One thing is that both a and b must be divisible by 6. Then reducing modulo 6 will give xy-(x^2-y^2)=25
#help-0
chrome tiger
Slightly simplified (?) the full square condition:
since 900 is $30^2$, $5k^2$ must be a sum of form $\Sigma_{j=30}^M (2j+1)$
ocean sealBOT
EQUENOS
chrome tiger
Also 5k^2 ends with either 0 or 5
unreal phoenix
What is k here?
chrome tiger
A positive integer
unreal phoenix
Oh, x/2
paper bough
I guess
I dont want to know the answer at all
My head is spinning already
These things like sigma and others were the most things I hated because it's a wide chapter of laws..
paper bough
**EQUENOS**
What does j means
balmy grail
I guess
I dont want to know the answer at all
My head is spinning already
Learning to write a simple python script to solve problems you don’t know how to solve by hand will be one of the most useful skills you will learn as an engineer
paper bough
Is it just instead of k because its used already?
chrome tiger
j is an integer that changes from 30 to M in the summation
paper bough
Learning to write a simple python script to solve problems you don’t know how to...
Yeah I think
But I will study programming next semester..
unreal phoenix
I could reduce the equation to xy-x^2+y^2=1. Can you find solutions for this?
chrome tiger
1,1
unreal phoenix
More solutions
paper bough
Or 0, 1
unreal phoenix
Some solution such that 30x and 30y are 4 digit numbers
paper bough
For =900 it can be something like 0,30
unreal phoenix
Nope, still ugly
paper bough
But yeah
unreal phoenix
Nah, this doesn't help at all. The solutions I want are still big numbers and I cannot reduce the equation further at all
paper bough
Yep..
unreal phoenix
I have a solution for (a,b), but I don't know why
paper bough
?
unreal phoenix
(1650,1020) works
paper bough
So, anyway we can know this is the only solution?
paper bough
Yeah 😂
unreal phoenix
Is it a JEE problem or something?
paper bough
The question asked like there is only 1 solution
paper bough
Is it a JEE problem or something?
Idk, its for my cousin, he is studying in high school..
What does JEE means tho
unreal phoenix
Ah, nvm
balmy grail
Here's my python script for you:
# Numerical Solution to the Total Value Problem.
from datetime import datetime
tv = 0
def findtv():
for a in range(1000,9999):
if a%500 == 0:
print(a)
for b in range(1000,9999):
if b%500 == 0 :
print(b) # Just so you know the program is doing things
tv = (a*b) - (a**2 - b**2)
if tv == 900: # If the value passes our goal:
print("-----")
print(f"{a}, {b}, {tv}") # Print the values of A, B, and the total value
return
tstart = datetime.now()
findtv()
tend = datetime.now()
print(f"total time: {tend - tstart}")
I managed to show that M here should be 1 mod 5, so M = 5q+1 for some integer q > 5
From this it's possible to show that 5(q+7)(q-5) should be a full square
(q+7)(q-5) should be divisible by 5, so either q+2 is divisible by 5 or q is divisible by 5
unreal phoenix
I managed to show that M here should be 1 mod 5, so M = 5q+1 for some integer q ...
A high school problem shouldn't be this 'ugly', should it?
paper bough
A high school problem shouldn't be this 'ugly', should it?
I dont think so 😂
chrome tiger
You either end up writing a script or using some sophisticated theorems
paper bough
If im the one who graduated from high school cant solve it and have no clue. I dont think it's normal for him, I wonder what is he doing
paper bough
You either end up writing a script or using some sophisticated theorems
Thats scary
unreal phoenix
You either end up writing a script or using some sophisticated theorems
Yeah, but the information doesn't look enough to use any good theorem really. The best I could think was reducing modulo some primes
chrome tiger
I was thinking of primitive roots but I forgot how to use them
paper bough
I was thinking of primitive roots but I forgot how to use them
Thats even more scary
Never heard of this
I loved math once before. Unfortunately, not anymore
After this day
balmy grail
After this day
it looks like the theoretical mathematician team isn't getting there, so the engineering solution is:
A = 1650, B = 1020
total time: 0:00:22.012609
paper bough
it looks like the theoretical mathematician team isn't getting there, so the eng...
I can understand 60% at least of what you guys are saying 😂
It's just my brain doesn't function the way to get the answer
balmy grail
You either end up writing a script or using some sophisticated theorems
it all boils down to this message, and writing a script is a hell of a lot easier than trying to remember crazy theorems and prime factorizations and stuff
honestly I wouldnt be surprised if the goal of this was to get the highschooler to write a python script to solve it for a programming class
paper bough
it all boils down to this message, and writing a script is a hell of a lot easie...
If I learn this in the future, how long do u think I need to write a code
Like this
balmy grail
If I learn this in the future, how long do u think I need to write a code
to write the script took me about 3 minutes, I was racing to get a solution before Equenos sent a message at 9:31
but I've been writing scripts since mid way through college, so a few years now
paper bough
but I've been writing scripts since mid way through college, so a few years now
Oh
So it might be around 12min for me, since I like to check too much
balmy grail
but the best way learn is to practice
balmy grail
I think, im gonna learn that today
have fun!
paper bough
If its math nothing can stop me 😂
vestal shell
Hii guys i have a question
lone heartBOT
Hii guys i have a question
tall topaz
I mean try for a few numbers n
vestal shell
i think that it isnt monotone
oak chasm
Why not?
vestal shell
cause lets call An = (-1/2)^n A(n+1) - An its not > 0 and its not < 0 so its not monotone right ?
oak chasm
Well, an easier way to think of monotone is that it's one of two things: "it never increases" or "it never decreases".
So, if you have a function that never increases, that's monotone.
If you have a second function that never decreases, that's monotone.
But if you have a function that increases and decreases, it's not monotone.
Here, we have it decreasing from 1 to -1/2 and then increasing from -1/2 to 1/4, so it's not monotone.
oak chasm
cause lets call An = (-1/2)^n A(n+1) - An its not > 0 and its not < 0 so its not...
What you said is almost right. Strictly monotonic needs > 0 or < 0. Monotonic needs >= 0 or <= 0.
lone heartBOT
@vestal shell Has your question been resolved?
sly summit
who is a beast at ap calculus ab ;-;
lone heartBOT
who is a beast at ap calculus ab ;-;
vague coral
just ask your questions tho
sly summit
I meant to write this in discussion I am just wondering maybe i'll ask one later
ok so
ok so nvm;-;
warm rock
How or where do we get it in French?
lone heartBOT
How or where do we get it in French?
warm rock
j'esperai
vale crag
alors c'est quoi ton truc ?
warm rock
j'ador les math (je voudrais en faire mon métier)
etj'aimerai programer aussi
*programmer
warm rock
tu connais khan academy déjà ou pas ?
je note
vale crag
ouais bha c'est un site pas mal (traduit en fr pour la plupart), pour tout ce qui est lycée et avant c'est bien
c'est des vidéos + des petits exos pas trop compliqués (c'est généré en automatique donc c'est assez répétitif)
warm rock
merci je regarde
vale crag
et puis yvan monka si tu connais pas non plus https://www.youtube.com/@YMONKA, tu peux juste regarder le programme des classes d'après comme ça
et pour le code, khan academy ils doivent avoir des trucs de base aussi
warm rock
il me mette qu'il y a une erreure
vale crag
et pour le code, khan academy ils doivent avoir des trucs de base aussi
et si tu veux plein d'exos https://www.france-ioi.org c'est excellent
vale crag
il me mette qu'il y a une erreure
qu'est-ce qui marche pas ?
vale crag
ouais
ah oui
c'est vrai que si t'es juste sur téléphone c'est un peu chaud
normalement tu peux quand même prendre des screen
faut savoir comment, c'est ça le problème
@warm rock toujours là ?
warm rock
oui j'ai fais autre chose, je suis sur ordi
vale crag
alright
vale crag
je pense qu'on peut fermer ce channel
si t'as des questions tu peux toujours les poser sur ce discord aussi
mais si t'as des difficultés en anglais je comprends que c'est chaud
c'est aussi l'occasion de s'entraîner
@warm rock
warm rock
oui comment on ferme ? merci beaucoup
vale crag
.close
forest burrow
hey. i'm currently trying to figure out how to map any point p1 with a range of [-1,1] to a point p2 also [-1,1] but so that if you drew all possible points (if that was possible) it would be a circle
forest burrow
i drew the problem in paint like this
you can see the more a point is on the x- or y-achsis the more it can stay the way it was, but the ones on the 45° angles have to move strongly to get into range
https://youtu.be/Sot2es78GhE?si=0biWRUU9jwq2ycHQ i made this little test application which modulates the x- and y-achsis nonstop so i can observe the effect of various remapping attempts. here we just see it interpreting the point linearly, so it has an overall rectangular range
lone heartBOT
@forest burrow Has your question been resolved?
prime badge
you can find how much you have to move depneding on direction, that thing you said directly
forest burrow
i did, but idk how to come up with the term for that. even though i do have the angle and the distance from origin
prime badge
harsh swallow
you want a function that takes all points that lie on the unit square and maps them onto the unit circle?
prime badge
OA and OB are 2 distances to the box, following the same direction,they can be found with cos and sin, picking the smaller result out of two
warm copper
Or are you trying to construct a circle which minimizes the distance between all points from some shape to that circle?
If you're just going to the unit circle, the angle should be enough.
harsh swallow
That's so much better than my idea
mine is just so complicated
i was thinking about constructing a vector from the point to the origin
normalizing it
then finding how big it needs to be in order to go to the correct location
you can just use a trig function
forest burrow
sry i was just trying something myself. also failed tho lol https://youtu.be/hdPcLqD3t3E?si=R5J1-CPDeOLT4ZaI
so what's the best approach now?
forest burrow
then finding how big it needs to be in order to go to the correct location
this is what i tried before, but either i did it wrong or it doesn't work, idk
harsh swallow
it's not the right way
you take any of your points
get the angle by using atan2
and then construct a point using cos(angle), sin(angle)
forest burrow
and then construct a point using cos(angle), sin(angle)
can you go more into detail about this pls?
prime badge
it's |1/sin x| and |1/cos x|, overlaid you;re interested in the stuff below sqrt2 (green line)
forest burrow
i don't understand your approach at all so far
prime badge
i think it's supposed to be what katharine said too
forest burrow
i kinda just get this diagonal spinning with this
prime badge
combine them with min()
forest burrow
on what
prime badge
no ok, nvm
x / min(abs(cos(angle)), abs(sin(angle)))
y / min(abs(cos(angle)), abs(sin(angle)))
try this
forest burrow
i do, but in the meantime let me show you this. it also looks really promising, but it just slightly clips for some reason https://youtu.be/VIBz8FSY29g?si=sBA18mt7vQbxhVo7
prime badge
right, it makes it bigger the idea was to make it smaller
maybe multiply instead of / then
prime badge
nice
forest burrow
i'd understand if it was just a bit rounded like a lens (left) but it does this edgy thing (right)
prime badge
it looks like what you described, 45° is a very shifted
forest burrow
what do you mean?
prime badge
i just think it's what you showed on your first diagram
i'm not sure, i think it's probably right
forest burrow
hmmm idk
let me show you smth real quickly
here you can see if you go around the rectangular xy pad on the most extreme values it looks alright
but moving on the inside there are sometimes weird points where the behaviour suddenly changes
forest burrow
idk, i kinda imagined the transition from placed where it maps hard and places where it stays where it is to be smooth
prime badge
i'll try to figure out if it's not what i meant to do
forest burrow
i mean i'm definitely glad it already meets the requirement to map any point of the rectangle into the circle
but don't you think those points, where it just suddenly changes direction in the middle of the circle act a bit weird?
ok maybe we just call it solved for now. it's pretty close to being solved and i wanna focus on smth else for now. thx for your help!
or do you still have an idea?
prime badge
i think it's what this method does
i can't find any mistakes, precision loss shouldn't be an issue either
forest burrow
nah bro, i want this orange line to become that yellow line basically
but atm it looks like smth like this happens
prime badge
sure, a different method then
forest burrow
i'm just totally out of ideas now, idk
my last straw is i could go into a bunch of game dev discords, because they often have projection matrices and all that
prime badge
nah bro, i want this orange line to become that yellow line basically
this thing looks like a sphere
forest burrow
yeah
forest burrow
what would be weird?
prime badge
it would just be a globe, it would have a north pole, every point with y=1 would map to one point
and if we avoid that somehow, then horizontal line would stay a horizontal line
if that second thing is fine, i guess it's possible
or maybe a horizontal line would lense inwards for some reason
forest burrow
nah it's totally what i have in mind
the vertical and horizontal lines should stay the way they are
forest burrow
i mean the x- and y-achsis should have the points fixed
but the more stuff is away from those the more it maps it
prime badge
ok gimme 2 minutes
forest burrow
oki
prime badge
y=y
x = x * sin(arccos(abs(y)))
prime badge
thanks for vids
sorry for not getting that immediately 🙂
also you can remove the abs
forest burrow
awesome
man that term is simpler than i imagined it to be
acos
i never remember that i could try that function
prime badge
so we didn't avoid the north pole actually
i just literally did the globe accidentally
or at least it has that problem too
lone heartBOT
@forest burrow Has your question been resolved?
harsh swallow
so what was the question about this in the end?
prime badge
🤷♂️
harsh swallow
@forest burrow
prime badge
what happens if you also do this for y
y = y * sin(arccos(x))
x = x * sin(arccos(y))
i can't see it
i hope it's a different kind of weird
ok, it just has 4 "poles" not very interesting
lone heartBOT
limpid turret
Lhopital?
frail grove
$\lim_{x\to a } \frac{f(x)-f(a)}{x-a} = f'(a)$
ocean sealBOT
Adam Chebil
marsh summit
Imagine a stock portfolio worth 110.000 with 100.000 loan borrowed against it. The margin level would be 100/110 = 90.9%. If my brokerage only allow max 85%. How much stock do I have to sell to reduce my debt to equity ratio to 85%?
marsh summit
really need help 🥺
wet linden
Just replace 110
With x
And find what x would be
And do your original amount - new amount
wet ravine
I need help whit problem number E:16714 ( a, b, c≠0)
If you cant understand something ask me
marsh summit
I need help whit problem number E:16714 ( a, b, c≠0)
I cant understand...like anything of that..
wet ravine
You need to show that the text there is true
marsh summit
Just replace 110
you mean 0.85 = 100000/x
wet ravine
Whit a,b,c≠0
marsh summit
Just replace 110
I dont understand 🥺
What is important to understand is that if I sell stock, the collateral I have will decrease by the amount I sell
lone heartBOT
I need help whit problem number E:16714 ( a, b, c≠0)
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
marsh summit
<@&286206848099549185>
whole tundra
Can't you just sell 90.9-85 = 5.9% of 110k?
marsh summit
Can't you just sell 90.9-85 = 5.9% of 110k?
Nah, wont be enough
It will reduce my collateral
Making it insufficient. Debt / Total Assets will still be more than 85%
I guess this question is too hard for this discord
whole tundra
marsh summit
Yeah totally that vibe just now
alpine sable
Imagine a stock portfolio worth 110.000 with 100.000 loan borrowed against it. T...
Hi!
alpine sable
Have you thought of needing to sell enough stock to decrease your loan amount?
alpine sable
How much we need to sell right?
marsh summit
Yes. How much stock do we have to sell in order for the debt side to be 85% in relation to the asset side
Right now its 90.9%
whole tundra
Theres no formula out here
marsh summit
Theres no formula out here
Yea, this is just real world problems
marsh summit
there is no formula
alpine sable
Well ok. i was supposed to tell you what I know but seems like no formula then.
marsh summit
i'm just a hard working man with a portfolio that is overleveraged right now and needs to be deleveraged by monday
marsh summit
Well ok. i was supposed to tell you what I know but seems like no formula then.
If you got one i would love to hear it
alpine sable
So to determine the amount of stock you need to sell, you have the stock worth 110 000 and the 100 000 loan. By subtracting 85% of the equity from the loan and dividing it by 0.85, you can find the approximate amount of stock you need to sell. Wait... let me show you
marsh summit
Just want to let you know that chatgpt 4 (paid version) failed to solve this problem. So if you solve it, youre smarter than chatgpt 4
alpine sable
Hahaha well it's kind of rude for you to warn me yet here you are asking help from people.
marsh summit
Sorry if you thought that was rude, i had no bad intentions with it
Im real with you Grace, I think we got off on the wrong foot here. Sorry for that. I really appriciate you helping me out
marsh summit
So to determine the amount of stock you need to sell, you have the stock worth 1...
I don't understand 🥺
alpine sable
Well then how did you find out what you got was wrong?
And with your chatgpt 4 paid version's answer?
marsh summit
Because I took the answers that chatgpt 4 gave me and put it into an equation:
0.85 = (100.000-x) / (110.000-x) where x is the answer i got from chatgpt 4
alpine sable
And?
alpine sable
Ok let me check mine
alpine sable
0.85 = (100.000-x) / (110.000-x) where x is the answer i got from chatgpt 4
Huh?
Why use this formula?
marsh summit
Because thats usually how i calculate my margin level. I just take how much debt I have and divide it by how much assets I have
and get the indebtness of the asset
If Chatgpts answer was right. I would sell 14k of my stock. And 14k of my loan would get amortized
and the end result would equal 0.85
But it didnt
It ended up with 86.000 (debt) / 96.000 (asset) = 89.58%
alpine sable
I understand that
I'm also checking it on my end
Well then if we use your checking formula 0.85 = (100.000-x) / (110.000-x)
Your x should be approximately 43,333.33
marsh summit
yo..
alpine sable
Check it
marsh summit
thats actually correct
Damn, thanks!
Thx for ur time really this was super important for me
alpine sable
So all you needed to do then is solve for x on your 0.85 = (100.000-x) / (110.000-x)
alpine sable
Happy that worked out for you!
marsh summit
.close
lone heartBOT
lone heartBOT
Available help channel!
tacit kestrel
Write the function as a sine function that has a positive "a" value:
f(x)= − cos (− x + π)
tardy stag
,tex .rocket trig
ocean sealBOT
hayley
tacit kestrel
,tex \.rocket trig
Im still so confused, I can't even find the right formula
tardy stag
look at the cofunction section
alpine sable
f(x) = a * sin(bx + c)
That is the function as a sine function with a positive "a" value
alpine sable
f(x) = a * sin(bx + c)
Take note of this form
What you're gonna do is to convert f(x) = -cos(-x + π) into a sine function
tacit kestrel
Sounds good give me a minute
alpine sable
You may use the identity cos(x) = sin(x + π/2)
Substitute this identity into the function
tacit kestrel
ok ok
alpine sable
So, what you got?
tacit kestrel
−sin(−x+ 3π/2) ???
alpine sable
Correct
tacit kestrel
actually?
alpine sable
f(x) = -sin(-x + 3π/2)
tacit kestrel
damn I got it thank you
alpine sable
You're welcome. Hope that helped
tacit kestrel
if i got it right it helped
alpine sable
Well hopefully! Tc
tacit kestrel
.close
tribal birch
i have a point which is the circle in the middle
lone heartBOT
i have a point which is the circle in the middle
tribal birch
this point is on earth, Latitude and longitude
given an angle draw a line a specific distance from the left and right
so in this picture it's 45 degrees
basically how can I find the two points of the line
tardy stag
i think they're trying to find the two endpoints of the line given its midpoint and angle
tribal birch
^
lone heartBOT
@tribal birch Has your question been resolved?
tribal birch
actually bing ai somehow managed to perfect do it first try
lone heartBOT
@tribal birch Has your question been resolved?
brisk kite
we had a question on a probability distributions test today, and only two people got the right answer and im trying to figure out why my solution wasnt right
brisk kite
we had this graph, and there was this person who was travelling from dot bottom left, to dot top right ALSO, the person can only move to the north or to the east, 50/50 chance
question a) was what is the probabilioty they pass the top left middle dot on the way to the top right
and b) was the same but just for the lower dot
my way of doing it was using binompdf(7,0.5,3) for a
and binompdf(6,0.5,4) *1/2 for b
brisk kite
my way of doing it was using binompdf(7,0.5,3) for a
since ur pathing 7 total, and 3 need to be successfully going to the east
brisk kite
and binompdf(6,0.5,4) *1/2 for b
since ur pathing 6 total and need 4 to be to the east, and then ur final needs to be up to pass the poing
lone heartBOT
@brisk kite Has your question been resolved?
lone heartBOT
@brisk kite Has your question been resolved?
smoky edge
What is the correct answer?
lone heartBOT
@brisk kite Has your question been resolved?
brisk kite
What is the correct answer?
I'm not sure...
lone heartBOT
I'm not sure...
brisk kite
I was wondering what the flaw in my reasoning was
lone heartBOT
@brisk kite Has your question been resolved?
lost spruce
hi
lost spruce
can someone teach me how to do this?
lower volume, recorded background music accidentally my apologize.
long axle
teach you how to do the entire packet?
lost spruce
https://gyazo.com/0dc9341f941fcc671aead1f2666b91b4
can be a similar problem
doesnt have to be the example one
long axle
well part a leading coefficient test is just something u memorize i think, and part b yea i can show you an example
lost spruce
just want to learn how to do this
ocean sealBOT
Stephen
lost spruce
teach you how to do the entire packet?
oh btw i believe the content of this entire video is related, no?
lost spruce
**Stephen**
so whats step 1
long axle
so let's say we have that function and we are given that x = 2 is one of the zeroes of the function
and now, we want to find the x intercept and the y intercept
first, to find the y-intercept, we plug in x=0 into our equation
so we get
$\psi (0) = 2(0)^3 + (0)^2 - 6(0) - 8$
ocean sealBOT
Stephen
long axle
following?
long axle
**Stephen**
right here
lost spruce
the entire problem?
long axle
wdym
lost spruce
nvm nvm
long axle
ok are u following the first step i took to find the y intercept
lone heartBOT
@lost spruce Has your question been resolved?
stable grotto
lone heartBOT
tacit arch
arctan(x) is bounded
stable grotto
arctan(x) is bounded
so?
junior vigil
arctan(x) has a limit as x->infinity...what is it?
stable grotto
pi/2
junior vigil
so what would be a good series to compare this one too?
lone heartBOT
lone heartBOT
Available help channel!
alpine sable
How do I solve 9e^-x + e^x = 8?
lone heartBOT
How do I solve 9e^-x + e^x = 8?
alpine sable
I tried to use the ln directly but idk if I can do that if there is a factor, can I?
Don't I have to isolate the e^x?
e^x = u
undone ledge
i was thinking first consider e^x as t , and form a quadratic
alpine sable
Hm, how would I know when to substitute and when not to?
What is the identifying factor here
alpine sable
Hm, how would I know when to substitute and when not to?
you can always substitute to make theexpression prettier
alpine sable
you can always substitute to make theexpression prettier
But why is it necessary here in particular?
undone ledge
i mean you actually dont have to substitute, but doing so lets you exactly see the quadratic you formed
alpine sable
But why is it necessary here in particular?
its not , its just more convinient to eyes
9/u + u -8 = 0?
you direcly factor it
undone ledge
yeah now , common base
alpine sable
9/u + u -8 = 0?
yes
alpine sable
its not , its just more convinient to eyes
hm
so I could solve this without substitution also?
yes
alpine sable
yeah now , common base
wdym
alpine sable
Oh I see what you mean
undone ledge
yeahh
alpine sable
yeah one second
alpine sable
yeah sounds good
but there's no easy solution for this
alpine sable
yeah
it'd be good if it were sqrt(64+36)
but it's sqrt(64-36)
cuz it's sqrt((-b)^2-4ac)
so sqrt((-8)^2-4 * 1 * 9)
alpine sable
think about it
I did, I must've made an arithmetic mistake somewhere then
alpine sable
thought we could easily split the middle term
the only issue here is
I am supposed to solve this without a calculator
undone ledge
yeah thats fine
use the quadratic formula ig
also recheck if the question you wrote is the question given
alpine sable
9e^-x + e^x = 8
undone ledge
cool
undone ledge
also factorise 28 , it would be a bit more neat
alpine sable
both are + no?
undone ledge
here yes
alpine sable
also factorise 28 , it would be a bit more neat
I didn't want to substitute in the first place
Would it be possible to solve this without that?
undone ledge
i mean you didnt have to , you make the quadratic in e^x and then solve for e^x and then find x
we just considered e^x as another variable to make it easier to deal
you see what i mean here?
alpine sable
yeah fair enough I guess
So I guess the "identifier" is to have e^-x and e^x
that way you'd multiply e^x
undone ledge
not rrl
alpine sable
and get u^2
undone ledge
like it could be 2^x too
alpine sable
like it could be 2^x too
how would that work
don't we need to multiply by u to make it squared?
like if I have 1/u + u -8 then yeah that makes sense
because *u gives me one u^2 one u and one u^0
undone ledge
not rrl , it can be anything
undone ledge
cool gl ig
undone ledge
anytime
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iron lion
How do i solve this? I've tried multiplying by its conjugate but I don't know what to do next...
junior vigil
How do i solve this? I've tried multiplying by its conjugate but I don't know wh...
!showwork
lone heartBOT
How do i solve this? I've tried multiplying by its conjugate but I don't know wh...
Show your work, and if possible, explain where you are stuck.
storm ridge
How do i solve this? I've tried multiplying by its conjugate but I don't know wh...
You don't need to do that idts
Just put the limits in
It becomes $\frac{0}{\sqrt{b} - 2}$
ocean sealBOT
Lorentz
iron lion
Yes i've noticed but it asks for the values of a and b hmmm
storm ridge
Here the numerator is 0 so you might think it's 0, but limit is 1
The only way it is possible is when the denominator is 0 too
junior vigil
(an indeterminate form)
iron lion
b = 4 would make it 0/0 yes???
storm ridge
Indeed
iron lion
wait so b is actually 4 in this case?
junior vigil
now you would do conjugate approach knowing b=4 :)
storm ridge
You don't need to do that idts
It is required after all, mb
But we had to find b first
iron lion
So a is also 4 right? cause after substituting b=4 into function:
$\frac{x(\sqrt{ax + 4} + 2)}{ax + 4 - 4} = 1$
ocean sealBOT
foresight
uneven kestrel
Yea a is 4, I divided the num and Denom by x, in your original question and got a as 4. b is 4 comes from the expression that Denom and num are equal as x approaches 0, since their ratio is 1.
fallow wadi
lim an = 0 <=> lim |an| = 0
lone heartBOT
lim an = 0 <=> lim |an| = 0
jagged cobalt
i believe so yeah, it cant converge to 0 absolutely if it doesnt normally and vice versa
lone heartBOT
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amber nymph
Need help with this particular problem
lone heartBOT
Need help with this particular problem
amber nymph
The work i did: I took the boundary of the solid S as the curve over which i will integrate i.e. x^2+y^2=1. I parameterized this surface as <cost, sint, 0> with 0<t<2pi. I evaluated F.dr and got 4sintcost and integrating that lead me to zero
Can anyone check my answer because a friend of mine said that it's wrong
lone heartBOT
@amber nymph Has your question been resolved?
scenic granite
Can anyone check my answer because a friend of mine said that it's wrong
im checking
amber nymph
im checking
Thank you
scenic granite
Need help with this particular problem
ok so this problem i believe you can do normal way of stoke's theorem but it will give you very complicated question
complicated expression inside integral
lone heartBOT
scenic granite
$\iint_{z<0}4x^4yz-6x^2zy^3-24z dxdy$ i think i got in the end
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yehuihe
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scenic granite
Need help with this particular problem
you want to use special surface on xy-plane. Look at this problem
scenic granite
in your question. $\curl{F} = <2yx^3z, -3x^2zy^2, -4>$ so $\curl{F} \dot n = -4dA$. So -4 times the area of the unit disc
ocean sealBOT
yehuihe
amber nymph
Uhh
Let me check
The unit disc in the xy-plane, how did that question thought of that
Oh
I found my mistake
This is my work
The second line should be <cost, sint>
r'(t) should be <-sint, cost>
-2sin^2t-2cos^2t=-2
-2*2pi
Thanl you so much @scenic granite
lone heartBOT
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slim chasm
Hi, can anyone help me with question c?
lone heartBOT
Hi, can anyone help me with question c?
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@slim chasm Has your question been resolved?
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@slim chasm Has your question been resolved?
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@slim chasm Has your question been resolved?
scenic granite
This is my work
Same answer. In fact your way is great. you integrate line integral instead of a surface integral. If you do surface integral of S it's very complicately. That's why do integral of the unit disc. gives you -4pi as well
amber nymph
Same answer. In fact your way is great. you integrate line integral instead of a...
Yup, thanks for the help
lone heartBOT
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lofty gorge
why have you multiplied by sin30° again
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@slim chasm Has your question been resolved?
mystic holly
i am unsure how to differetiate the second part
lone heartBOT
i am unsure how to differetiate the second part
ionic jewel
chain rule
tardy stag
,tex .diff rules
ocean sealBOT
hayley
warm copper
These guys are fast.
tardy stag
ok nvm i hate that table but yes chain rule
ionic jewel
These guys are fast.
thats why we get paid the big bucks
specifically, its $e^{f(x)}$, where $f(x) = -5x$
ocean sealBOT
warm copper
I will begin restoring my collection of LaTeX statements.
mystic holly
but there is a variable next to the 5 which is why im confused
midnight herald
de^(ax)/dx = ae^ax
mystic holly
tardy stag
but there is a variable next to the 5 which is why im confused
do you mean x?
mystic holly
something like taht
midnight herald
whenever you get a function like this to differentiate, assume the function f(kx) to be f(X)
for eg, here assume e^(-5x) to be e^X
now derivative of e^X is e^X. but now multiply dX/dx
here d(e^(X))/dx= e^X * d(X)/dx
re subdtitute X=-5x
d(e^(-5x))/dx= e^(-5x) * d(-5x)/dx
therefore we get
d(e^(-5x))/dx= -5e^(-5x)
weary radish
@tacit lichen
lone heartBOT
<@870103388216516609>
quartz agate
wtf
lone heartBOT
@weary radish Has your question been resolved?
tacit arch
<@870103388216516609>
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river bloom
hi! here's the problem i'm working on:
lone heartBOT
hi! here's the problem i'm working on:
somber panther
Maybe I'm reading it incorrectly but it says there are 10 people and you need to prove there are equal or less than 10 groups?
It's that just given
Wait duh
they can be in multiple
river bloom
this is where i've gotten so far:
- a friend group can be expressed as a vector composed of 10 elements in Z_2 (1 representing a student in the group, 0 representing a student not in the group for each student in the class)
- given 2 arbitrary friendship groups a and b, a.b=0 because the intersection will always be even, and an even number mod 2 = 0
- this means all friendship groups must be orthogonal to one another
- this also means all groups must be linearly independent / they form a basis
- then the last step would be something like the basis of something must <= the number of elements it has?? but i'm having trouble articulating/proving this step...
unkempt mica
thats very good reasoning
if they indeed form a basis you are done, because all bases have the same number of elements (i.e. the dimensions of the vector space)
the dimension being 10 in this case
river bloom
if they indeed form a basis you are done, because all bases have the same number...
how do i prove this?
unkempt mica
that they form a basis?
river bloom
that the number of elements in its basis is the same as the dimension of the vector space
unkempt mica
its the definition of dimension
but you havent shown its a basis yet
youve convinced me that they are linearly indenpendant (great argument) but its not enough to show its a basis
for example (0,0,1) and (1,0,0) are linearly independant but they do not span R^3
so they do not form a basis
unkempt mica
im not sure you can
maybe theres only one friend group
then all the conditions would be met
but it wouldnt be a base
unkempt mica
i wouldnt have thought of what you did but its really great
you are essentially done
you dont need them to form a base
if a set of vectors is linearly idenpendant, it has less elements than a base of the vector space
less meaning less or equal to
river bloom
oh ok so that's just a rule
unkempt mica
i wouldnt say its a rule but its easy to show
river bloom
could you show me haha
unkempt mica
we know there exists a base with ten elements
sorry yes my wifi is lagging
you can make a proof by contradiction
any set of 10 linearly independant elements will be a basis for your vector space
(because it is of dimension 10)
so if you had a set of 11 linearly independant vectors, you could extract a basis from it (take any 10 elements)
but then the 11th element could be described as a linear combination of the 10 others (its the definition of a basis)
but if it can be written as a linear combination of the others it is clearly not linearly independant
do you see the contradiction?
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vagrant sphinx
Okay, I seriously don't understand how to get from 5 to 6
lone heartBOT
Okay, I seriously don't understand how to get from 5 to 6
remote heron
can you show the original problem
frigid mirage
$\int dx = x$
ocean sealBOT
nebula40
remote heron
theres a definite integral, right
frigid mirage
,w 2.34 - 0.818
ocean sealBOT
ocean sealBOT
Result:
1.522
is cleaner fyi
vagrant sphinx
oh, does the + C not interfere with anything here?
hushed locust
you end up with +C - (+C) so not in definite integrals, but indefinite integrals it is important
vagrant sphinx
you end up with +C - (+C) so not in definite integrals, but indefinite integrals...
Oh, I have, come to a revelation, thank you.
Actually, thank all of you.
tight locust
Do parallelograms with integer coordinates always have integer areas
tight locust
@here
dire tiger
there will never be a negative area
He doesn't mean that
dire tiger
Do parallelograms with integer coordinates always have integer areas
I don't think so
weak field
Do parallelograms with integer coordinates always have integer areas
No
However it will always be terminating in 1 decimal place
lone heartBOT
@tight locust Has your question been resolved?
tacit arch
Do parallelograms with integer coordinates always have integer areas
Do you know the area of a parallelogram in terms of its base and height
weak field
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weak field
I feel the only possible value of f(2023) is 2022
lone heartBOT
@weak field Has your question been resolved?
weak field
<@&286206848099549185>
unkempt mica
have you looked at some smaller examples?
like f(2), f(3) etc
f(1)=0 and f(n)=n for all other n>1 would work
omg nvm
f(1)=1 so no
f(1)=1 and f(n)=n-1
if 0 is in \N
we must have $f(1)+f(n)=kn$ for some $k \in \mathbb{N}$ so $f(n)=kn-1$
ocean sealBOT
LF
unkempt mica
and actually we must have k=1 because for n=2, we must have f(1)+f(2)=2 (since 1 and 2 are its only divisors) so $1+(2k-1)=2 \implies 2k=2 \implies k=1$
ocean sealBOT
LF
lone heartBOT
@weak field Has your question been resolved?
unkempt mica
you can also just consider that 2023=7*17^2 so one of
- f(1)+f(2023)=2023 ;
- f(7) + f(17^2) = 2023 ;
- f(7x17) + f(7) = 2023.
is true
you will see that 2 and 3 lead to a contradiction
for example, for n=7, we must have f(1)+f(7)=7 so f(7)=6, similarly, f(17)=16
also for n=17^2 we must have either f(1)+f(17^2) = 17^2 or f(17)+f(17)=17^2 but we know that f(17)=16 so clearly f(17^2)=17^2-1
and then $f(7)+f(17^2)=6+17^2-1\neq2023$ so case 2 is impossible
ocean sealBOT
LF
unkempt mica
proceed similarly for case 3
thin hull
you can also just consider that 2023=7*17^2 so one of
1. f(1)+f(2023)=2023 ;
2. ...
This is incorrect. The problem says divisors. Not two divisors multiplying to n.
There are already two possible values for cases as small as f(p^2) when p is odd.
thin hull
.close
lone heartBOT
unkempt mica
This is incorrect. The problem says divisors. Not two divisors multiplying to n....
for n=2023 you must be able to find divisors d1,d2 such that f(d_1) + f(d_2) = 2023
what is incorrect?
thin hull
No, they are not. Offhand, you can pick d_1 = 2023 and d_2 to be any divisor less than 2023. That expands your first case to 5 cases.
tame granite
so how would the solution go?
thin hull
All of which should lead to valid assignments.
unkempt mica
hmm ok nvm youre right
but for a prime p we must have f(p)=p-1
that can be useful
upper ibex
GM yall
thin hull
so how would the solution go?
f(1) is given. f(p) is fixed. f(p^2) already has multiple possible values. Do the casework for the prime powers divisors of 2023 and continue from there.
tame granite
f(1) is given. f(p) is fixed. f(p^2) already has multiple possible values. Do th...
but we want f(2023), so why would we take n=2023?
are we saying that f(2023) can be 2023-f(d), where d|2023?
that isn't necessarily true
thin hull
but we want f(2023), so why would we take n=2023?
Do the casework. It is easily seen that when d_1 and d_2 are both proper divisors of 2023, you will never get that 2023 = f(d_1) + f(d_2). So for the property to hold, you must have 2023 = f(2023) + f(d) for some proper divisor d.
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alpine sable
Hi I’m confused with this representation of the above taylor series
alpine sable
If it’s (2N)! At the bottom
And n is equal to 2
Wouldn’t it be 4! Instead of 2!?
frigid mirage
Wouldn’t it be 4! Instead of 2!?
yes, idk why your n is going in increments of 2
n = 0, 1, 2, 3 ... should be what it is
alpine sable
yes, idk why your n is going in increments of 2
My prof was doing it, so she’s wrong then?
frigid mirage
My prof was doing it, so she’s wrong then?
the above sum and the sigma form are consistent
the second term should be n = 1
the third with n = 2
I think I worded that weirdly
what I mean is everythin is correct except for the n = 2, n = 4 part written above
alpine sable
Are you able to help dumb down what this means? I’m a little confused reading this and understanding what it means
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turbid gazelle
tan90=(20sinA)/(20+20cosA) =>1/0= (20sinA)/(20+20cosA) => 20+20cosA = 0 => cosA = -20/20 => A = 180
Is that a solving method right? Or how can we solve the equation?
storm ridge
tan90=(20sinA)/(20+20cosA) =>1/0= (20sinA)/(20+20cosA) => 20+20cosA = 0 => cosA ...
What's the original problem?
zealous lichen
lone heartBOT
@turbid gazelle Has your question been resolved?
turbid gazelle
What's the original problem?
actually I want to know that how to solve the equation. Is there any way and how ?
@storm ridge
gray isle
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@turbid gazelle Has your question been resolved?
versed rock
sup
versed rock
need ur help with:
-2log6 2 -log6 9= -2 and not just 2?
like I dont get why the minus stays behind the log
vale wigeon
$-2 \log_6(2) - \log_6(9)$
ocean sealBOT
Ann
vale wigeon
this?
versed rock
Like here it says that r belongs to R
vale wigeon
so you tried to calculate this and got positive 2 as your answer, yes?
versed rock
so you tried to calculate this and got positive 2 as your answer, yes?
yeah
vale wigeon
show your work
vale wigeon
$\frac{1/4}{9} \neq 36$
ocean sealBOT
Ann
versed rock
$\frac{1/4}{9} \neq 36$
now I kinda get it lol, thanks man, but I still got an question
why is the minus supposed to stand behind the log?
.close
fiery violet
Is this teh correct way of applying a chain rule?
lone heartBOT
Is this teh correct way of applying a chain rule?
fiery violet
Since my theacher showed it like this, but I cant really find out the next step
lone heartBOT
@fiery violet Has your question been resolved?
lone heartBOT
@fiery violet Has your question been resolved?
lone heartBOT
@fiery violet Has your question been resolved?
chrome tiger
Since my theacher showed it like this, but I cant really find out the next step
Leibnitz rule + chain rule
fiery violet
Is this teh correct way of applying a chain rule?
But is this also an appropiate way to do it?
chrome tiger
But is this also an appropiate way to do it?
No, because $\frac{d^2 f}{dx^2} \neq (\frac{df}{dx})^2$
ocean sealBOT
EQUENOS
chrome tiger
For example look at f(x) = x^2
Second derivative is 2
The square of the first derivative is 4x^2
fiery violet
Okay that makes sense
fiery violet
But how is this step working, I really can't find it out
fiery violet
But how is this step working, I really can't find it out
in this case its
sullen pelican
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misty bobcat
Point B is chosen uniformly at random on a circle with center (0,0) and radius 1. (In other words, B is chosen on the boundary of the circle with center (0,0) and radius 1 so that the angle determined by the points (1,0), (0, 0), B has a uniform distribution on the interval [0, 2π].) Let S denote the area of triangle determined by the points (-1,0), (1,0), B. Find the distribution function, density, and expected value of the random variable S.
misty bobcat
can someone give me a hint how to tackle this problem?
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blissful breach
lone heartBOT
blissful breach
Can anyone help me with these two, the instructions are to multiply or divide
tall topaz
You can do long division, for example.
tall topaz
For the second one you can rewrite it as
[\qq\qq\q
\wrb*{\4{x-2}{x-2}+\48{x-2}}
]
ocean sealBOT
Pure
blissful breach
Why?
tall topaz
I got 2x -3/2x^2-1 for the first one
Show your work this doesnt seem right.
blissful breach
tall topaz
Why?
Did you mean why can we rewrite it like that or why does rewriting it like that help?
blissful breach
Did you mean why can we rewrite it like that or why does rewriting it like that ...
Why did you rewrite it like that?
tall topaz
remember that you have ti wrute 0x as well
for example
,tex\polylongdiv{6x^3+4x^2+2}{2x^2+1}
ocean sealBOT
Pure
tall topaz
Well, here it leaves a gap where the 'x' term should be.
tall topaz
Why did you rewrite it like that?
what is (\77{\4{x-2}{x-2}})
ocean sealBOT
Pure
blissful breach
0
ocean sealBOT
Pure
blissful breach
1
tall topaz
Okay so what's (\77{\4{x-2}{x-2}})
ocean sealBOT
Pure
blissful breach
1
tall topaz
[
\wrb*{\4{x+6}{x-2} = \4{x-2}{x-2}+\48{x-2} = 1 + \48{x-2}}
]
ocean sealBOT
Pure
tall topaz
Got this?
lone heartBOT
@blissful breach Has your question been resolved?
wet vector
could someone explain to me why they picked n = 1 as the subset
why didnt they pick n = 2 or n = 3?
pseudo ice
Because the initial condition x(0) = 1, so you have 1 in the interval W_1
wet vector
Because the initial condition x(0) = 1, so you have 1 in the interval W_1
but u could have (-3pi/2, 3pi/2), when n = 2
1 is still in that interval
pseudo ice
but u could have (-3pi/2, 3pi/2), when n = 2
The interval isn’t quite right: n=2 gets you (3pi/2, 5pi/2), and remember where the discontinuities of tan are
wet vector
The interval isn’t quite right: n=2 gets you (3pi/2, 5pi/2), and remember where ...
oh yh 1 isnt included in that interval
yh mb
so is (-pi/2,pi/2) the only interval that contains 1 for this function?
pseudo ice
Yep, any other ones wouldn’t have 1 in it (the intervals are like formed of “consecutive odd numbers”, as a super brief motivation why)
wet vector
Yep, any other ones wouldn’t have 1 in it (the intervals are like formed of “con...
ok cool that makes sense
thanks alot
.close
fast geyser
idk if this is the right place to ask but i am considering submitting a scholarly article i wrote on knot theory with an advisor at my school as a research supplement to be reviewed by colleges like harvard, yale, and columbia. could anyone offer me their feedback on it?
pseudo ice
Might be better to ask in say #discussion #serious-discussion #math-discussion
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keen pasture
<@&268886789983436800>
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keen pasture
Thx
lone heartBOT
Available help channel!
dense matrix
lone heartBOT
dense matrix
12 question a)
reef ice
ask terence teo