which still makes no sense
#help-36
outer yacht
tranquil pine
why not tho
outer yacht
because i just realised
(a)(4a) = 4a²
answer should be 3 or -3 for k
which i tested and its correct
wild plank
<@&286206848099549185>
tranquil pine
what
wild plank
Ask dan
wild plank
Yes
tranquil pine
how -3 tho
strong kindle
Can anyone help me to know how can I develop my math skills?
tranquil pine
Can anyone help me to know how can I develop my math skills?
yeah sure
what grade are you in
strong kindle
Grade 10
tranquil pine
im not that great but ill try
strong kindle
Egypt
tranquil pine
oh nice
so what do you struggle with
any questions or so you want help trying to solve?
wild plank
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wild plank
Thanks for the help
tranquil pine
why
wild plank
What
tranquil pine
that dude wants help
wild plank
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strong kindle
so what do you struggle with
I just want to be good at math in general
wild plank
that dude wants help
Can't he just open a new help channel?
tranquil pine
i guess
warm python
yeah, do that. #❓how-to-get-help
tranquil pine
i can dm you bro
strong kindle
Like I want to know about the skills that I need to know for being nice at math
wild plank
Like I want to know about the skills that I need to know for being nice at math
Just do repetitions for related topics
Practice makes perfect
tranquil pine
I can give yall a really good qn
wild plank
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tranquil pine
kind of good
strong kindle
Ok
There's some problem
In my school, I learn mathematics in Arabic
So I think it's difficult some how for me to understand mathematics in English
So it needs time to get uses to it
So can you give me easy qn to practice at it
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devout dock
how would i differentiate the probability generating function for a binomial distribution X-B(n,p)?
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how would i differentiate the probability generating function for a binomial dis...
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civic valve
δy = (u + δu)(v + δv) – uv
= uv + uδv + vδu + δuδv – uv
=uδv+vδu+δuδv
Why do we need to subtract uv
marble agate
context?
timid pollen
δy = (u + δu)(v + δv) – uv
= uv + uδv + vδu + δuδv – uv
=uδv+vδu+δuδv
Why do ...
To avoid double counting
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ruby bough
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ruby bough
what happened between the second to last step
and the last step
like
how did he end up with sin/cos - cos sin
oh i see
yeah thanks
ruby bough
yup
i have to put a negative sign outside the integral correct ?
so i could get ln
as the product
of the integral
or not ?
ivory vessel
wdym
ruby bough
like
the derivative of cos is negative sin
and they're in a fraction
and the integral of anything divided by it's derivative is ln
west berry
You mean derivative divided by anything?
ivory vessel
and the integral of anything divided by it's derivative is ln
uh no not really
this is sinx/cosx
which is tanx
integral of tanx is -ln|cosx|, which is a fairly common integral
ruby bough
yeah well it's the same idea
like the integral of 4x/2x^2 would be ln|2x^2|
bec the derivative of the denominator is the numerator
ivory vessel
yes
ivory vessel
!done
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sterile swan
Good morning, I'm having trouble with some math in my class that looks like setting a function equal to another function. Here, lg refers to log_2.
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Good morning, I'm having trouble with some math in my class that looks like set...
sterile swan
Does it actually make sense to say that one function is equal to a modified form of the function? Can I do math on that function in the same way I would with an equation?
For instance, if 2T(n/2) + n = n log_2(n), then does T(n/2) + n = 2n log_2(n)?
To ask a simple version, if f(x) = x + 7, then does f(x) - 7 = x? I was under the impression we must go from x to the outputs of x, not the other way around.
timid pollen
Does it actually make sense to say that one function is equal to a modified form...
I don't think that's a valid assumption
sterile swan
I don't think that's a valid assumption
That's what I'm thinking as well. This is computer science related. Is there a specific place to ask for help on that topic?
timid pollen
That's what I'm thinking as well. This is computer science related. Is there a s...
Not sure
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warm python
My thoughts:- So the ways it can have two solns is that it just touches the x axis once
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My thoughts:- So the ways it can have two solns is that it just touches the x ax...
warm python
and intresects the other time
so the derivative must ne negative at some point
so the answer is B ?
mint orbit
I think thats the answer
ocean lintel
I'd recommend drawing the cubic and then drawing its derivative
mint orbit
im not certain i follow your logic
warm python
so basically, the derivative must be negative on some interval
mint orbit
maybe its easier to think of critical points than signs
warm python
as cubics map from R to R, it can't always be negative, or always positive
ocean lintel
but it is B yes, because you need two sign changes
warm python
I'd recommend drawing the cubic and then drawing its derivative
I'll try that, thanks
oh yeah, that works very well
thanks both of you!
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warm python
so in case 1, the function will have to be a straight line $\frac{\left(y-8\right)}{x-10}=\frac{3}{5}$
soft zealotBOT
Why am. I here
warm python
when mapped from R to R instead
spare folio
why straight line
warm python
there are 10 inputs
5 outputs
oh
right
hmm, in case(1) It need not necessarily exist , I think
i.e f(n)=n
same goes for case 2
so B is the answer?
desert mantle
why do you think so
if it doesnt need to exist then surely you can give such an example function
warm python
oh
right
for case 1, f(n)=n is necesssary
as there are only 6 number between f(2) and f(10)
desert mantle
7 numbers
warm python
and 10 inputs to be mapped
desert mantle
why does that mean that an input needs to be mapped to itself?
desert mantle
ok and? if the points werent from 0 to 10 but instead from 10 to 20 then it clearly wouldnt hold
desert mantle
yes but you havent used that in your argument so far
warm python
OK, so there are 10 elements to be mapped to 7 elements ,such that 7 elements are identical, now , f is increasing on Z. If it's constant, function at f(n)=n is ensured.
if not
f(n)=n is still ensured as there aren't evough elements(Not sure of how I'd prove this) to ensure $f(n)\neq n$
soft zealotBOT
Why am. I here
ocean lintel
try drawing the function
warm python
how would I do that?
ocean lintel
take an example
warm python
for a constant function, (except at the endpoint), f(n)=n is true
ocean lintel
try drawing the function
if you wanna be efficient, try making a function that doesn't work
If you can, you're done
If you can't, you should now know why
spare folio
draw y = x
but not linear
just mark up to (1,1) (2,2) (3,3).. (10,10)
and
draw a function whose y value doesnt greater than 8 when it is between 0<x<10
tiny gorge
here's something that might be useful
let g(n) = f(n) - n
observe that g(n+1) - g(n) >= -1
now compute g(0) and g(10) for your two examples
tiny gorge
hmm maybe this doesn't work after all, lemme think again
oh right, it does work
haha sorry, operating on like 2 hours of sleep
warm python
how did you come up with that?
tiny gorge
just playing around
notice that in the first example, you have
g(0) = f(0) - 0 = 2 and g(10) = f(10) - 10 = -2
so g has to go from 2 to -2
can it avoid 0?
it can't decrease by more than -1 at a time
so no, it can't
spare folio
it can't decrease by more than -1 at a time
why
ocean lintel
how did you come up with that?
if you're looking for a fixed point and don't think of looking at f - Id, you lack experience
desert mantle
let g(n) = f(n) - n
and as a general strategy, its often better instead of f(n)=n where both sides vary, to consider f(n)-n=0 where only one side varies
warm python
if you're looking for a fixed point and don't think of looking at f - Id, you la...
yeah, I do, never solved a problem like this before
hmm
ok
yeah, this sort of makes sense
spare folio
```
g(n+1) - g(n) = f(n+1) - (n+1) - f(n) + n
= f(n+1) - f(n) - 1
...
great
warm python
```
g(n+1) - g(n) = f(n+1) - (n+1) - f(n) + n
= f(n+1) - f(n) - 1
...
I follow until the second step, what did you do in step 3
tiny gorge
I follow until the second step, what did you do in step 3
just used that f is nondecreasing, which means f(n+1) >= f(n)
warm python
just used that f is nondecreasing, which means f(n+1) >= f(n)
ah, got it
spare folio
f(n+1)-f(n) is always greater than or equal to zero
so plus -1 is always greater than ot equal to -1
warm python
ok, got it
let me think of something similar for function 2
yeah, in function two it's definitely not necessary
there are more points in the Image set than in the preimage set
so it's possible to create a function such that $f(n) \neq n$
soft zealotBOT
Why am. I here
ocean lintel
then create it
warm python
$f(0)=f(1)=f(2)....f(9)=-2$ and f(10)=12
soft zealotBOT
Why am. I here
tiny gorge
simple but effective
spare folio
haha yes
warm python
though I'd like to think of a more rigourous proof
tiny gorge
for (b) you just needed a single example, and you provided one
warm python
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bold coral
There is a site/file with all known primes?
final saddleBOT
There is a site/file with all known primes?
celest crane
The number of prime numbers are infinite.
But you can find relatively small lists of prime numbers online though.
bold coral
Yes, but I need to download list(because i found site with 1000 billion primes, but i can`t download all list)
zenith pollen
we know more primes than there is storage space lol
tardy sigil
The number of prime numbers are infinite.
prove it
bold coral
The number of prime numbers are infinite.
yes
chrome pawn
there is a collection of the 5000 largest known primes
which is updated hourly i think
tiny gorge
is there a practical upper bound that you can take advantage of
like, there are files containing all primes that fit into a 32 bit integer for example
chrome pawn
if it's that urgent u can write a simply python code to limit primes upto a 32 bit integer and then write it onto a file
i think we can use the Sieve of Eratosthenes algorithm
glad steeple
anyone has an Idea how to integrate this beauty. I have the feeling substitution might be a thing. but I cant think of any idea how.
vast summit
x=sin theta or cos theta, either one works
final saddleBOT
tiny gorge
it seems not natural to me
!help
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it seems not natural to me
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glad steeple
ah maybe because you know that the derivative of arcsin has something to do with that sqrt expression?
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ivory barn
Question leads: Use the first-order Talylor evolution for a linear approximation of
the value of ln(6/5). Then make an estimate of the maximum error (with
sign) in this approximation and also sketch the graph of the function ln 𝑥
along with the linear fit so that the sign of the error estimate
appears.
So sorry if the english is awful
The conclusion choses a value for a = 1 wich I don't really get why they do! I get to f(a) + f´(a)(x-a) but the cheat sheets answer is ln(6/5) wich i don't get
final saddleBOT
Question leads: Use the first-order Talylor evolution for a linear approximation...
floral nova
They choose a = 1 because 6/5 is approximately equal to 1 and you can calculate ln(1) without a calculator.
If there is another value you know that is closer to 6/5 that you can calculate exactly without a calculator, you can use that instead.
ivory barn
Ahhh ok I get that how do they get it so the first-order is equal to ln(6/5) I don't know if my calculations are way off or if I am doing something wrong here
floral nova
It won't be equal to that. You are linearly approximating a curve that is not a line.
ivory barn
sorry I'm just confused on how they get to the conclusion
f'(x) is 1/x I accidentaly cut it out
hoary oxide
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hoary oxide
I am confused for the second statement
I know that the answer is True, but WHY?
I thought dimension is number of vectors in a basis
there are only 3
how can it be greater?
low cargo
it doesnt say only containing 3 linearly independent vectors. it could be a 5 dimensional space which will contain 3 lin independent vectors (as well as 2 more)
formal trail
any subspace (other than the subspace only containing the zero vector) will have infinitely many vectors, so it must contain more than just the 3 vectors overall
so there may or may not be additional linearly independent vectors in the space (if there aren't then it's 3D, if there are it's higher dimensional)
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@hoary oxide Has your question been resolved?
slate jasper
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warm wraith
!status
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What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
You could divide it. That would spare you using the quotient rule
But either way you would get to the same result
fallow folio
Differentiation
Do you know how to differentiate the function you posted?
slate jasper
Yes u/v
slate jasper
But what about this method rationalization
fallow folio
you get the same result but you still need to differentiate
you should get a fraction with numerators having roots 4 and 16
after you differentiate
replace x = 4 into your original eq., so f(4) = 1
then go for f(16) = 25
slate jasper
(x+3) + 36/(x-10)
If i differentiate it
fallow folio
you need to use the quotient rule to differentiate that
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@slate jasper Has your question been resolved?
edgy ore
what did I do wrong?
final saddleBOT
what did I do wrong?
edgy ore
answer sheet says a = 16 and b = 4
I know there are different ways of solving this, but I wanted to know what was the mistake here
pseudo knot
what is that
-8-r
they're said to be in gp and ap but it is not said that the common ratio and common difference are equal
those are 2 separate quantities
limber isle
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limber isle
this is a new concept for me so i feel i ought to check if im getting it right before i move forward
i only get the answers back once the teacher grades them unfortunately and im going to be completing the unit today so no such luck
sturdy cypress
the first one is weird
i think the formula would have 0.011
the second one is extra super dumb
the last one is hard to guess
it does work for negatives, and it wouldn't make sense if x >= 0 is right but not y >= 0
so i would guess all real numbers
but maybe you guessed right
limber isle
i thought the same for the 1st
by sumb u mean crazy simple right?
or am i missing smth
limber isle
<@&286206848099549185> second opinions?
hm..
they seemed fine to me
if not a little simple
onyx lagoon
Yeah
sturdy cypress
they aren't telling you anything about the function in the second one, you have no way to know it's actually guessing
limber isle
you have to make the function no
sturdy cypress
the last one is interesting there's like meta deduction, it can't be option 2 because then option 3 is wrong, it can only be option one
just it would be a wrong guess, i suppose
onyx lagoon
Just chilling
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tranquil charm
why is $\sum^{\inf}{n=1} \frac{1}{n+2}$ divergent sum when $\frac{1}{n+2} \leq \frac{1}{n^2}$ for $n \geq 3$ and $\sum^{\inf}{n=1}\frac{1}{n^2}$ is convergent?
final saddleBOT
why is $\sum^{\inf}_{n=1} \frac{1}{n+2}$ divergent sum when $\frac{1}{n+2} \leq ...
solar glade
Put between $
soft zealotBOT
Slowaq
thorny tendon
If n = 100, that inequality is false
tranquil charm
ah yes my bad
so how should i show that it is divergent?
ah nvm got it
.close
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sonic crystal
I’m not sure what I did wrong
final saddleBOT
I’m not sure what I did wrong
sonic crystal
I don’t know what to do from here
royal gust
Consider a u-sub instead
sonic crystal
Ohhhh
yeah that would work from the start
I forgot I could just do that
This chapter is about IBP so I was only thinking in terms of that method lol
Thanks
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royal tusk
How would I do 11?
final saddleBOT
How would I do 11?
royal tusk
Everything after the integral I used mathway to help me, but I’m not sure how it even got these values nor how I can isolate y
magic sparrow
Everything after the integral I used mathway to help me, but I’m not sure how it...
#11 is a seperable ODE
do you know how to solve those
magic sparrow
that is exactly how you solve these
it's even what you started doing in your work on the right
You don't need to isolate y
to have a solution
royal tusk
So where should I stop?
magic sparrow
,w y'=e^(x)sin(2y)
soft zealotBOT
royal tusk
I was taught to answer this by separation of variable method
magic sparrow
ah, looks you can solve for y explicitly somehow
magic sparrow
I was taught to answer this by separation of variable method
yes, because it is a "seperable" ODE like I said earlier
your method is right
you just need to figure out how to simplify it, assuming you did your integrals properly
royal tusk
I plug integral of dy/sin2y into mathway but got this weird ln(…) as an outcome
magic sparrow
that is the correct integral
royal tusk
Oh ok
But then I got stuck on (1-cos2y)/sin2y= e^(2e^x+c)
How would I go from there?
magic sparrow
cos(2y) is a trig identity you should know
royal tusk
There are a couple
I did this
Would this be correct?
Oh wait it should arctan not arcsin
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north spear
hi
north spear
so its says the plane Π contains the points (−1, −3, 2) and (1, 0, 1) and is parallel
lelt with the vector
a) i have solved
but on b
it say count the distance between the point (10, 1 ,1) to II
i dont understand how to do that
!help
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spare bone
Is there an algorithm to check periods of xorshift with different parameters? Like different shifts or number of rounds. It's hard to bruteforce because input is 64bit.
final saddleBOT
Is there an algorithm to check periods of xorshift with different parameters? Li...
@spare bone Has your question been resolved?
paper hamlet
I'm struggling alot with quadratic equation (grade 10)
final saddleBOT
I'm struggling alot with quadratic equation (grade 10)
paper hamlet
Ever since they started the chapter I've not been able to do it without lots of helps
paper hamlet
Example of the kind of stuff I get
karmic kindle
better photo plz
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dense pumice
(a_1 a_2 a_3 a_4) + (a_2 a_3 a_4 a_5) + ... + (a_n a_1 a_2 a_3) have n terms , since each of these terms are either +1 or -1, and the sum of all n terms equals 0, there are equal number of +1 and -1 terms in this sum, this implies n is even, that means n is either of the form 4k (divisible by 4) or 4k+2 (not divisible by 4). I am trying to come up with an explanation for why n = 4k+2 would not work, but I have not got anything so far, can someone help me out?
final saddleBOT
(a_1 a_2 a_3 a_4) + (a_2 a_3 a_4 a_5) + ... + (a_n a_1 a_2 a_3) have n terms , s...
cobalt lodge
how many products are there if n=4k+2
dense pumice
how many products are there if n=4k+2
4k+2
cobalt lodge
oh wait a minute i thought it didn’t wrap
vital surge
(a_1 a_2 a_3 a_4) + (a_2 a_3 a_4 a_5) + ... + (a_n a_1 a_2 a_3) have n terms , s...
simple way to get started is to consider what happens when n = 6
dense pumice
simple way to get started is to consider what happens when n = 6
alright, there should be two more terms a_7 and a_8
vital surge
huh?
dense pumice
For n = 6
vital surge
where are you getting 7 and 8 from
the sequence only goes up to n, meaning there are 6 terms
dense pumice
Yeah that's what I'm saying, it doesn't work, we need two more terms for it work,
vital surge
(a_1 a_2 a_3 a_4) + (a_2 a_3 a_4 a_5) + ... + (a_n a_1 a_2 a_3) have n terms , s...
for n = 6 (i'm omitting the "a"s)
1234 + 2345 + 3456 + 4561 + 5612 + 6123
i'm not sure what you mean by "it doesn't work"
do you mean the statement cannot be true? yes that's what the problem tells us. it's also what we wish to prove
dense pumice
Ohh my bad I did some mistake in laying out cases
cobalt lodge
ok proof by contradiction works to eliminate n=4k+2
by counting the number of all 4(4k+2) values that must be -1
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daring juniper
The area of Laatoka is approximately 18,300 km2. Calculate the area of Laatoka with a map ball with a diameter of 30 cm. The diameter of the Earth is 12,700 km.
map scale
final saddleBOT
The area of Laatoka is approximately 18,300 km2. Calculate the area of Laatoka w...
warm ether
how have you been going about it
daring juniper
i got 0 clue
warm ether
you need to find the area scale of the map to reality
even though big E isnt a sphere
anywho, how do you think you could do that
daring juniper
2 people tried to help and failed too
daring juniper
you need to find the area scale of the map to reality
even though big E isnt a s...
i gotta do the comparison then do parabels and cross them
ygm?
warm ether
maybe
tall mantle
I think what you can do is assume your area is a disk sitting on the sphere. When you ratio down the radius of the sphere, assume you ratio down the radius of the disk in the same way
the area of your disk should be shrinking something quadratic with r, not linear
daring juniper
I think what you can do is assume your area is a disk sitting on the sphere. Whe...
so what do i do
tall mantle
A' = A(r'/r)^2 where A is the "old area" and r is the "old radius"
the primes are the "new"
make sense?
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@daring juniper Has your question been resolved?
daring juniper
the primes are the "new"
what r primes
final saddleBOT
@daring juniper Has your question been resolved?
daring juniper
tall mantle
I don't understand the issue, but you should check that it's been resolved
low magnet
I need help understanding items 3, 4 and 5. I have tried solving for items 1 and 2 but idk if they're correct
final saddleBOT
I need help understanding items 3, 4 and 5. I have tried solving for items 1 and...
warm ether
,calc (1.610^(-19))/(8.85410^(-12))
soft zealotBOT
Result:
1.8070928393946e-8
1 is fine
warm ether
what were you doing in 2
ah i see
seems alright
for 3 what does gauss law state
for 4, thats quite simple if you just work out the area of that section
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amber crane
Hi! these are 2 questions for our homework. The problem is, our professor purposefully doesnt teach the appropriate lesson or math concept beforehand. So far, ive been doing okay in answering the activity, but I'm having a bit of trouble in terms of how to approach these 2 items.
For the first one, I tried doing 6! / 6 as my solution but I'm not too sure I'm understanding the question right, particularly the part where it says "non crossing"
For the second one, what I tried doing is dividing the area hidden by the total area of the smaller rug, this gave me 25% going directly off the numbers provided. I am just not sure if its right to assume that 1/4 of the smaller rug is automatically the hidden area just because it said that the corner falls on the center.
Any insight or help would be greatly appreciated! tyia
final saddleBOT
Hi! these are 2 questions for our homework. The problem is, our professor purpos...
chrome pawn
in the first problem i think non crossing could mean that the line segments joining two points dont intersect?
amber crane
in the first problem i think non crossing could mean that the line segments join...
ohh makes sense
do u think 6!/6 would still be a possible solution ?
chrome pawn
what i would do is probably first calculate all possible hand shakes which is 6!/6 since its a ciruclar permutation
and then subtract the crossing handshakes
amber crane
and then subtract the crossing handshakes
how would i be able to calculate all possible crossing handshakes?
amber crane
hmm, i still seem to be stuck. im trying to figure out a formula to solve this based on what u said
chrome pawn
wait i think i was wrong
its not gonna be 6!/6 thats the number of ways 6 people can sit in a circle
the number of handshakes possible is 6 choose 2
@amber crane
chrome pawn
so since each person is adjacent to only two people those are the only non crossing handshakes possible
amber crane
i notice that if two dots are adjacent there is no crossing
but im not sure how id come up with a formula for calculating all possible crossing handshakes based on what u said
amber crane
the answer is 9\
oh this is already with the crossing handshakes subtracted?
chrome pawn
yep
may i ask what grade math is this tho
because it was easy but i confused myself
amber crane
im in 12th grade
we have this maths subject but no one really knows the exact concepts it covers
its pretty random
chrome pawn
oh ok
sterile vector
Guys anyone want to see my face
inland kettle
please don't spam/occupy help channels if it isn't relevant.
sterile vector
U saying me?
round hinge
i mean lerty
amber crane
im not that sure about the 2nd one
all good no worries. thanks for helping me with the first ques!
round hinge
😔😔
amber crane
i mean lerty
yup I just need some verification that my approach to the 2nd item that I sent is valid
round hinge
yup I just need some verification that my approach to the 2nd item that I sent i...
i was about to answer
amber crane
i was about to answer
wdym
round hinge
nothing
amber crane
wait @chrome pawn sorry follow up question if thats alright
chrome pawn
like tbh sinces it only 6 it was easy to manually count it but i guess we can derive a formula for it as well
6 choose 2 total number of handshakes
then total number of crossing handshakes
and then total number of non crossing handshakes
since its the difference
is that fine?
amber crane
like tbh sinces it only 6 it was easy to manually count it but i guess we can de...
but i manually counted 9 crossing handshakes. orrr am i counting this the wrong way
chrome pawn
yeah thats what i got
9 crossing
and 15 total
so u subtract
and u get 6
or u could just count the total number of adjacent pairs
amber crane
9 crossing
but non crossing would be the adjacent ones no?
chrome pawn
ye sorry
amber crane
ahhhh
chrome pawn
the problem is that since its 6 its easy to count them manually
royal horizon
GM
manic void
chrome pawn
,rotate
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midnight hill
how to express y as a fucntion of x : 1/x + 1/y =1/f
final saddleBOT
how to express y as a fucntion of x : 1/x + 1/y =1/f
stone wagon
how to express y as a fucntion of x : 1/x + 1/y =1/f
subtract 1/x from both sides
and then isolate y
midnight hill
oh yeah yeah i did that but i have a hard time isolating y how do you flip 1/y like does it become -y?
zealous holly
cross multiplication
stone wagon
oh yeah yeah i did that but i have a hard time isolating y how do you flip 1/y l...
no
cross-multiply or raise both sides to power of ^-1 (flip)
midnight hill
i am doing this right my answer is y/1 = fx/y - (x-f)/fx
oh nevermind is it y = xf -x -f
hushed dust
Hello, I have to find the solutions of the following trigonometric equation.
hushed dust
The solutions according to the book are:
But I came to this:
Here is my resolution, I don't know how to get to the solutions in the book:
sen is the same as sin
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hushed dust
?
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hushed dust
?
analog zealot
yo
hushed dust
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tawny dagger
i dont really understand how the teacher worked this out
the second hand of a watch moved from 2pm to 7pm the same day, if the length of the hand is 12 cm taking pi is 3.14, calculate:
a) the length of an arc defined by this movement
b) the area of the minor sector formed by this movement
final saddleBOT
i dont really understand how the teacher worked this out
the second hand of a w...
zenith pollen
the idea is that 2 to 7 is 5/12 of the clock, so the length and area would be 5/12 of the circumference and circle area
tawny dagger
could you explain the formulas for this question pls 😶
neon slate
you just need the formulas for area and circumference of a circle, do you remember those?
tawny dagger
yes!
neon slate
so if the length of the clock's hand is 12cm as stated in the problem, what would be the area\circumference of the whole circle?
(we can afterwards get the 5/12 part from that)
@tawny dagger you understanding the circle we are talking about?
tawny dagger
so for circumfrence 2x3.14x12 = 75.36 and area is 3.14x12x12 = 452.16
tawny dagger
<@1074098745131663423> you understanding the circle we are talking about?
a bittt i js need help along the way
ok yay i got that part
neon slate
so for circumfrence 2x3.14x12 = 75.36 and area is 3.14x12x12 = 452.16
yes that's exactly right, so that's the circumference \ area of the circle traced by the clock's hand if it was moving all the way around the clock
but between 2pm and 7pm, it goes just between 5 of the numbers on the clock (out of 12) so all you would have to do is calculate 5/12 of each of those numbers
tawny dagger
but between 2pm and 7pm, it goes just between 5 of the numbers on the clock (out...
ohhhh
wait im lost 💀
neon slate
neon slate
wait im lost 💀
you just multiply the area\circumference you got by 5/12 lol
theres not much to it
if it was like...half the clock...you would just multiply by 1/2 right cause it would be half of the area and half of the circumference right?
but in this case the part that youre interested in is 5/12 so thats what you multiply by
so circumference: 75.36 (5/12)
area: 452.16 (5/12)
@tawny dagger does that make sense?
tawny dagger
ok ok so multiply 75.36 x 5/12 and 452.16 x 5/12?
neon slate
ok ok so multiply 75.36 x 5/12 and 452.16 x 5/12?
yes like...the circumference is divided into 12 parts right? (the arc length between each hour on the clock) and you go between 5 of them, so total of 5 out of 12
and same with area, it's like a pizza of 12 slices, but youre only eating 5
tawny dagger
i think if you did the formula like
2x3+2x1
6+2 = 8
i would understand more 😭 im so confused like i just need a working out of this so i can practice more
neon slate
i think if you did the formula like
2x3+2x1
6+2 = 8
i would understand more 😭...
what's the confusion?
it's just 5 parts out of a total of 12
it's just 5/12 times whatever the whole thing is
neon slate
ok ok so multiply 75.36 x 5/12 and 452.16 x 5/12?
you already have the answer here
tawny dagger
you already have the answer here
would that be for a and b
neon slate
one is the arc length one is the area yes...
tawny dagger
alrightt ty!!
i got ittt i got another one :>
A clock is reading 11:30 hr. The radius of a circle forming the face of a clock is 15 cm, taking pi is 3.14, calculate:
a) the length of the minor arc defining time
b) the area of the minor arc defining time
in this working out 165 was divided by 360 x etc i js wanna know how the area 165 was derived
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limber isle
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limber isle
makes sense?
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<@&286206848099549185>
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verbal karma
Express the probability distribution of the random variable of the sum of the outcomes on rolling 2 dice. The sample space of the discrete random variable for the sum of the outcomes on rolling 2 dice is 6
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Express the probability distribution of the random variable of the sum of the ou...
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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.
verbal karma
what do you mean the sample space is 6
It's whats stated in the instructions so im asking for help since I dont get it either
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eager stirrup
how in the world would i do this?
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how in the world would i do this?
eager stirrup
could i get a hint please
mint orbit
could i get a hint please
i believe this has a name
if thats helpful
its a form of the ||leibniz integral rule|| but i could be mistaken
eager stirrup
I’ll search it up but I don’t think we learned it
ivory vessel
pretty sure this can be easily proven by FTC and chain rule
eager stirrup
pretty sure this can be easily proven by FTC and chain rule
Do FTC on what?
The integral?
ivory vessel
yes
eager stirrup
I wonder if chain rule will produce the same result though
eager stirrup
Because it would become F(h(x))-F(g(x))
Oh wait
Yeah this is easy
Thanks!
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thick swan
real quarry
Hello! Could you guys give me a hint about where this solution is wrong?
real quarry
The steps, I mean, I was able to solve it by difference of squares
However I must correct the first solution, but I cannot find the error
marble agate
how x^2+x became x^2(1+1/x)?
fast heart
Factorised out x^2
fast heart
I don't understand the step after, facyorising x out of the square root
cobalt lodge
under what conditions does it hold that lim f(x)g(x) = lim f(x) lim g(x)?
real quarry
under what conditions does it hold that lim f(x)g(x) = lim f(x) lim g(x)?
is it because both f and g must be continuous?
cobalt lodge
no
and as far as we’re concerned f and g are continuous in the region we’re interested in here
for a sillier example
$\lim_{x \rightarrow \infty} 1 = \lim_{x \rightarrow \infty} x \cdot \frac{1}{x} = \lim_{x \rightarrow \infty} x \cdot 0 = 0$
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IV
cobalt lodge
spot the error
neon slate
you have lim (x) = infinity and lim of what was evaluated to the right is 0, but thats an indeterminate form (i.e. lim f(x) = infinity and lim g(x) = 0, you do not have lim [f(x)g(x)] = 0, it is indeterminate and you have to look for some other way to evaluate it
real quarry
spot the error
I see the error clearly, but I can't justify exactly why it's wrong in a solid conceptual way
cobalt lodge
under what conditions does it hold that lim f(x)g(x) = lim f(x) lim g(x)?
at which point we go back to this
you probably want to either look at notes or google limit laws
real quarry
you probably want to either look at notes or google limit laws
I'm doing exactly that, ashhashas, I'm still trying to understand what's the case here
neon slate
I'm doing exactly that, ashhashas, I'm still trying to understand what's the cas...
this isn't equals to 0, this only evaluates to 0 if you take the limit
you split the limit in 2 then you evaluated the limit of the right part
but then you slide that 0 back inside the left limit
as if it wasnt a separate limit
but the left factor is giving you a limit of inifnity and the right factor is giving you a limit of 0, which is indeterminate
real quarry
but then you slide that 0 back inside the left limit
which 0?
neon slate
which 0?
yes, you cannot randomly slide a constant into a limit if doesn't exist, and well lim as x-> infty of x doesn't exist
so sliding that 0 back into the left limit isnt valid
before trying to evaluate the limit
@real quarry are you familiar with lim x-> 0 of sin x / x ?
neon slate
ok so what happens if you consider the limits separately:
lim x to 0 (sin x) * lim x to 0 (1/x )
if you decide the first one is 0
then multiply that 0 back in and decide 0 * 1/x is 0, now try to evaluate the limit...you'd get 0, but the lim of sin x / x = 1
this product law for limits is ONLY valid if the limits exist, so you cannot think of it that way
the 1/x limit doesnt exist, so you cannot think of it as the product of two separate instances in this case, because if you do the individual limits of sin x and 1/x you get 0 and infinity, again 0 * infinity is an indeterminate form, so the sin x / x limit must be evaluated some other way, not considering it as a product of two limits
do you get your mistake yet @real quarry ?
real quarry
do you get your mistake yet <@543937185938931723> ?
I believe I'm almost there, give me a minute
Ah, so the error is considering 1 + 1/x as a valid limit, but it doesn't exist given its one sided limits?
neon slate
I believe I'm almost there, give me a minute
how did you get 0? you split up the red thing into two parts and decided that the limit of f(x)g(x) is equal to the limit of f(x) * the limit of g(x) and evaluated the limit of g(x) to be 0, but the limit of f(x)g(x) is equal to lim of f(x) * lim g(x) ONLY if the limits of f and g exist, but they dont (at least not both), so this assumption you can split off the big product and evaluate the factors separately is erronous
real quarry
how did you get 0? you split up the red thing into two parts and decided that th...
But why doesn't the limit of g(x) exist?
neon slate
its the limit of f(x) = x that doesnt exist...
real quarry
its the limit of f(x) = x that doesnt exist...
Ahhh
got it, got it
because otherwise it would be infinite * 0, which, as you said, is not determined
neon slate
right, those various limit theorems you learn only apply when the limits exist, important fine print
real quarry
right, those various limit theorems you learn only apply when the limits exist, ...
Thank you! I believe the main problem was that I didn't know 0 * infinity is undefined, but those will surely help
neon slate
Thank you! I believe the main problem was that I didn't know 0 * infinity is und...
note that limits that evaluate to "+/-infinity" use a different definition than the standard delta epsilon stuff and function a bit differently. some textbooks will say "the limit doesnt exist, but this kind of limit describes the behavior of the function," some might say the limit exists and is infinite or something, but important to know it is a distinctive type of limit than the ones that actually evaluate to a number. I personally like to stick with the idea that the limit doesnt exist but if we have the lim -> infinity then its more describing what the function does
real quarry
note that limits that evaluate to "+/-infinity" use a different definition than ...
Ah, okay. I will read some stuff on that specific matter because it has got me curious now
Thank you so much for your help (and patience!)
and also thanks to @cobalt lodge
cobalt lodge
it’s the tiny details that matter
and 0*(+-)infty is the only case where product law doesn’t apply
cobalt lodge
that’s surprisingly fine, -infty
real quarry
I read a less rigorous but clear explanation. 1/x (Usually aproximated to 0) is not exactly zero but something very small, which, multiplied by infinity gets arbitrarily big and thus, 0 * infinity is not defined
Is it a wrong explanation? Or okay-ish?
cobalt lodge
uhhhhh
neon slate
i dunno if that's a good way to think about it, kinda fudgy at best
cobalt lodge
if you write a justification like that, probably 0 marks, maybe 1
but if it helps with understanding sure
real quarry
if you write a justification like that, probably 0 marks, maybe 1
but if it help...
Oh, yeah, definetely, ashhasheashs. I was more worried if it was actually true, even though it's not a mathematical proof
Thank you again, guys!
.finish
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flint perch
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flint perch
how did they find the line segments?
I know when you plug in 0 you get the point (-5,-3) and 1 you get (0,2)
but how did they find the parametric representation
tulip coyote
Are you familar with the whole parametric a + t(b - a) equation for a line segment from the point a to the point b (with t being from 0 to 1)? If so then it's just that but slightly reframed
flint perch
this one?
Ive definitely learnt this before in lin alg I think?? but I forgot lol
I'll do a quick search
for a quick reminder
tulip coyote
this one?
Yea that's the one 
Replace r0 with (-5, -3) and r1 with (0, 2) and then split the line equation into the x and y components and it should hopefully be clearer
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flint perch
staying here for a bit..
although i think I'll sleep soon because im very sleep deprived
have been for a few weeks now but mideterm season is over!!
so yea time to become a normal human again
i do realize tho, because Im lacking so much sleep I can't think properly anymore cause everything just feels foggy
ok thats my little rant for the day
tulip coyote
although i think I'll sleep soon because im very sleep deprived
Me too 
only slept for less than an hour yesterday
(also sorry, I fell asleep on you the other day 
)
tulip coyote
i do realize tho, because Im lacking so much sleep I can't think properly anymor...
Awwww 
definitely can get that. make sure you get some rest soonish 
tulip coyote
lol off topic whyd you change your profile pic?
Just felt like changing it haha
Also hi @magic sparrow 
flint perch
Ahh i liked your old one lol
everytime I see it im like
ahh
thats chartbit
yayyyyyyyyyyyyy
tulip coyote
Awwww maybe I might put it back at some point 
flint perch
lol ok
also its soo funny but basically there was a question on the real analysis midterm and it was like xn = (-1)^n and yn is cauchy, will xn(yn) also be cauchy.. smth like that
I literally showed how xn(yn) could diverge
and then I was like yup
thats CAUCHY🤩
I dont remember the exact conditions
I think they also gave some other detail but I literally proved and concluded the opposite
tulip coyote
also its soo funny but basically there was a question on the real analysis midte...
Awww was it like a "it must be true/must be false/may be either true or false" type question or something?
flint perch
yea, but I dont know why I thought they strictly wanted us to prove xn(yn) is also cauchy
but after discussing it with some friends after exam, I was like oh...
yea so I guess it was a must be true/must be false type of question
tulip coyote
Awww I see 
flint perch
we'll see how I do..
All I want to do, is to get better than class average for real analysis
hahahahhaa
but yea
but also the class size is super small and everyone is pretty smart
last exam I got the class average grade😂
this time... we'll have to see
but not much hope cause I messed up that question
and we literally had 3 questions total😂
opaque ember
T/F questions are the worst
they can also be pretty bad to grade 
unless you dont ask for counterexamples, then its just binary credit
flint perch
ahhhahahha ok I'll be back
I might do more stuff or I might just sleep
we'll see
likely the latter
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snow flax
hi, could someone help me with the steps on how to solve this? im struggling to think after working on assignments all day and am burning out😭
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hi, could someone help me with the steps on how to solve this? im struggling to ...
snow flax
or if there is some type of video or content online i can read/watch to come across my answer, please link it 🙏🏾
magic sparrow
What is your doubt
signal shell
How to evaluate $\int_{-\infty}^\infty f'(t)e^{-st}dt$?
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rbmuk
signal shell
Using IBP
signal shell
😮
@snow flax you should try that
I would expect that would lead to a swift answer
(One line after this)
snow flax
<@912798847804276817> you should try that
so integrate $\int_{-\infty}^\infty f'(t)e^{-st}dt$?
soft zealotBOT
weezy🤴🏾
snow flax
this is another form of $\mathcal L(f')(s)$ am i correct?
signal shell
The lower limit should be 0 (I misremembered)
soft zealotBOT
weezy🤴🏾
signal shell
But this should just be the definition of the laplace transform applied to the function f'
snow flax
$\mathcal L(f')(s)=\int_0^\infty f'(t)e^{-st}dt\
=\int_0^{f'}e^{-st}dt\
=-\frac1s[e^{-sf'}-e^0]\
=\frac1s[1-e^{-sf'}]$
soft zealotBOT
weezy🤴🏾
snow flax
But this should just be the definition of the laplace transform applied to the f...
i used a littlesomething from my notes, how does this look
i feel like i might have gone wrong on the f'?
or is this good?
signal shell
No
You cant put the function as the top index
@magic sparrow
Let me have my sir explain
magic sparrow
@snow flax
Let me help clear your doubt
Do you know how to do integration by parts for a simpler function like say maybe, $$\int_{0}^{\pi}x\cos{x}dx$$
soft zealotBOT
Austin
snow flax
Do you know how to do integration by parts for a simpler function like say maybe...
yes if im not wrong, take u=cos x and du the derivative
magic sparrow
That's not right
do you know what integration by parts is?
It's not the same as u-substitution
snow flax
ohh whoops i know what youre saying
integration from 0 to pi for x then integration from 0 to pi for cos x?
snow flax
bruh dang i thought ive done it before
snow flax
yes it looks very familiar
signal shell
magic sparrow
basically yes
but you have to evaluate the bounds still
which is a mistake you were making earlier
I'll let my protegee take over from here @signal shell
signal shell
My friend try watching that video on integration by parts to refresh your memory.
snow flax
mr sir and mr protege @magic sparrow @signal shell i might have gotten it
hows this ??
magic sparrow
I think you left offf the bounds of integration
and why did you say du=0
you have not gotten it
hate to be the bearer of bad news
snow flax
I think you left offf the bounds of integration
ahh thats another part i need a brush up on
snow flax
and why did you say du=0
is du just e^-st again? this e rule is so crazy
magic sparrow
..
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rotund glen
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rotund glen
Can someone lend a help with part a pls
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rotund glen
<@&286206848099549185>
jagged cosmos
Start by differentiating the function f(x) using Fundamental Theorem of Calculus
$$\dfrac{d}{dx} \int_0^x f(t)dt =f(x)$$
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Ericsson
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rotund glen
<@&286206848099549185>
jagged cosmos
Write
jagged cosmos
$$f'(x) = \dfrac{1}{\sqrt{2\pi}} e^{-x^2/2}$$
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Ericsson
rotund glen
I completely agree, i think i am a bit lost how u got that