how is that not true
#help-23
stoic raptor
brave wolf
for example the function e^(-1/x^2) is extremely flat at the origin, it has all derivatives = 0
and yet it's not the 0 function
so yeah, common sense can sometimes be misleading
stoic raptor
dayum
math indeed is always right
ok thanks @brave wolf i appreciate the insight
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brave wolf
btw its a pretty cool exercise to try and figure out how this works
You can try taking a polynomial, and making sure that the derivatives at 0 match the derivatives of sin
stoic raptor
i fear i may not be at that lvel yet
cuz i just started learning these higher order derivatives
maybe when i reach undergraduate i could have a fair fight against it
stone sedge
hello guys
brave wolf
cuz i just started learning these higher order derivatives
I see, you dont really need a lot of knowledge for it though.
you can start with ax^3 + bx^2 + cx + d and make sure that at 0 it = sin(0). That already guarantees d = 0. Then compute the first derivative and make sure it equals the derivative of sin at 0, that'll make c = 1 if you actually compute it...
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stone sedge
anyone jee aspirant here?
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anyone jee aspirant here?
brisk shard
anyone jee aspirant here?
yes?
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@stone sedge Has your question been resolved?
stone sedge
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void berry
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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 don't know where to begin
earnest nacelle
what do you know about direct and inverse variation?
void berry
y=kx not much
earnest nacelle
that's direct. what about inverse?
void berry
is it y=k/x
earnest nacelle
yes, cool
now, you are told x varies direvtly with y and inversely with z
if you put aside k for the moment what equation can you set up?
void berry
50=k410
earnest nacelle
don't put values yet
just make an equation with x, y, and z
and leave k aside for the time being, we'll bring it back in later
main point is the equation with x, y, z
void berry
x=50 y=410 z=420
earnest nacelle
nono, one equation that describes the relationship between x, y, z
not their values
do not think about their values right now, just focus on having x, y, z in the same equation with nothing else
void berry
what do mean same equation?
earnest nacelle
for example, if I ask for an equation with a, b, c in it, a = bc is an example
notice no numbers
it's just literally a, b, and c in one equation
can you do the same for x, y, and z given the conditions in the question?
void berry
i'm still a bit confused how would i solve it like what would the first step be?
earnest nacelle
forming the equation with x, y, and z that fulfills the relationships in the question
hence why I'm asking you to try doing that
void berry
ok so i should replace the variables with the values?
earnest nacelle
no, I said not to think about values right now
void berry
oh
earnest nacelle
that would be after you've formed the equation
void berry
ok so it would be 410= ? X 50
earnest nacelle
no values, mate. no values.
is there a language barrier perhaps? is your native language English?
earnest nacelle
English, Mandarin, Japanese. but either way, may I know if my wording regarding "no values" was unclear to you?
if it was, let me rephrase it this way: your equation right now should have no numbers in it whatsoever, only letters, the equal sign and possibly a fraction
nothing else
graceful lichen
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graceful lichen
What will I get if I multiply P^T with A ?
tardy mango
Try finding $P^{-1}$
flat frigateBOT
Civil Service Pigeon
tardy mango
and/or recall that the transpose of an orthogonal matrix is the same as the inverse
tardy mango
tardy mango
and/or recall that the transpose of an orthogonal matrix is the same as the inve...
(because of this)
tardy mango
and/or recall that the transpose of an orthogonal matrix is the same as the inve...
(which I said here)
cobalt aurora
(which I said here)
sorry I didn't notice TwT
tardy mango
sorry I didn't notice TwT
there's probably other help channels that are completely open
and/or #1021175428326633542
cobalt aurora
there's probably other help channels that are completely open
yea imma go there
tardy mango
yea imma go there
👍 yeah please try to not barge into help channels where things are already under control
because no telepathy -> things can get driven off course
and also too many cooks in the kitchen can confuse the person asking for help
cobalt aurora
and also too many cooks in the kitchen can confuse the person asking for help
true mb
graceful lichen
Please show me what is value of P^T*A
I am not able to use my mind to get its value even after your hint
tardy mango
Please show me what is value of P^T*A
Wait why are you doing $P^T A$
flat frigateBOT
Civil Service Pigeon
tardy mango
tardy mango
$C$ should just boil down to $A^{10}$
flat frigateBOT
Civil Service Pigeon
graceful lichen
Why I can't see it boils down to A^10
tardy mango
$$P^{-1} BP=P^{-1} PAP^{-1}P=IAI=A$$
$$P^{-1} B^2 P=P^{-1} PAP^{-1} PAP^{-1} P=IAIAI=A^2$$
etc.
flat frigateBOT
Civil Service Pigeon
graceful lichen
Inverses?
nimble wyvern
AAᵀ=I
tardy mango
^ for an orthogonal matrix A, that holds
then multiply both sides by the inverse of A
tardy mango
and/or recall that the transpose of an orthogonal matrix is the same as the inve...
which is what I referenced here
@graceful lichen you good?
tardy mango
I still don't see where $P^T A$ is coming from
flat frigateBOT
Civil Service Pigeon
tardy mango
**Civil Service Pigeon**
can you show me where it would arise in the examples I gave you here
graceful lichen
can you show me where it would arise in the examples I gave you here
How can I show it in your examples if I don't understand it yet
graceful lichen
Here can you see we need to multiply (P^T)(PAP^T)(PAP^T) .... (PAP^T)P
tardy mango
Here can you see we need to multiply (P^T)(PAP^T)(PAP^T) .... (PAP^T)P
Regroup it as $(P^T P) A (P^T P) A \dots A (P^T P)$ since matrix multiplication is associative, which it looks like you did in the image. So all you have now is $I$'s and $A$'s, which is again why I'm asking where the need to compute $P^T A$ comes from.
graceful lichen
Oh shit
flat frigateBOT
Civil Service Pigeon
graceful lichen
I wasn't regrouping it the way it has to be regrouped
tardy mango
oh
graceful lichen
Yes
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dim socket
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earnest nacelle
you can consider a vector space in R^3 with the standard basis. let A have dimension 1 and B have dimension 2
you'll quickly find out there's a way to debunk this statement
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dim socket
you'll quickly find out there's a way to debunk this statement
It is wrong
Because if I take x axis for dim 1
And i consider yz plane for dim2
clearly dimA<dimB but....A is not subset of B
earnest nacelle
exactly
that's why I said you can debunk this statement
it's false as written, as you've proven yourself
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frosty leaf
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frosty leaf
can someone please explain to me how we calculate the max range here?
earnest nacelle
note down which division has teams in this case
and which does not have teams
then assume that the lowest division with a team has a player at the min age, and the highest division with a team has a player at the max age
earnest nacelle
mhm
frosty leaf
and what about min range?
earnest nacelle
assume that the lowest division has all players at max age and the highest division has all players at min age
frosty leaf
20-12 = 8 ?
earnest nacelle
yeah looks correct
frosty leaf
ONE LAST QUESTION
i recall this idea of MIN range being : whatever smaller circle fits in the larger circle
sort of like a venn diagram idea
earnest nacelle
never heard of this idea
frosty leaf
set containment.
earnest nacelle
still never really heard of it. perhaps others would have, and you can wait for others to comment
sorry
astral glacier
i recall this idea of MIN range being : whatever smaller circle fits in the larg...
Hm?
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stoic raptor
can the slope of a normal line just be written as m and then subscript perpendicular sign?
safe radishBOT
can the slope of a normal line just be written as m and then subscript perpendic...
fair helm
can the slope of a normal line just be written as m and then subscript perpendic...
You can call it whatever you want
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covert yoke
ok thanks big pout
I would probably just write it as -1/m
because that's just the value (assuming m isn't 0)
stoic raptor
ok thanks for the clarification omnipotententity
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lament dirge
how the heck did they get (what i circle in red) as the displacement form?
wary cape
think its typo on the first line
it should be 4sin 30° j
the answer is then correct
lament dirge
think its typo on the first line
it should be 4sin 30° j
the answer is then corr...
pls how did u get this
and where does the 2 come from
wary cape
and where does the 2 come from
2 is typo
should be 4
stoic raptor
ya
wary cape
yea hold up
lament dirge
thank you
lament dirge
okay i think i am confused because i am not looking at the picture properly
is 4m the
dotten line?
OMDDD
bro nvm
i dumb
.i get it now
.close
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whole geode
how to find every prime number within a given interval
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how to find every prime number within a given interval
whole geode
in wikipedia ??
plucky elk
reading is good for you
whole geode
thank youu
plucky elk
especially when it answers your question
whole geode
there's another method i think it's with sqrt
plucky elk
there's another method i think it's with sqrt
first read the wiki, then decide if your "other method" is actually different
whole geode
first read the wiki, then decide if your "other method" is actually different
it's the same method right ....
plucky elk
no idea what "other method" you're thinking of
whole geode
yoo this method make alot of sense
i get it you cross out every multiple i get itttt
thank you man
plucky elk
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tardy mango
thank you man
!done
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thank you man
If you are done with this channel, please mark your problem as solved by typing .close
tardy mango
.solved
shrewd linden
Let the initial integer vector be
[
(a_0, b_0, c_0, d_0) = (0, 1, 1, -1),
]
and define the iteration for each (n \ge 0) as
[
(a_{n+1}, b_{n+1}, c_{n+1}, d_{n+1})
= \big(c_n (2+n),; d_n (2+n),; a_n - c_n (1+n),; b_n - d_n (1+n)\big),
]
Is it true that
[
\gcd(a_n, b_n, c_n, d_n) = 1
]
for every (n \ge 0)?
flat frigateBOT
rozehip
shrewd linden
I created this script: ```python
import math
a, b, c, d = 0, 1, 1, -1
for n in range(1000):
print(f"{'Passed' if math.gcd(a, b, c, d) == 1 else 'Failed'} {n}")
a, b, c, d = c*(2+n), d*(2+n), a - c*(1+n), b - d*(1+n)
And for first 1000 it works.But I'm not sure how to prove it
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shrewd linden
<@&286206848099549185>
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<@&286206848099549185>
fair helm
<@&286206848099549185>
Speak
shrewd linden
**rozehip**
.
mossy nexus
what i usually do for questions like these is write down the 1st few values of n
and then see if there is any sort of series being made
for example an AP GP, AGP HP etc
shrewd linden
n = 0, (0, 1, 1, -1)
n = 1, (2, -2, -1, 2)
n = 2, (-3, 6, 4, -6)
n = 3, (16, -24, -15, 24)
n = 4, (-75, 120, 76, -120)
n = 5, (456, -720, -455, 720)
n = 6, (-3185, 5040, 3186, -5040)
n = 7, (25488, -40320, -25487, 40320)
n = 8, (-229383, 362880, 229384, -362880)
n = 9, (2293840, -3628800, -2293839, 3628800)
n = 10, (-25232229, 39916800, 25232230, -39916800)
n = 11, (302786760, -479001600, -302786759, 479001600)
n = 12, (-3936227867, 6227020800, 3936227868, -6227020800)
n = 13, (55107190152, -87178291200, -55107190151, 87178291200)
n = 14, (-826607852265, 1307674368000, 826607852266, -1307674368000)
n = 15, (13225725636256, -20922789888000, -13225725636255, 20922789888000)
queen ingot
can we conjecture that a_n = 1-c_n ?
that should give you gcd = 1, and maybe it can be proven by induction
shrewd linden
also b_n = -d_n
shrewd linden
can we conjecture that a_n = 1-c_n ?
[
\begin{cases}
a_{n+1} = (n+2)c_n,\[2mm]
c_{n+1} = a_n - (n+1)c_n.
\end{cases}
]
Substitute (a_n = 1 - c_n):
[
c_{n+1} = a_n - (n+1)c_n = (1 - c_n) - (n+1)c_n = 1 - (n+2)c_n.
]
And
[
a_{n+1} = (n+2)c_n,
]
so indeed:
[
a_{n+1} + c_{n+1} = (n+2)c_n + [1 - (n+2)c_n] = 1.
]
flat frigateBOT
rozehip
shrewd linden
Ahh so g=gcd(a, b, c, d), then g|a, g|c => g|(a+c) and because a+c=1, then g|1 => g=1
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modest copper
how do i solve this?
safe radishBOT
how do i solve this?
hard crest
3x + 1 is equal to 3x - 1 + 1 + 1
modest copper
3x + 1 is equal to 3x - 1 + 1 + 1
i see the 3x + 1 comes from the first part, 3x - 1 comes from the second
but where does the extra +1 and +1 come from
flat frigateBOT
schrödinger's kitten
modest copper
i see but why do we make that a + 2
timid ridge
i see but why do we make that a + 2
3x + 1 = 3x - 1 + 2, yes?
modest copper
yeah
timid ridge
ok great
you just rewrote the exponent in a different way so it might be easier to solve now
$2^{3x-1} \cdot 2^{2} - 2^{3x-1} \cdot {1} = 768$
flat frigateBOT
tten ʚɞ
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silk saffron
hi
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.
molten acorn
,rccw
flat frigateBOT
silk saffron
I'm not sure how to go about making boolena statements from here, I tried making Karnaugh maps but realized I had no clue how to do that here as well
I tried putting it in chat gpt and its giving me some Q0,Q1 but when i look at my notes we didn't use any other variables and stuck with our state names
if someoen can just let me know how to make boolean statements from this or if I might've done this incorrectly
this is the questions I should've maybe posted this:
Alyssa P. Hacker’s snail from Section 3.4.3 has a daughter with a
Mealy machine FSM brain. The daughter snail smiles whenever she slides over the
pattern 1101 or the pattern 1110. Sketch the state transition diagram for this
happy snail using as few states as possible. Choose state encodings and write a
combined state transition and output table using your encodings. Write the next
state and output equations and sketch your FSM schematic.
<@&286206848099549185>
do i put my states horizontally instead of vertically? Im seeing some examples do it my way and some examples do it horizontally and im getting confused
anybody know where i can get computer architecture help
earnest nacelle
maybe #theoretical-cs may help, or if not you may check the list of affiliated servers in #old-network and see if one fits
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high perch
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high perch
Why is the radius x squared
I'm still new to the concept and confused
I thought the radius was 1
timber karma
the radius is the function y = x
median vigil
the area of each disk is pi * r^2
high perch
Oh
high perch
the radius is the function y = x
I'm still confused
I thought the radius was the circle
This part
Is this part y = x?
Would that part be y = x but with 1 plugged in?
as x'
median vigil
it's a shape made out of stacking a bunch of circles on top of each other
each circle is at a position x, and its radius is also x
high perch
Oh I get it
Y is the height and the radius
I have to turn y in terms of x
Am I right?
Ok
So Y is pretty much the height and the radius here
But Y can be converted into X, so I have to turn y in terms of x right? for all values
Ik if i want to derive with x then I have to turn to x
Did I answer my own question?
I don't get this at all
high perch
it's a shape made out of stacking a bunch of circles on top of each other
Oh
I think I finally get it
.close
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dire idol
for question e and f is it necessary to factorise it then describe the transformation or both ways is ok
safe radishBOT
for question e and f is it necessary to factorise it then describe the transform...
earnest nacelle
not necessary to refactor the equations
both of them fit the form af(bx - c) + d precisely
dire idol
i rememebr theres situations where i have to factorise
can u plss giv eme an example i forgot
earnest nacelle
x^2 + 2x + 1 would be one of them
factors to (x+1)^2, so base function is f(x) = x^2
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dire idol
.reopen
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✅ Original question: #help-23 message
dire idol
@earnest nacelle sorry
what about question e i cant get the right answrer without factorising
earnest nacelle
why do you need to factor for e though? it's again in the form y = af(bx - c) + d
stiff magnet
Just alter the graph
earnest nacelle
!noping
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Please do not ping individual helpers unprompted.
dire idol
okok
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@dire idol Has your question been resolved?
dire idol
no 🙁
glass carbon
What is the problem?
What you need to do is identify transformations applied and apply them to coordinates
For e) you can rewrite it as y = -2f(2(x-2)) - 3
so here you have horizontal compression, horizontal translation about two units right, vertical stretch and reflection over x-axis, then finally translation about three units down
dire idol
For e) you can rewrite it as y = -2f(2(x-2)) - 3
Can i do without rewriting
dire idol
horizontal compression scale factor of 1/2, vertical compression scale factor of -2, horizontal translation of 4 and vertical translation of -3
@glass carbon is it right
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silent roost
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silent roost
not sure where to start forgot what all this meant
delicate shore
can you figure out the dimension of the space
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@silent roost Has your question been resolved?
silent roost
can you figure out the dimension of the space
sorry that i was afk
silent roost
can you figure out the dimension of the space
is the dimension just how many variables?
like 1 by 3 idk
delicate shore
Mate if you don't know what the word dimension means then I don't know how to help you
silent roost
it cant be that bad 😭
delicate shore
The question quite literally asks for the dimension of the space
silent roost
dimension like xyz
earnest nacelle
dimension is a number OP
delicate shore
The dimension of a vector space is the size of any of its bases
You should review what all the terms mean before you come back
silent roost
ok
prisma field
I'm stuck on the proof of this formulation of Dirichlet's approximation theorem in my number theory book (alpha, or just a - is irrational, p and q are whole, wherein 1=<q=<n, and n is natural). Online I've found formulations of the theorem where the RHS is 1/nq or 1/q^2, and those are proved by the pigeonhole principle and I understand the proofs.
However, this proof I don't understand - the book suggests that this result can also be proven by the pigeonhole principle by considering the fractional part of the irrational number {ma} for m ranging from 0 to n. Thus we get n+1 numbers (including 0) which are in the interval [0, 1). Then it simply states "And so by the pigeonhole principle it follows that two of them are at a distance less than 1/(n+1)". But how could this be? We have n+1 numbers (including 0), and they divide the section [0, 1) into n+1 parts - the amount of numbers and sections match, so where do we use the pigeonhole principle?
safe radishBOT
I'm stuck on the proof of this formulation of Dirichlet's approximation theorem ...
prisma field
I'm stuck on the proof of this formulation of Dirichlet's approximation theorem ...
Before the pigeonhole argument, the expression is reformulated to this (I forgot to send it, but I understand this part):
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peak estuary
if none are distance less than 1/(n+1) then all would have to be exactly distance 1/(n+1) from which you should be able to derive a contradiction probably
no wait, another off by one error. hmm
prisma field
Yeah, I was thinking if something forces them to line up to 1/(n+1), and so on, then it would be a problem since that's the remainder of an irrational number (so it can't be expressed as a fraction)
peak estuary
are we considering the distance on a circle?
so e.g. 0.9 and 0.1 would have distance 0.2?
prisma field
Well, later on they use the absolute value of the difference between the two fractions that are closer than 1/(n+1) being less than 1/(n+1)
So it should be on a line, since abs(0.9-0.1) can't be 0.2
If we find two numbers m2, m1, closer than 1/(n+1), then the proof goes on to say this:
And then we let p = m1 - m2, and q = (the part after a) and we're done
peak estuary
I feel like you should be able to adapt this and be able to consider the distance on a circle. but hmm thats certainly not what they meant
[x] means rounding down here, yes?
prisma field
yes, the whole part
On art of problem solving I can find this proof for the theorem, which is the same proof as in the textbook, except they claim it with only 1/n, instead of 1/(n+1)
or, no, actually, in the textbook they include 0 in the numbers in step 1, and then divide into n+1 intervals, so there is a difference
peak estuary
dividing [0,1) into N=2 subintervals of length 1/2 and having 2 numbers certainly does not guarantee that two are in the same subinterval
so that proof is also wrong
prisma field
Yeah, that's what I was thinking, if we test with small numbers, you need 3 numbers in the interval [0, 1) to guarantee distance <1/2
prisma field
If we find two numbers m2, m1, closer than 1/(n+1), then the proof goes on to sa...
perhaps if we do use an interpretation of a circle somehow, it works, but then I don't know how this last part will work out. If you know how this can be proven with adapting on a circle, please do share
peak estuary
difference of the fractional parts is the fractional part of the difference
thats certainly not true
if you are doing it on the circle you just need a bit more bookkeeping if your pair just decided to look like 0.9 and 0.1
for one of them you would have to round down and for the other up
something along those lines
I dont really want to work it out tbh
(well I'm hoping anyway that it works out. I could be wrong)
prisma field
for one of them you would have to round down and for the other up
Alright I'll see if it works out with this perhaps?
prisma field
> difference of the fractional parts is the fractional part of the difference
Well if 1/2 - 1/4 = 1/4, and the fractional part of 1/4 is 1/4, what's the issue there?
peak estuary
but its certainly weird that your textbook got it wrong. textbooks are usually better, at the very least for common proofs like this
1/4-1/2=-1/4
order is important
prisma field
oh, right
peak estuary
and they specified m<n but not {ma} < {na} which really is what they probably meant
all around thats not a good proof
prisma field
It's from this Bulgarian textbook "640 problems in number theory". It's useful for the problems, I guess, but the part where they teach the theory is sometimes difficult/lacking
Ok, so I'm thinking something along the lines of:
Since we are working on a circle (or, equivalently, on a line with a wrap-around at the end, which wraps back around to 0, so if we have 0.9, that's 0.1 away from 0 here), when we have n+1 intervals, we get that:
- the numbers 1/(n+1), 2/(n+1), ..., n/(n+1) also split the line in n+1 intervals
- If the fractional part of the irrational number is less than 1/(n+1), so {a}<1/(n+1), then the distance between {0a} and {1a} is less than 1/(n+1) and those are our selected numbers.
Otherwise: the fractional part must be greater than 1/(n+1) (it cannot equal it, since then the number wouldn't be irrational). This then means the intervals in which a splits the line are bigger than the interval with length 1/(n+1), then the last fractional part {nalpha} ends up in the interval from n/(n+1) to 1, which, because we are on a circle, means its distance to 0 is <1/(n+1)
This is how I imagine the second case (where the fractional part is bigger than the even split of the intervals)
prisma field
If we find two numbers m2, m1, closer than 1/(n+1), then the proof goes on to sa...
This would prove at least two numbers are at a distance less than <1/(n+1). In the first case (where we have the first number and 0), we can follow what's done in the book here, since the difference between them really is <1/(n+1).
I'm not certain what to do in the second case, since then, if I use the idea you suggested with floors/ceilings to adjust for the fact we're on a circle, the floor of {na} becomes just 0, which is our second number, and so we don't get two distinct numbers for the |(m1-m2)a - [m1a] + [m2a]| part
prisma field
This is how I imagine the second case (where the fractional part is bigger than ...
Plus I'm not sure if this can be considered a general case for the fractional part being bigger than >1/(n+1), since a part of that is the possibility of the fractional part {a}>2/(n+1), at which point remainders wrap around the line and we certainly need different reasoning than the distance from 0
peak estuary
the whole point is that the fractional parts will be somewhat randomly on the interval
we really cant say anything about where they are
just go and compute the fractional parts of {m sqrt2} and see where they end up. it looks somewhat random (of course it isnt technically but whatever)
prisma field
just go and compute the fractional parts of {m sqrt2} and see where they end up....
Yeah, I see that
prisma field
Since we are working on a circle (or, equivalently, on a line with a wrap-around...
So this isn't the right approach, I reckon? What could be?
safe radishBOT
@prisma field Has your question been resolved?
safe radishBOT
@prisma field Has your question been resolved?
prisma field
Right now I'm trying to go through this proof:
At the bottom it quite literally says the lighter version of the approximation theorem with 1/n instead of 1/(n+1) can be proved more easily with the pigeonhole principle (so I'm guessing that implies the version with 1/(n+1) can't)
But again, the proof simply states probably the most important part "Since the
n+2 numbers 0, r_a, 1, all lie in the same unit interval, some two of them differ (in absolute value) by at most 1/(n+1)" without showing why, and I can't understand why that must be true
safe radishBOT
@prisma field Has your question been resolved?
peak estuary
But again, the proof simply states probably the most important part "Since the
...
well now we have n+2 values so everything works out
also now we only care about <=, not <
safe radishBOT
@prisma field Has your question been resolved?
fervent bane
What is a general way to solve thses kind of questions like f)?
safe radishBOT
What is a general way to solve thses kind of questions like f)?
buoyant shadow
wait what
buoyant shadow
the first number they give is always useless
honest perch
is x=-4.8 vertical or horizontal?
fervent bane
I'd assume horizontal since its x
fervent bane
udersrtand what?
honest perch
use a graphing calculator if u want to help u learn
fervent bane
i dont have one
fervent bane
wait is this really neccassary tho?
honest perch
i think this is the best way to learn
fervent bane
Surely theres a different way. Im in Year 10 and they never mentioned anything abt graphic calcs
I got y=3 for e
the previous one isnt that correct?
honest perch
the smart people u know who get these questions visualize the graph in their head
honest perch
I got y=3 for e
yeah this is correct
fervent bane
the smart people u know who get these questions visualize the graph in their hea...
whaaat??
ok wait
im picking up on a trend here based on the previous answers
would f be y=-3?
bcs of the y cord it passes?
fervent bane
i acc dont know the reason but its based on the pattern from other questions
honest perch
would f be y=-3?
mhm
fervent bane
ok so can you explain how that would be?
fervent bane
I got y=-2/3x + 4/3
safe radishBOT
I got y=-2/3x + 4/3
fervent bane
yet the correct answer is just tweaking the y-intercept to 5/3
I'm not sure what I did wrong, they looked perpendicular in hindsight
my graph btw
.close
safe radishBOT
safe radishBOT
Available help channel!
fringe dock
safe radishBOT
fringe dock
i dont understand why he crosses out the value of k = -1 as it "diverges"
but doesnt it get smaller and smaller
-1, -2, -9
like that's getting smaller
peak estuary
but it goes towards -infinity
it needs to get smaller in absolute value
if thats what you mean
properly you really should compute the common ratio in both cases
and check whether |common ratio| < 1
fringe dock
it needs to get smaller in absolute value
so it just gets bigger and bigger because if i take absolute value of each it should look like:
1, 3 , 9
fringe dock
and check whether |common ratio| < 1
oh yeah
that makes sense
the person didnt explain that part
so i was a lil confused
peak estuary
but well you can read off the common ratio from the first two terms
for 5,3,9/5 its clearly 3/5 with |3/5| < 1
and for -1,-3,-9 its 3
west bramble
can anyone help
safe radishBOT
can anyone help
hard crest
well now solve for x
buoyant shadow
this is 4
buoyant shadow
the idea is you find something that works
west bramble
since that's the sq of two
buoyant shadow
and you assume that nothing else works
west bramble
the idea is you find something that works
ion understand 😭
burnt notch
why can't i post answers smh
!noans
safe radishBOT
why can't i post answers smh
The purpose of this server is to help you learn; please don't ask for direct answers. Ask for guidance, explanations, or feedback instead.
hard crest
$\sqrt{2\sqrt{2\sqrt{\dots}}} = x$
$\sqrt{2x} = x$
flat frigateBOT
schrödinger's kitten
hard crest
see how i replaced a copy of the expression with x
winter whale
Genius
west bramble
**schrödinger's kitten**
is x 1.414
west bramble
see how i replaced a copy of the expression with x
yeah
hard crest
no, use your algebra and figure it out
winter whale
Petition to just start giving answers to people without explaining anything
hard crest
i see a very annoying square root, how do you get rid of square roots
hard crest
seems right to me. now.... its a little unclear how to decide which one but which one makes more sense to you? or do they both seem reasonable?
considering the original problem
west bramble
seems right to me. now.... its a *little* unclear how to decide which one but wh...
feel like its 2
hard crest
yeah, 0 doesn't really make sense
safe radishBOT
safe radishBOT
Available help channel!
rich dawn
Five balls are placed at random in five buckets. What is the probability that each bucket
has a ball?
safe radishBOT
Five balls are placed at random in five buckets. What is the probability that ea...
open wedge
Five balls are placed at random in five buckets. What is the probability that ea...
!status
safe radishBOT
Five balls are placed at random in five buckets. What is the probability that ea...
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
yeah but i dont know how to find the total number of scenarios
brave wolf
I'd try to imagine placing the balls one by one instead, then there'll be more than 1 valid scenarios, but it will be easier to count
floral yew
Five balls are placed at random in five buckets. What is the probability that ea...
first find the total cases for your question
rich dawn
first find the total cases for your question
yes but how do i go about finding that
brave wolf
yes but how do i go about finding that
How many options do you have for the first ball? For the second ball? ...
floral yew
think how many choices does each ball have?
rich dawn
think how many choices does each ball have?
5
rich dawn
ah 5^5 ?
floral yew
yeah
rich dawn
ahhhh okay so its 1/(5^5)
open wedge
,calc
flat frigateBOT
open wedge
ahhhh okay so its 1/(5^5)
Nope not 1
floral yew
ahhhh okay so its 1/(5^5)
no
open wedge
,calc 5^5
flat frigateBOT
Result:
3125
wait does it matter if ball A goes int bucket 1 rather than ball B going into bucket 1
open wedge
These 5 balls are different
open wedge
wait does it matter if ball A goes int bucket 1 rather than ball B going into bu...
Yes it matters
rich dawn
ah okay got you
open wedge
So as @brave wolf said, there would be more than 1 valid scenario
rich dawn
so is it 5! / (5^5)
floral yew
does your question state the condition as each box has to have "atleast" one ball or what?
open wedge
does your question state the condition as each box has to have "atleast" one bal...
I mean, there's 5 balls, 5 buckets, what do you expect?
brave wolf
does your question state the condition as each box has to have "atleast" one bal...
that'd mean the probability would be 1, which is probably not what they want
rich dawn
does your question state the condition as each box has to have "atleast" one bal...
okay guys thank you very much for your help
open wedge
I mean, there's 5 balls, 5 buckets, what do you expect?
Each bucket must have exactly 1 ball or there would be at least 1 empty bucket
rich dawn
.close
safe radishBOT
covert jungle
I mean, there's 5 balls, 5 buckets, what do you expect?
lol true, what if the balls were identical instead, how would you go about counting those scenarios
open wedge
lol true, what if the balls were identical instead, how would you go about count...
same fucking thing
covert jungle
same fucking thing
prob is the same but counting scenarios uses stars and bars, what's the total then
safe radishBOT
Available help channel!
mighty cairn
why does constructive interference of electrons leads to increase in probability of finding an electron between the two nuclei for bonding molecular orbitals and why does destructive interference cause the electrons to be outside the two nuclei??
safe radishBOT
why does constructive interference of electrons leads to increase in probability...
mighty cairn
gpt gave me the explanation that the cross term in the addition of psi a and psi b whole squared leads to them being in between the nuclei
safe radishBOT
safe radishBOT
✅ Original question: #help-23 message
safe radishBOT
@mighty cairn Has your question been resolved?
white pebble
Hello guys, i need help on how to do this task especially where do i even start. The task is translated from german, so its hopefully understandable. Its e)
safe radishBOT
Hello guys, i need help on how to do this task especially where do i even start....
long copper
Hello guys, i need help on how to do this task especially where do i even start....
you integrate growth speed (velocity/speed) to get growth height (displacement/distance)
with respect to time
and you can use the g=120 at t=2 thing to find out what the +c is if that makes sense
$\int v(t) \dd t = g(t)$
flat frigateBOT
I can't believe you've done this
white pebble
oh i need integrals for this?
long copper
yes i believe so
white pebble
what do i input at the top and bottom of the integrals? 0 and 2 ?
long copper
no top or bottom because youre only finding the function
you will get something like $g(t) = at^3 + bt^2 + ct + d$ and you get $a, b, c$ from doing the integral and use $g(2) = 120$ to find $d$
flat frigateBOT
I can't believe you've done this
long copper
that last bit is from the part where it says when t = 2 the plant is 120 cm tall
white pebble
okay imma try
wait
now i got g(t) and now input 2 in g(t) ?
so i gotta do a2^(3)+b2^(2)+c*2 + d and that has to add up to 120 or what?
so the part without d (a2^(3)+b2^(2)+c*2) is 104.67 which means i gtg 120-104.67, so d is 15.33?
long copper
so the part without d (a2^(3)+b2^(2)+c*2) is 104.67 which means i gtg 120-104.67...
yeah sounds right to me
white pebble
yeah sounds right to me
but whats the end result then
long copper
if you want to double check you can differentiate and see if u get v(t)
long copper
but whats the end result then
just the expression but with a b c and d in it
write out g(t) thats the answer
white pebble
oh
white pebble
if you want to double check you can differentiate and see if u get v(t)
wym differentiate, how
long copper
wym differentiate, how
like check $\frac{\dd}{\dd t} \left(g(t) \right) = v(t)$
flat frigateBOT
I can't believe you've done this
white pebble
**I can't believe you've done this**
wait it isnt
60 != 50
oh wait
huh
it should be 60 and 50
which means its wrong?
merry owl
which means its wrong?
share what your g(t) is
safe radishBOT
@white pebble Has your question been resolved?
safe radishBOT
@white pebble Has your question been resolved?
ionic spear
This is a simple question: In a geometry exercise, if I have got 4 different points in a 3 dimensional space. Can I justify if between the four of them there is a plane by calculating just two vectors (that include all the points, such as vector AB and CD) and cheking if they are linearly dependent?
safe radishBOT
This is a simple question: In a geometry exercise, if I have got 4 different poi...
brave wolf
This is a simple question: In a geometry exercise, if I have got 4 different poi...
Not really?
that'd be much stronger condition than just being in one plane
If two vectors are linearly dependent, they are parallel
covert jungle
This is a simple question: In a geometry exercise, if I have got 4 different poi...
parallel vectors work but they could also just intersect and be coplanar
ionic spear
And i could see if they are part of a plane in some way, but using just two?
brave wolf
You'd have to known both the vectors and their position
from the vectors alone, it cannot be determined
Easy way to see this imagine shifting the vectors - you can always shift them in a way that makes them lie in a common plane
ionic spear
I understand
timid ridge
do you need to use 4 points? whats this for
ionic spear
I need the "spatial" position of both
timid ridge
what does that mean
don't you have the "start points" of the vectors?
its just one of the points
covert jungle
And i could see if they are part of a plane in some way, but using just two?
to check for a plane you usually need three vectors from one point like AB AC and AD
brave wolf
I think it'd be easier to choose one point A, and then compute the vectors AB, AC, AD and check whether those are LD (for example by putting them in a 3x3 matrix and checking whether the determinant is 0)
ionic spear
do you need to use 4 points? whats this for
This can be used to make shapes, for example to build a parallelepiped with the vectorial product
ionic spear
to check for a plane you usually need three vectors from one point like AB AC an...
I know, I wandered if could function with just two
brave wolf
I know, I wandered if could function with just two
you cant, not enough info unfortunately
daring sluice
know if you want to know if points are coplaner or not you could use the volume of parallelepiped formula if you get a volume of zero then the points are coplaner
ionic spear
I think it'd be easier to choose one point A, and then compute the vectors AB, A...
But they wouldnt be LD bc they arent parallel, no? I confused with your first reply
daring sluice
as i remember it only work to check three points
brave wolf
But they wouldnt be LD bc they arent parallel, no? I confused with your first re...
that was for 2 vectors
2 vectors are LD iff they span the same line iff they are parallel
ionic spear
that was for 2 vectors
I understand it
brave wolf
3 vectors are LD iff they span the same plane iff they are coplanar
4 vectors are LD iff they span the same 3-space iff they are cospatial ig
...
ionic spear
cool
brave wolf
ill try drawing a pic
these vectors are clearly not parallel (so not LD), and yet the points are coplanar
they'd be parallel only if your points formed a parallelogram / trapezoid
but if they are parallel, you can conclude coplanarity
daring sluice
isnt the volume of the parallelepiped formed by any combination of these points vectors equals to zero?
brave wolf
isnt the volume of the parallelepiped formed by any combination of these points ...
if you take any 3 of the vectors, then yeah
if you take only 2 of them, then it doesnt make sense to talk about parallelepiped formed by them
brave wolf
what are we even proving? 
ionic spear
That with two vectors we cant confirm if 4 points are coplaner
brave wolf
Oh, well, here is an example of 2 of these vectors, and the points are coplanar
imagine taking one of those vectors with its points and shifting it back behind the plane
the vector doesnt change, but suddenly the 4 points wont be coplanar anymore
this proves that the 2 vectors cannot be enough to determine whether the points are / arent coplanar
daring sluice
but arent they coplaner if the two vectors are parallel?
covert jungle
this proves that the 2 vectors cannot be enough to determine whether the points ...
nice explanation, also looks like your latex had a stroke lol
brave wolf
i didnt do any latex 
ionic spear
the vector doesnt change, but suddenly the 4 points wont be coplanar anymore
I suddenly catched it very much clearly
brave wolf
but arent they coplaner if the two vectors are parallel?
If the vectors are parallel, then the points are coplanar
but if the points are coplanar, the vectors are not necessarily parallel
it's just a one way if, not iff
ionic spear
we need the third bc is the one that confirms that the two other vectors are in the same plane
safe radishBOT
covert jungle
I close it then?
yeah if you're clear on it now you can close it
safe radishBOT
Available help channel!
crude oar
Hey!
Im on a minecraft community which had a competition to win rewards!
The Competition is now over and the owner said we're allowed to ask around for quiz answers but he wtill wont tell himself since uhh he wants us to learn how.
Here is the full section of it
crude oar
Please ping me on every response since I have notifs disabled!
normal moss
What good does pinging do then
timid ridge
Please ping me on every response since I have notifs disabled!
please tell me you know the first answer
crude oar
please tell me you know the first answer
20 😭
crude oar
What good does pinging do then
It say "1" next to the server
timid ridge
why is this quiz about search for a world that doesnt exist
also just lowk look up the probability of grass tick online
i also dont think its a set probability
mortal sandal
These are just questions about Minecraft mechanics lol
mortal sandal
Well some of the questions rely on math but you can't solve them without answering the other questions first which are just about Minecraft mechanics
crude oar
Well some of the questions rely on math but you can't solve them without answeri...
true
someone here gotta know mc mechanics
ik some
but not probability
not fully
im still learning
statistics gcse
timid ridge
bud the owner just put you on a rabbit chase
crude oar
bud the owner just put you on a rabbit chase
?
crude oar
bud the owner just put you on a rabbit chase
so u know where the vid originates from?
timid ridge
it's all scripted
crude oar
yeah wifies
timid ridge
so like what's the point
crude oar
a manager on wifies' server made this
i doubt they're trolling
they even exteneded time
cuz most ppl got wrong
timid ridge
the second question is already written in such a vague way
as i said the tick probability has so many factors
and since the rest of the questions seem to be based off of jt
how would you solve it
covert jungle
and since the rest of the questions seem to be based off of jt
actually @crude oar earlier @dreamy hazel mentioned that cot-csc term, q45 is just reverse product rule for f(t)csc(t)
timid ridge
what
crude oar
I mean I don't have full context idk if this is the same question
I don't think so
dreamy hazel
yeah actually I scrolled up and im confused lol
what does this have to do with that other question
crude oar
Hey!
Im on a minecraft community which had a competition to win rewards!
The C...
mines to do with this
crude oar
Hey!
Im on a minecraft community which had a competition to win rewards!
The C...
HEre is more info:
Description
in wifies' recent video (i strongly apologize if i spoil it for you but if you're here and still haven't watched the video, what are you doing??), d3rlord places a grass block next to a dirt block and uses it to determine if an entity has loaded the chunk while he was gone.
we will ignore the fact that this fact is wrong, and pretend that render distance is the deciding factor. #865224345379012618 message
in the video, he realizes that the grass block has grown after 90 seconds of it being loaded. assume this value is correct, you do not need to check the video.
there is surprisingly little documentation online about how grass spreads in Minecraft. from decompiling the code, I obtained:
if a grass block is chosen to be randomly ticked, then it will pick 4 blocks that can be at most:
1 block away on the x/z axes, and
3 blocks downwards or 1 block upward on the y axis.
these are not necessarily distinct, and can also be the grass block itself.
4 conditions are checked (that can be found on the wiki, and for the purposes of this question, we can consider them insignificant), and if all 4 are true, and if the chosen block is a dirt block, it will turn into grass.
basically, the block picking occurs first, and then it is checked if the picked block is dirt. dont mix this up!
timid ridge
what about the 3 block ticks per chunk per second
covert jungle
what about the 3 block ticks per chunk per second
it's actually 3 ticks per sub-chunk per game tick, so 60 per second usually
safe radishBOT
@crude oar Has your question been resolved?
timid ridge
alternatively just run 10 million simulations of a subchunk and find the probability
safe radishBOT
@crude oar Has your question been resolved?
safe radishBOT
@crude oar Has your question been resolved?
bold plank
guys
vague steppe
im so bad at maths
burnt notch
im so bad at maths
!redir
safe radishBOT
im so bad at maths
This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.
glacial cairn
can someone explainn
,, a > b \implies a^2 > b^2
flat frigateBOT
Nel
glacial cairn
Do you agree with this, when both a and b are positive?
glacial cairn
!done
safe radishBOT
If you are done with this channel, please mark your problem as solved by typing .close
sharp tangle
Well $18 - 2 = 16$, $35 - 19 = 16$, $42 - 26 = 16$. What can you do with this information?
flat frigateBOT
Ajay
safe radishBOT
@bold plank Has your question been resolved?
indigo scaffold
-2 sin (x+1) -1
safe radishBOT
-2 sin (x+1) -1
obsidian oracle
what are you trying to find?
obsidian oracle
-2 sin (x+1) -1
The max and min of this function?
quiet plume
It's correct now.
safe radishBOT
safe radishBOT
Available help channel!
clever karma
e^(5-2x)=2
safe radishBOT
e^(5-2x)=2
empty gyro
e^(5-2x)=2
!status
safe radishBOT
e^(5-2x)=2
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 dont even know how to conceptually start ths
empty gyro
1 i dont even know how to conceptually start ths
Are you familiar with logarithms?
clever karma
like i dont get logs and ln and e
empty gyro
like i dont get logs and ln and e
A logarithm just undoes an exponent.
By definition, $\log_a a^b=b$
flat frigateBOT
SWR
empty gyro
Also by definition, $\ln x$ is just $\log_e x$
flat frigateBOT
SWR
empty gyro
It's just a number
clever karma
im sorry i get that ln is log base e but is there anything just e is equal to?
empty gyro
$e\approx 2.71..$
flat frigateBOT
SWR
clever karma
so how would i begin to solve that e^5-2x=2
empty gyro
,calc e
flat frigateBOT
Result:
2.718281828459
flat frigateBOT
SWR
empty gyro
so how would i begin to solve that e^5-2x=2
Try undoing the e exponent
clever karma
how do i do that
im sorry i dont even understand a little bit of e
m teacher taught it pretty badly
flat frigateBOT
SWR
clever karma
i dont thin my teacher wants me to solve for x as is e equaled to a number
like im supposed to change it to ln and simplify as much as i can
but i dont understand how to turn it into ln or simpkify it
empty gyro
i dont thin my teacher wants me to solve for x as is e equaled to a number
you do want to solve for x
empty gyro
but i dont understand how to turn it into ln or simpkify it
There's a rule with logarithms: If $a=b$, then $\log_c a=\log_c b$
flat frigateBOT
SWR
empty gyro
That is, you can take the log of both sides of an equation, and the equality remains.
empty gyro
You literally just write$\log_a e^{5-2x}$, but you need to decide what base you want $a$ to be.
flat frigateBOT
SWR
empty gyro
can i js do log base 10
You can, but that would be a little hard to work with
clever karma
oh shoot really i was just taught to default ten
whats the bbest base to choose?
oh wait
log base e of e?
empty gyro
exactly
clever karma
okay so it would become log base e of e^5-2x=log base e of 2
empty gyro
okay so it would become log base e of e^5-2x=log base e of 2
Yes
clever karma
so what do i do fromthere
empty gyro
so i can do lne^5-2x=ln2
Yes
clever karma
what do i do from there?
empty gyro
simplify $\ln e^{5-2x}$
flat frigateBOT
SWR
empty gyro
A logarithm just undoes an exponent.
👆
clever karma
wait so like do i have to put it into exponential form
empty gyro
wdym?
empty gyro
yes
empty gyro
yeah
clever karma
so its 5-2x=ln2
so its ln2-5/-2
omg ur a savior
a literal savior
like a goat
my goat
safe radishBOT
clever karma
.reopen
safe radishBOT
✅ Original question: #help-23 message
empty gyro
how would u go abt solving ln(4x+7)=4
exponent undoes logarithms
That is, $a^{\log_a b}=b$
flat frigateBOT
SWR
flat frigateBOT
SWR
clever karma
why dos ln become an exponent
empty gyro
But, incidentally, they're both equal to 4x+7
clever karma
like how does ln just become e to the power of ln
empty gyro
why dos ln become an exponent
We take advantage of another rule: If $a=b$, then $c^a=b^a$
flat frigateBOT
SWR
flat frigateBOT
SWR
empty gyro
So, if $\ln{4x+7}=4$, then $e^{\ln{4x+7}}=e^4$
flat frigateBOT
SWR
clever karma
okay wait so my a=ln4x+7, my b=4
and i can choose anything to be my c?
in this case e?
or is e chosen as the c for a specific reason
empty gyro
okay wait so my a=ln4x+7, my b=4
$a=\ln{4+7}$, not just $4x+7$
flat frigateBOT
SWR
clever karma
so if it has ln in it you always change the base to e
empty gyro
or is e chosen as the c for a specific reason
e is chosen specifically to get rid of the natural log
clever karma
**SWR**
okay so once we getthis
bc they have the same base we can just do 4x+7=4?
okay so i feel like thats not right when doing that i got -3/4, but the answer is (e^4-7)/4
okay wait ln and e cancel out so it would become 4x+7=e^4
empty gyro
looking good
clever karma
so for like ln(x+1)=3 the first thing to do is make both e
also thx i finshed that problem! :-)
so it would be e^lnx+1=e^3
and e and ln cancel out so x+1=e^3
also it if it says find the solution of each equation correct to four decimal places i can use a calc righ
empty gyro
yes