So that means that we don’t have any asymptotes ?
#help-19
tall veldt
Youre looking for non-vertical asymptotes
Horizontal asymptotes fall under this category
leaden light
So horizontal asymptote is x = 0 ?
tall veldt
Yes
leaden light
Make sense , but how do I suppose to write an answer ?
tall veldt
Prove that as x tends to infinity f(x) tends to 0
Then you can conclude x=0 is a horizontal asymptote
odd edgeBOT
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wide nova
odd edgeBOT
wide nova
Hey all, I'm struggling getting started here
When I set y^2 = 2y+1 I get y = 1, 2
oh what
sorry I thought I had the channel
shut mantle
.close
odd edgeBOT
odd edgeBOT
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odd edgeBOT
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rocky edge
!status
odd edgeBOT
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
odd edgeBOT
@rocky edge Has your question been resolved?
rocky edge
<@&286206848099549185>
visual sigil
can you think of a "rule" for this equivalence relation?
rocky edge
No
visual sigil
theres clearly a pattern right
rocky edge
Ye
visual sigil
can you express that pattern in plain english
visual sigil
can you deduce something about any of the elements in each set
rocky edge
is it something to do about the last element or first element on each set
rocky edge
for the first elements of each set i.e
1,2,4,7,11 they increase by 1 then 2 then 3 then 4
visual sigil
can you find a closed form for those?
rocky edge
closed form as in mathematical notations?
visual sigil
yeah
ill give you a hint
might be easier to find a closed form for the max of each set
rocky edge
max as in size?
visual sigil
yeah
rocky edge
ok
visual sigil
the last element of each set
misty terrace
i need help with 6b. i just need to know if i even need to do long division cuz it seems pointless??
misty terrace
fractions but partial
mint mirage
i need help with 6b. i just need to know if i even need to do long division cuz ...
No you don't need to do long division
misty terrace
aight thanks
mint mirage
You do it when the power of the numerator is equal to or greater than the power in the denominator
misty terrace
oh right 💀 i didn't notice the numerator is less than the denominator
thanks thanks
.close
pearl patio
odd edgeBOT
pearl patio
Is there a nicer way to do this instead of just listing out?
It'd get messy if the number was something other than 11 so that's why
odd magnet
well I'd probably try by first finding a possible sequence of numbers
pearl patio
well I'd probably try by first finding a possible sequence of numbers
yes i'm aware
i'm curious about another way rather than listing out numbers
odd magnet
I think there probably is, but it's going to be a hell of a lot harder
pearl patio
I think there probably is, but it's going to be a hell of a lot harder
yeah there probably is a "trick"
i'm looking for that
pearl patio
I think there probably is, but it's going to be a hell of a lot harder
11 is 5+6
so everything else has to cancel out
1,2,3, and 4 cancels out with -1,-2,-3, and -4
okay there
late dust
You got a list of 10 consecutive integers but you could have just taken all the integers between -10 and 11 included
summer cradle
wait that pfp omg lol
odd edgeBOT
@pearl patio Has your question been resolved?
pearl patio
You got a list of 10 consecutive integers but you could have just taken all the ...
yeah but i want the least cardinality of the set right to make a comparison
pearl patio
wait that pfp omg lol
kuromi pfp too cute 
late dust
yeah but i want the least cardinality of the set right to make a comparison
Oh right, you want to find a sequence of fewer than 10 terms
Well you need and odd number of odd numbers in it
pearl patio
If there is one yeah
None here i guess since the lowest cardinality it can have is 11 iirc
late dust
So you can try 2,3,4 but that's too small
1,2,3,4,5 is too big
So you necessarily have to go into the negatives
late dust
I don't think there's a nicer way
pearl patio
isn't 5+6 one the nicer way?
I just saw it on some site
I did it like you, but i was confused until i translated
oh maybe it just worked for this problem but you can't extrapolate?
without some work at least ig
late dust
I mean if you replace the 11 with a 9, you can find 4+5 and so you can have the sequence -3, -2, ..., 4, 5
But you could have just taken 2,3,4
pearl patio
since 10 + 11 = 21
yeah indeed lol
okay thanks
could i get help on this?
This one is confusing me
I have to compare the quantities in a similar fashion
Like i have an intuitive feel that Quantity A > quantity B
but that's really it
more of the areas are bunched up towards the middle so the value at the 75th percentile is closer to 60th percentile than it is to the 90th percentile
late dust
Not sure about that
pearl patio
aww
@summer cradle would you be kind enough to help me like last time or if you're busy its okay~~ (sorry for ping)
late dust
Oh the change of curvature occurs one standard deviation away from the mean
Hm actually I'm not sure this solve that
summer cradle
<@984319941417250907> would you be kind enough to help me like last time or if y...
i was gonna try to take a nap sorry T_T but it might be that you can’t determine
late dust
I'm relatively sure you are correct but only because the 90th percentile isn't far enough
pearl patio
i was gonna try to take a nap sorry T_T but it might be that you can’t determine
it's okay thanks for looking
the answer is i think A
as in Quantity A> Quantity B
pearl patio
I'm relatively sure you are correct but only because the 90th percentile isn't f...
Damn
odd edgeBOT
@pearl patio Has your question been resolved?
odd edgeBOT
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inland cape
Consider 20 statements:
"I have exactly 1 sister." "I have exactly 1 brother."
"I have exactly 2 sisters." "I have exactly 2 brothers."
"I have exactly 3 sisters." "I have exactly 3 brothers."
"I have exactly 4 sisters." "I have exactly 4 brothers."
"I have exactly 5 sisters" "I have exactly 5 brothers"
"I have exactly 6 sisters" "I have exactly 6 brothers"
"I have exactly 7 sisters" "I have exactly 7 brothers"
"I have exactly 8 sisters" "I have exactly 8 brothers"
"I have exactly 9 sisters" "I have exactly 9 brothers"
"I have exactly 10 sisters." "I have exactly 10 brothers."
Find the largest natural number n such that each of the n siblings can make a different one of these 20 statements and be right. (all siblings have same parents)
ans: n=4 - say x is number of sisters and y number of brothers, there are only 4 possible statements: man can say I have x sisters and y-1 brothers and woman can say I have y brothers and x-1 sisters. 4 possible statements = max. of 4 siblings
inland cape
Could someone please tell me if it is correct?
I found it kinda easy and Im worried that it is some kind of tricky question
boreal crag
Yeah that should be right
odd edgeBOT
karmic hearth
Since I can’t find this question online
And also if I got it wrong,may you tell me where I went wrong
honest hawk
how do i do this?
odd edgeBOT
how do i do this?
zealous fossil
consider the function $f(t)=e^t-1$
clever fjordBOT
Pure2
zealous fossil
there exists some c in (0,x) such that it conforms to the MVT:
$e^c=\frac{e^x-1}{x}$
clever fjordBOT
Pure2
zealous fossil
then: Take the natural logarithm of both sides and then multiplying by 1/x
u can make some observation, ie c is between 0 and x, and x>0, it follows some nice inequalities to prove the thing
@cold urchin CALC
odd edgeBOT
@honest hawk Has your question been resolved?
cold urchin
Nice one my disgraced student
zealous fossil
Nice one my disgraced student
np
zenith tartan
can i be pure 3?
zealous fossil
can i be pure 3?
yes, i permit
zenith tartan
thanks
odd edgeBOT
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Available help channel!
mystic saffron
hi, can I ask here?
odd edgeBOT
hi, can I ask here?
odd edgeBOT
@mystic saffron Has your question been resolved?
odd edgeBOT
mystic saffron
.reopen
odd edgeBOT
✅
odd edgeBOT
@mystic saffron Has your question been resolved?
odd edgeBOT
@mystic saffron Has your question been resolved?
forest solstice
Fisher's exact test can be used as a quick test for correlation between two variables X and Y, each of which has at least an ordinal scale of measurement. Divide the scatterplot of the N values of (X,Y) with a vertical line at the median of X, and a horizontal line at the median of Y, and count the number of observations in each of the four quadrants. note that the row and column totals are N/2, and are not at random. Suppose 16 observations of X = age of marriage of a husband, and Y = age of marriage of his father, result in 7 pairs where both ages were above the median. Are the two variables positively correlated?
I've made this table
+---------------------------+--------------+--------------+-------+
| | Above Median | Below Median | Total |
+---------------------------+--------------+--------------+-------+
| Husband's age of Marriage | X | 8-X | 8 |
| Father's age of marriage | 7-X | 1+X | 8 |
| | 7 | 9 | 16 |
+---------------------------+--------------+--------------+-------+
I don't understand how to proceed from here on, without the value of X
forest solstice
<@&286206848099549185>
odd edgeBOT
odd edgeBOT
Available help channel!
winged jacinth
Someone help me solve this
odd edgeBOT
Someone help me solve this
mystic saffron
is this from chatgpt?
chat gpt can make images?
mystic saffron
!status
lavish jackal
chat gpt can make images?
ye
mystic saffron
what's up with the bots today
lavish jackal
when showing you a math problem solution
gray dome
i see now
lavish jackal
k
nimble delta
do the higher ups know about it?
mystic saffron
about the bot?
mystic saffron
do the higher ups know about it?
the elites know everything
oh yeah the whole system is sown
tall veldt
yeah its happened before
last time it eventually fixed itself
would need mniip to look at it i imagine
nimble delta
last time it eventually fixed itself
wow
mystic saffron
such a coincedence
that it is happening now
lol
when I have a math question
must be the opps
no wannder why their is less help channels
lavish jackal
??
lavish jackal
no wannder why their is less help channels
ik but your message didn't make sense here ^
mystic saffron
yeah ik
odd edgeBOT
odd edgeBOT
Available help channel!
near ore
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distant tartan
odd edgeBOT
distant tartan
How do I solve AU=B if A has no inverse?
drifting valley
write U = (x, y, z), do the multiplication and solve the system
distant tartan
write U = (x, y, z), do the multiplication and solve the system
so like for the top one it would be
3y -3z = 9
2y -2z =6
x - y -z = -5
?
drifting valley
yes
spare hornet
odd edgeBOT
spare hornet
Then
fair prism
What do you get
fair prism
Yeah so since you can cancel x-1 from numerator and denominator what type of discontunuity is that? Since you can't cancel x+2 but its still undefined, what type of discontinuity is that?
fair prism
When you can cancel a factor in numerator and denominator it means that value is discontinuous at a point
if you cant it means its an asymptote discontinuity
spare hornet
Yes I get a hat but that but how they get 1/3
fair prism
0/x+2
this should be 1/x+2 but yeah thats the simplified form
Then 1/3 follows from plugging in 1
fair prism
Use formula for circumference, and multiply it by the appropriate scale factor so you are only talking about the given length (100cm). Then you can solve for the radius of the smaller circle arc. Then you can probably do the rest from there
fair prism
You have any ideas for how to do it?
spare hornet
You have any ideas for how to do it?
No
spare hornet
How to factor after
fair prism
sin^2x=sinxsinx. How would you factor 2sinxsinx+sinx
spare hornet
Sorry of it's a dumb question
fair prism
What thing do both of the terms share
opal lantern
using trigono identity
spare hornet
Sinx
opal lantern
?
spare hornet
using trigono identity
Did not learn that yet but teacher is said we have to do these questions
No
fair prism
What value is the left side equal to when sinx=0
spare hornet
Pi and neg pi
spare hornet
Ohh
fair prism
Do the same thing for 2sinx+1 now (when 2sinx+1 is 0, the entire left side is 0)
or technically u could look at the answers and see only option 4 has -pi
fair prism
Yeah including negative pi, but not positive pi
odd edgeBOT
fair prism
bot broken or smth
spare hornet
😭
odd edgeBOT
Available help channel!
sharp thistle
odd edgeBOT
cold sage
what have you done
odd edgeBOT
@sharp thistle Has your question been resolved?
sharp thistle
what have you done
Just imagined and feel about its domain
cold sage
you just went on a spiritual adventure with the functions?
whats the definition of uniform continuity
sharp thistle
It should be increasing continuously
sharp thistle
real analysis?
Yes
cold sage
have you tried applying the defintion on them to see if they fulfull it
sharp thistle
have you tried applying the defintion on them to see if they fulfull it
I don't understand how to apply the definition
cold sage
youll do it as normal
you get your e>0 and f=...
you say for all x,c in interval with |x-c|<f then...
then just do the |f(x)-f(c)|..... stuff
if you can get it so that delta has no dependence on c (or x by extension) then its uniformly continuous
sharp thistle
Can we try an easy example so that i can understand the concept?
Suppose if we take sin(1/x)
I know that x=0 is not existing
Rest of all points it will be continuous
sharp thistle
.close
odd edgeBOT
tawny notch
Nvm
odd edgeBOT
tawny notch
.close
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Available help channel!
tawny frost
how to calculate g1(y) and g2(y) without sketching?
odd edgeBOT
how to calculate g1(y) and g2(y) without sketching?
tawny frost
like without sketching, idk if g1(y) = y/8 or g2(y) = y/8
quasi sparrow
Why can't you sketch
quasi sparrow
Yup
odd edgeBOT
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weak dew
i need help with trigonometry
if cosθ=3/5, and 0°<θ<90°, find tanθ-(1/sinθ)
odd edgeBOT
@weak dew Has your question been resolved?
jolly halo
i need help with trigonometry
if cosθ=3/5, and 0°<θ<90°, find tanθ-(1/sinθ)
cos theta is 3/5 so sin theta is?
jolly halo
bet
weak dew
.close
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eager iris
- The centers of four circles (in the plane) of radius 1 are the vertices of a square of side 1. Through how many points do at least two of these circles pass? Explain with the help of a neat figure.
sturdy perch
tried drawing it?
eager iris
no I don’t understand how to draw it
sturdy perch
we are going to draw 4 circles, one at a time, pick your favorit vertex on the square with side length one. Then draw a circle where that vertex, is the center, and the circle has radius one, the same length as the side of the square
eager iris
so the vertex is the center?
sturdy perch
yes
eager iris
I drew one
sturdy perch
now, do this three more times, for each vertex
eager iris
done
sturdy perch
let me se
eager iris
sturdy perch
perfect!
eager iris
so the answer is 8?
sturdy perch
"Through how many points do at least two of these circles pass?" is a bit weird, we need to mark all intersections, then see if it is between atleast two circles, to count this write numbers next to the intersection to make sure to not miss any or over count
i think thats all of them?
eager iris
Do you also have to count the circles?
sturdy perch
no
eager iris
so 8?
sturdy perch
12 intersections of at least two circles
eager iris
im confused
sturdy perch
1: black and red intersects
2: black and blue intersects
7: black and green intersects
10: black and red intersects again
9: black and blue interects again
5: black and green intersects again
eager iris
the answer thing says 8
sturdy perch
weird
sturdy perch
Shoot
sturdy perch
What language?
eager iris
Which inequality is wrong? (Explain graphically without SSM)
(A) sin 300° < sin 350°(B) cos 300° < cos 350°
(C) sin 300° < cos 350°(D) tan 300° < tan 350°
(E) cot 300° < cot 350°
Dutch
sturdy perch
Time to draw a big circle
eager iris
damn
sturdy perch
aight lets skip drawing
we can just stare at this instead
familiar with the unit circle?
sturdy perch
so first coordinate is cos, second coordinate is sin
so, now we can read of values to check the inequalites
eager iris
yes
sturdy perch
ah, here, more numbers and sign of the functions
we can start by checking those since postive is greater than negative
eager iris
okay
sturdy perch
(A) sin 300° < sin 350°(B) cos 300° < cos 350°
- < -*+ < +
(C) sin 300° < cos 350°(D) tan 300° < tan 350°
- < +*- < -
(E) cot 300° < cot 350°
- < -
Dam didnt reveal anything
eager iris
the drawing sucks so hard
sturdy perch
ye use the first one
sturdy perch
when you have cos and sin then its quick to calculate tan and cot
eager iris
but it needs to be graphically
thorn pecan
what i got was
a. 30
b. 14880
but apparently its wrong?
zenith tartan
show ur work women lover
thorn pecan
i did the calculator stuff on google so im unsure how to exactly show my work 😭
zenith tartan
u can explain what u did
cold urchin
a is right
nimble blaze
it seems you ignored pi for part b)
odd edgeBOT
odd edgeBOT
Available help channel!
unborn flicker
I want a function from 1 to 128, I do not care what is beyond of those values, where 1 is 32 and 128 is 128. I think the linear function shall be good.
unborn flicker
It is, probably, something as: "(128-32)/something", yet I do not see what.
void yew
hmmmmmm
unborn flicker
I see it, I do not see the logic behind.
cold urchin
Do you mean like f(1) = 32 and f(128) = 128
unborn flicker
If x is 1, y is 32, if x is 128, so is y, in 128 they cross.
cold urchin
Wdym they cross
unborn flicker
One function, values cross, in that point x is y, beyond that x is probably bigger.
cold urchin
What do you mean by values cross and x is y
jolly halo
..
unborn flicker
A fucntion has two values, not just one.
jolly halo
If x is 1, y is 32, if x is 128, so is y, in 128 they cross.
i mean this statement litterally means what pure said a line above doesnt it?
unborn flicker
I do not know.
jolly halo
For x = 1
y = 32
OR f(1) = 32
For x = 128
y= 128
OR f(128 ) = 128
and you need this f(x)
?
unborn flicker
Yes. That is what I want.
I did try learning such codes, I failed. I can only read the very basic.
If x passes 128, the y passes 96, x is 1,33..., or is y, times greater, I can do it.
unborn flicker
No, it is just 96 because it already starts with 32 when other is 1.
Bingo. Now just to convert it into actual formula.
X/(1+1/3)+32 is the y I want, probably.
cold urchin
so you just wanted a straight line that passes through (1,32) and (128,128)
unborn flicker
Yes.
jolly halo
oh my god.
jolly halo
wow
cold urchin
unborn flicker
I think this is called linear function.
This is your thank. People in Indo-China, I forgot which land exactly, are collecting, what I remember as lilies.
.close
odd edgeBOT
jolly halo
I think this is called linear function.
yeah a straight line
odd edgeBOT
Available help channel!
jolly halo
did you get the equation as
odd edgeBOT
did you get the equation as
unborn flicker
did you get the equation as
Oh no, no more questions! I barely understood this amount. Please.
jolly halo
.close mb didnt realise i opened a chat
jolly halo
odd edgeBOT
clever fjordBOT
jolly halo
(from what i thought i think we can use rolle's theorem but im not sure how exactly)
as f prime here would just be linear
chilly epoch
Maybe check all the options one by one
jolly halo
wont work
too many unkowns
specially option c 
cant seem to proof that otherwise too
noble forge
look at the discriminant of 3ax^2+2bx+c
chilly epoch
D = b²-3ac= a² -ac +c²
noble forge
and then the signs of a,b,c
jolly halo
we do not know a / b / c it can be anything really
unless we get like a perfect square or adition of suares perhaps
chilly epoch
D = b²-3ac= a² -ac +c²
From this you can check that the given exp is always non negative
jolly halo
we cant say for sure ig
noble forge
we do not know a / b / c it can be anything really
well draw a rough graph and then mark the vertex and make cases (only 2)
chilly epoch
For a,c are real
noble forge
a>0 and a<0
chilly epoch
So option C is incorrect
jolly halo
fair
chilly epoch
so for option A
Check f(0).f(1)
chilly epoch
And to make worst there is none of these in options
jolly halo
IKR!
chilly epoch
Substitute value of c
jolly halo
as -a -b?
chilly epoch
f(0).f(1)= -(a+b)(2a+b)= -(2a²+3ab+b²)
jolly halo
not sure what im looking for here..
chilly epoch
Wait
jolly halo
what will multiplies them do
chilly epoch
I was trying to get expression which is always +ve or -ve
chilly epoch
D = b²-3ac= a² -ac +c²
You see how i got this
jolly halo
yeah ofc
already played with the discriminant a lot
im overstimulated
the dumb book doesnt have any other similar question
the book threw a curve ball right at my face and i had no prep
no way
no way
jolly halo
(from what i thought i think we can use rolle's theorem but im not sure how exac...
it is just rolle's theorem.
because i want to check if roots lie in the interval
i think i should consider THIS as f'(x)
to find f(x) i can just integrate it
ax^3+ bx+2 +cx+ C = 0
C-> arbitary constant
for f(0 )
we get C
for f(1)
we get a + b + c + C = C ( as a+b+c = 0 )
oh everything is fitting so perfectly now
and since f(0) = f(1)
fprime should have a root in interval 0 to 1
due to rolle's theorem
thanks for trying i think i got the solution , should be A
chilly epoch
I have not studied rolle's theorem
jolly halo
oops forgot to close the chat
np
thanks for responding !!!!
( also this theorem was mentioned like so behind this question i swear , and no other question used this, had to read everything )
.close
odd edgeBOT
https://gyazo.com/fe339f446d017690dd3b36a2ecd9b56d
rocky edge
!status
odd edgeBOT
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
4
l composed r = {(a,3), (c,3), (b,1)} ?
i'll do r composed l later, just checking l composed r first
crisp wadi
You can't define composition of l with r
Applying r first gets you an element from {1, 2, 3}, but you need that to be in the domain of l
rocky edge
Wht
crisp wadi
l composed r = {(a,3), (c,3), (b,1)} ?
This would be correct if you wrote r composed l
rocky edge
Ye
crisp wadi
And is l(1) defined?
rocky edge
Na
crisp wadi
Neither is $l \circ r$
clever fjordBOT
A Lonely Bean
spiral frigate
$s(f,c)=\left(\floor{\frac{f}{c}}+1\right)\left(c+73-(c\mod{16})+\ceil{\frac{\log_2{c}}{8}}\right)$
clever fjordBOT
Kris
spiral frigate
for a given f, I want to find the c which produces the minimum s(f,c)
is it possible to create a formula that can do that, and how would i go about doing it?
right now, I just have some code that brute forces all values for c within a range, but it would be computationally cheaper and more scalable to solve the problem with a formula
also - f, c and the output to the function are all natural numbers
sudden ledge
no theres no closed form solution for this
this is an integer programming problem google that
spiral frigate
no theres no closed form solution for this
how do you know, is it provable?
spiral frigate
this is an integer programming problem google that
and I don't know what this is, sorry
I looked up the wikipedia article and it has way too many things I don't understand, I'm not very smart
late dust
There seems to be a pretty easy solution to this
If f < c then floor(f/c) = 0 and the answer is a constant (if c can't be 0 then the minimum is at c=1)
Hm I can't find a way to explain the rest
spiral frigate
If f < c then floor(f/c) = 0 and the answer is a constant (if c can't be 0 then ...
the problem is about breaking a file down into chunks, where f is the size of the file and c is the size of the chunk, so if the size of the chunk is bigger than the filesize then there will just be one chunk and you can ignore the first bracket. I don't see how the output would be a constant but you only need to consider cases where 1 <= c <= f (or f+15? idk), sorry I should've mentioned that
f is the size of the file in bytes, so an integer greater than 0. c is the size of the chunk in bytes, so an integer greater than 0 and less than or equal to the file's size. the function presented in the latex output the size of the file in bytes after you've chunked it, added metadata, etc. so you're trying to use that function to find the optimal chunksize for reducing the size of the output file
spiral frigate
for a given f, I want to find the c which produces the minimum s(f,c)
i.e. this
spiral frigate
Hm I can't find a way to explain the rest
while an explanation would be nice, all i really want is a formula that can be used to find the best c (since a formula is pretty much always gonna be faster than brute force)
or, at the very least, some kind of optimisation for brute forcing, like "only test odd numbers" or something like that (i'm not saying that is something that would work it's just an example)
but yeah. a formula. or how to make one because i don't know where to start.
late dust
Then it looks to me like c = ceil((f+1)/2) gives the minimum
spiral frigate
based on my testing that doesn't seem to work, but I'm curious how you got that
late dust
I may have ignored a term 
spiral frigate
rip
late dust
Ok first thing to notice, c - (c mod 16) is just 16*floor(c/16)
spiral frigate
h u h
late dust
It starts at 0 and jumps up by 16 every 16 units
spiral frigate
yeah i just tested it on desmos and it works but i can't wrap my head around why
late dust
In [0,15], (c mod 16) is just c
So that's c - c = 0
In [16, 31]. (c mod 16) is c - 16
So that's c - (c - 16) = 16
And so on
spiral frigate
right
late dust
floor(x) jumps by 1 every 1 unit
floor(x/n) jumps by 1 every n units
Did that clear things up?
late dust
ceil(log_2(c)/8) starts at 1 and jumps up by 1 after 256^n where n starts at 1 and is just incremented every time
spiral frigate
yeah, it's "how many bytes does it take to represent the integer chunksize"
late dust
So let's ignore this term, solve for c < 256 and then try to put it back in
spiral frigate
i know it's not the correct way to do things but it's such a small term that it doesn't have much impact, so even if you can solve it without that term, that's better than nothing
spiral frigate
So let's ignore this term, solve for c < 256 and then try to put it back in
but yeah okay
late dust
Ok, now floor(f/c) + 1 = floor((f+c)/c)
spiral frigate
i know it's not the correct way to do things but it's such a small term that it ...
ignore this actually it does make more difference than i thought
spiral frigate
Ok, now floor(f/c) + 1 = floor((f+c)/c)
why is that? is it like... floor((f+c)/c)=floor((f/c)+(c/c))=floor((f/c)+1)=floor(f/c)+1 or something like that? idk i haven't done maths in a while
late dust
Yeah
late dust
I probably won't be there in 30 min
Close this and open a new channel when you're back if you need
I have a feeling the minimum will be something like c = ceil((f+1)/(1+n)) where n = ceil(log_256(c)) or something
Otherwise ask for guidance with integer programming
I'm not sure I can actually solve this correctly
odd edgeBOT
@spiral frigate Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
hollow wasp
When I have this signal, how should I read the values for x[n]?
hollow wasp
south plume
wdym how?
hollow wasp
is the first value cos(pi/2 *0) ?
coral heath
im not sure if this is right
odd edgeBOT
im not sure if this is right
coral heath
leaden widget
the 2/3 exponent should be outside the parenthesis for one
leaden widget
ya
odd edgeBOT
odd edgeBOT
Available help channel!
odd edgeBOT
Available help channel!
gilded jewel
Question: What does it mean to find the rank of the derivative of a vector-valued function? For context, we recently covered implicit function theorem and rank theorem in my real analysis II class.
tall veldt
the derivative will be a matrix, so its just the rank of that matrix
or the rank of the matrix at an evaluation at a point rather
odd edgeBOT
@gilded jewel Has your question been resolved?
gilded jewel
the derivative will be a matrix, so its just the rank of that matrix
Yeah I took the jacobian and found values for which f' is invertible (by setting determinant = 0)
But that doesn't tell me the rank of f' in general
tall veldt
you just have to determine a maximal set of linearly independent columns like normal
mystic saffron
I really really need help
odd edgeBOT
I really really need help
lavish jackal
mystic saffron
so, I asked my teacher in thursday "wait, how they figured out that if we have a list, and we sum all the values of that list and we divide the output by the number of elements, we get the average?", and she didn't answer... so I am trying to answer that, and I got that the average between two numbers is (x+y)/2, and now trying to do that for 3 numbers, I got (x+y+2z)/4, and I am trying to prove that it is equal to (x+y+z)/3
can someone help me with that? I have been strugling with it the whole day ( I am not very good at math, like, I am 14 years old, but I have learned some math by watching 3b1b and other channels )
south plume
define average
in your context
what you are finding is a mean, one of the types of averages
mystic saffron
we are studying statistics
south plume
yes
mystic saffron
like, the average value between a list like [1, 2, 3, 4, 5] ( idk how to write it in math way, I am a programmer :( )
mystic saffron
can you see what's wrong with (x+y+2z)/4
not really, I did avrg2(avrg2(x, y), z) -> ((x+y)/2+z)/2 -> ((x+y+2z)/2)/2 -> (x+y+2z)/4
south plume
like, the average value between a list like [1, 2, 3, 4, 5] ( idk how to write i...
how would you find the average of a list/array in whatever programming language you use?
mystic saffron
how would you find the average of a list/array in whatever programming language ...
float v = 0;
for(int i = 0; i < arr.size; i++)
{
v += arr[i];
}
v /= arr.size;
I know how
I want to know why
south plume
not really, I did avrg2(avrg2(x, y), z) -> ((x+y)/2+z)/2 -> ((x+y+2z)/2)/2 -> (x...
well now that's the average between (average between x and y) and z, which isn't average between x y and z
okay
mystic saffron
well now that's the average between (average between x and y) and z, which isn't...
ohhh, ok that explains
south plume
first condition: the order must not matter
so it must be symmetric
so no x+y+2z, because that's not symmetric between x y z
mystic saffron
mhhh, true
but how would I find the mid point? for x and y is easy cuz i just did, c ( the middle between x and y ) is equal to x+d, and I want to know what d is, so the distance between x and y is y-x, and then I want the half of it, so d=(y-x)/2, then c=x+(y-x)/2, that is just c=x+y/2-x/2, and that is c=x/2+y/2 -> c=(x+y)/2
south plume
woah
first we were doing statistics, now this is geometry
but yes, these 2 things are related
the arithmetic mean of 2 points' coordinates is their midpoint
mystic saffron
wait wait wait, wouldn't the actual avrg3 be something like avrg2(avrg2(x, y) avrg2(y, z))?
mystic saffron
cuz we find the middle between x and y, and then between y and z, and we find the middle between those?
south plume
not gonna work
mystic saffron
I will trust you
but now I am just doing trial and error to find what works and trying to see what fails
south plume
cuz it again gives bias to a variable
arithmetic mean is defined to be sum of series over its length
mystic saffron
I started doing this since 9am or smth, now its 9pm, my brain is just hurting
mystic saffron
arithmetic mean is defined to be sum of series over its length
but why that works?
south plume
you can't use combinations of avrg2 to get avrgn
south plume
but why that works?
wdym why it works
we use it as one of the measures of the average
mystic saffron
why if I do number + number ... (n times) / n = average
mystic saffron
we use it as one of the measures of the average
yeah but why they found out that it works?
south plume
mean, median and mode
mystic saffron
how?
mystic saffron
mean, median and mode
yeah I know, that is what my teacher was talking about
and I asked "but how did people come out with this?"
south plume
for example
mystic saffron
and I asked "but how did people come out with this?"
no answer
south plume
the mean * the length of array will be the sum of the whole thing
here's a person asking the same thing as you
mystic saffron
yay
I mean he is asking "Why it works", I want to know "How they come up with it"
but I think yeah, the answer of one will answer the other in some way
south plume
that's history of math
mystic saffron
but how did people just woke up one day and said "wait, if i sum all this things together and I divide that number by the number of things i summed up, I get the """average value""" between the numbers in this thing"
what is the thinking you had to do to get that
mystic saffron
but how did people just woke up one day and said "wait, if i sum all this things...
also, is there a prof that it will always work? for any array size?
south plume
any array size
but also again
i'm not sure what you want the proof of
an "average" of a list is a human invented thing
mystic saffron
how they realized it worked for any array size?
also, what about an array with no elements inside?
that question is dumb but
south plume
an "average" of a list is a human invented thing
it's not like it will lead to a contradiction
mystic saffron
I wanted an answer
mystic saffron
an "average" of a list is a human invented thing
I mean everything is human invented so /:
south plume
also, what about an array with no elements inside?
you'll be dividing by 0 there :)
mystic saffron
you'll be dividing by 0 there :)
exactly
and 0/0 is "undefined" in most fields of math
my teacher said "it just works with any list size", and I was going to answer "what about a list with no elements?"
but I said "nah, this will lead to nothing"
south plume
i see you are a little smartass 13 year old
(it's a good thing, keep going)
like seriously i wish i was as cool at 13 lol
mystic saffron
like seriously i wish i was as cool at 13 lol
oh, thanks!
no way this site is just stackoverflow but with people that know math
mystic saffron
damm I hate stackoverflow
mystic saffron
a site full of smart people that just answer with vague questions or just don't answer at all and just act like they are supperior
south plume
i agree
mystic saffron
when I started learning programming it was a pain in the ass
anyways, now I think I got an answer
but
mhhh
I really need that math lore
cuz I just can't see how people come up with tis
well, maybe is just like coding, they tried different algorithms at random until they got values they liked and said "this is good to analize this thing" and it stuck around
mystic saffron
i agree
anyways, thanks a lot man
I really needed that answer, or at least a way of trying to figure it out, I don't have a clear answer, but I can start looking for info
and ask the right questions
I think this could be a really interesting topic to make a yt video about!"
( cuz I didn't find any info while searching there )
like those VSauce videos
south plume
it does sound interesting
mystic saffron
yeah
south plume
in any case, if your question has been answered, type .close
mystic saffron
and there is no info in spanish either so I could do it in spanish and english ( so I can show it to my nerd friend that likes math )
mystic saffron
in any case, if your question has been answered, type .close
I think it is, for now
.close
visual tide
Since when in linear algebra are we allowed to add columns to other columns in a matrix like wtf
summer river
Since when in linear algebra are we allowed to add columns to other columns in a...
why not
wouldn't you expect A + (-A) = 0
visual tide
i dont understand ur example
like ive never seen in my life someone doing column operations
how is that even legal
summer river
I mean break the determinant up
and you will see that if they have the same two columns
then det(A) = 0
ex the determinant of this is 0
so you can safely subtract a column from one to another and add one to another
and get the same determinant
visual tide
ok but that only works cuz detA = 0?
summer river
ok but that only works cuz detA = 0?
well it works for any matrix
visual tide
k but thats whats confusing
like in linear equations u cant just add an x column to a y column
yk? 😭
latent scaffold
Well the determinant of the transpose is the same yes?
And the rows of the transpose are the columns of the original one
summer river
k but thats whats confusing
just reocgnize that you can break it up linearly
and that if there is a repeat column
you find that the determinant is zero
let me write it out if you really want
but I have to whip out my notebook
visual tide
ok
summer river
ok
you want me to get my backpack
and take out my notebook
and send a pic to you?
visual tide
yes pls
so like we can just alternate between row and column operations on the same matrix with no problems?
that seems rly weird to me
summer river
so like we can just alternate between row and column operations on the same matr...
I'm sending the page
pls don't use my handwriting for forgery or anything
visual tide
um i wont
latent scaffold
nosqldb probably has a good example coming. To me it seems like you're confusing row reducing and determinant computation. Row reducing forces you to only do operations on rows because it represents the simplification of linear equations. You don't have this restriction on determinants as they represent a scaling factor of a unit n-cube.
visual tide
so its only for determinants we can do row operations?
i mean
colum
column operations
summer river
so its only for determinants we can do row operations?
my example will come up, but trivially you can see usually if you can do column operations, you can also do row operations
since
det(A) = det(A^T)
my example will give an intuitive explanation on why you can do column operations
but a precursor, if a matrix A has two identical columns, then det(A) = 0
if you want the proof for that lmk
visual tide
is the proof for that cuz theres gonna be a column of 0 when reduced
so the det would be 0 because the diagonal has a 0
summer river
is the proof for that cuz theres gonna be a column of 0 when reduced
if you change two rows or columns, you change the sign
summer river
but notice that you get the same matrix if you change the columns that are equal
so
let det(A) = b
then $b = -b \implies b = 0$
clever fjordBOT
nosqldb
summer river
bc it's a real matrix
visual tide
um why r u allowed to add them like that
summer river
um why r u allowed to add them like that
well expand along the 3rd column
and you will see
visual tide
what does expand along the column mean
summer river
what does expand along the column mean
do you know what an laplacian expansion is
visual tide
no
summer river
@latent scaffold do you wish to explain
visual tide
this is introductory linear algebra 💀
summer river
this is introductory linear algebra 💀
I also take introductory linear algebra
I thought this was a common topic
old whale
How do you prove that e^x > x^n
odd edgeBOT
How do you prove that e^x > x^n
latent scaffold
You can show their ratio goes to infinity for large x
odd edgeBOT
@old whale Has your question been resolved?
distant tartan
odd edgeBOT
distant tartan
how do I integrate this if I dont know what the function is?
odd edgeBOT
@distant tartan Has your question been resolved?
gleaming dew
I= integrate (cos^2023 x) dx from 0 to 2pi |
odd edgeBOT
I= integrate (cos^2023 x) dx from 0 to 2pi |
upbeat drum
!status
odd edgeBOT
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
(change bounds to use even/odd function properties)
odd edgeBOT
@gleaming dew Has your question been resolved?
quasi sparrow
@gleaming dew did you understand the hint
odd edgeBOT
@gleaming dew Has your question been resolved?
gleaming dew
<@1125652195367452813> did you understand the hint
I'm really not very good at English so I hope everyone can explain in detail 🥲
I'm really grateful
quasi sparrow
I'm really not very good at English so I hope everyone can explain in detail 🥲
Do you know what odd and even functions are
gleaming dew
Do you know what odd and even functions are
This is it, right?
help me pls
or this
lethal gale
What’s the formula to the Pythagorean theorem?
odd edgeBOT
What’s the formula to the Pythagorean theorem?
blissful musk
mint mirage
What’s the formula to the Pythagorean theorem?
You mean a^2 + b^2 = c^2? A very common formula that you can google
lethal gale
You mean a^2 + b^2 = c^2? A very common formula that you can google
THANK YOU
lethal gale
Yesss
odd edgeBOT
Available help channel!
drifting edge
drifting edge
.close
ruby nacelle
i am stuck on c, i dont know how can i use part a to help me
ruby nacelle
sharp oak
Maybe not useful, but note sin(π/10) = sin(9π/10)
sharp oak
We will get a polynomial from this process, I'm sure a is useful
I would instead consider x = π/10. However, I have not actually tried this yet so take me with a grain of salt.
odd edgeBOT
@ruby nacelle Has your question been resolved?
spiral atlas
SOS
round bone
Distribution
Or just test square numbers
You want x to be square and x+5 to be square
Nvm
formal ermine
i would expand this first
then you can probably do a substitution where a = root(x) and solve from there (may not be exactly root(x))
noble forge
SOS
notice that sqrt(x^2+5x) factors as sqrt(x)*sqrt(x+5)
That may not make this problem a piece of cake but definitely should help in some simplification
toxic monolith
$\left( \sqrt{x+5}-\sqrt{x} \right)\left( 1+\sqrt{x^{2}+5x}\right)=5\\\text{ Let's note that the domain of the equation is }[0,\infty )\text{ then we get that: }\\\frac{5\left( 1+\sqrt{x^{2}+5x} \right)}{\sqrt{x+5}+\sqrt{x}}=5<=>1+\sqrt{x^{2}+5x}=\sqrt{x+5}+\sqrt{x}\\<=>\sqrt{x+5}\left(\sqrt{x}-1 \right)-\left( \sqrt{x}-1 \right)=0<=>\left( \sqrt{x}-1 \right)\left( \sqrt{x+5}-1 \right)=0\\<=>x = 1 \vee x=-4\text{, but }x\geqslant 0\text{. then solution is: }x=1$
clever fjordBOT
Joanna Angel
noble forge
well aren't you providing the entire solution to just be copied by the OP
toxic monolith
well, i have just decided to show solution, since it is tricky, little bit
noble forge
but yeah you did a good observation at STEP 1
(derationalizing sqrt(x+5)-sqrt(x))
toxic monolith
yes, wanted to avoid gettign polynomials of he vry high degrees
odd edgeBOT
@spiral atlas Has your question been resolved?
spiral atlas
yo im back
spiral atlas
$\left( \sqrt{x+5}-\sqrt{x} \right)\left( 1+\sqrt{x^{2}+5x}\right)=5\\\\\text{ ...
i do not understand this by one bit nor the fact if this was even a 9th grade solution
how about this, i found an existing solution but there a part in it that i dont understand
toxic monolith
i made solution shorter to decrease number of liens ) but ask
spiral atlas
lemme find it
toxic monolith
solution is x = 1, you can easily verify it
first i have applied Conjugate (square roots)
because i have noticed also that number 5 wil be reduced
spiral atlas
nvm i get the whole thing
spiral atlas
high school
but technically its middle school as in my place we still consider 9th grade to be middle
toxic monolith
i see, i am trying to compare to our schools, but ok
irrational euqations, reuqire knowledge of many tricks
and mslty they are not pleasant )
odd edgeBOT
odd edgeBOT
Available help channel!
ruby nacelle
odd edgeBOT
ruby nacelle
i dont know what to do next
and also idk how to use the results of part a
how is part a useful
zenith tartan
can u just post the pic of the question agani please? @ruby nacelle