quadruple it instead of dividing by 4
lone void
ig u can do that as well
untold marlin
now do x-(x/4)
oh word lemme see
limpid lodge
It would js give a negative gp upon subtraction then
lone void
It would js give a negative gp upon subtraction then
didnt u have helper role
limpid lodge
didnt u have helper role
Huh?no why
untold marlin
now do x-(x/4)
so i kinda got why u did dat
but like can u explain why so like i dont have any doubts or nun
lone void
Huh?no why
ohh mb i think it was @stoic saddle
limpid lodge
but like can u explain why so like i dont have any doubts or nun
To convert it into a gp.
limpid lodge
When you're subtracting u subtract the ones with common denominators
untold marlin
i think i fucked sumn up
limpid lodge
And as u can see the subtraction of numerators would give one
(I explained tht so bad ngl)
limpid lodge
so i def fucked sumn up cuz dats impossible
Yh
untold marlin
ig redo it
limpid lodge
Are u finding 4x or x/4
untold marlin
4x was easier to calculate cuz less fractions
limpid lodge
Okay
untold marlin
so i got 4x-3x=(1+8/16+12/64+16/256+...)-(3/4+6/16+9/64+12/256+...)
limpid lodge
4x-3x?
untold marlin
yea
limpid lodge
Why
limpid lodge
But we already have x?
untold marlin
act good point
limpid lodge
What did u get for 4x?
untold marlin
so i got 4x-3x=(1+8/16+12/64+16/256+...)-(3/4+6/16+9/64+12/256+...)
i got the left side of ts equation
1+8/16+...
limpid lodge
(is "word" some slang?🫠)
limpid lodge
so simplifize it
Yh
untold marlin
aight so i got 1+2/4+3/16+1/64+...
limpid lodge
aight so i got 1+2/4+3/16+1/64+...
How about u write 1/2 as 2/4
I said don't budge the numerators at all
limpid lodge
You'll understand why ,when we get the answer
limpid lodge
do i change 1 to 2/2 too?
No tht would change the original numerator
Now just do 4x-x
Only subtract terms with like denominators
untold marlin
word
limpid lodge
omg wdym by word?
untold marlin
nah
flat frigateBOT
Viͥђaͣnͫ
limpid lodge
Only subtract terms with like denominators
Here, dont budge denominators
untold marlin
yeah
untold marlin
Here, dont budge denominators
word mb its takin a lil long i do it in my head
fickle yoke
its smth like $x = \sum_{n=1}^{\infty} \frac{n}{4^n}.$
flat frigateBOT
Viͥђaͣnͫ
untold marlin
holy fuck what is dat
fickle yoke
holy fuck what is dat
u didnt read summation yet?
limpid lodge
**Viͥђaͣnͫ**
U kinda have a direct formula for this. But i suppose udk tht
untold marlin
ive only seen sigma in physics for now
limpid lodge
ive only seen sigma in physics for now
Wait a sec do yk GP?
untold marlin
gary payton
fickle yoke
ive only seen sigma in physics for now
yk about series? geometric series
untold marlin
nah havent learnt it yet
limpid lodge
word mb its takin a lil long i do it in my head
What'd u get
limpid lodge
nah havent learnt it yet
Then who gave u this problem😭
fickle yoke
nah havent learnt it yet
bro ur teacher is cooked
untold marlin
What'd u get
so i got 3/4+6/16+9/64+12/256
limpid lodge
so i got 3/4+6/16+9/64+12/256
Ehh u sure sure?
limpid lodge
Now just do 4x-x
For this?
untold marlin
bro ur teacher is cooked
lowkey stealing is a more ethical way to get money than ts mf teaching
yeah
what did i fuck up😭
limpid lodge
How would u get tht
fickle yoke
this mf didnt teach u geometric series it would take a lot of time to solve this
limpid lodge
Are u doing it on a pen and paper?
untold marlin
Are u doing it on a pen and paper?
yeah
untold marlin
icl i cant
im on pc rn and my phones camera dont work
what should it equal so i can figure out what i did wrong
untold marlin
this mf didnt teach u geometric series it would take a lot of time to solve this
i got my terms tmr yall am i cooked😭
limpid lodge
(2/4 - 1/4)+ (3/16- 2/16).....
fickle yoke
i got my terms tmr yall am i cooked😭
wait lemme teach u a formula
limpid lodge
i got my terms tmr yall am i cooked😭
If u dont know a thing about series and sequences then yes
untold marlin
(2/4 - 1/4)+ (3/16- 2/16).....
what shouldnt it be 4/4-1/4
charred summit
word
untold marlin
didnt i time it by 4
limpid lodge
aight so i got 1+2/4+3/16+1/64+...
This is 4x
untold marlin
yeah
limpid lodge
**Boogie**
This is x
untold marlin
the 1 is 4/4
fickle yoke
I SAID DONT BUDGE THE NUMERATORS 😭
bro how the hell he gonna solve this rn???
untold marlin
I SAID DONT BUDGE THE NUMERATORS 😭
word mb gng
limpid lodge
a ques, where is this question from?
untold marlin
*a ques, where is this question from?*
my teachers exam from like 5 years ago
fickle yoke
my teachers exam from like 5 years ago
broooo
limpid lodge
Okay , do yk which topic it is from?
fickle yoke
fuck ur teacher question its old
untold marlin
Okay , do yk which topic it is from?
uh i think telescopic fractions?
fickle yoke
literally he sure taught geometric series to them
untold marlin
omm idk what dat is
fickle yoke
omm idk what dat is
look bro
notice that
lemme explain
A geometric series is a sum of numbers where each number is multiplied by the same ratio to get the next one
for example
1 + 2 + 4 + 8 + 16 + ...
limpid lodge
Anyways did u get 4x-x?
limpid lodge
uh i think telescopic fractions?
Its not telescoping
fickle yoke
Here, every number is multiplied by 2 to get the next one. The 2 is called the common ratio
fickle yoke
Its not telescoping
lemme explain geometric to this guy and let this shit end
untold marlin
Anyways did u get 4x-x?
i redid it and it was the same shit i said i think
limpid lodge
(2/4 - 1/4)+ (3/16- 2/16).....
This simplifies to that again??????
I really would need ur work tbh
fickle yoke
1 + 2 + 4 + 8 + 16 + ...
@untold marlin
limpid lodge
Honestly its the same thing
But if u want to go ahead
And again DONT BUDGE THE NUMERATORS IN THIS STEP
untold marlin
word
fickle yoke
i aint fucking with this shit anymore do anything u want
limpid lodge
Woah thts ryttt
untold marlin
ok so what now
limpid lodge
But wait thts 4x-x
untold marlin
yeah
limpid lodge
Not x- (x/4)
untold marlin
i meant i added it up again
limpid lodge
Now write the denominators in the form of 4ª
limpid lodge
Now write the denominators in the form of 4ª
Leave out 1.
fickle yoke
$ S_\infty = \frac{a}{1-r} + \frac{d r}{(1-r)^2} $
tf
$S_\infty = \frac{a}{1-r} + \frac{d r}{(1-r)^2}$
flat frigateBOT
Viͥђaͣnͫ
fickle yoke
ah
untold marlin
(=\frac{1}{4}+\frac{2}{16}+\frac{3}{64}+\frac{4}{256}+...)
flat frigateBOT
Boogie
untold marlin
what no
mb
it didnt copy
i write my shi in a calc and paste it so i get the correct fraction symbols
limpid lodge
Smart
fickle yoke
$1, 2, 3, 4, ...$ is the AP term and $\frac{1}{4}, \frac{1}{4^2}, \frac{1}{4^3}, \frac{1}{4^4}, \dots$ is the GP term
flat frigateBOT
Viͥђaͣnͫ
untold marlin
(\frac{1}{4^{0}}+\frac{1}{4^{1}}+\frac{1}{4^{2}}+\frac{1}{4^{3}}+)...
flat frigateBOT
Boogie
limpid lodge
gary payton
Had to google tht person but okay
fickle yoke
$S_\infty = \frac{a}{1-r} + \frac{d r}{(1-r)^2} = \frac{1}{1 - 1/4} + \frac{1 \cdot (1/4)}{(1 - 1/4)^2} = \frac{4}{3} + \frac{1/4}{(3/4)^2} = \frac{4}{3} + \frac{1/4}{9/16} = \frac{4}{3} + \frac{4}{9} = \frac{16}{12} + \frac{4}{9} = \frac{4}{9} \text{(after simplification)}$
the answer
flat frigateBOT
Viͥђaͣnͫ
fickle yoke
after using AGP
limpid lodge
(Mate, i got an exam tmrw i shouldn't be here)
untold marlin
fuck it im js memorizing the anwser😭
limpid lodge
https://youtu.be/gua96ju_FBk?si=69yBdnrZZ4x22aYk
Watch this, sir.
fickle yoke
fuck it im js memorizing the anwser😭
dont fuck with the question at all if they didnt teach u
limpid lodge
also would u tell me your syllabus for the tes?
untold marlin
*also would u tell me your syllabus for the tes?*
idk lowkey whats a syllabus
limpid lodge
idk lowkey whats a syllabus
As in what topics or units will be asked in the test
limpid lodge
Okay and?
limpid lodge
Thts all?
untold marlin
yea
limpid lodge
Well
untold marlin
the book is like 8 lessons
limpid lodge
This is a part of Sequence and series
short jewel
how does e and b -> d?, i would understand if it was d and e -> b , like (d v e...
Mb, yea that should've been e and d -> b
limpid lodge
And will not be asked in ur test
So I'd recommend u wait till ur teacher teaches this topic
near atlas
If $a_1,...,a_7$ are not necessarily distinct real numbers such that $1<a_i<13$ for all i, then show that we can choose three of them such that they are the lengths of the sides of a triangle.
safe radishBOT
If $a_1,...,a_7$ are not necessarily distinct real numbers such that $1<a_i<13$ ...
flat frigateBOT
T&C
near atlas
hi this is my first time solving questions such as these. I'm actually practicing from a problem compendium without the help of any mentors.
all that comes to mind is triangle inequality and some combinatorics when i think about tackling this. but i don't quite know how to begin.
rigid blaze
vectors eh
near atlas
hi this channel is already occupied. you can create your own help channel. go through #❓how-to-get-help
rigid blaze
ok back to the original problem
I’m pretty sure there is a theorem that says the sum of two sides of a triangle is always greater than the third side
rigid blaze
so there are 11^7 possible combinations
Oh wait it’s real numbers
yeah both of our approaches are the absolute same
near atlas
hence i rejected the combinatorial angle. but if we restrict ourselves to the naturals maybe we can use some combinatorics
near atlas
sure
rigid blaze
it might be pretty dumb
take intervals between two umbers
yeah that’s also equally useless
wait
I think yiu can do proof by contradiction
near atlas
oh can you tell me how
rigid blaze
but the statement would be proven false
however
there is a bit of a catch here
yeah that doesn’t work as well
I was thinking you could take some particular values and prove that no single combination forms the sides of a triangle
near atlas
im so confused rn. im thinking of several ways at the same time
rigid blaze
im so confused rn. im thinking of several ways at the same time
I’m literally in the same state as you
timid token
Mb, yea that should've been e and d -> b
ah okay, ty i understand!
near atlas
say for now, we stick to naturals.
then we have the numbers {2,3,...,12}
can we figure out the number of ways to choose 3 numbers so that the sum of any two is always greater than the third. then can we use the IEP?
autumn sun
I have an idea of a proof by contradiction by sorting the seven values in non-decreasing order (b_1 lowest, b_7 highest).
then, suppose no triple forms a triangle. then, for all i < j < k, b_i + b_j <= b_k (where b_i <= b_j <= b_k)
consider all five consecutive triples (which gives the largest possible LHS), and bound all five of them below using the above inequality, then express all of those inequalities in terms of b_1 and b_2.
might come across something here
near atlas
we have to choose 7 btw
7?
rigid blaze
yeah the question says to pick a set of 7 out which any 3 must form a tringle
near atlas
yeah the question says to pick a set of 7 out which any 3 must form a tringle
oh yeahh right mb
near atlas
I have an idea of a proof by contradiction by sorting the seven values in non-de...
okay im sort of getting this. ill try
rigid blaze
I have an idea of a proof by contradiction by sorting the seven values in non-de...
This seems to be the method that works rn
autumn sun
I will have to note that the final contradiction requires you to remember the strict inequality of b_i < 13.
near atlas
I have an idea of a proof by contradiction by sorting the seven values in non-de...
btw why are we considering 5 consecutive triples?
autumn sun
(b1, b2, b3), (b2, b3, b4), etc.
near atlas
ah i see
autumn sun
as for why not something like (b1, b3, b4), because b2 >= b1, so even if we disprove b1 as a candidate element in a triple where b4 is largest, we cannot yet disprove that a triple with b4 largest cannot exist, because b2 is possibly larger than b1 and therefore could satisfy a triple with b4 largest
a similar argument works for any triple with a largest element that isn't b3.
so we are picking the triples with the largest possible LHS
(for each candidate largest element in the triple*)
near atlas
ohhh i understand now. this is such a smart proof. thank you so much. I'll try to redo it myself now from the beginning
rigid blaze
so we are picking the triples with the largest possible LHS
Ohhh
autumn sun
glad to have given you some insight
languid monolith
hello. so i wanna convert z_2 to rectangular coords and i let z = z_2 ^(1/24) to convert that into polar and then evaluate z^24 to get z_2. Is my method wrong? I cant evaluate the angle and it should be staged for the angle to work so i mightve gone wrong somewhere
safe radishBOT
hello. so i wanna convert z_2 to rectangular coords and i let z = z_2 ^(1/24) to...
manic radish
hello. so i wanna convert z_2 to rectangular coords and i let z = z_2 ^(1/24) to...
hint: convert your complex number inside the (...)^24 into re^it form
languid monolith
i mean thats what i tried in the pic no?
i found r and tried to find t
unless thats not the method to find re^it. i searched it up on google but didnt find what i wanted
it only showed me calculators and no methods
languid monolith
oh i can just write our wanted z as 2-√3 +i ? and we concern ourselves with 1/2 later?
its alright
manic radish
But, basically, given x + yi, we have r^2 = x^2 + y^2 and t = arctan(y/x)
which you've done. ok I see what your problem is now.
sorry, I jumped the gun
languid monolith
hahah its okay
so if this way doesnt give convenient results is there a different one?
manic radish
this would be the easiest way
languid monolith
hmm
manic radish
otherwise, you'd need to do (x+yi)^24 which is a huge polynomial to evaluate
languid monolith
mayb our prof wrote smth wrong bc were not supposed to use inverse trig functions yet
languid monolith
otherwise, you'd need to do (x+yi)^24 which is a huge polynomial to evaluate
nono she told us to use what weve learnt in complex analysis to solve it
anyway ill ask her tomorrow
thank you
.close
safe radishBOT
manic radish
the angle is 5pi/12, but I'm not sure what trig you know to show this
languid monolith
ill work it out and see if its possible
safe radishBOT
Available help channel!
rocky pond
I might be romanticizinf math a bit but what went wrong
safe radishBOT
I might be romanticizinf math a bit but what went wrong
plucky elk
You can check your graph in desmos
brave wolf
It seems like u completely ignore negative r
brave wolf
I might be romanticizinf math a bit but what went wrong
and at pi/2, u forgot to multiply by 2
otherwise u just need to fix the sign (it doesnt change much, the circle will just be under the x-axis)
safe radishBOT
@rocky pond Has your question been resolved?
safe radishBOT
safe radishBOT
Available help channel!
errant shuttle
can anyone help me to solve this puzzle? it's not necesarry but i will accept any kind of help.
safe radishBOT
can anyone help me to solve this puzzle? it's not necesarry but i will accept an...
errant shuttle
i can tell more info if anyone helps
short jewel
i can tell more info if anyone helps
I suggest you just lay it all down here so that if somebody who knows see it, they can help
errant shuttle
hmm right
novel frost
I can't read your handwriting
errant shuttle
normal sudoku rules aply+ the squares connected with the lines must difer min. by 5+ the squares connected with the dark dots must be x-2x + the squares connected by the empty dots must be X--X+1
errant shuttle
I can't read your handwriting
its not even fully in english
novel frost
Ah that's why I was confused 😭
errant shuttle
anybody?
novel frost
I don't know what the lines in the boxes mean. That's different from sodokus I do
The ones I do just have numbers
Still numbers 1-9?
errant shuttle
Still numbers 1-9?
yes and each printed square(not which i drew with my pencil)counts as a regular sudoku square
novel frost
Ohhhh ok lemme grab a piece of paper. You're 100% sure it's solvable?
errant shuttle
Ohhhh ok lemme grab a piece of paper. You're 100% sure it's solvable?
idk i got it from the math-discussion chanel yesterday
novel frost
Ohhh ok. Well, we'll see
errant shuttle
the only thing i know is that the squares connected by the line cant be 5 because then theres no number biggr or smaller by 5
chat gpt say that its solvable-didn't ask for sollution tho
novel frost
Just to confirm, dark dots could be 2 and 4, and light dots could be 4 and 5?
That's what it means?
errant shuttle
not excatly : the squares connected by the dark dots are like 1:2 :one of them is twice as much as the other, the white dot: one of the squares is one less(or more(doesn't mater))than the other
novel frost
Ok. So my example works?
errant shuttle
the dots are not numbers
novel frost
Oh, yeah that makes sense
I meant the boxes could be that sorry
But I understood it right lol
novel frost
Id start with the middle left column and the middle middle. Where they intersect
Ohhh ok
Seems like there are lots of dots and lines there
desert juniper
chat gpt say that its solvable-didn't ask for sollution tho
never use chatgpt
errant shuttle
hmm yea it would be really good if i would have even one number writen in 🙂
desert juniper
also, the original puzzle is unreadable
desert juniper
you used it to tell you that it's solvable. So the information of "it being solvable" is suspect, since it came from gpt which is terrible
errant shuttle
even chat gpt said that he wasn't sure, can you tell me then?
desert juniper
not until you actually put the puzzle in readable form. As i said, your original one is unreadable
errant shuttle
not until you actually put the puzzle in readable form. As i said, your original...
theres no need for reading
desert juniper
ah yes. You definitely dont need to read the instructions to solve a problem
errant shuttle
normal sudoku rules aply+ the squares connected with the lines must difer min. b...
the instructions are here man
and heres the nicer image for you
desert juniper
that's not a set of instructions. That's unreadable and incoherent notes
errant shuttle
that's not a set of instructions. That's unreadable and incoherent notes
tell me what you don't understand
desert juniper
literally nothing is understandable there
"normal sudoku rules apply" on something that has no numbers already fails to be understandable
errant shuttle
"normal sudoku rules apply" on something that has no numbers already fails to be...
do you know sudoku?
desert juniper
yes
novel frost
Oh good point sudoku do normally start with some numbers. This one is really difficult
errant shuttle
Oh good point sudoku do normally start with some numbers. This one is really dif...
yep thats the hard part
i think tipmix is the key to victory 🙂
desert juniper
so what you're saying is, this is a sudoku with extra restrictions?
errant shuttle
and no starting numbers
desert juniper
okay, lemme try to translate your crappy notes
when you say "the squares connected with the lines" do you mean ONLY the endpoint squares of the lines, irrespective of any angles within the lines?
also on those, does that mean they need to be a pair 1-6, 1-7, 1-8, 1-9, 2-7, 2-8, 2-9, 3-8, 3-9 or 4-9?
with dark dots one of them needs to be twice the other, and with empty dots one number is the next of the other?
errant shuttle
when you say "the squares connected with the lines" do you mean ONLY the endpoin...
the ends and the difference is minimum 5
desert juniper
with exactly 5 being valid?
errant shuttle
with dark dots one of them needs to be twice the other, and with empty dots one ...
if you mean next to like 1,2,3,4,5,6,7,8,9 then yes (one more/+1)
errant shuttle
with exactly 5 being valid?
yes
errant shuttle
5 is the only number which cannot be connected with the line(5-5=0/5+5=10
I think i will need to ask a math expert to say if its solvable or not 🙁
desert juniper
where did you get this from?
also, a puzzle is not necessarily "math"
but it feels like if it has a solution, it is not unique
novel frost
I give up on this puzzle lol. I don't have the time to solve it
errant shuttle
they sent this to me in the math-discussion chanel yesterday
safe radishBOT
@errant shuttle Has your question been resolved?
untold charm
<@&286206848099549185>
safe radishBOT
<@&286206848099549185>
novel frost
Just ask the question don't ping yet the mods will get you
untold charm
visual linden
!15m
safe radishBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
novel frost
We need a clearer picture
novel frost
You're over 13... Right???
untold charm
yup
plucky elk
,calc 3/100
flat frigateBOT
Result:
0.03
calculators are your friend
noble mango
Aside from that, it looks like you already converted all the numbers into decimals?
untold charm
oh :3
noble mango
Now you just have to order each of the numbers based on their decimal value :)
untold charm
to least to greatest
noble mango
So which one's the biggest? Is it:
0.3
2/5 (which is 0.4)
0.68
5/8 (which is 0.625)
plucky elk
i cant use calculators on this
you can't use calculators but you can ask people for help?
noble mango
to least to greatest
Yep.
plucky elk
sounds wrong
untold charm
the biggest is 0.625
noble mango
the biggest is 0.625
mmmm are you sure?
untold charm
yeah
noble mango
Remember that when we are counting decimal closest to the decimal point is larger.
untold charm
So which one's the biggest? Is it:
0.3
2/5 (which is 0.4)
0.68
5/8 (which is 0.6...
5/8
ok
noble mango
Let me ask you a question,
untold charm
ok
noble mango
Which number is bigger?
0.62 or 0.68?
untold charm
0.68
noble mango
Good, why?
untold charm
beacuse theres is an 8 and the other one has a 2
noble mango
beacuse theres is an 8 and the other one has a 2
Good!
But, if you wanted to be more specific,
The second decimal place of 0.68 is larger than the second decimal place of 0.62
untold charm
noble mango
I.e 0.68 is larger than 0.62.
Now, that being said,
Which one is bigger?
0.68 or 0.625?
untold charm
becuase 0.625 is it on there???
noble mango
wdym
untold charm
or it to big
noble mango
Not sure what you mean
untold charm
0.625 is to big
untold charm
i know
noble mango
The fact that the 8 is bigger than 2 means that anything after the 2 doesn't matter.
So for example,
0.68 is bigger than 0.625 because the 8 in 0.68 is bigger than 0.625.
untold charm
ok
noble mango
nice
noble mango
So, would you agree 0.68 is the biggest? What goes next?
untold charm
then 2/5 goes next
noble mango
then 2/5 goes next
wait
Are you sure?
2/5 is only 0.4
What's the next number smaller than 0.68?
untold charm
it 0.3\
untold charm
fine
noble mango
0.3,
2/5 (which is 0.4),
0.68,
5/8 (which is 0.625)
After 0.68, what is the next biggest number?
untold charm
0.628
noble mango
wait wait
Should be the other way around
Because it's
... < ... < ... < ...
Like
0.68 goes at the right
... < ... < ... < 0.68
Because the < means
Smaller < Bigger
So for example, 0.625 < 0.68
noble mango
Other way
Swap the 0.68 and 0.625
Because 0.68 is bigger than 0.625
So it should go on the other side
untold charm
so o.68 should take 0.628 side
noble mango
so o.68 should take 0.628 side
Yes
untold charm
done
noble mango
Good, now fill in the rest according to their order :)
untold charm
ok
noble mango
Just to be consistent with the original question
noble mango
Try it first. Again, convert all the numbers into decimals.
noble mango
how do i do that
Do you know long division?
untold charm
no :3
noble mango
How did you convert these numbers into decimals then?
untold charm
idk i just had someone to help me
noble mango
😭
noble mango
As mentioned earlier, the easiest way to find decimals is to use a calculator. However, if you are not allowed to use a calculator, the next best strategy is to use long division. Now, long division is a pretty long method, so it's best if you learn it via youtube or another source.
https://www.youtube.com/watch?v=usxTJbQbAIg
untold charm
noble mango
For example, in order to convert 4/5 into a decimal, you would do 4 divided by 5.
untold charm
im just watching it on discord
untold charm
0.3
noble mango
Yeahhhh well
Technically
1/3 is 0.333333....
But for convenience,
I'm going to convert it to just 0.33
So 1/3 is close to 0.33
untold charm
ok so0.48 is the largest
noble mango
So nice, you have:
4,
4/5 (which is 0.8),
0.48 and
1/3 (which is around 0.33).
So, which one is the greatest?
noble mango
ok so0.48 is the largest
nope
noble mango
nope
untold charm
...
noble mango
Look carefully at each of the numbers
Very carefully
There should be a number that is much bigger than the others
untold charm
4 is the largest
untold charm
so put it at the end
untold charm
ok
noble mango
What is the next largest number?
untold charm
0.8
noble mango
There you go!
Remember
The number closest to the decimal places is the largest
So for instance
untold charm
ok
untold charm
ok
noble mango
80 is bigger than 48, so 0.80 is bigger than 0.48
noble mango
Yep
untold charm
time for 6
noble mango
This one's a little tricky, but let's see how you go :)
noble mango
does 5.7 go fisrst
Good! Why?
untold charm
beacus eit lower
noble mango
oh whoops I didn't read the question
Well hold on
Remember
The first thing we need to do with these questions is..?
untold charm
least to greatest
untold charm
to figure out the demicals
noble mango
Exactly
So figure out the decimals first, then tell me
Remember also that the signs flip again
untold charm
ok
noble mango
So the lowest will go first and the highest will go last.
untold charm
0.6
untold charm
0.66
noble mango
Hint: ||Use addition||
untold charm
idk
untold charm
5.6
noble mango
There's one more number you haven't converted into a decimal
noble mango
wait where'd you get that?
untold charm
counted :3
untold charm
how many time 3 can go into 5
noble mango
These are the numbers, so
You have 5.7,
Oh I mean
5 3/5 is equal to 5.6
What's the other number that we need to convert?
tardy mango
You need to convert this number too :)
orz
noble mango
<:happy:908558103992225822> orz
hi pigeon
untold charm
I NEED HELP I DONT KNOW
noble mango
As mentioned earlier, the easiest way to find decimals is to use a calculator. H...
Using the method here