i can't tell you shit before you show it to me lol
#help-23
quasi bison
lean otter
i can't tell you shit before you show it to me lol
kkk
this was sm extended euclidian alg work
quasi bison
,rcw
flat frigateBOT
quasi bison
100y+x - 68 = 2(100x+2y)?
lean otter
100y+x - 68 = 2(100x+**2**y)?
yeah, the teller switched up dollars and cents, so replace y with x, and when he spent 68¢ he had double the amount
of the original cheque
quasi bison
that would make the rhs 2(100x+y) or 200x + 2y, but you wrote 200x + 4y
quasi bison
$2(100x+2y)$
flat frigateBOT
Ann
quasi bison
you wrote this on the right
lean otter
you wrote this on the right
well everything else is fine, that 2 didnt affect the latter
quasi bison
it sounds like you treated it as if the other 2 weren't there anyway though
even number of mistakes
lean otter
it sounds like you treated it as if the other 2 weren't there anyway though
without the 2 it simplifies to -199x+98y=68 so uhh😭 ignore it 😭
its correct afterwards😭
quasi bison
so you ended up with the dio eq -199x + 98y = 68
lean otter
so you ended up with the dio eq -199x + 98y = 68
yepppp
quasi bison
its correct afterwards😭
as i said, even number of mistakes (2 in this case)
quasi bison
,calc 199 * 93 - 98 * 67
flat frigateBOT
Result:
11941
ok so your bézout representation for the gcd is wrong somehow
time to locate where the error is in that one
lean otter
gosh 😭😭 not an ARITHMETIC error😭
quasi bison
,calc 199 * 33 - 98 * 66 - 98
flat frigateBOT
Result:
1
wait no im the fool here
lean otter
wait no im the fool here
😭
quasi bison
yes sorry, typo on my part
lean otter
whatever
quasi bison
how many million more sob emojis should i expect from you today
,calc 199 * 33 - 98 * 67
flat frigateBOT
Result:
1
,calc 199 * 2244 - 98 * 4556
flat frigateBOT
Result:
68
yeah i did check that enough number of times
quasi bison
so it looks like you got (x,y) = (-2554, -4556) as a possible sol
thus the general is x = -2554 + 98t, y = -4556 + 199t
lean otter
so it looks like you got (x,y) = (-2554, -4556) as a possible sol
thus the gener...
yeah, and we need the minimum
quasi bison
x=2254-98t and y=4554-199t,
this seems to have gotten infected with typos
-2554 + 98t > 0 => 98t > 2554 => t > 2254/98
,calc 2254/98
flat frigateBOT
Result:
23
x = -2244 + 98t
lean otter
heck, the numbers
quasi bison
,w simplify -199(-2244+98t) + 98(-4556+199t)
flat frigateBOT
quasi bison
,calc 2244/98
flat frigateBOT
Result:
22.897959183673
yea
flat frigateBOT
Result:
10
,calc -4556 + 199 * 23
flat frigateBOT
Result:
21
oh god
quasi bison
and typos can and do prove fatal
quasi bison
thats over 22.89 tho😭
what?
safe radishBOT
@lean otter Has your question been resolved?
serene sequoia
how to solve that without trigonometric solutions?
safe radishBOT
how to solve that without trigonometric solutions?
zenith orchid
radiant canopy
45+x+a(for alpha)+75=180
x+a =180-120
ig that's enough i have not calculated further
i need a pen and book
i don't even know if u can do it without trig
radiant canopy
how to solve that without trigonometric solutions?
any parallel lines or smth
safe radishBOT
@serene sequoia Has your question been resolved?
serene sequoia
cus i have already done with the sin rule. 
serene sequoia
need smt diff. 
radiant canopy
not possible then
serene sequoia
lean swan
safe radishBOT
@serene sequoia Has your question been resolved?
lean otter
<:sad:532803514892812288>
,rccw
flat frigateBOT
safe radishBOT
@serene sequoia Has your question been resolved?
iron herald
The closest you can get is using trigonometric ratios
You would eventually need trigonometric ratios to convert those angles into lengths of side
iron herald
The closest you can get is using trigonometric ratios
That too I am not exactly sure
safe radishBOT
safe radishBOT
Available help channel!
copper temple
hi , what's a hypothesis in math
safe radishBOT
hi , what's a hypothesis in math
copper temple
?
upbeat swan
basically
a hypothesis is a statement that is assumed to be true for the purpose of argument or investigation.
upbeat swan
hh?
copper temple
hh?
If we can assume for everything to be truth and they are not we can falsifie all math truths
and we make truth all false propositions
upbeat swan
yeah
if you can prove a hypothesis is false
then its false
and your assumption was wrong
copper temple
Yes , but I did'nt understand
how a false proposition is supposed truth and truth proposition is supposed false ?
copper temple
No
upbeat swan
,w assume
flat frigateBOT
upbeat swan
we "pretend" that something is true
quasi bison
what's the German word for assumption?
upbeat swan
and then if it leads to a contradiction or false statement
then it means that the original ssumption was false
quasi bison
this will be a bit embarrassing if i turn out to be wrong in thinking timo is German
copper temple
we "pretend" that something is true
But rigourous way to say pretending in math ? , Because in mathematics there must be a mathematical way to state that ?
copper temple
In math there's a formal language
flat frigateBOT
Googoo Gaga
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
quasi bison
In math there's a formal language
if you think mathematicians spend all day talking entirely in a sea of $\forall$, $\exists$, $\land$ etc then you are very wrong
flat frigateBOT
Ann
upbeat swan
so our hypothesis, our assumption was false
math also works with words
it's not only symbols
copper temple
Here saying ,lets suppose sqrt(2)=p/q is'nt saying sqrt(2)=p/q is true
but sqrt(2)=p/q
copper temple
if you think mathematicians spend all day talking entirely in a sea of $\forall$...
There is thouse who spend years to proof 1+1=2
bertrand russell with north white head
with 350 pages .
copper temple
But it's better
to turn words to symbols at least having a complet formal language
Is'nt it ?
upbeat swan
i think words bring clarity
i mean
for a human it's much easier to understand proofs that contain words
for a computer it might be better to just use symbols
but i think words are always helpful becuase they can explain what you are doing and why you are doing it
copper temple
Yes
brave wolf
There is thouse who spend years to proof 1+1=2
They didn't do it because they doubted that 1 + 1 = 2, nor did they do it because they thought purely symbolic proofs are superior to proofs with words.
I think that their intention was to create an axiomatic / formal system, in which all theorems could be proved almost algorithmically. They probably didn't think that when they create such system, every mathematician will start working in it (because words are just simpler). But such system could be interesting anyway, what could such a system prove? Could it prove everything? If not everything, could it prove at least most of the current mathematics? Is it possible to reduce everything (or at least almost everything) we know about mathematics to something, which is essentially just a set of symbol with rules of purely typographic manipulations?
...
Symbolic proofs are hard to make and hard to follow. Using words is much simpler, and equally valid. As long as the word-proof makes logically sense, there's nearly no doubt that it could be translated into symbolic proof, if needed
Though nowadays, we have proof assistants such as Lean, which can make writing "symbolic" proofs much less painful
copper temple
Though nowadays, we have proof assistants such as Lean, which can make writing "...
Yes , but in
formal definition what is hypothesis ? ,
could we make a hypothesis without using it as an introduction part for a proof ?
brave wolf
formal definition what is hypothesis ? ,
I don't think that the word "hypothesis" has any fixed meaning in formal logic
Depending on the context, it could be the P in a sentence of form P -> Q, or in context of natural deduction, it could be the premise of subproofs..
I wouldn't think of "hypothesis" as a formal mathematical term with one precise definition, it's an english word that means roughly "something that is assumed, from which something else follows / can be proved"
but the precise meaning varies depending on the context
copper temple
Thanks a lot ,subproofs are proofs inside a proove ?
brave wolf
Thanks a lot ,subproofs are proofs inside a proove ?
Yep
they are mostly used in context of natural deduction
The first
|
|
|
is the proof itself, and the nested ones are the subproofs
obtuse star
if you have a game of p player nim where each player has to make {a,b,c...} moves, how many outcome classes will there be (an outcome class is a type of outcome, think of 2 player hackandbush having 4 outcome classes, left wins, right wins, first wins, second wins)
safe radishBOT
if you have a game of p player nim where each player has to make {a,b,c...} move...
@obtuse star Has your question been resolved?
obtuse star
<@&286206848099549185>
daring flume
OP, you may want to try posting your problems in #game-theory. the community there might be able to better help you with your problems.
astral glacier
I'm pretty sure they have posted there
I think it might help a bit to elaborate on what the game of nim is
daring flume
ah I see, I apologize.
quasi bison
OP, you may want to try posting your problems in <#1364706668960546906>. the com...
they've posted questions of this kind here like 20 times and received no response ever as far as i can tell
daring flume
I see. I did notice from time to time, but I'm way out of my depth.
obtuse star
they've posted questions of this kind here like 20 times and received no respons...
Twice, but yeah
Should I close it and just ask in game theory?
daring flume
I'm not sure closing it is necessary but you should definitely consider asking in #game-theory, yes.
obtuse star
Combitorial game theory!!!
safe radishBOT
@obtuse star Has your question been resolved?
twin dew
/tts hi
safe radishBOT
@obtuse star Has your question been resolved?
obtuse star
I’ve found that for XvX games O(XvX)=2 and for XvY games where X and Y are not equal, O(XvY)=4
$O(\overset{n}{\overbrace{1 ...1}})=\text{win for n}\
O(\overset{m}{\overbrace{m ...m}})=\text{win for m}\
\text{for }m>n$ logic for second one
flat frigateBOT
TheHoneycombTiling ReadMyStatus
obtuse star
the other two cases are trivial
safe radishBOT
@obtuse star Has your question been resolved?
safe radishBOT
@obtuse star Has your question been resolved?
obtuse star
Ok like how does the {1,2,3} game work
last heath
why are you a likely spammer
pine mountain
why are you a likely spammer
Read his their custom status
obtuse star
Read ~~his~~ their custom status
*their
solar hazel
blud has never talked to a woman
pine mountain
blud has never talked to a woman
I mean as in the gender pronoun that I default to as gender-neutral without thinking 😓
...I'll see myself out
safe radishBOT
@obtuse star Has your question been resolved?
quasi bison
I mean as in the gender pronoun that I default to as gender-neutral without thin...
yeah that's. no. male as default is mega stank
lean otter
blud has never talked to a woman
i always fear calling he/him to someone regardless they are a women people tend to break out on me 🥀
mortal sandal
So for 2-player nim, the answer would be 2 outcome classes? (first player win, second player win)
I would expect the answer to be p because it would always be of the form [the ith turn player wins] but idk the details of how p-player games have well-defined strategy
obtuse star
So for 2-player nim, the answer would be 2 outcome classes? (first player win, s...
Yes
obtuse star
I would expect the answer to be p because it would always be of the form [the it...
This is true when there are no teams
But like, in 2v3 nim, there are 4 because 0, 11, 3, and 333 are all different outcome classes
obtuse star
**TheHoneycombTiling ReadMyStatus**
The two extra outcome classes in nvm nim
obtuse star
Also a p player game has a maximum of p^(p!) outcome classes
obtuse star
i wrote code to do this for me
twin dew
raven acorn
**TheHoneycombTiling ReadMyStatus**
Ofc i totally understand what this means
obtuse star
Ofc i totally understand what this means
The outcome of an n versus m game with n one stacks is a win for n; the outcome of an n versus m game with m stacks with m objects is a win for m
obtuse star
Do you know how to play nim?
obtuse star
I feel like I’m on to something
safe radishBOT
@obtuse star Has your question been resolved?
lean otter
<@&268886789983436800>
exotic anvil
what
exotic anvil
There's no rule setting a maximum amount of time a channel can be open for
lean otter
I see 
obtuse star
Also literally no one has even tried to help
exotic anvil
Believe it or not the goal of the server is not "close help channels as quickly as possible" despite what some people think
obtuse star
I may close it if I get no help today as well
Just because then I don’t think there will be anyone willing/able to help, and let other people get help rather than me
Altho there are some other help channels that have been open for just as if not longer
I have been making slow progress, but I think having another head could really help
obtuse star
I will
lean otter
I am no good in game theory myself
main mural
but also i hope you understand that what you are asking is niche to say the least, MSE or some other space might be of more help
exotic anvil
I mean its also not like we have a lack of help channels. Iirc the limit is something like 50 open at once
lean otter
I only see like 4 open left for me tho i have no question for now
exotic anvil
I only see like 4 open left for me tho i have no question for now
Only 4 are available to be claimed at a time
most are kept in Math Help (Hidden) until those 4 are used
main mural
lean otter
Damm i see the point it will look horrible otherwise
exotic anvil
help-13 hasn't been used since the 26th of october last year
so yeah no need to worry about a lack of help channels
obtuse star
I’m gonna write a big explanation soon, to get people up to speed
scenic phoenix
i wrote code to do this for me
the code is bieng so anoying istg
scenic phoenix
Some data: I need to find or disprove the missing values
LMML(RR)(LM)
MLLM(RR)
LRMR(RR)(LM)
MRLR(RR)
RLRM(RR)(ML)
RMRL(RR)(ML)
LLMM(RR)(LM)(ML)
MMLL(RR)(LM)
1313(11)(22)
2121(11)
1212(11)(22)
2222(11)
3131(11)(33)
3333(11)(33)
1111(11)(22)(33)
2323(11)(22)
This is for the 1,1,2 game
safe radishBOT
@obtuse star Has your question been resolved?
soft wedge
4
vivid sparrow
🫃
solar hazel
safe radishBOT
quasi timber
Bot just felt the need to confirm 
scenic phoenix
Should I make a new channel? Or should I just leave it at this point
median vigil
you can keep using it until the bot comes back online i guess
it won't close while the bot is offline anyway
safe radishBOT
Available help channel!
drifting sierra
I get that f'(0)=0 and f(0)=0
And since |f'(x)|≤ f(x)
f(x) should not lift above 0
But Idk how to write it
??
drifting sierra
<@&286206848099549185>
safe radishBOT
brave wolf
And since |f'(x)|≤ f(x)
One way could be writing |f'(x) / f(x)| < 1, and then try to do something with that ||Hint: integrate||
Or alternatively, you could focus on the extreme case f'(x) = f(x) first and then use it to solve the original question
solemn vault
does || MVT || work?
drifting sierra
Well why would we assume f(x) is always positive?
brave wolf
Well why would we assume f(x) is always positive?
If it was negative, what would |f'(x)| be?
also negative?
solemn vault
Well why would we assume f(x) is always positive?
|| f(x) >= |f'(c)| >= 0 ||
brave wolf
does || MVT || work?
not sure
solemn vault
so its always positive
delicate shore
does || MVT || work?
It does
brave wolf
Oh, yeah, it does, that works too
drifting sierra
Or alternatively, you could focus on the extreme case f'(x) = f(x) first and th...
That's everywhere ig
brave wolf
there are probably lots of ways to do this
delicate shore
Fix some x in (0, 1), then |||f(x)| <= x |f(x_1)| for some 0 < x_1 < x, then iterate ||
safe radishBOT
safe radishBOT
Available help channel!
remote walrus
Yo do u guys also explain whole chapter?
safe radishBOT
Yo do u guys also explain whole chapter?
quasi bison
unlikely
#study-discussion maybe, or if you post a specific part of the theory or a specific question you're stuck on, then we can help
remote walrus
Oh ty!
austere goblet
so do you still have questions for this channel?
austere goblet
you may close the channel then. welcome to the server!
quasi bison
then .close this channel, and come back when you get a specific question
safe radishBOT
safe radishBOT
Available help channel!
keen pond
if i take the biggest base on top and bottom it gives me 2x cubed/x can i simplify it into 2x square ?or do i start over and factorise by x squared on top to reach a normal expression?
safe radishBOT
if i take the biggest base on top and bottom it gives me 2x cubed/x can i simpli...
plucky elk
Yea 2x^2 goes to ? as x goes to inf
keen pond
isnt it an undetermined form since it would be -infinity/+infinity
glacial cairn
The usual way is to divide both the numerator and denominator by some power of x
keen pond
The usual way is to divide both the numerator and denominator by some power of x
i could factorise both sides by x
safe radishBOT
safe radishBOT
Available help channel!
copper temple
safe radishBOT
https://discord.com/channels/268882317391429632/1364708617072148591/146973557610...
glacial cairn
I'm not going to read behind those links without context, but "if P then Q" is the same as "P implies Q"
normal moss
What formaly means if then ?
In proofs
Say we have if P then Q
This is the same as $P \implies Q$
flat frigateBOT
USS-Enterprise
normal moss
But we don't care about truth values here
Like false implies true is true
In proofs, if we have a statement implies another statement
We operate under the assumption that P is true
And if P is true, then Q must be true as well
We aren't saying P is true at all. We are saying if it is true, then Q is as well
normal moss
Yes, formally and logically they are the same
copper temple
P is truth implie Q is truth is same as P implie Q .
copper temple
Yes, formally and logically they are the same
Thanks a lot, because there's the paradox of material implication is :
All Q,P , (if P is false so Q ) truth .)
False proposition implie all propositions
Truth and false one .
And a truth proposition is implied by all propositions .
And there's no nessecerely a causal relation neither meaning neither time order
Between P and Q
But only truth table of it .
glacial cairn
Propositional logic does not deal with causality
manic patrol
what you stated is the principle of deductive explosion, and it is a thing, but it doesn't serve much purpose because most all theorems in math don't care about implications with a false antecedent.
copper temple
what you stated is the [principle of deductive explosion](https://en.wikipedia.o...
This is used in
Proof by contradiction .
manic patrol
eh... I would say not really in the current wording.
in deductive explosion, you start with a contradiction and prove anything.
in a proof by contradiction, you are assuming a falsehood to be true and shows that it leads to a contradiction. you do not infer anything from the contradiction. that would more lean towards the law of noncontradiction (that is, either a premise or its negation is true).
why did this embed work but not the previous one...
glacial cairn
Right but the law of noncontradiction exists at least partly because of the principle of deductive explosion
manic patrol
ah, fair point. I'm sorry I didn't catch that at first.
glacial cairn
I mean you're right, the law is what directly enables (as in makes possible) proofs by contradiction
manic patrol
I was more cautioning against thinking that deductive explosion is directly used in proofs by contradiction because it can then lead to various... nonsense proofs if abused.
but I also get your point that this law exists because of deductive explosion, so I apologize for not getting that at first.
weary latch
Yesterday, I finally understood how rotations around the unit circle worked, and that was a huge breakthrough.
Now, I'm working through word problems that use 2pi*n (I believe, since that's a full rotation), but I keep on getting them wrong. I think I mess up around where I stopped here.
Can someone help me with the next steps so that I see where I'm failing?
(Also, I have a feeling this isn't a 2pi(n) problem because this would only be half the way around the unit circle, as we're looking for equivelant cos values...)
safe radishBOT
Yesterday, I finally understood how rotations around the unit circle worked, and...
plucky elk
do you know what the period is of A(t) ?
plucky elk
cos(Bt) has period 2pi/|B|
where |B| means absolute value of B
one way to answer is to find the time "compress accordian completely" then add that time to "stretch it back out to a length of 50cm"
do you know how to find the first time?
weary latch
Hmmm... well, I thought about dividing 2.2142... by pi...
plucky elk
i don't see how that follows from "compress accordian completely"
weary latch
Wait a minute...
It's just 1/4th of the period, right?
No, wait, this is cos.
But if we're talking about going from fully stretched out to fully compressing it, that would be 1/2 of the period.
In that case, 1/2 of the period would be 1.
plucky elk
yea t=1 is right for the first part
plucky elk
one way to answer is to find the time "compress accordian completely" then add t...
try doing the second half of this
weary latch
Oh! Okay, so we already started the second half.
There we go, we have the first t value.
Now we just have to add 1 to it, right?
... the answer doesn't seem to be correct.
Oh, nevermind.
It's 1.3 because 0.7 is when it's going up, but we're going down.
I'll close this, but thanks for the help!
.close
safe radishBOT
safe radishBOT
Available help channel!
grim plover
question
grim plover
uhh, what the ?
why was the gas cloud treated like a solid sphere?
shell thrm applies to only connected surfaces or smth no?
yes closed surfaces
plucky elk
more of a physics question really
manic patrol
the shell theorem applies to any spherically-symmetric (by mass) object.
plucky elk
A spherically symmetric body affects external objects gravitationally as though all of its mass were concentrated at a point at its center.
https://en.wikipedia.org/wiki/Shell_theorem
grim plover
the shell theorem applies to any spherically-symmetric (by mass) object.
o
but in the proof we choose a closed surface 
grim plover
more of a physics question really
well i dont really understand how we prove shell theorem from gauss's law
or how we got gauss law for gravity from newtons law either
manic patrol
there is a paper about proving both parts of the shell theorem, which may help you here.
grim plover
this is the issue for me rn
mint plume
the choice of a closed surface stems from choosing a gaussian surface
u choose it so gauss law applies!
grim plover
the choice of a closed surface stems from choosing a gaussian surface
now wth is a guassian surface
as per my understanding a closed surface is any surface with a boundary?
and that has no holes
mint plume
yes but the gas cloud boundary itself is not your surface
when applying gauss law, u enclose the gas cloud with a imaginary sphere
that imaginary sphere is closed
mint plume
(not imaginary in the sense of complex numbers, i mean literally imaginary)
grim plover
(not imaginary in the sense of complex numbers, i mean literally imaginary)
yes i understand that much🙏
mint plume
u could choose any closed shape but we often pick ones that help us exploit symmetry
i could pick a closed panda and apply gauss law
grim plover
u could choose any closed shape but we often pick ones that help us exploit symm...
like spheres
grim plover
i could pick a closed panda and apply gauss law
what really?
grim plover
because bad surface integral?
mint plume
yes
grim plover
i see
well i dont think i'll be applying gauss law in either of these forms
atleast till electrostats
maybe then i might dabble it with a bit
mint plume
yeah its often introduced there more rigidly but a lot of force laws from electricity carry over to gravity
grim plover
yeah its often introduced there more rigidly but a lot of force laws from electr...
yeah my teacher did say that
grim plover
uhh, what the ?
tho ngl who would think about justifying this in exam 😭 i'd do this regardless if it was 'correct' or not
also another unrelated question: is $\omega_{BA} = \frac{v_B-v_A}{r_B-r_A}$ or $\frac{v_B}{r_B}-\frac{v_A}{r_A}$
flat frigateBOT
rak³en
grim plover
here BA mean B relative to A, omega is ang vel, v is linear vel, r is radius of circular orbit
grim plover
probably the latter
well then wtf is this
mint plume
what is the context behind that
grim plover
two satellites a and b in circular orbits of radii r_a and r_b
what is the omega_a relative to b when they are closest
mint plume
yeah im not sure how you'd get that formula for W_AB from that
best i can conclude is still w_a - w_b
grim plover
best i can conclude is still w_a - w\_b
jee mains 
time to sleep its 1 am for me
ty!
.close
safe radishBOT
safe radishBOT
Available help channel!
mighty gyro
I need help answering a,c,e
safe radishBOT
I need help answering a,c,e
silk tendon
!status
safe radishBOT
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
I dont know where to begin
silk tendon
try to turn all to y = something first
mighty gyro
wait is that just the answer for a?
silk tendon
yea
mighty gyro
oh alrighty
what would I write down for the answer accordingly to what the question is asking
mighty gyro
thats fair
silk tendon
so for c we need more information: what have you learnt in class
mighty gyro
the problem is I missed a week and half of school because of class swapping so im now trying to catch up
silk tendon
uhh yea but its hard to figure out if i dont know what kind of equation is that
mighty gyro
looking at the answer key in the back of the book what you told me was right
silk tendon
like linear equations are very different from trigonometric equations
mighty gyro
I think linear
silk tendon
ok for linear equations
if its f(x-a)
then its shifting a to the right
thats the golden rule.
if is outside
f(x)+b
then its shifting up
mighty gyro
actually I think I understand what im doing for now ill come back if I need more help
silk tendon
remember, when inside, its always opposite direction but when outside, its the same direction as the axis
mighty gyro
I figured ill keep it in mind thank you
silk tendon
np
safe radishBOT
Available help channel!
latent tendon
Hello, can someone pls help me understand the disrepency between my answer vs the solution book answer.
safe radishBOT
Hello, can someone pls help me understand the disrepency between my answer vs th...
quasi bison
images uploading?
safe radishBOT
@latent tendon Has your question been resolved?
latent tendon
<@&286206848099549185>
snow robin
Right
The channel closed before i could talk
When you look at $\delta(x \cos(\theta))$ and $\delta(y \sin(\theta) - l)$ do you see single variable functions?
flat frigateBOT
Katharine
snow robin
specifically the $\theta$ @latent tendon
flat frigateBOT
Katharine
snow robin
$\theta$ is a function of both $x$ and $y$
flat frigateBOT
Katharine
latent tendon
Which couples both x and y, so its not seperable?
snow robin
yes
and their answer
is when you look at specific cases with cos(θ) = 0
then you can separate them
but in general it is coupled
latent tendon
but thats kind of confusing no? like saying when costheta = 0 or sin theta =0 , then its no longer coupled?
Like i understand sin (0)= 0 and cos (0)= 1 means they are different but lets say sin (3)= 0.05 and cos (0.05) = 0.99 so they still are different
ig reading the answer key kind of confused me
i get theta affects both simultaneously which is why its not seperable, but its seperable when one is 0?
@snow robin
safe radishBOT
@latent tendon Has your question been resolved?
latent tendon
<@&286206848099549185>
safe radishBOT
@latent tendon Has your question been resolved?
safe radishBOT
@latent tendon Has your question been resolved?
unique thicket
i think the above helper misunderstood θ and tbh it's not clear in the textbook. but no it's not a function of x, y and is in fact a constant. δ_l looks like 0 everywhere except on a line where it is equal to ∞. this line is parametrised by θ and l. the textbook is saying that δ_l is separable if and only if this line is either perfectly horizontal or perfectly vertical.
safe radishBOT
@latent tendon Has your question been resolved?
hearty sable
i have to prove this formula
safe radishBOT
i have to prove this formula
safe radishBOT
@hearty sable Has your question been resolved?
hearty sable
<@&286206848099549185>
safe radishBOT
@hearty sable Has your question been resolved?
safe radishBOT
@hearty sable Has your question been resolved?
safe radishBOT
safe radishBOT
Available help channel!
fiery olive
Anyone able to link me videos so I can solve these? The textbook is unclear and I missed the lesson
safe radishBOT
Anyone able to link me videos so I can solve these? The textbook is unclear and ...
fiery olive
Yeah, but that one was so short so I was wondering if someone got a longer one
safe radishBOT
Available help channel!
jade bane
Hi, could I please have some help on this, I approached it by contradiction, I was wondering, suppose that e is a rational so e = p/q, then show T is an intger and also a rational which is a contradictin, To show T is a rational i know tat the RHS summation is < 1/q + 1/q^2 + 1/q^3 +... < 1/q right?
Is that a correct upper bound i can use?
safe radishBOT
Hi, could I please have some help on this, I approached it by contradiction, I w...
safe radishBOT
safe radishBOT
Available help channel!
sick zealot
help
sick zealot
First time doing volume math I want to know how to do the math on the examples please help
wispy adder
for 3d objects like the bottom two u wanna do volume = area of the base * height
so for the cylinder in part a we need to find area of circle (coz thats the base) * heigh of the cylinder
area of circle is pir^2 we know r is 5 so its 25pi, and the height of the cyliner is 5
so answer is 125pi u^2
for part b u know base is a rectangle which is 22*7 = 154 and t hen times the hight which is 8
1232
safe radishBOT
@sick zealot Has your question been resolved?
wispy adder
yeah so ur formula is right
but do u know what those letters mean?
pi is a number
r is the radius of the circular base
h is the height
so looking at the diagram u can see arrows labelling each of these
r is radius which is half the diameter
the diameter is the entire length of the circle which is 10 so radius would be half of that hwich is 5
h is height which is 5
so plug it into the formula and u get ur volume
same with the bottom one
lwh
l is length
w is width
h is height
u have 3 numbers on that rectangular prism
each number corresponds to a letter
mutliply all 3
and u get ur volume
safe radishBOT
sick zealot
yeah so ur formula is right
Can you like download my picture and draw on it how it’s done I’m more of a visual learner
.reopen
safe radishBOT
✅ Original question: #help-23 message
@sick zealot Has your question been resolved?
safe radishBOT
@sick zealot Has your question been resolved?
south steppe
rigid meteor
safe radishBOT
Asking the actual question right away is more likely to get responses.
Asking "Can I ask...?" or "Does anyone know about...?" doesn't give people enough information to decide whether they can help, and answering can feel like a promise to help with the actual question, which they might find themselves unable to.
rigid meteor
@tawny igloo bestie what’s your question
safe radishBOT
safe radishBOT
Available help channel!
nocturne zephyr
Prove that given any real number m >=1, ther exists some value p(natural) such that for all integers n>= p
safe radishBOT
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
1
i generally attempt to solve universal into existential quantifer proofs by writing the existential bit in terms of the universal but idk how to do that here...
void path
(it's not)
why?
nocturne zephyr
yes i am trying to prove it true and it is true
light shoal
try n = 1 and m = 2, for example
void path
Prove that given any real number m >=1, ther exists some value p(natural) such t...
he's trying to prove this
void path
so forall m exists p forall n > p
misty nest
.
light shoal
he's trying to prove this
in addition to having nothing to do with the screenshot, this is also strange, what does m have to do with anything
void path
i generally attempt to solve universal into existential quantifer proofs by writ...
anyways usual way to prove existential statements is either constructing the candidate or proving by contradiction (if you assume lem)
nocturne zephyr
in addition to having nothing to do with the screenshot, this is also strange, w...
what do you mean
tardy mango
void path
and m is never mentioned again
it is in the ss
nocturne zephyr
m is in the equation
light shoal
i give up, have fun with this
void path
any ideas guys lol
i'm thinking but induction seems to work quite well?
nocturne zephyr
mhm i have yet to learn mathematical induction
void path
ah ok
nocturne zephyr
our previous lecture went over it and i haven't had the time to go over it since i missed it
unfortuante
void path
oh but you are allowed to use it?
nocturne zephyr
yes
void path
because proofs on naturals like these are commonly solved by induction so it may be the intention here
safe radishBOT
@nocturne zephyr Has your question been resolved?
void path
i just dont know how lol
okay i think something like this should work without induction if you're able to prove that m < p^m for some p
nocturne zephyr
@void path thank you so much
safe radishBOT
Available help channel!
safe radishBOT
safe radishBOT
@fringe dock Has your question been resolved?
hard crest
weight is mass * the force of gravity
frosty leaf
what am i doing wrong
safe radishBOT
what am i doing wrong
hard crest
it would be:
rate * birds * time = birdseed
quasi bison
... where rate is the amount of seed eaten by ONE bird in ONE month
manic patrol
5 what? might want to be careful with units especially in problems like this, lest you end up confusing yourself with a bunch of numbers.
also, recall that you may prefer to work with the rate per bird in terms of cups of birdseed per a single month.
hard crest
does your answer of about half a month seem reasonable? like using your skills of estimation
frosty leaf
yes
hard crest
cool seems good then
hard crest
me? i'd probably do something like
5 cups - 18 birds - 1 month
5/18 cups - 1 bird - 1 month
80/18 cups - 16 birds - 1 month
1 cup - 16 birds - 18/80 month
2 cup - 16 birds - 9/20 month
but like. we get the same result by multiplying the same things
i'd just write out less because i'm more comfortable with these problems
frosty leaf
can i avoid calculating the rate of 1 bird
and use the proportional rule directly
18 birds = 5 cups per 1 mo
16 birds = 2 cups per ? mo
and solve
why should we use 1 bird in the first place
hard crest
idk i just went through one bird because i was less likely to mess it up
youc ould do it that way too
frosty leaf
is there a caveat here
i see many solutions go first through 1 "worker"
in this case 1 bird
manic patrol
you're less likely to mess up a simple multiplication if you first find out the rate of one entity than to have to handle multiplication and division at the same time by directly using proportion. it's not impossible, but it's more error-prone.
safe radishBOT
@frosty leaf Has your question been resolved?
exotic anvil
Please don't ping mods for that
radiant isle
<@&268886789983436800> bot broke
yes we're aware
exotic anvil
We're aware the bot is currently running a bit slow
Please only ping mods for actual moderation issues
steep magnet
Alrighty
granite viper
<@&286206848099549185>
proud tree
where are you having trouble?
granite viper
where are you having trouble?
It’s in my book I will take a picture wait
Q2 a and b
proud tree
okay next time send your question first and wait 15 minutes
granite viper
okay next time send your question first and wait 15 minutes
Sure
flat frigateBOT
proud tree
what have you tried for part a @granite viper
granite viper
what have you tried for part a <@1147514251339108372>
I tried like diving by 14 then I got stuck
Both sides. Not the middle
proud tree
okay so you get $\cos(x+75^\circ)=\frac{1}{2}$
flat frigateBOT
Green
proud tree
well for what values of x is cos x = 1/2
granite viper
okay so you get $\cos(x+75^\circ)=\frac{1}{2}$
Yea then I think I need to put it in shift cos then get it then
proud tree
shift cos?
granite viper
I study trig
proud tree
ik
granite viper
So like to get the angle of it something something
proud tree
is shift cos supposed to mean inverse cos
granite viper
is shift cos supposed to mean inverse cos
Yea yea
proud tree
well for what values of x is cos x = 1/2
@granite viper
granite viper
okay well that won't give you all the solutions here (on the principal branch)
Yea then I need to do some steps that involve 360
proud tree
ye
granite viper
I will try complete it and I will see if there’s any mistakes
honest idol
I need help here with the first one. (This is a practice test not an actual one)
mystic nexus
These problems are basically just taking a big force and splitting it into pieces that actually matter for the slope.
and btw this is physics ryt
@honest idol
honest idol
and btw this is physics ryt
No calc 3
Well it is physics but the class isn’t physics centered
honest idol
These problems are basically just taking a big force and splitting it into piece...
I just don’t understand the wordings
mystic nexus
The car's weight is pushing straight down, but because it's on a $15^\circ$ hill, that weight gets split into two parts: one trying to slide it down the hill and one squishing it into the pavement.a) Force to keep it from rolling: This is the "parallel" force. You just take the weight and multiply by the sine of the angle.
Calculation: $5800 \times \sin(15^\circ) \approx 1501$ lbs.So you need about 1501 lbs of force to keep that thing from becoming a runaway projectile.b) Force perpendicular to the slope: This is how hard the car is actually pressing against the road. Use cosine for this one.Calculation: $5800 \times \cos(15^\circ) \approx 5602$ lbs.The road is feeling a massive 5602 lbs of pressure.
flat frigateBOT
Innocent Zero
honest idol
The car's weight is pushing straight down, but because it's on a $15^\circ$ hill...
Like this ?
Wait no probably this
Idek
mystic nexus
The Weight Vector: In your drawing, the red arrows represent the components, but the "main" force (the car's weight) always points straight down towards the center of the Earth, regardless of the hill.
The Triangle Logic: Those two red arrows should actually be the "legs" of a right triangle where the car's 5800 lb weight is the hypotenuse.
The Angle: In your second drawing, you marked 30°, but the problem specifically says the car is on a 15° slope.
honest idol
The Weight Vector: In your drawing, the red arrows represent the components, but...
Oh yea angle is 15
Did I get the component vectors correctly tho?
mystic nexus
not quite correct for a standard physics vector diagram.
honest idol
not quite correct for a standard physics vector diagram.
Well is it still correct practically
mystic nexus
your new diagram is getting much closer, but it's still a bit "messy" logically. You’ve got the right idea with the angles now, but your force values and directions are still tripping you up.
honest idol
your new diagram is getting much closer, but it's still a bit "messy" logically....
Wdym
mystic nexus
there are me correction but this diagram is pretty close
honest idol
Ok
mystic nexus
Is this AI generated?
the image is ai generated i am too lazy to draw but the concept is correct i double chked it carefully
honest idol
So I had an issue with my other vector
I see
From there it’s just trig right @mystic nexus
mystic nexus
From there it’s just trig right <@1225769778338070562>
ye
mystic nexus
So I had an issue with my other vector
ur perpendicular was correct but the direction were opposite
safe radishBOT
Available help channel!
west hedge
Honey
light shoal
you ok over there? 😁
west hedge
you ok over there? 😁
Two points A and B and there are another movable point P on the given circle which satisfies that given equation. How many possible P there are? 0, 1, 2….
The problem is the given equation PA^2-PB^2=-13 would not be a easy reach algebraically speaking
So I have to rely on a geometric approach
But I’m not sure what the equation means geometrically, which gets me stuck
Ahhh
Abhhhhhh
Nooooo
I love North Korea
calm cloak
??
west hedge
Ppl outside North Korea are too blunt to solve this one
rustic goblet
west hedge
My arguments:
- because North Korea do not have internet, local people spend most of their time on learning math which results in a greater capability of math for them compared to people in other countries.
2.people in North Korea are more resilient. In North Korea, food shortages, water shortages, and power outages are commonplace which makes a lot inconvenience and trouble for local people. Those people able to survive through this tough and unbearable circumstances without giving up are mentally strong enough to cope with complicated math quizzes. With greater mental resilience, they are more likely to have better academic achievements in math field compared to people in the rest of the world.
safe radishBOT
@west hedge Has your question been resolved?
velvet nebula
The problem is the given equation PA^2-PB^2=-13 would not be a easy reach algebr...
We know P is closer to A than B, what I would do is start by plotting points on the circle and calculating PA^2-PB^2 and see how it compares to -13
west hedge
We know P is closer to A than B, what I would do is start by plotting points on ...
You mean choose a random point in the circle and start calculate
velvet nebula
Yeah, there are 8 such points with integer coordinates, not too hard to go through these
safe radishBOT
@west hedge Has your question been resolved?
midnight plume
Hello! I'm stuck on this question, specifically at 2x = 1 - (3/x+2). Im unsure how to continue working, is anyone able to help?
safe radishBOT
Hello! I'm stuck on this question, specifically at 2x = 1 - (3/x+2). Im unsure h...
hard crest
generally it's a good idea to clear denominators
can you tell me what you did so far?
midnight plume
i said that im stuck at 2x=1 - (3/x+2), i think i did what you asked? not sure tho
hard crest
can you tell me how you got there?
midnight plume
i can send a picture of my work?
hard crest
what steps have you taken so far?
midnight plume
just cancelled out the bottom numbers on the fractions (idk what the terms are sorry)
hard crest
okay, that's what i was afraid of. I don't understand why you thought you could just do that.
When you're solving an algebraic equation, you can do whatever you want to one side, as long as you do the same exact thing to the other sdie
for example, you could multiply both sides by 2
but you have to multiply the entire thing by 2
it seems like what you were trying to do was to multiply both sides by (x^2 - 4)?
midnight plume
I know this is a terrible picture but this is what I did specifically, I thought I did the same process the teacher told me to
hard crest
right okay, it does seem like you were trying to multiply both sides by (x^2 - 4)
so let's do that
starting with
$\frac{2x}{x^2-4} = \frac{1}{x^2-4} - \frac{3}{x+2}$
flat frigateBOT
schrödinger's kitten
hard crest
$\orange{(x^2-4)}\lp \frac{2x}{x^2-4}\rp = \orange{(x^2-4)}\lp\frac{1}{x^2-4} - \frac{3}{x+2}\rp$
flat frigateBOT
schrödinger's kitten
hard crest
do you see how i'm multiplying the entire thing by (x^2 - 4)?
midnight plume
yes i see
hard crest
okay. on the left, we have something that fits the pattern of $\rsq * \frac{\bsq}{\rsq} = \bsq$ so we can simplify that
flat frigateBOT
schrödinger's kitten
hard crest
so now we have
$2x = \orange{(x^2-4)}\lp\frac{1}{x^2-4} - \frac{3}{x+2}\rp$
flat frigateBOT
schrödinger's kitten
hard crest
on the right, we're going to have to distribute that orange thing across the two terms
$2x = (x^2-4)\lp\frac{1}{x^2-4}\rp - (x^2-4)\lp\frac{3}{x+2}\rp$
flat frigateBOT
schrödinger's kitten
hard crest
now do you see another spot we can apply the rule we know, of $\rsq \cdot \frac{\bsq}{\rsq} = \bsq$ ?
flat frigateBOT
schrödinger's kitten
midnight plume
uhmm
lemme see
sorry i think im still a little lost
but i looked back at my notes and i think i figured out what i did wrong earlier
.close
safe radishBOT
safe radishBOT
Available help channel!
winged flare
is there a sensible basic calc way to evaluate\\
$\int _{-\infty} ^ {\infty} \frac{R^2}{2(R^2 + x^2)^{3/2}} dx$
safe radishBOT
is there a sensible basic calc way to evaluate\\\\
$\int _{-\infty} ^ {\infty} \...
flat frigateBOT
median vigil
trig sub?
safe radishBOT
winged flare
thank you though
tired spindle
safe radishBOT
Available help channel!
hybrid forum
Hello guys, I have a question. Is a logarithm an irrational number? Can you calculate a logarithm without a calculator?
safe radishBOT
Hello guys, I have a question. Is a logarithm an irrational number? Can you calc...
tall hearth
It depends on the argument of the logarithm
hybrid forum
It depends on the argument of the logarithm
What's an argument?
tall hearth
The number you take the log of
so like x is the argument for log(x)
like log_10(100)=2, but log_10(2) is irrational
so it depends
open wedge
True
tall hearth
Also you can calculate any logarithm w/o a calculator to any precision you want but its a lot of computation
peak estuary
its worth noting that even the calculator still only computes an approximation
quasi bison
Hello guys, I have a question. Is a logarithm an irrational number? Can you calc...
extremely dependent on what the base and input are
safe radishBOT
@hybrid forum Has your question been resolved?
open wedge
And that's why we write logs instead of their decimal representation, we write: $\log_{m}{a}$
flat frigateBOT
1 divided by 0 equals Infinity
open wedge
Just like we don't write as $1.414$, we write as $\sqrt2$. It's because we can't write all digits of it out, because it's infinite
flat frigateBOT
1 divided by 0 equals Infinity
safe radishBOT
open wedge
Or people don't write as $0.1428570142857\dots$, people found a lot of alteratives to this, or they just wrote it as $\frac17$
safe radishBOT
Available help channel!
compact pasture
someone help pls
safe radishBOT
someone help pls
compact pasture
hard crest
that looks like it might be separable? have you tried?
compact pasture
that looks like it might be separable? have you tried?
yeaa so my friend once posted it here i have adoubt regardin the soln
can u guide me
compact pasture
that looks like it might be separable? have you tried?
soo umm this was the soln given #help-2 message
but i think the guy assumed wrong
for if u take the 2 bracket t
the 1 bracket doesnt become dt
can u please try
i think the question is wrong like they put it wrong in 1 brackde
hard crest
i can't tell which part you're doubting
but try differentiating the solution given and see if it matches
compact pasture
i can't tell which part you're doubting
umm like the asnwer is by when u take the second part 2
the 1 part isnt dt
compact pasture
but try differentiating the solution given and see if it matches
good idea
compact pasture
but try differentiating the solution given and see if it matches
not matching for me
can u please reconfirm
hard crest
seems to match for me i think?
brave wolf
,w find derivative, ln(1+2sin(y)) = 1/2 ln(4+sqrt(9+sqrt(x))
compact pasture
ohh
hard crest
coefficient might be slightly off
flat frigateBOT
compact pasture
when the right root x goes insise it becomes xrootx
so umm how is it matching
like the rightest inside the second rightest
compact pasture
heres its only x and 9 root x
compact pasture
when the right root x goes insise it becomes xrootx
@hard crest im sorry but im a like understandable like idk if i am able to convey what i want to say
compact pasture
yeah, it does seem kinda weird
yeaa i think like the question was trying to make the same equation the guy found out but i think they messed up the roots somewhere
hard crest
idk i'm doing this without paper so it's tricky for me to check
brave wolf
that sqrt(x) multiplies to the root
brave wolf
$\sqrt{\sqrt{x} + 9} \sqrt{x} = \sqrt{x + 9 \sqrt{x}}$
flat frigateBOT
MathIsAlwaysRight
brave wolf
wont it be x^3/2
oh yeah im stupid
brave wolf
,w y' = (1+2sin(y))/(16sqrt(x+9sqrt(x))(4+sqrt(9+sqrt(x)))cos(y))
compact pasture
i think its unsolvable in that form
lmao
😭
bro just moved the items in multiplication
AB = BA AHH
😭
flat frigateBOT
brave wolf
thanks wolfie
short lark
just to provide some context by the way, they expect us to solve this in about 2 minutes
compact pasture
just to provide some context by the way, they expect us to solve this in about 2...
thats a diff question but they arent even providing a valid equation the question is wrong smh
brave wolf
Not even wolfram can solve it apparently
compact pasture
brave wolf
maybe this was the intended question
safe radishBOT
@compact pasture Has your question been resolved?
twin prawn
safe radishBOT
twin prawn
hello, no need to simplify any further right
summer coral
yeah that looks right, id just write it in order A B C idk if its required
safe radishBOT
Available help channel!
mellow lodge
I've been working on this for a while. I think I've been able to successfully eliminate a portion of this limit but I'm not sure how to proceed in evaluating what's left
safe radishBOT
I've been working on this for a while. I think I've been able to successfully el...
@mellow lodge Has your question been resolved?
safe radishBOT
safe radishBOT
Available help channel!
brazen nimbus
find the zeropoints of the function depending on q, and their type
brazen nimbus
can someone help me holy shit this is so hard
flat frigateBOT
riemann
plucky elk
plug in a, b, c and simplify
glass carbon
Well, they depend on q, so you're rather supposed to find discriminant and then check when D > 0, D = 0 and D < 0
safe radishBOT
@brazen nimbus Has your question been resolved?
brazen nimbus
Well, they depend on q, so you're rather supposed to find discriminant and then ...
yes exactly but
brazen nimbus
Well, they depend on q, so you're rather supposed to find discriminant and then ...
my D in this case is the -5q right?
glass carbon
my D in this case is the -5q right?
Not really, show you work if possible
D is b^2 - 4ac, not just c
safe radishBOT