If a times b yields a positive value, what are the possible values (positive/negative) for a and b?
#help-36
versed cargo
ebon sigil
Both minus and both plus..?
ebon sigil
I'm in a bit of thought
versed cargo
you also need to solve x<0, x-3<0
ebon sigil
I see
versed cargo
And find their intersection
ebon sigil
Look at the answers not language. Is the last answer it? Because it includes the negative but how could 3 and 0 be answers
The last question
Is the one I'm solving
versed cargo
you also need to solve x<0, x-3<0
What did you get by solving this?
versed cargo
Why did you include (0;3)?
ebon sigil
Hold on let me process this ofc why did I
But the next thing in my mind also isn't in the answers
It's less and more than 0, not 4
versed cargo
Hold on
ebon sigil
But bigger than 4...
versed cargo
From both numbers are positive case you should get x>3
x<0 for negative
ebon sigil
So I don't need to put x<3
versed cargo
Yes, cuz you only include the intersection
ebon sigil
It isn't in my next theory too tho, since x belongs in less than 0 and more than 0 I just dropped it
I got only with the 4 but there isn't such answer
versed cargo
Do you perhaps know russian?
versed cargo
I advise you to learn how to solve inequalities
versed cargo
But do u know the answer? It'll help me find how the equation is solved
Yes it's D)
I mean Г
ebon sigil
What do you mean by this
Make it into a graphic with the lines
I don't
I find it hard a lot
main mirage
What do you mean by this
Like, the shape of the graph y = x^2 looks like this:
,w graph y = x^2
soft zealotBOT
ebon sigil
How do I read it
If y is this number then x is that number
Therefore why the arch
If y is 0 then x is 0
main mirage
Well if you are trying to solve the inequality x^2 - 3x > 0, this is essentially asking us when the graph of this function is above the x axis. So, you can just read that by looking at the given graph.
Although if you don't know how to graph functions, then this isn't really useful advice.
The alternate strategy you can use is to use the sign test which I think is what you were trying to use in your question. You have the equation:
y = x^2 - 3x
And you know it has roots at x = 0 and x = 3.
That means in order to solve x^2 - 3x > 0, you need to find where this expression is positive and negative.
ebon sigil
X=0 is a game changing knowledge rn I was just thinking this
main mirage
I.e, it will look something like a numberline.
main mirage
I.e, it will look something like a numberline.
We want to check whether x^2 - 3x is positive below 0, between 0 and 3, or after 3.
So, is x^2 - 3x positive or negative when x is between 0 and 3?
ebon sigil
So besides x^2-3x bigger and lower than 0, it can also equal?
ebon sigil
We want to check whether x^2 - 3x is positive below 0, between 0 and 3, or after...
Thinking rn
main mirage
So besides x^2-3x bigger and lower than 0, it can also equal?
Yeah, it can equal 0.
ebon sigil
Positive but why does this matter
main mirage
Although, the important fact we are trying to find is where it is positive or negative.
main mirage
Positive but why does this matter
We're solving for x^2 - 3x >= 0 right?
ebon sigil
Yes
main mirage
This question is literally asking us - where is this function positive?
And so, that's what we are doing - we are looking for where it is positive.
ebon sigil
WAIT X IS BIGGER AND EQUAL THAN 3 THEREFORE WHY 3 IS ALSO AN ANSWER
main mirage
WAIT X IS BIGGER AND EQUAL THAN 3 THEREFORE WHY 3 IS ALSO AN ANSWER
Wait wait, this is true - but I want to make sure you understand why.
ebon sigil
Like I'm a bit in a hurry rn and I won't be able to log in back
ebon sigil
Wait wait, this is true - but I want to make sure you understand why.
I will look at it myself I promise u I'll find out why
main mirage
hmm okay, well perhaps it is better if you review inequalities another time. However, consider this:
Give me a random number that is bigger than 3
ebon sigil
hmm okay, well perhaps it is better if you review inequalities another time. How...
5
It can't be 4
In my case
main mirage
I will look at it myself I promise u I'll find out why
I'll leave this here for when you come back:
If you have a random number such as x = 5 and you plug it into the equation, you get:
(5)^2 - 3(5) = 10
So clearly, when x is bigger than 3, the equation is positive.
That means if we take the interval from when x > 3, we know that the equation x^2 - 3x is positive.
So the way to go is, you mark this region (where x > 3), with a positive symbol. Now, what you need to do is pick another random number from each region, and see whether it is positive or negative.
ebon sigil
2
main mirage
Good! What happens when you put x = 2 into the equation x^2 - 3x?
main mirage
And if it's 3 it's 0 so how is 3 also an answer
Because we are solving for x^2 - 3x >= 0, so we are actually including the roots.
ebon sigil
OHHH because earlier we said x=0
main mirage
This makes sense because the square root of 0 is ... 0! So it's perfectly fine.
main mirage
ebon sigil
Thank you so much
main mirage
Good! So, when x > 3, x^2 - 3x is positive.
When x is between 0 and 3, x^2 - 3x is negative.
How about that last interval?
ebon sigil
Like below 0?
main mirage
Amazing.
main mirage
main mirage
So everything in the plus regions is an answer
Exactly! We are trying to solve for when x^2 - 3x >= 0, so everything that's positive or zero is part of our answer.
So, now, let me ask you - where is x^2 - 3x >= 0?
ebon sigil
Like where x belongs?
main mirage
Like where x belongs?
Yep.
ebon sigil
Everywhere between negative infinity and(plus)3, from 3 to 4, and from 4 to positive infinity
main mirage
Just like soley based on this image
ebon sigil
Haha
main mirage
Where would x^2 - 3x >= 0 based on the diagram?
main mirage
I gotta go
No worries :) Cya!
main mirage
Everywhere you've marked with +
When you come back - yep! But, how would you say "everywhere you've marked with +" in terms of a mathematical statement?
ebon sigil
I have no idea tbh
main mirage
I have no idea tbh
Well, can you give me a sentence on how you would write my diagram?
Like, for example, the + sign on the right. What does that mean?
final saddleBOT
@ebon sigil Has your question been resolved?
next thorn
. @severe flower send your work here! preferably the one we jsut discussed.
.I need to study myself so perhaps others can assist you!
severe flower
final saddleBOT
https://media.discordapp.net/attachments/1443779983096025138/1443887299476852787...
raven marsh
Greetings.
raven marsh
https://media.discordapp.net/attachments/1443779983096025138/1443887299476852787...
Could you tell me your progress?
severe flower
Could you tell me your progress?
car said
raven marsh
Your first equation is wrong
severe flower
@next thorn
next thorn
<@858810915663511553>
yes?
next thorn
the first equation is very wrong, let @raven marsh walk you through it!
severe flower
Balancing
severe flower
x+y = 35
y=4x
for x and y?
raven marsh
x+y = 35
y=4x
for x and y?
Indeed.
raven marsh
So 35 = 4(y)
x + y = 4y?
bold turtle
Do you know how substitution works?
severe flower
Yes
bold turtle
To whom is that directed?
severe flower
Do you know how *substitution* works?
This
raven marsh
@severe flower Bro answer me please
raven marsh
So you are saying 5x = 12x?
Is this what you are saying
Because it follows from your logic
bold turtle
You've _just_ said that y = 4x
If you're substituting using this, then that means wherever you see "y", you replace with "4x"
raven marsh
what video now
raven marsh
My solutions are correct
bro what solution did you get
next thorn
ok
raven marsh
next thorn
he's trolling
raven marsh
Is this a joke
next thorn
😭
bold turtle
Man's watching an INTEGRATION video for this?
raven marsh
Nono
One sec
@severe flower i think this is a good starter excercise
To solve your original problem
You could try this as a prerequisite
severe flower
Try that?
severe flower
I don't know where to begin
next thorn
the last time i thought someone was trolling they were just young
next thorn
ill assume you lied to me about your native language being english and delusionally give you the ebenfit of the doubt.
next thorn
https://m.youtube.com/watch?v=aO4PPaqYG4Q&pp=ygUYdGhlbWF0aHNvcmNlcmVyIGludGVncmF...
how was this of relevance to what you just did?
to the question
to your logic
next thorn
why did you send an integration video?
bold turtle
If you're substituting using this, then that means wherever you see "y", you rep...
[COUGH]
bold turtle
yes, mach weiter
-# yes, continue
next thorn
So, x + 4x = 35?
actually yeah.
proven radish
right
severe flower
x + 4x = 35
x = 35
plucky rover
...no
plucky rover
...both sides?
plucky rover
Where are these both sides you speak of
bold turtle
Are these both sides you speak of in the room with us?
You have ONE lot of something, and you add it to FOUR lots of something; how many lots of something do you have?
severe flower
5
next thorn
5x = 35
x = 7
FIRE
bold turtle
next thorn
can you get y now?
severe flower
Answer is 7?
proven radish
Answer is 7?
x is 7
next thorn
...?
proven radish
?
severe flower
Can he be trusted?
bold turtle
No, because he "has bald head"
polar agate
irrelevant to discussion, and his later vids are 50-50, but his math-related stuff are ok.
next thorn
Can he be trusted?
you cant trust a calculus video about algebra 1!!!!!
proven radish
right
next thorn
perfect! now for clarity, say
"the first number is 7"
"the second number is 28"
oy you dont really have to if you named them x and y
severe flower
severe flower
next thorn
idk what you
proven radish
woah woah
bold turtle
No shit
severe flower
I thought u meant from online.
next thorn
bold turtle
What the fuck else would he have meant.
next thorn
what did you do here and what was your brain process?
severe flower
This is correct
bold turtle
This is not correct
That it might not be true is something you are told; you get no marks for asserting as much.
The marks come from the demonstration itself that this might not be true
polar agate
writing "could be" without reasoning is a special branch of post-graduate math known as vibe mathing. do not do that.
bold turtle
"it" being...?
next thorn
writing "could be" without reasoning is a special branch of post-graduate math k...
did he even do anything that is relevant to the question? I dont even understand his logic or what he is trying to get to
bold turtle
Because that's NOWHERE in the question
polar agate
did he even do anything that is relevant to the question? I dont even understand...
my friend, i called it vibe mathing for a reason
bold turtle
"Anthony bought some apples. Explain why they could still cost him £10"
"Because he may have bought bananas instead, and bananas are more expensive than apples"
This is exactly the same logic on display here
bold turtle
No
next thorn
.
bold turtle
You don't "get mark"
severe flower
1/2
raven marsh
wait bro can you like take this a bit more seriously @severe flower
were trying to help you please dont waste our time
next thorn
if im the examiner, this scores a "?"
raven marsh
thanks
bold turtle
It's a FACT in my example that Anthony bought apples; you saying that he bought bananas instead directly contradicts this fact.
In much the same case, Ben's H:M ratio is 5:1, and this is stated as fact
polar agate
anyway, does OP know what a ratio is?
bold turtle
You cannot then claim that it could be 4:2
next thorn
You cannot then claim that it could be 4:2
oh yes, you CANNOT add and substract numbers from a ratio, 5:1 ISNT equivalent to 4:2.... what did you do? add and substract one? that doesn't work with ratios.
final saddleBOT
@severe flower Has your question been resolved?
next thorn
@severe flower
he has promised to be professtional and serious from now on
and would like his work checked on these problems
next thorn
<@1148521630864257054>
you may stop dming me now ❤️
steep hatch
.close
final saddleBOT
steep hatch
@severe flower you have been timed out for DM behaviour and trolling. DM modmail if you’d like more detail
final saddleBOT
Available help channel!
barren pebble
a,b,c≥0. ab+bc+ca>0. Prove that:
final saddleBOT
a,b,c≥0. ab+bc+ca>0. Prove that:
barren pebble
Let (x,y,z)=(1/a,1/b,1/c) and (p,q,r)=(x+y+z,xy+yz+zx,xyz) then we need to prove f(q)=(p³+r³)q+p²r(3-4r)≥0
But it's linear in q so the minima is reached when 2 of the variables are equal
That's what i've got so far
final saddleBOT
@barren pebble Has your question been resolved?
barren pebble
<@&286206848099549185>
barren pebble
Let (x,y,z)=(1/a,1/b,1/c) and (p,q,r)=(x+y+z,xy+yz+zx,xyz) then we need to prove...
So basically I now have to prove (x²+2xy)+1/(x²+2xy)²≥(4-3x²y)/(2x+y)
For x>0, y≥0
proven radish
a,b,c≥0. ab+bc+ca>0. Prove that:
apply am hm to ab, bc, ca
ull get sm relations whichll help but not directly solve the qn
barren pebble
I don't think they're strong enough
barren pebble
You mean ab+bc+ca≥9/(1/ab+1/bc+1/ca)?
proven radish
You mean ab+bc+ca≥9/(1/ab+1/bc+1/ca)?
1/a +1/b + 1/c should b written there instead of 1/ab+1/bc+1/ca
rest all what uve written is right
barren pebble
Also i've tried Schur's and other strong inequalities. I literally used EV above too
It's not as simple as just classical inequalities
barren pebble
So basically I now have to prove (x²+2xy)+1/(x²+2xy)²≥(4-3x²y)/(2x+y)
This is where's im at after applying Tej's Theorem (q-lemma)
proven radish
This is where's im at after applying Tej's Theorem (q-lemma)
then ill take my leave
barren pebble
I appreciate your intent to help btw, thanks
proven radish
tis all which u js said isnt comprehendable to me at my curent lvl of math
barren pebble
tis all which u js said isnt comprehendable to me at my curent lvl of math
Tej's theorem is the one about symmetric 3 variables functions
Usually used in uvw-method too if you're more familiar with that maybe?
proven radish
Usually used in uvw-method too if you're more familiar with that maybe?
nvm mate
continue
i only know am gm hm ineq n a bit of cauchy nothing else so
barren pebble
All good man
final saddleBOT
@barren pebble Has your question been resolved?
final saddleBOT
@barren pebble Has your question been resolved?
barren pebble
.close
final saddleBOT
final saddleBOT
Available help channel!
bronze grove
yo
bronze grove
that will be an example tho
versed crater
Yes but the example tells you what the idea is
You asked how to start these kinds of proofs not how to do this proof in particular
bronze grove
well for the second one
pliant shore
- is easiest either by proving the contrapositive, or by contradiction
bronze grove
we can just take n and every sub goes to 0
versed crater
12. is easiest either by proving the contrapositive, or by contradiction
There’s a simple construction proof too
bronze grove
12. is easiest either by proving the contrapositive, or by contradiction
by assuming thats its bounded?
pliant shore
ah really?
pliant shore
by assuming thats its bounded?
no, assume it's unbounded and that no subsequence has lim(1/x_(n_k)) = 0
versed crater
Yeah you just construct ||s_n = |max{x1, …, xn}|, this is monotonic and grows without bound, 1/s_n will get arbitrarily close to 0||
bronze grove
we can just take n and every sub goes to 0
is this right example
pliant shore
Yeah you just construct ||s_n = \|max{x1, …, xn}\|, this is monotonic and grows ...
damn
okay that idea is neat
versed crater
we can just take n and every sub goes to 0
Huh?
bronze grove
Yeah you just construct ||s_n = \|max{x1, …, xn}\|, this is monotonic and grows ...
damn thats nice
versed crater
damn thats nice
Okay yoy were supposed to try it yourself before looking
I typed that for south to read :/
versed crater
What does it mean the sequence will be n
bronze grove
1,2,3,4,5,6,7,8..
bronze grove
xn = {n, n > 1}
bronze grove
wdym jump around
versed crater
So perhaps 0 1 -0.5 2 -0.25 3 -0.125 4 …
bronze grove
unbounded and divergent
versed crater
sequence will be n so for any sub k 1/k will -> 0
You can see here that if you find a subsequence that monotonically increases then that subsequence will go to infinity
bronze grove
You can see here that if you find a subsequence that monotonically increases the...
yesss
versed crater
Such a subsequence is what you need for this 1/xnk
bronze grove
i understand it now damn
versed crater
So we need to figure out how to get a monotonic subsequence
bronze grove
So we need to figure out how to get a monotonic subsequence
i think there is a theorem
lemme check
versed crater
Well if xn is bounded from above then any monotonically increasing subsequence will be monotone and bounded -> converges which we don’t want
If it’s bounded below … same argument
bronze grove
versed crater
If xn is unbounded then it has to be unbounded below or above or both
versed crater
A very lose definition of monotone here
Too weak
We need it to say strictly monotone otherwise lim 1/xnk mightn’t go anywhere
bronze grove
If xn is unbounded then it has to be unbounded below or above or both
yess
bronze grove
A very lose definition of monotone here
so we cant use this gotcha
versed crater
Yeah
bronze grove
We need it to say strictly monotone otherwise lim 1/xnk mightn’t go anywhere
all he has to do is go to 0
versed crater
But with the unbounded ness it’ll be fine
versed crater
all he has to do is go to 0
We need the xnk to go to + or - infinity or bounce between them
But it can just do + or -
If xn is unbounded above then you can take the max of the first n terms
It may not be strictly monotonic but it grows without bound because it is unbounded from above
bronze grove
If xn is unbounded above then you can take the max of the first n terms
yess
versed crater
If it’s unbounded below you take min same thing
bronze grove
It may not be strictly monotonic but it grows without bound because it is unboun...
makes sense ngl
versed crater
Yeah you just construct ||s_n = \|max{x1, …, xn}\|, this is monotonic and grows ...
Here I just did both at once
bronze grove
If it’s unbounded below you take min same thing
so we will take two cases
versed crater
A little bit cheating because perhaps |max{x1, …, xn}| is not in the sequence but yet the idea is there
<@&268886789983436800>
bronze grove
A little bit cheating because perhaps |max{x1, …, xn}| is not in the sequence bu...
lmaoo
versed crater
I just wanted to jot the idea down for south lol
bronze grove
i think i kinda understand it now
versed crater
1,2,3,4,5,6,7,8..
But do you see how this idea comes from looking at an example
bronze grove
But do you see how this idea comes from looking at an example
kind of ngl
versed crater
Try to do the same with the first question, I’m gonna be asleep tho
bronze grove
Try to do the same with the first question, I’m gonna be asleep tho
good night !! thanks for ur help 
bronze grove
Try to do the same with the first question, I’m gonna be asleep tho
yess lemme just try it
we can do it to the same way right
first one
inf(sn) is just the upper bound of the sequence
and if we prove that a subsequence is increasing
then it diverges to its supremum i.e inf{sn}
final saddleBOT
@bronze grove Has your question been resolved?
bronze grove
.close
lapis rapids
If im asked to prove arccos(x)=pi/2 - arcsin(x). Can i use sin(pi/2 - theta) = cos(theta) directly or not?
final saddleBOT
If im asked to prove arccos(x)=pi/2 - arcsin(x). Can i use sin(pi/2 - theta) = c...
@lapis rapids Has your question been resolved?
bronze grove
If im asked to prove arccos(x)=pi/2 - arcsin(x). Can i use sin(pi/2 - theta) = c...
yes
frosty sigil
If im asked to prove arccos(x)=pi/2 - arcsin(x). Can i use sin(pi/2 - theta) = c...
Yes, you can but it depends more on what is instructed for you. (Some professors would want an explaination to it)
final saddleBOT
final saddleBOT
Available help channel!
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tired walrus
!status
final saddleBOT
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
tranquil pine
Let $a$ and $b$ be two non-zero relatively prime integers and let $(u_0, v_0) \in \mathbb{Z}^2$ be a Bezout pair such that $au_0 + bv_0 = 1$.
\begin{enumerate}
\item Determine all pairs of integers $(u, v) \in \mathbb{Z}^2$ such that: $au + bv = 1$.
\item If $a, b \in \mathbb{N}^*$, show that there exist two integers $(u, v) \in \mathbb{Z}^2$ such that: $au + bv = 1$ and $\begin{cases} |u| < b \ |v| \le a \end{cases}$
\end{enumerate}
soft zealotBOT
Drk
soft zealotBOT
Drk
shadow marlin
there are multiple ways to go about this:
- try to make u or v "minimal" by doing a euclidean division
or - look at the set {bv - 1, |v| <= a} and see what the bezout relation means for bv - 1 . You will need some knowledge about modular arithmetic for this one
tranquil pine
there are multiple ways to go about this:
- try to make u or v "minimal" by doin...
hmm let me try
shadow marlin
the first method follows from the previous question
desert mantle
I think the pair you get from eea is already minimal
so that could be another alternative way to do it
final saddleBOT
@tranquil pine Has your question been resolved?
tranquil pine
there are multiple ways to go about this:
- try to make u or v "minimal" by doin...
thanks!
worked out
well
.close
final saddleBOT
final saddleBOT
Available help channel!
solar crest
can someone help
final saddleBOT
can someone help
solar crest
im so confused on how i can find the coordinates
cuz I thought i look at symmetyr
like symmetry about pi/2, pole, and polar axis
celest crane
A negative radius can have the same position as (2, pi/7).
celest crane
im so confused on how i can find the coordinates
.
(r, θ) = (-r, θ + (2n+1)π), I think that's right.
flint sleet
can someone help
what are you even given
in terms of different polar coordinate systems
i am unsure of what the task is
celest crane
The question is asking for OP to find three polar coordinates, (r; θ), that are equivalent to the polar coordinate (2, π/7) on the interval -π <= θ <= 2π.
final saddleBOT
@solar crest Has your question been resolved?
flint sleet
The question is asking for OP to find three polar coordinates, (r; θ), that are ...
whats the convention on "polar coordinates" here
final saddleBOT
flint sleet
because the one i was subject to was that r ≥ 0 and \theta is an angle starting from the +x axis going CCW
final saddleBOT
Available help channel!
warm python
final saddleBOT
rustic wedge
https://math.stackexchange.com/questions/5111248/a-block-generalization-of-factorions
in context of this (bit of a coding question)
final saddleBOT
https://math.stackexchange.com/questions/5111248/a-block-generalization-of-facto...
rustic wedge
import math
from scipy.special import gammaln
F=2
def logaddexp(a,b):
return max(a,b)+math.log1p(math.exp(abs(a-b)))
def check_fctrn(Z):
buf = str(Z)
l = math.log(Z)
log_sum = 0
while len(buf)>F:
log_sum = logaddexp(log_sum, gammaln(int(buf[-F:])))
buf = buf[:-F]
if log_sum > l:
break
else:
log_sum += gammaln(int(buf))
return abs(log_sum-l)<10
return False
N = int(input())
dct = dict()
for x in range(1, N+1):
for n in range(10**(F*x-1), 10**(F*x)):
dct[n] = check_fctrn(n)
if dct[n] == True:
print(n, dct[n])
print(f'Loop for x = {x} done.')
Wrote this bad boy. For some reason according to this 1001 is a 2-factorion?
which well it clearly isnt?
(n-factorion means a number which is equal to the sum of the factorials of consecutive blocks of n integers made from the number. eg. 2763 is not a 2-factorion since 27!+63! >>>> 2763)
final saddleBOT
@rustic wedge Has your question been resolved?
leaden moon
1! + 001! = 2
10! + 01! > 1001
100! + 1! > 1001
1001! > 1001
huh????
import sys
sys.setrecursionlimit(1000000)
class FactorialMachine:
def __init__(self):
self.MEM = {}
def calculate_factorial(self, n):
if not isinstance(n, int):
raise TypeError
if n in self.MEM:
return self.MEM[n]
if n == 0:
self.MEM[0] = 1
return self.MEM[0]
res = 1
tmp = n
while n > 0:
if n in self.MEM:
self.MEM[tmp] = res * self.MEM[n]
return self.MEM[tmp]
res *= n
n -= 1
self.MEM[tmp] = res
return self.MEM[tmp]
fm = FactorialMachine()
def check_factorion(n):
if not isinstance(n, int):
raise TypeError
if n < 0:
raise ValueError
first_str = str(n)
second_str = ""
while len(first_str) == 1:
char = first_str[-1]
first_str = first_str[0:-1]
second_str = char + second_str
if fm.calculate_factorial(int(first_str)) + fm.calculate_factorial(int(second_str)) == n:
return True
return False
print(check_factorion(1001))
try this
and we don't have to worry about how big an int is because python already handles that
rustic wedge
back
leaden moon
?
try this one
class FactorialMachine:
def __init__(self):
self.MEM = {}
def calculate_factorial(self, n):
if not isinstance(n, int):
raise TypeError
if n in self.MEM:
return self.MEM[n]
if n == 0:
self.MEM[0] = 1
return self.MEM[0]
res = 1
tmp = n
while n > 0:
if n in self.MEM:
self.MEM[tmp] = res * self.MEM[n]
return self.MEM[tmp]
res *= n
n -= 1
self.MEM[tmp] = res
return self.MEM[tmp]
fm = FactorialMachine()
def check_factorion(n):
if not isinstance(n, int):
raise TypeError
if n < 0:
raise ValueError
if len(str(n)) == 1:
return n in (1, 2)
first_str = str(n)
second_str = ""
while len(first_str) > 1:
char = first_str[-1]
first_str = first_str[0:-1]
second_str = char + second_str
if fm.calculate_factorial(int(first_str)) + fm.calculate_factorial(int(second_str)) == n:
return True
return False
print(check_factorion(1001))
```\well i fixed my code
rustic wedge
```
import math
from scipy.special import gammaln
F=2
def logaddexp(a,b):
re...
the issue was abs(log_sum-l)<10, 10 was way too large a value
with 0.1 it does get fixed
theres also some more errors
but i wont get into those
let me try yours
actually wait u understood the definition wrong
rustic wedge
```
1! + 001! = 2
10! + 01! > 1001
100! + 1! > 1001
1001! > 1001
```
10!+01! is the only valid one here
we dont have to check 1! + 001! or 100!+1!
its why i implemented blocks (or in ur code the str slicing part) the way i did
chunking off n integers at the end one by one
rustic wedge
no as in
rustic wedge
we dont have to check 1! + 001! or 100!+1!
this
10! + 01! is the only valid 'split' for 1001
but for eg. for 100101
leaden moon
but they don't add up to 1001
rustic wedge
yes they dont i agree so its not a factorion but ur code also checks 1! + 001!
which is wasteful
leaden moon
i just wanna be sure
rustic wedge
but for eg. for 100101
this has two splits: 10!+01!+01! and 100! + 101! neither of which sum to 100101 therefore its neither a 2-factorion nor a 3-factorion
rustic wedge
i just wanna be sure
well i mean i have given my opinion 🤷
and my issues fixed so i'll close this now
ty for ur effort tho!
final saddleBOT
final saddleBOT
Available help channel!
exotic shale
can someone explain this or what it looks like
final saddleBOT
can someone explain this or what it looks like
winter grail
can someone explain this or what it looks like
What are you stuck with?
severe canyon
Any vector of the domain
formal trail
{y : y = Ax} is the set of all vectors y which can be written as the product of A and some vector x
exotic shale
so x in R^N or x in R^M
severe canyon
is the rows/columns
!xyproblem
final saddleBOT
is the rows/columns
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
winter grail
what is x supposed to be
The vector 𝑥 is any element of ℝⁿ
exotic shale
exotic shale
The vector 𝑥 is any element of ℝⁿ
where n is what ?
winter grail
𝑥 ∈ ℝⁿ
formal trail
if A is M × N, then you can figure out what size column vectors can or cannot be multiplied on the right
exotic shale
you mean N as in the amount of columns?
winter grail
where n is what ?
represents the number of columns of the matrix $\mathbf{A}$
soft zealotBOT
𝙲𝚘𝚛
exotic shale
if A is M × N, then you can figure out what size column vectors can or cannot be...
so R^N
but why column vectors
severe canyon
you mean N as in the amount of columns?
Of course, since your matrix A is M×N
exotic shale
and not row vectors
severe canyon
Because... that's how multiplication with matrices works
formal trail
but why column vectors
only column vectors could possibly be multiplied on the right. row vectors would have to be multiplied on the left
tired walrus
columns not rows
exotic shale
columns right
so the maximum dim(A) = N?
when all columns are linearly independent
exotic shale
dim(im(a))
tired walrus
and the biggest possible rank aka the biggest possible value of what you just said, is min(m,n)
tired walrus
oh you are using capital M and N my bad
tired walrus
if we are multiplying with x E R^N shouldnt it not be N?
it means the image has dimension not bigger than N
dim <= N
but also dim <= M because we land in R^M
exotic shale
i get the first one
but not the M one
yea just the M thing i dont understand where it comes from
timber plume
final saddleBOT
timber plume
How do I solve b
tired walrus
how do you write "fails within the first 5000 hrs of use" as an inequality involving the failure time?
winter grail
How do I solve b
Compute $$
P(X < 5000).
$$
soft zealotBOT
𝙲𝚘𝚛
winter grail
Then standardize
tired walrus
Compute $$
P(X < 5000).
$$
mmmm you kinda answered the question i was hoping for OP to answer himself
timber plume
….
tired walrus
Then standardize
also i think you've got the order of things mixed up.
timber plume
!nosol
tired walrus
how do you write "fails within the first 5000 hrs of use" as an inequality involving the failure time?
timber plume
how do you write "fails within the first 5000 hrs of use" as an _inequality_ inv...
f=h<5000
timber plume
f is failure
h is hours
I’m just wondering how the last sentence of question b is relevant
tired walrus
f is failure
h is hours
mmmmmmm
timber plume
They brought “3000 units are sold in a year” randomly
tired walrus
okay no, the 3000 units/yr thing is not random.
ok, so here is the idea
you first find the probability that a refund is issued on any one specific machine
you do this by saying: let T be the time taken for a unit to fail. we get a refund if and only if T < 5000,
so we will want P(T < 5000).
once you work that out, do you see how to find the expected number of refunds?
i want you to PLAN but NOT EXECUTE here.
don't do ANY calculations yet,
but only TELL me what you'll do.
@timber plume are we understood
timber plume
Yeah I am reading this
tired walrus
i want to repeat once again that i want you NOT TO EXECUTE anything UNTIL I TELL YOU TO.
timber plume
so we will want P(T < 5000).
What’s that? Probability of time less than 5000?
tired walrus
probability of failure time less than 5000, yes.
timber plume
I see
tired walrus
once you work that out, do you see how to find the expected number of refunds?
i wanna stress again that you dont need to have worked out the third decimal place of P(T<5000) in order to answer this PLANNING question.
timber plume
What’s that? Probability of time less than 5000?
Well this gives us the amount of a specific machine to fail before 5000, correct
tired walrus
probability is probability, probability is not amount, probability is probability
timber plume
yea I meant that its referring to the probability of a specefic machine to fail before 5000
tired walrus
I just need help what the last sentence of the question is asking me to do
and im trying to actually get you to think about your plan from then on.
but ok, i see it's not really working out.
so let's set this question aside for a moment.
imagine a different model of equipment your factory is producing is known to have, say, a 2.4% defect rate.
meaning that if you pull a unit off the production line at random, the probability it's faulty is 0.024
in a batch of... let's say 8,000 units, how many defects do you expect to find?
@timber plume you here?
soft zealotBOT
timber plume
192?
tired walrus
ok, so
yes
same shit here.
P(T < 5000) will be the refund rate -- in other words, it'll give you the percentage of units that will need to get refunded.
in part b of your original question, the batch size is 3K units.
timber plume
the question says how much expect to pay
tired walrus
can you read what the question says
EXACTLY AND IN FULL
cause you're having a "devil in the details" moment
timber plume
so this must be the answer if u did get 2.4 % from the table
polar agate
they are tricky
have you written down what you're given and required to do? also, at some point, maybe it's time to back down to algebra word problems and build intuition on how to tackle them from there
maybe this is not the first time you've heard someone tell you to go back to basics, but having heard many people tell you this should give you a sense of why exactly you should do this, if you've never thought of doing it until now.
timber plume
have you written down what you're given and required to do? also, at some point,...
yeah true
I will tackle the basic word problems
iron mist
Ann how do I get good at word problems
- Read carefully
- Explore (both in terms of one particular problem and in terms of many problems)
- Come up with a game plan per problem
faint locust
It might be helpful to think in terms of Polya's four-step-approach to problems
polar agate
I was about to bring that up
timber plume
It might be helpful to think in terms of Polya's four-step-approach to problems
whats that
faint locust
He has a book called 'How to Solve it', he gives a lot of examples of this process; how he would guide a student through a problem; it's a nice read, you can lend it out, the problems he discusses are all high school level (though his 'methods' generalize)
polar agate
but let me quote something that you should try
timber plume
Ill make sure to check it out
polar agate
if stuck, try the I SEE + SUCK method of answering questions until you have enough familiarity with them
if you dk what that is:
I SEE:
Identify: what is the problem asking for? what is the problem NOT asking for? what do i need (formulas, theorems, laws, etc.) to solve this problem?
Setup: how do i use what i need to solve this problem? are my steps justified? why (not)? what other concepts do i need?
Execute: do the calculations.
Evalute: further divided into SUCK:
Size: are the answers the right size? is it too big? small? what do you expect if you did the circuit or experiment in real life?
Units: are the answers the right units? did i do any illegal unit operations?
Calculation: did i do the calculations right? did i miss any steps? can i explain everything? (your worst nightmare, as i see it)
'K' (Context): is everything framed in the right context? are my steps justified within the context of the problem?
(ok this one is a little specialized, because it's directed at my engineering friend, but the main ideas apply to you just as well.)
you can also skip units most of the time, as you rarely work with them
timber plume
I see
polar agate
also, I have been told by a contact of mine in here that you used to read material way beyond your level by throwing them into ChatGPT and asking it to summarize it for you. never do that.
tired walrus
this is good
this is exactly what i was yapping about with planning vs execution
the book says "carry out" instead of execute, but it's the same thing
timber plume
also, I have been told by a contact of mine in here that you used to read materi...
I dont really do that
faint locust
yeah
timber plume
Ik chat gpt is terrible
tired walrus
basically for this question, part b of your original post
polar agate
timber plume
oh that I remember
tired walrus
the plan was:
- find P(T < 5000)
- find number of refunds as
batch size * refund rate
polar agate
that is what I'm referring to. if you are still doing that, esp. with your lessons, please don't.
tired walrus
the thing i was trying to drive home is that logically speaking step 2 gives exactly 0.0 shits about any details of how step 1 went
faint locust
Oh and also something interesting about Polya, the author: Hardy was really set on changing how the Tripos exam in Cambridge worked, since before, it was favoring speed and brute-force methods. He changed it to favor understanding more and asked Polya to take it. He did and to his surprise, received the highest score (that would've made him the Senior Wrangler) - so he really is quite good at problem solving
tired walrus
they are tricky
they're tricky because you routinely do them without much of a plan.
you do them without much of a plan because you're shaky on understanding what the problem wants you to do.
you're shaky on understanding what the problem wants you to do because your basics are rusty.
timber plume
my answer said 18.6 refunds, is it safe to say 18 refunds?
tired walrus
i would have imagined the proper rounding is 19 not 18
but also it's all approximate anyway
final saddleBOT
steep plank
.reopen
tired walrus
.reopen
this isnt your channel. you can only .reopen your own channel while it still has your name on it
if you have a question of your own, go to another channel that doesn't have a name on it, and post your question there
steep plank
Ok, thx for help
final saddleBOT
Available help channel!
keen vector
Hii I know this is a mechanics question but in the physics hub people reply to me very slowly. I was wondering why despite B being heavier than A, A moves down and B moves left? These are the model answers thanks
final saddleBOT
Hii I know this is a mechanics question but in the physics hub people reply to m...
keen vector
final saddleBOT
@keen vector Has your question been resolved?
safe oyster
Hii I know this is a mechanics question but in the physics hub people reply to m...
as indicated by the direction of a, A moves with a vertical acceleration
and B moves to the ‘right’ (but angled)
since a is positive both move in the same direction we assume which according to the image is to the right but angled down
smoky bramble
Hii I know this is a mechanics question but in the physics hub people reply to m...
even if B is heavier, there is no friction
this means that it can move however
B will only stay still if there's enough friction to hold it down
imagine a ball connected to another ball in a pulley
vs
a man standing holding a thing from a pulley
if the thing is heavy enough, the man will move
final saddleBOT
final saddleBOT
Available help channel!
zealous wasp
2 alike series 1+2+3+4+5.... take first of the clones and (1+2)+(3+4)+(5+6)...... 3+7+11..... the latter is still 1+2+3+4+5.... 3>1,7>2,11>3...... hence first one is greater when they were exactly same to begin with
final saddleBOT
2 alike series 1+2+3+4+5.... take first of the clones and (1+2)+(3+4)+(5+6)........
zealous wasp
unable to understand how this works
fluid blaze
what do u not understand?
zealous wasp
what do u not understand?
that the first series is said to be obviously greater than 1+1/2+1/2....
fluid blaze
yeah thats the point
since 1 +1/2+1/2+... doesnt converge
why will a series greater than that converge?
zealous wasp
why will a series greater than that converge?
can you dumb it down a little i dont get it
that 1+1/2+1/3+1/4 is greater than 1+1/2+1/2
fluid blaze
like it doesnt attain a specific value right
zealous wasp
yes
tired walrus
2 alike series 1+2+3+4+5.... take first of the clones and (1+2)+(3+4)+(5+6)...... 3+7+11..... the latter is still 1+2+3+4+5.... 3>1,7>2,11>3...... hence first one is greater when they were exactly same to begin with
do you want an explanation for why this is wrong
fluid blaze
that 1+1/2+1/3+1/4 is greater than 1+1/2+1/2
look at the partiations
zealous wasp
> 2 alike series 1+2+3+4+5.... take first of the clones and (1+2)+(3+4)+(5+6)......
yes
tired walrus
you silently assumed that the series 1+2+3+... converges to something finite at all (call it S)
your argument proves S > S
so you just have a contradiction
the right conclusion is that your assumption of "S is finite" was false
royal gust
that the first series is said to be obviously greater than 1+1/2+1/2....
The first series is "greater" when taken term-by-term. I think that's all they mean.
The series itself isn't greater, they're both infinite. If that's what you're noticing, you're correct.
zealous wasp
The first series is "greater" when taken term-by-term. I think that's all they m...
oh
ok
do i close?
royal gust
If everything makes sense!
tired walrus
you decide when to close the channel
if you have nothing else to ask then yes, close
zealous wasp
i still dont understand but i dont want to annoy anyone
royal gust
Not annoying at all
zealous wasp
why is my example wrong because i tried to do the same thing as in the pdf
they also grouped i also did
but it isnt right but still shwoing first one is greater than second
soft igloo
why is my example wrong because i tried to do the same thing as in the pdf
what was ur example
zealous wasp
what was ur example
2 alike series 1+2+3+4+5.... take first of the clones and (1+2)+(3+4)+(5+6)...... 3+7+11..... the latter is still 1+2+3+4+5.... 3>1,7>2,11>3...... hence first one is greater when they were exactly same to begin with
soft igloo
2 alike series 1+2+3+4+5.... take first of the clones and (1+2)+(3+4)+(5+6)........
but ur using the same series to compare
tired walrus
why is my example wrong because i tried to do the same thing as in the pdf
i didnt say your example is wrong
i EXPLAINED THE LOGIC behind it
in order to compare two series like this, we have to assume they converge -- you can't do any comparisons with known divergent series
zealous wasp
i didnt say your example is wrong
I am trying to know why it is wrong
tired walrus
girl...
i said...
or rather
i DIDN'T say it was wrong
in as plain language as possible
zealous wasp
in order to compare two series like this, we have to assume they converge -- you...
but the book is comparing two divergent ones
soft igloo
I am trying to know why it is wrong
it not wrong but since ur series are already known to be divergent
so yeah
tired walrus
but the book is comparing two divergent ones
no
soft igloo
but the book is comparing two divergent ones
we assumed 1
tired walrus
well
kinda yes, but not really
since at the start we dont know yet that 1+1/2+1/3+... diverges
it's unknown
royal gust
I wish your book didn't say "thus the given series is greater". The given series is not greater. It was a thoughtless thing to say.
zealous wasp
I wish your book didn't say "thus the given series is greater". The given series...
should i ignore that
royal gust
Every term is greater, that's all they mean.
icy tulip
it's unknown
But it tends to a value
tired walrus
... WHO, exactly, tends to WHAT value.
final saddleBOT
final saddleBOT
Available help channel!
neon pendant
Five men and 5 women are ranked according to
their scores on an examination. Assume that no
two scores are alike and all 10! possible rankings
are equally likely. Let X denote the highest rank-
ing achieved by a woman. (For instance, X= 1 if the top-ranked person is female.) Find P{X = i},
i= 1, 2, 3,... , 8, 9, 10.
final saddleBOT
Five men and 5 women are ranked according to
their scores on an examination. Ass...
tired walrus
!status
final saddleBOT
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
@neon pendant
winter lava
i think you can choose 4 from the ranks less than i
then count the ways of sorting the five men, and likewise for the women
neon pendant
<@1143949449622732871>
didnt understand the whole question lol
tired walrus
we have 5 men and 5 women shuffled randomly and assigned ranks 1-10
then the women gather among themselves, and figure out what the top rank is among them
for example, let's give them names like: ♂️ Aaron, Bart, Carl, David, Eric; ♀️ Alice, Barbara, Cheryl, Diana, Emma
and say the final ranking was as follows:
- David
- Cheryl
- Aaron
- Barbara
- Alice
- Diana
- Bart
- Eric
- Carl
- Emma
the women's ranks are 2, 4, 5, 6, 10
and so the value of X as the problem defined it will be 2
does that make the problem setting clear now?
tired walrus
that i can't answer with confidence, because i really don't know what you mean here.
neon pendant
we can choose the first woman in 5 ways
tired walrus
also i think you meant men not "mans"?
neon pendant
also i think you meant _men_ not "mans"?
yes men
tired walrus
i think i may see where you're going with this
neon pendant
same thing
tired walrus
if the top-ranked woman appears in rank i,
then the i-1 places above her are taken by men
neon pendant
if the **top-ranked woman** appears in rank i,
then the **i-1 places above her**...
yeah
look
tired walrus
so we can construct a ranking that results in X=i in three steps:
- choose which of the 5 women gets rank i
- arrange (i-1) men above her in the ranking
- arrange the remaining (10-i) people into the ranks below i
neon pendant
so we can construct a ranking that results in X=i in three steps:
1. choose whic...
u are goddamn right i wanted to say this
so the whole answer is (5 * ( P(5, i-1) ) * ( (10-i)!))/10! right?
tired walrus
so it seems, yes.
and you can also very clearly see the biggest value that X can possibly take is 6
which happens if all the women end up at the very bottom -- the highest among them will rank 6th
neon pendant
which happens if all the women end up at the very bottom -- the highest among th...
so for i <= 6 its the formula
neon pendant
o/w 0
neon pendant
i did (10-i choose 4)*5!5!/10!
C(10-i , 4)?
winter lava
ye
i think P and C are defined 0 when you go outside the proper range so you don't really need a piecewise function
neon pendant
why 5!5!?
winter lava
5! ways to sort men and 5! ways to sort women
neon pendant
5! ways to sort men and 5! ways to sort women
we cant use C(10-i, 4) it will overcount same as 5!5!
its a permutation problem
order matters
final saddleBOT
neon pendant
.reopen
final saddleBOT
✅ Original question: #help-36 message
neon pendant
@tired walrus
tired walrus
yes?
neon pendant
yes?
An integer N is to be selected at random from
{1, 2,... , (10)^3} in the sense that each integer
has the same probability of being selected.
What is the probability that N will be divis-
ible by 3? by 5? by 7? by 15? by 105? How
would your answer change if (10)^3 is replaced
by (10)^k as k became larger and larger?
tired walrus
ok so there's a different problem now
i thought you had a follow-up about the first one
neon pendant
i thought you had a follow-up about the first one
nope
tired walrus
k
why are there unnecessary brackets around every instance of 10
also what's your progress on this one
im kind of tired right now so i dont want to have to pull this out of you like rotten teeth
neon pendant
why are there unnecessary brackets around every instance of 10
copied it thats why
tired walrus
you could have also sent a screenshot
this way there would not be any awkward newlines
neon pendant
also what's your progress on this one
should we take floor(10^3/k)?
tired walrus
why are you dividing by k
neon pendant
you could have also sent a screenshot
cant mate discord is boycotted in iran
tired walrus
you definitely arent using k in the same way as the question does
tired walrus
cant mate discord is boycotted in iran
you're able to access it now but you cannot upload images?
manic nimbus
Hi
tired walrus
ok anyway i think im gonna go
neon pendant
you definitely arent using k in the same way as the question does
i meant 3, 5, 7, 15 and 105
tired walrus
Hi
hi, this channel is occupied, if you have your own question then claim your own channel please
neon pendant
you're able to access it now but you cannot upload images?
dude i cant
neon pendant
ok anyway i think im gonna go
tc
manic nimbus
hi, this channel is occupied, if you have your own question then claim your own ...
Sure
tired walrus
dude i cant
do not call me "dude".
tired walrus
I don't have question Now
then go to #discussion or #chill.
neon pendant
.close
fathom owl
I haven't done this in a while but
12 and 13 are nightmare fuel. (Not really, I just can't seem to find the appropriate logic to solve them)
final saddleBOT
I haven't done this in a while but
12 and 13 are nightmare fuel. (Not really, I ...
tidal vale
every year, each day moves forward by one (but two for leap years)
so if july 3, 1977 was a sunday then july 3, 1976 was a saturday
rugged geyser
I haven't done this in a while but
12 and 13 are nightmare fuel. (Not really, I ...
It is ez sub 1 per year and 2 for leap
final saddleBOT
so if july 3, 1977 was a sunday then july 3, 1976 was a saturday
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
fathom owl
I think I'm stupid
rugged geyser
I think I'm stupid
You arent
rugged geyser
I did solve it but I just did addition instead of subtraction
Crazy....
radiant carbon
hey
radiant carbon
why is the point of inflection not ALWAYS found at f''(x) = 0
can someone give me some examples
eager shore
f(x) = x^4
You specifically need f'' to change sign at x
If that happens then f''(x) = 0, but the converse is not always true
hybrid heath
why is the point of inflection not ALWAYS found at f''(x) = 0
Are you asking why point of inflection does not always imply f"(x)=0 or why f"(x)=0 does not always imply point of inflection?
radiant carbon
Are you asking why point of inflection does not always imply f"(x)=0 or why f"(x...
why f"(x)=0 does not always imply point of inflection?
.close
final saddleBOT
final saddleBOT
Available help channel!
radiant carbon
final saddleBOT
next thorn
why is it 4
(I genuinely dont know if this is actually what you're supposed to do, but...)
the tallest height reached is 8 and the smallest is (supposedly?) 0... median should be (8+0)/2 no?
I'm very unsure! maybe its a just coincidence
vital crag
Find the cumulative distribution function then evaluate at 0.5
radiant carbon
I'm very unsure! maybe its a just coincidence
yeah this is what i was thinking
radiant carbon
Find the cumulative distribution function then evaluate at 0.5
what does that mean
cumulative distribution function
soft zealotBOT
rugged merlin
Which amounts to [
F(x) = \int_{-\infty}^xf(t)\dd t
]
In the continuous case and [
F(x) = \sum_{t\le x} f(t)
]
In the discrete case
soft zealotBOT
plucky rover
Find the cumulative distribution function then evaluate at 0.5
His flair says pre-uni, I doubt any of this is at his level
iron mist
mark scheme says you can find it by symmetry
You’re using the quadratic model
Which yes is symmetric
plucky rover
and how would you do this
There are 256 seedlings. Do you remember the formula for median
final saddleBOT
@radiant carbon Has your question been resolved?
glass wren
How do I calculate a cubic equation with a parameter in it? Im noob at math bro
mint orbit
Can you show an example of the kind of problem youre talking about?
mint orbit
whats the goal with this expression?
glass wren
Oh yea
mint orbit
$f(x) = 2x^3-4x^2-4x+m$
soft zealotBOT
jan Niku
mint orbit
no I know what you mean
glass wren
mint orbit
So maybe you've seen the cubic equation? like the quadratic equation
glass wren
the one i wrote above that
mint orbit
well, maybe formula is the right word
glass wren
hahhha
mint orbit
the one i wrote above that
no its really long and bad
glass wren
OH
mint orbit
you know how like, for a quadratic, we can just write out the roots
mint orbit
yea its hard usually cubics are really hard
you either have to rely on special forms or be lucky
mint orbit
**jan Niku**
like here, say you could pick m, can you make the problem nice?
mint orbit
Oh thats sad
we can just write down the answer, if youre into that kind of thing, but its a mess
glass wren
mint orbit
this is why its usually special cases
glass wren
mint orbit
i dont think so
well can you think of what might need to happen?
glass wren
Nope
mint orbit
so lets thing of like
mint orbit
$ax^3+bx^2+cx+d$
soft zealotBOT
jan Niku
mint orbit
so lets try ...
glass wren
Mhm
mint orbit
$x^2(ax+b)+(cx+d)$
soft zealotBOT
jan Niku
mint orbit
here's an easy one