i think bayes theorem actually might be easier here btw
#help-33
cunning fractal
Oh okay
latent coral
actually i'm not sure since bayes would require you to find P(she stopped | last flip heads)
which doesn't seem all that easier
cunning fractal
Even then I still feel like the answer is wrong
Because we're assuming specific sequences like HH or TTT
But in reality she could do HTTHTHH
Or something else of the sort
marsh citrusBOT
@cunning fractal Has your question been resolved?
hot slate
Hi everyone. I hit my chatgpt and claude limit, so I am coming here to ask something. In this example, on the definition of the set H, H is a direct image right? Even if it was a subset of R(real numbers), within the function definition, there won't be any inverse image, right? So why in this example, it took the direct of the inverse image of H and it was equal to {y:0<=y<=1} ?
marsh citrusBOT
Hi everyone. I hit my chatgpt and claude limit, so I am coming here to ask somet...
whole thorn
tldr
hot slate
bruh
hot slate
tldr
it's literally two questions bro i can't sleep if i go to sleep with this question unanswered
whole thorn
i apologize
quaint elm
Hi everyone. I hit my chatgpt and claude limit, so I am coming here to ask somet...
H is not necessarily a direct image of any set
whole thorn
my nitro ran out btw
hot slate
H is not necessarily a direct image of any set
yeah but still if i try to get the inverse image of H, that means some number squared has to be -1, right? that's confusing to me
quaint elm
it will help to start by calculating f-1(H)
no, not necessarily
the inverse image of H is all real numbers x such that f(x) is in H
hot slate
so that means basically all numbers f(x) that is in H would be [0, 1] ?
that makes sense, because there is no number that will be squared to -1, so we will just take the numbers x that f(x) is in H. Okay got it.
i forgot the command that closes this channel, anyone?
quaint elm
.close
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sacred rivet
I found my eigenvalues to be λ= 0, λ = 25, λ = -18
and the corresponding eigenvectors to be:
[4/3 0 1]^T
[-3/4 0 1]^T
[0 1 0]^T
Do I simply normalize these vectors to make P and just use the eigenvalue along the diagonal for D?
I don't have to perform gram-Schmidt because Each eigenspace has dimension 1, so all we need to do is normalize the eigenvectors?
glass silo
They're already orthogonal, so you just need to normalise them
sacred rivet
Well how do we know they are already orthogonal?
glass silo
Try it 
valid cape
glass silo
(last is clearly orthogonal to the first two, the first two you can see it works out 
)
glass silo
Because, weirdly enough, a matrix is orthogonal iff its columns are orthonormal (and not just orthogonal) 
sacred rivet
I'm not getting the first two vectors to be orthogonal
glass silo
So we need to make sure that those eigenvalues are orthonormal, them being nonzero orthogonal is most of the way there
sacred rivet
the dot product is not 0 for the first 2
glass silo
It's not? How are you doing them?
glass silo
Happens to us all 
sacred rivet
umm i'm still slightly confused
why we need to normalize
i understand that
normalizing makes it orthonormal
but doesn't the question only want orthogonal?
glass silo
It wants the matrix to be orthogonal, but you need the columns to be orthonormal for that 
sacred rivet
I don't have to perform gram-Schmidt because Each eigenspace has dimension 1, so...
Is this also true?
glass silo
good question, I can't remember
I feel not but I don't have a counterexample to hand for that 
Actually, if you have all your eigenvalues being distinct, then the corresponding eigenvectors are automatically orthogonal, so then it's just needing to normalise them that would be left
sacred rivet
yaa
okay thank you!
wait hmm
even without normalizing tho
our matrix P is orthogonal
so why is normalizing coming into play?
wait
nvm
you are right!
glass silo
Yep you need them orthonormal, it's an iff 
On a related note, whoever chose the naming should be shot 
sacred rivet
hahahahaha
sacred rivet
mhm, thank you so much!
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weak wind
i need help on this question
marsh citrusBOT
i need help on this question
sand fable
nope. not a single person
marsh citrusBOT
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sand fable
.close
subtract the fractions starting from smallest denominator
i.e. 13/42 - 1/2!, is this less than 0? if yes, then a_2 = 0 and move on to 1/3!. if not, then subtract again, etc
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steel breach
I tried various different methods but I just can't solve this integral.
still temple
I tried various different methods but I just can't solve this integral.
assume this integral is I
and then apply kings rule
and observe the result
steel breach
observe the result?
still temple
what did you get after applying kings rule?
steel breach
this?
elfin berryBOT
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reaction for more information.
(You may edit your message to recompile.)
broken zealot
,,\int_{-1}^1 \frac{e^x x^2){e^x+1}
elfin berryBOT
Bair
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broken zealot
bruh
steel breach
\int_{-1}^1 \frac{e^x x^2}{e^x+1}
steel breach
yes
still temple
do you have one iintegral i.e this
and other which is the same but with e^x in the numerator
steel breach
yes
but how should I get rid of the e^x
since like I have to sub the I back right?
still temple
check what happens when you add both the integrals
since both are the same
you have 2I = ....
still temple
check what happens when you add both the integrals
inorder to get this idea you have to observe
👁️
lol
paper cedar
marsh citrusBOT
amber birch
!status
marsh citrusBOT
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
2
paper cedar
I have a solution here but it might be wrong
Can you guide me like from the 1st step
amber birch
I have a solution here but it might be wrong
post your solution and I'll tell you where you might have gone wrong
otherwise I might be telling you things that you already know
paper cedar
Alright let me write it again
marsh citrusBOT
@paper cedar Has your question been resolved?
whole hinge
whereis the value of di came from?
marsh citrusBOT
whereis the value of di came from?
amber birch
whereis the value of di came from?
can you send the full question?
marsh citrusBOT
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marsh citrusBOT
whole hinge
can you send the full question?
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whole hinge
the question If the temporary average of the data is 27 million rupiah, then the calculated average of the data (in millions of rupiah) is shown by the formula
marsh citrusBOT
the question If the temporary average of the data is 27 million rupiah, then th...
whole hinge
pendapatan means salary, jumlah means sum, frekuensi means frequency
amber birch
the question If the temporary average of the data is 27 million rupiah, then th...
ah so I think you're just listing the order of the pendapatan
cause 27 (million) is in the category 25 to 29, so you set that weight to be 0
it's a very clever method
,calc 5 * 1 + 8 * 2 * 10 * 3 + 12 * 4 + 7 * 5 + 3 * 6
elfin berryBOT
Result:
586
hmm
whole hinge
whereis the value of di came from?
nonono im asking wheres the di came from
-3,-2,-1
amber birch
I'm not too sure actually
whole hinge
can you solve the problem?
amber birch
looks like this but different
amber birch
can you solve the problem?
I don't know what the question is asking actually
like what is a temporary average and a calculated average
whole hinge
looks like this but different
naahh this is how to search average
whole hinge
https://www.youtube.com/watch?v=cZfawFEnbSU
bro r u indonesian?
amber birch
bro r u indonesian?
no
whole hinge
oo
amber birch
unfortunately I don't know why the formula given in the video works
whole hinge
oo i see , so we have to search the mid point first and after that we hv to reduce mid point and temporary average
amber birch
and it doesn't help that your teachers are like "shut up and memorise it"
whole hinge
wwww
elfin berryBOT
Result:
11.666666666667
thats the way to search the average
amber birch
,calc (30 + 270 + 650 + 350)/(3 + 9 + 13 + 5)
elfin berryBOT
Result:
43.333333333333
the way to search temporary average is a bit difffrent
amber birch
yeah so that's the same as (sum of fi di) / (sum of fi)
amber birch
the way to search temporary average is a bit difffrent
yeah then I don't understand this
whole hinge
yayayaya
amber birch
but your question is asking for the calculated average right
amber birch
oh wait what I was doing
that's rata hitung right
not rata-rata sementara
interesting
but then can't you apply the same method for both
amber birch
looks like this but different
you just need to find the midpoints as stated here
whole hinge
naahh broo youre right
amber birch
I just don't know how Indonesian maths works
maths is maths I know but there are plenty of differences in style and content
maths isn't super universal
marsh citrusBOT
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marsh citrusBOT
@small stream Has your question been resolved?
flat junco
can somebody help me how to calculate eigenvalues by hand? actually its a bonus task for my assignment
marsh citrusBOT
can somebody help me how to calculate eigenvalues by hand? actually its a bonus ...
fervent rampart
could you show the original problem?
marsh citrusBOT
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flat junco
could you show the original problem?
its part of complex assignment
this is just a characteristic polynomial of sample covariance matrix
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rancid glen
modern lintel
what is your question
rancid glen
Solve Derivatives
modern lintel
so you want the derivative of that function?
rancid glen
Yes please
modern lintel
then first, each term on the numerator has a common denominator so try splitting it up into 3 different parts
modern lintel
yeah oaky so split it into your 3 terms
late geode
no need to split
modern lintel
why not
late geode
just apply quotient rule
modern lintel
but also depends what level they are at
late geode
even if you were to split, you'd need to follow with product rule with neg exponents or quotient rule, so why not just do that directly
marsh citrusBOT
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rancid glen
but also depends what level they are at
Grade 12
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serene ermine
i need a full solution for this
marsh citrusBOT
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serene ermine
.end
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muted grail
how can i show that this series is a cauchy series?
marsh citrusBOT
how can i show that this series is a cauchy series?
amber birch
<@&268886789983436800>
amber birch
how can i show that this series is a cauchy series?
note that $|a_n - a_m| < a_n$ for all $m, n \in \mathbb N$
elfin berryBOT
southlander!
elfin berryBOT
southlander!
amber birch
we can assume this condition without loss of generality
muted grail
ok
amber birch
**southlander!**
sorry this is not quite right
muted grail
so we need to show that the sum of all the terms 1/k^2 from k = m to k = n can be as small as we want it to
amber birch
so we need to show that the sum of all the terms 1/k^2 from k = m to k = n can b...
yeah I know
ah can't you bound $|a_n - a_m|$ above by $(m - n + 1) \frac{1}{n^2}$
elfin berryBOT
southlander!
amber birch
basically if we have 1/4^2 + 1/5^2 + ... + 1/10^2 for example
bound this above by 1/4^2 + 1/4^2 + ... + 1/4^2
muted grail
i might be wrong can we maybe use the fact that n>=m>=N_e and say that 1/n^2=<1/m^2 =< 1/N^2
amber birch
and there will be 10 - 4 + 1 or m - n + 1 terms
amber birch
the experts are coming great
hushed egret
,, \sum_{k=m}^n \f 1 {k^2} \le \sum_{k=m}^n \f 1 {k(k-1)}
elfin berryBOT
hushed egret
🔭
hushed egret
your bound doesn't work because n is unbounded
hushed egret
i've given you what you need
amber birch
,, \sum_{k=m}^n \f 1 {k^2} \le \sum_{k=m}^n \f 1 {k(k-1)}
ah shit ofc
muted grail
.reopen
marsh citrusBOT
✅
muted grail
@hushed egret hey so
I understood what you meant
but I'm stuck again
<@&286206848099549185>
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gray iron
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terse basin
I'm not sure how to start on that
you're doing general sin equation or wtvr right
to find the second solu you do pi -x
amber birch
I'm not sure how to start on that
if u is a solution of sin(u) = k
then note that pi - u is also a solution
cause sin(u) = sin(pi - u) for all real u
,w pi - arcsin(-0.45)
elfin berryBOT
amber birch
oh and then add 1
gray iron
Sorry if my notation is messy
This seems correct
Thanks guys I really appreciate the help :)
.close
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gloomy merlin
Are the Fourier coefficients of a scalar the scalar itself?
marsh citrusBOT
Are the Fourier coefficients of a scalar the scalar itself?
gloomy merlin
my book says the following, but how do you justify it using the mathematical representation of the Fourier coefficient series
marsh citrusBOT
@gloomy merlin Has your question been resolved?
marsh citrusBOT
royal sable
Are the Fourier coefficients of a scalar the scalar itself?
Yes, because given a function $f(t) \in L_2([0,2\pi])$ one can calculate the coefficients as
$$a_k = \frac{1}{2\pi}\int_0^{2\pi}f(t)e^{-ikt}dt,$$
and hence when $f(t)\equiv c$ we have
$$a_0 = \frac{1}{2\pi}\int_0^{2\pi}cdt = c, \quad a_k=\frac{1}{2\pi}\int_0^{2\pi}c e^{-ikt}dt=0, \ k \ge 1.$$
elfin berryBOT
EQUENOS
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wicked ridge
How do you do newtons cooling with changing environmental temperature
wicked ridge
Like a block heated to 100 degrees C is placed into water that is 18 degrees C
when will the temperature stabilize
marsh citrusBOT
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wicked ridge
Sorry it wouldnt be newtons cooling
The mass of the water isnt enough to keep its temperature constant
How would we come up with a coupled differential to solve this
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unborn condor
!original
marsh citrusBOT
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.
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median flare
Hello, I need some help with converting units of measuerement
marsh citrusBOT
Hello, I need some help with converting units of measuerement
median flare
So I have 0.00001pm³ and I need to convert it to Tm³
Now I understand I have to use division because pm is a smaller unit than Tm and that I have to do it 3 times because it's ^3
But like... how do I calculate it?? What numbers do I put in
main idol
Do you know how many pm equals 1 Tm?
median flare
I don't, I don't really understand that part. I just have this table and I know that pm=10^-12 and that Tm=10^12
But what do I do with that information?
median flare
Yeah
main idol
1 pm = 10^(-12) m
You can multiply 10^12 to both sides to solve for 1m
median flare
I got 1×10^31m
main idol
I got 1×10^31m
For what
median flare
10^-12?
main idol
No
median flare
What do you mean by both sides?
main idol
Then cube both sides if you want to solve for pm^3 in terms of m^3
like 2.4cm = 1in. Multiply both sides to get 1 foot = 12*2.4cm
median flare
How did you get 12 in 12×2.4
median flare
Hahahahaha I know it probably is but I never used American measurements in my life
main idol
You can multiply 10^12 to both sides to solve for 1m
Does this make sense now
"multiplying both sides" by a number should not be a new concept
median flare
I don't know what to multiply with
what number
I thought it was maybe first about converting pm to m and then m to Tm
main idol
I specifically said 10^12
median flare
Is 1Tm=10^12m?
main idol
I thought it was maybe first about converting pm to m and then m to Tm
This is the first half of what you said
main idol
1 Tm = 10^12 m
.
median flare
I guess we have different ways of solving because I dont know what it means
Let me tell you an easy one I solved
For example when I wanted to convert 0.5cm² to m²
I just did 0.5÷100÷100
main idol
median flare
And got 5×10^-5m²
Which is correct and I understand that
So I used the same logic for every other task but when I came to these weirder measurements it stopped working
that is it probably still works but I don't understand those measurements how to convert them since I never heard of them up until now
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median flare
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keen echo
GUYS WHATA 9!
marsh citrusBOT
GUYS WHATA 9!
keen echo
WHAT ARE !
grizzled sonnet
GUYS WHATA 9!
$n! = \prod_{i=1}^{n} i = 1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot ... \cdot n$
elfin berryBOT
Karma
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buoyant jetty
marsh citrusBOT
buoyant jetty
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buoyant jetty
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wary lichen
problem: no answer is correct, at least according to my math
the z values for the first condition are
z = 1, z = -1, z = i, z = -i
sooo, in easier terms, the powers of i
we both speak spanish, lol
bueno, cuestion, no hay ningún argumento que corresponda a los argumentos de las potencias de i
esos son arg(z) = 0, π/2, π, and 3π/2
la unica que cumple con las condiciones es z_3 = i, que tiene parte imaginaria mayor a uno, pero su argumento no tiene nada que ver
elfin berryBOT
zzz0nnn
wary lichen
si entendes que las soluciones de z^n a una de estas ecuaciones forman un poligono de n lados, entonces resulta en que las aristas del "cuadrado" equivalen a las potencias de i
marsh citrusBOT
@buoyant jetty Has your question been resolved?
buoyant jetty
si entendes que las soluciones de z^n a una de estas ecuaciones forman un poligo...
de argentina brou?
wary lichen
de argentina brou?
si
wary lichen
answer key says 5pi/8 and pi/8 bro
idk
buoyant jetty
ye, I think I will try it again tomorrow bro 
is too late today
or maybe I will leave it open idk
like there is some argument properties that we can use directly
no need to use demoivre mayhaps
idk
craggy terrace
solar heron
@buoyant jetty the first thing that we did was evaluate $(1+i)^{10} = 32i$. Once we had that, then we knew that we had to divide the argument of this complex number by $4$ to obtain the first positive solution of $\pi/8$. There are definitely four solutions to the problem, but only two of the angles have $Im(z)>0$, so the other solution must be $5\pi/8$
elfin berryBOT
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wispy ledge
marsh citrusBOT
wispy ledge
Is ii right?
crystal lintel
,rotate
elfin berryBOT
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ruby matrix
hi i dont understand how the bottom inequality is achieved
marsh citrusBOT
hi i dont understand how the bottom inequality is achieved
vocal rune
How many fractions are there in the middle?
And can you find an easy lower and upper bound for these fractions.
ruby matrix
And can you find an easy lower and upper bound for these fractions.
sorry i still dont understand
i tried doing this
but i dont see why it can be generalized
vocal rune
From 2^n to 2^(n+1) - 1, there are 2^n numbers, so you have 2^n fractions in the middle. Do you agree?
ruby matrix
yep
vocal rune
Each fraction in the summation gets smaller, so 1/(2^n) > 1/(2^n + 1) > ... > 1/(2^(n+1) - 1)
An upper bound for all these fractions is 1/(2^n), so the sum is at most 2^n * 1/(2^n) = 1
Because we have n>1,, we have at least 1 fraction smaller than 1/(2^n), so the sum is strictly lower than 1.
A lower bound for these fraction is 1/(2^(n+1)), so their sum is bigger than 2^n * 1/(2^(n+1)) = 1/2
marsh citrusBOT
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cunning oak
suppose we write down all the permutations of all the arrangements in the letters in MATHEMATICS, and rearrange that in alphabetical order. what would be the 92nd permutation?
marsh citrusBOT
suppose we write down all the permutations of all the arrangements in the letter...
cunning oak
not sure what to do
marsh citrusBOT
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marsh citrusBOT
devout mauve
divide num and denominator by x
if you then "plug in" x=0 you would have number/0 which doesnt exist unless the number is 0
small stream
Ooh I guess that I understand
small stream
Why is it 0?
marsh citrusBOT
Why is it 0?
glass silo
How do you have o(x^3) defined? 
small stream
How do you have o(x^3) defined? <:pikathink:972100841748185208>
It's like x^4, x^5 etc
glass silo
It's like x^4, x^5 etc
Fair 
(I'd think it's along the lines of "stuff that goes to zero as x goes to zero, even when divided by x^3", right?)
At which point, dividing both numerator and denominator terms by x^3, the numerator still goes to 0, the denominator goes to -25/2, which is nonzero
small stream
Thanks charbit!
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full arrow
how
late geode
can you show your attempt
full arrow
can you show your attempt
just discarded that sheet of paper sadly, but this is another result i reached
late geode
it might be better to start from the more complicated right side
valid wing
have you tried making a2-b2?
full arrow
it might be better to start from the more complicated right side
alright, will have a crack at it!
valid wing
not any closer sadly
really?i thought it would work
full arrow
componendo dividendo?
not too sure what that is 😄
valid wing
it won’t work anyway so its ok
clear basin
how
i'd let tan = sinx/cosx and i'd let secx = 1/cosx and then substitute
then you should get a big RHS, you can then simplify it down and get the answer, i just did it @full arrow
let me know if you need help
full arrow
ill give it a try.
so to clarify, the general good approach in sums like these would be to tackle the trickier side right
as its easier to simplify
clear basin
so to clarify, the general good approach in sums like these would be to tackle t...
honestly i just learned this like 2 days ago lol
but from what i've learned that's the case
marsh citrusBOT
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full arrow
giving it a try right now!
full arrow
haha, thats the rhs of this one
clear basin
haha, thats the rhs of this one
wait im so stupid lol
i combined the two photos without realising
im sorry 💀
grand radish
@full arrow Still need help?
grand radish
how
For this take 1 = sec^2(x) - tan^2(x), then use a^2 - b^2 formula
^RHS
in numerator
marsh citrusBOT
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timid mesa
$\int_{0}^{\frac{1}{2}}\int_{0}^{x}\frac{1}{x}\times \frac{1}{1-y}dydx$
elfin berryBOT
Tail
timid mesa
Can I get an explanation on how to evaluate this?
I'm not really sure where to start.
Oh also it's like the first or the second time using this bot so correct me for wrong uses
lucid zenith
Oh also it's like the first or the second time using this bot so correct me for ...
You don't need the times in there, just write it as one fraction
Also use \dd{x} for differentials
timid mesa
Also use \dd{x} for differentials
nice tip, will keep that in mind
lucid zenith
$\int_0^\frac1{2}\int_0^x\frac{\dd{y}\dd{x}}{x(1-y)}$
elfin berryBOT
kheerii
lucid zenith
Anyways you can write this as an iterated integral
timid mesa
I haven't heard of it, is it about the notation or how to go about solving it?
would like to hear more about it or get related resources either way.
lucid zenith
**kheerii**
You can write this as $\int_0^\frac1{2}\left(\int_0^x\frac{\dd{y}}{1-y}\right)\frac{\dd{x}}{x}$
The inner integral can be worked out easily because it's just in terms of y
elfin berryBOT
kheerii
timid mesa
The inner integral can be worked out easily because it's just in terms of y
$\int_{0}^{\frac{1}{2}}-\frac{\ln(1-x)}{x}\dd{x}$
elfin berryBOT
Tail
timid mesa
like this?
marsh citrusBOT
@timid mesa Has your question been resolved?
light cloak
does anyone know why we combined (2) and the first two equations in (3) and not just all three equations in (3)?
marsh citrusBOT
does anyone know why we combined (2) and the first two equations in (3) and not ...
wheat carbon
where do u see that
gloomy merlin
does anyone know why we combined (2) and the first two equations in (3) and not ...
Read what they said below (3) directly. "However, the last equation is superfluous, since it is the difference of the first two". What this means is that it's not an independent equation. It doesn't provide you new information that the first two don't already do
Including it would be redundant in that sense
marsh citrusBOT
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sinful hinge
Hi! I'm supposed to prove inequalities like these using the Mean Value Theorem, but am stuck on what to pick for f(x). Does anyone know how to pick an appropriate f(x) to go off of?
marsh citrusBOT
Hi! I'm supposed to prove inequalities like these using the Mean Value Theorem, ...
@sinful hinge Has your question been resolved?
proud ice
@sinful hinge choose any two integers that surround r
sinful hinge
what do you mean by that??
Maybe I didn't word it right, but my professor solves it by making a function f(t). I'm just trying to figure out how to decide on what it would be
proud ice
what do you mean by that??
Okay let's do problem a
If i recall, bernoullis inequality is just $1+nx\le (1+x)^n$ for $n\in\bN$, right?
elfin berryBOT
SWR
proud ice
Naw it still works for n=1
sinful hinge
oo okay
proud ice
Okay now let's consider $r$. We are given $r>1$. So if $r$ is an integer, then $r\in\bN$, and we just have bernoulli inequality. So now let's consider when $r$ is not an integer. I forget the name of the identity, but we know that there exists an $n\in\bN$ such that $n-1<r<n$
elfin berryBOT
SWR
sinful hinge
okay?? i'm sorry if im not seeing the big picture here but i dont really get it right now
proud ice
This might not lead where i wanted it to lead
sinful hinge
😢
i was supposed to solve it using mvt!! if that helps a little
i dont know if wht you were doing leads to that
proud ice
These are easy to prove with Taylor series but yeah mvt is baffling
sinful hinge
😢
proud ice
Yeah i was trying to use mvt, and the idea i had i thought would work, but it doesn't really use the "1+rx" part
Damn
sinful hinge
if you want i can show you how my professor did it 😭 though i'm more so wondering how to get the thought process of solving inequalities like these myself
proud ice
Yeah what did your prof do
sinful hinge
so she does this (continuation is her doing it for the (iii) part, too)
i just wondered why she picked f(t)=(1+t)^r for this case, but for an example question she ended up using f(z) = z - sin z
like based on what do we pick an f(t)? is kind of the root of my question i guess
the rest of it i can draw conclusions on why she'd do it, but its just that specific part that confuses me
do we pick just pick any function thats differentiable on (a,b) and continuous on [a,b] (did i say it right?)?
proud ice
I'm still here. I'm just reading it through
I think i see the idea, but i must be sure
sinful hinge
I'm still here. I'm just reading it through
thank you 😭
proud ice
Okay i see what she did for the proof to a)
sinful hinge
ive tried watching so many videos but nobody really explains how they come up with their functions 😢
proud ice
It'll take a bit of writing to explain, and i am on mobile right now, so I'll have to wait until i get to my pc
sinful hinge
It'll take a bit of writing to explain, and i am on mobile right now, so I'll ha...
its alright!! take your time
proud ice
I also have to bake some pies today for thanksgiving, so permit me some time to get back to you for a proper response
sinful hinge
I also have to bake some pies today for thanksgiving, so permit me some time to ...
haahaha enjoy baking those pies!!
i might close this channel if nobody else decides to answer. its getting a bit late here 😞 but i really appreciate you trying to help!!
proud ice
@sinful hinge okay here's what I can figure out
For part a, you prof broke down into three cases, the x=0 case, I imagine you do not need help with
sinful hinge
For part a, you prof broke down into three cases, the x=0 case, I imagine you do...
youve got that right lol
proud ice
so let's look at her $x\in(0, 1)$ case
elfin berryBOT
SWR
sinful hinge
yess
proud ice
She's going to use MVT in the interval $[x, 0]$. For this, she is chosing any $c\in(x, 0)$ (it will be important to us later to rememberthat this means $x<c<0$, so just keepo that in mind)
elfin berryBOT
SWR
proud ice
Oops: correction, she is not "choosing" a $c\in(x, 0)$
elfin berryBOT
SWR
proud ice
She is saying that a specific $c\in(x, 0)$ $\textbf{exists}$ such that it satisfies the MVT condition $\frac{f(0)-f(x)}{0-x}=f'(c)$
elfin berryBOT
SWR
proud ice
We recall that $f(x)=(1+x)^r$, and we can thus calculate $f(0)=1$ and $f'(c)=r(1+c)^{r-1}$.
nocturne dune
Help
marsh citrusBOT
Help
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
elfin berryBOT
SWR
proud ice
**SWR**
So, we can simplify this MVT condition down to $\frac{1-(1+x)^r}{-x}=r(1+c)^{r-1}$
elfin berryBOT
SWR
proud ice
Does all of that jive with you so far, @sinful hinge?
sinful hinge
yess
Here's the continuation by the way, in which I'm honestly starting to not understand why she does certain things
proud ice
Here's the continuation by the way, in which I'm honestly starting to not unders...
No worries
sinful hinge
as in why show r(1+c)^{r-1} < r, and the entirety of what's below 'Then,'
proud ice
**SWR**
Let's rewrite parts of this a bit.
We can multiply both sides by $-x$, giving us $1-(1+x)^r=-rx(1+c)^{r-1}$. Then we can rearrange some terms to get $$1+rx(1+c)^{r-1}=(1+x)^r$$
elfin berryBOT
SWR
proud ice
That's just some simple algebra, so I hope that at least that much is easy to understand right now
sinful hinge
oh my god i see it
youre right 😭 i understand the entire bottom part now!!! thank you
just a tiiny little question.. whats the reason behind choosing the interval [x,0]? i'd understand it for part (iii) where she's looking at x>0, as in that the interval would (hopefully...) be [0,x], but i'd had thought this one would have something to do with the -1
to be entirely honest, i'm really sleepy so i might just overlook something really obvious right now so im sorry if its a really dumb question
as in i thought the interval would be [-1,x]
proud ice
just a tiiny little question.. whats the reason behind choosing the interval [x,...
I think it has to do with crossing from negative to positive, but I am not 100% certain
sinful hinge
i think i'll just have to bombard my professor with alot of questions this time
😞 MVT.... my enemy
Thank you so much for helping me, though @proud ice. I appreciated it alot!! But I think I'm going to dip for tonight and rest up
.close
marsh citrusBOT
proud ice
i think i'll just have to bombard my professor with alot of questions this time
Always a good choice
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buoyant jetty
The tangent line to the graph of ( f(x) = (ax + 2)e^{ax} ) at the point ( (0, 2) ) is given by ( y = 6x + 2 ). Then ( a ) is:
[
\boxed{2} \quad \boxed{-2} \quad \boxed{-4} \quad \boxed{4}
]
marsh citrusBOT
The tangent line to the graph of \( f(x) = (ax + 2)e^{ax} \) at the point \( (0,...
elfin berryBOT
Renato Chavez
buoyant jetty
the tangent line at a point (0, 2) is the first degree taylor polynomial centered around zero
y = f(x_0) + f'(x_0)(x-x_0)
y = 6x + 2 = f(0) + f'(0)(x-0)
y = 6x + 2 = f(0) + xf'(0)
f(0) = 2
f'(0) = 6
elfin berryBOT
Renato Chavez
buoyant jetty
,, f'(0) = a + 2a
elfin berryBOT
Renato Chavez
buoyant jetty
a = 3
odd crest
and have an expression for f'(0)
elfin berryBOT
Result:
2
I messed up real bad, I need to level up my arithmetic
I guess this is it
.close
marsh citrusBOT
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hoary lake
hi I don't understand what they did to get this particular line
marsh citrusBOT
hi I don't understand what they did to get this particular line
hoary lake
just for some background im going into physics fresh and don't know the arithmetic
specifically this part
distant peak
hi I don't understand what they did to get this particular line
they just summed everything ?
hoary lake
they just summed everything ?
what are they the sum of
distant peak
all the things that are written before the equation you underlined in red
distant peak
0.3 × 380 (T_f - 80) + 0.2 × 4200 (T_f - 20) = 0
hoary lake
0.3 × 380 (T_f - 80) + 0.2 × 4200 (T_f - 20) = 0
I mean what specifically was added to get tf-9120 and tf-16800
not the whole line
I get that 114 is from 0.3*380
hoary lake
114 T_f - 9120
okay how did they get the number 9120
copper raven
like what was added to get 9120 and 16800
,calc 0.3 * 380 * -80
elfin berryBOT
Result:
-9120
,calc0.2 * 4200 * -20
elfin berryBOT
Result:
-16800
why did u do that
hoary lake
so you distributed the values from the first two sets of brackets into the third?
hoary lake
why don't you distribute the 3rd into the second and change that value
distant peak
3rd what
hoary lake
is there a good article or video I can use to refresh my memory on this
distant peak
look for algebra course on khan academy I guess
hoary lake
look for algebra course on khan academy I guess
what would I search to find this specific topic
expanding?
copper raven
distant peak
algebraic expression
hoary lake
damn 6th grade math I feel like a late french person
alright Ill look into that
oh i already know this
the reason why im so confused is because somehow the tf is now outside the bracket
and now it's minus some other number that's from multiplying two other numbers
so why isn't tf affected why is it still tf
copper raven
so why isn't tf affected why is it still tf
what do you think should happen to tf then? it's just a name for some number we're looking for
hoary lake
what do you think should happen to tf then? it's just a name for some number we'...
I left it alone because I had no clue what to do
so why is it next line there is only one tf instead of two
copper raven
with the 954 you mean ?
hoary lake
what with the 954?
hoary lake
oh yeah that one
copper raven
yeah well they just rounded up all the Tf's they got
114 Tf's + 840 Tf's
,calc 114+840
elfin berryBOT
Result:
954
that's 954 Tf's
hoary lake
that's 954 Tf's
okay so they deed the like terms? Then what about the tf, how did they do anything with it if we don't know the value
copper raven
well the goal is to get Tf alone
then we know it's value
that's why they're doing all of this
to find what Tf is
hoary lake
well the goal is to get Tf alone
okay but aren't there two tfs with different values?
wait a second
Recall, both Tf values will be the same because the mixture of water and brass will come to an equilibrium temperature.
copper raven
yea
copper raven
weird formatting on their part idk
hoary lake
do you mind if I complete it on my own and then close the ticket
copper raven
I guess it's confusing if you remove the parentheses and keep the units
114 J/°CTf now it's barely readable
copper raven
do you mind if I complete it on my own and then close the ticket
yea sure
there's no time limit as long as you speak a bit in the channel
marsh citrusBOT
@hoary lake Has your question been resolved?
versed agate
I don’t understand equations of a line with a curve
marsh citrusBOT
I don’t understand equations of a line with a curve
versed agate
I don’t understand equations of a line with a curve
like say there’s a graph with a curved line
I don’t know how to write the the equation
wary inlet
need an example
marsh citrusBOT
@versed agate Has your question been resolved?
weary condor
Cant really find the equation of a curve can you
Unless maybe its a sin wave or logarithmic or something like that but also you cant be sure
marsh citrusBOT
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void iron
so im on the circled step, however i'm not sure how the hell you get to the next few
marsh citrusBOT
so im on the circled step, however i'm not sure how the hell you get to the next...
wary inlet
25-25 =0
then divide h cause it’s in the numerator and denominator
then plug in 0 for h to evaluate the limit
wary inlet
😭😭
void iron
😭
wary inlet
void iron
alright i appreciate the support lol
wary inlet
all g
void iron
.close
marsh citrusBOT
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sonic palm
would this be correct?
marsh citrusBOT
@sonic palm Has your question been resolved?
mild hearth
Let $\omega$ be the principal root of $z^7=1$ \newline Find the exact value of the following: \newline $(1+\omega+\omega^2)^7+(1+\omega)^7(1+\omega^2)^7$
marsh citrusBOT
Let $\omega$ be the principal root of $z^7=1$ \newline Find the exact value of t...
elfin berryBOT
BOHO
mild hearth
is there a trick to do this without letting w=e^i(2pi/7) ?
like using $1+\omega+\omega^2+\omega^3+\omega^4+\omega^5+\omega^6=0$
elfin berryBOT
BOHO
marsh citrusBOT
@mild hearth Has your question been resolved?
marsh citrusBOT
@mild hearth Has your question been resolved?
cunning fiber
is there a trick to do this without letting w=e^i(2pi/7) ?
Using geometric series, this is the same as $$\frac{1}{(\omega-1)^7} [(\omega^3 - 1)^7+(\omega^4 -1)^7]$$ $$=\frac{1}{(\omega-1)^7} \left[ \left(\omega^3-1 \right)^7+\left(\frac{1}{\omega^3} -1 \right)^7 \right]$$ By symmetry, this is the same as $$\frac{1}{(\omega^5-1)^7} \left[(\omega-1)^7+\left(\frac{1}{\omega}-1 \right)^7 \right]$$
elfin berryBOT
Civil Service Pigeon
cunning fiber
See if you can finish it from here
mild hearth
See if you can finish it from here
how did you get the last line using symmetry?
marsh citrusBOT
how did you get the last line using symmetry?
@mild hearth Has your question been resolved?
marsh citrusBOT
@mild hearth Has your question been resolved?
marsh citrusBOT
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latent whale
@mild hearth I can't speak for the person above but I didn't need to use geometric series for this
marsh citrusBOT
<@548367428854349834> I can't speak for the person above but I didn't need to us...
latent whale
like using $1+\omega+\omega^2+\omega^3+\omega^4+\omega^5+\omega^6=0$
Your observation here was very helpful, try to see how this can help
I would also mention that with some substitution and factoring I was able to get a form of (F1 (w)) * (F2 (w)) where F1 and F2 are polynomials with respect to w, and you can show that one of them must reduce to 0 so the whole thing is 0
marsh citrusBOT
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marsh citrusBOT
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drowsy stirrup
if A is a matrix is 3A = A3 true?
marsh citrusBOT
if A is a matrix is 3A = A3 true?
marsh citrusBOT
amber birch
if A is a matrix is 3A = A3 true?
yes you can change the order if you have a scalar multiple
it's just matrix multiplication where changing the order would give you a different answer
drowsy stirrup
.reopen
marsh citrusBOT
✅
drowsy stirrup
wait so if its like matrix multiplication then 3A =/= A3
drowsy stirrup
it's just *matrix* multiplication where changing the order would give you a diff...
if we consider 3 a 1x1 matrix and A a 3x3 matrix then how is the multiplication even possible?
amber birch
if we consider 3 a 1x1 matrix and A a 3x3 matrix then how is the multiplication ...
don't consider a scalar as a 1x1 matrix
otherwise yeah that multiplication is impossible
this is the rule btw
marsh citrusBOT
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faint birch
Im supposed to use either direct comparison or limit comparison. Every graph ive thought of for comparison felt like i was getting an inconclusive result. For #21
marsh citrusBOT
Im supposed to use either direct comparison or limit comparison. Every graph ive...
faint birch
I know that if the bigger expression converges, then the smaller one if its the original one converges too.
I know that if the smaller one diverges, and the original one is bigger, it diverges too
I guess i could try limit comparison maybe? I think if i use 1/n, i could use lhospitals rule?
This is what AI said lol
quaint hill
.close
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simple pollen
How can I solve this question? The ramps height is sin(10) * 3.5m = 0.6077686m
simple pollen
the energy gained by the box is mgh = 9.81m/s^2 * 10kg * 0.6077686m = 59.6221018 Joules
I would try W = F * d = 200N * 3.5m but that doesn't seem right
200N * 3.5m * sin(10) gives 121.553724 Joules, which would give an efficiency of 49.05%, but I am not sure if that is correct
the normal force on the box should push with a force of 10kg * 9.81m/s^2 * sin(10) = 17.0348862N down the ramp
rocky lark
How did you find the height of the ramp?
simple pollen
How did you find the height of the ramp?
sin(10) * 3.5m = 0.6077686m
rocky lark
What does that 30 in the figure represent
simple pollen
What does that 30 in the figure represent
that is a typo, its meant to be 10 degrees
simple pollen
yes
rocky lark
Is there no friction?
simple pollen
there is no friction on this ramp, there is the normal force from gravity
rocky lark
But does the box have to reach up to the top?
simple pollen
yes, it will travel ramps length of 3.5 meters
simple pollen
I doubt velocity is relevant
same with acceleration
how do i calculate the efficiecny of the ramp?
rocky lark
You had to calculate the work of the applied force and that of the weight force
simple pollen
You had to calculate the work of the applied force and that of the weight force
the applied force at 10 degrees or the applied force in the X direction?
marsh citrusBOT
@simple pollen Has your question been resolved?
rigid lodge
Hi, I need a little (lot) of help here. I'm reading Bartle's book on Lebesgue Integration so Phi and Psi are simple functions
marsh citrusBOT
Hi, I need a little (lot) of help here. I'm reading Bartle's book on Lebesgue In...
@rigid lodge Has your question been resolved?
devout mauve
you need to be more specific about what you need help with
have you done a sketch of these functions?
rigid lodge
you need to be more specific about what you need help with
I'm curious about how they got that double sum expression
marsh citrusBOT
@rigid lodge Has your question been resolved?
static quarry
I'm curious about how they got that double sum expression
If x is in both E_j and F_k, then what is phi(x) + psi(x)? There's not much more to it than that
note that the representation for phi + psi is not necessarily the standard one
haughty token
hi
rugged spindle
the easiest ones are definitely trigonometry, applied statistics (assuming it's not calc based, still would be rather easy if it was), then calculus 1 and 2
haughty token
the easiest ones are definitely trigonometry, applied statistics (assuming it's ...
am doing calc 1 and i already finished trig
i should go for calc 2 next? is the the easiest?
rugged spindle
then probably calc 2 or linear algebra, but probably calc 2 first
unless linear algebra is a proof-based course (some colleges have their introductory linear algebra courses be proof-based, other have theirs computation based), then it might be pretty much same level as discrete math
haughty token
what about numerical analysis
rugged spindle
i'm not sure what exactly it is by that name
if it's supposed real analysis, then it's far more difficult than calc 2
still temple
I think "numerical analysis" is when you study computational methods for doing integration, solving ODEs/PDEs, and so forth
So yea probably on the more advanced side
marsh citrusBOT
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still temple
please ive tried these problems all day and i dont know how to do it. i just want some extra credits😭
marsh citrusBOT
please ive tried these problems all day and i dont know how to do it. i just wan...
amber birch
please ive tried these problems all day and i dont know how to do it. i just wan...
do you see how $f(t) = 610(1 + 0.047/12)^{12t}$?
elfin berryBOT
southlander!
still temple
no i have no idea what his mean or how to start
amber birch
no i have no idea what his mean or how to start
you need to watch a video then
or your textbook
marsh citrusBOT
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Available help channel!
gentle owl
marsh citrusBOT
gentle owl
I have no clue what this means
Can someone send resources for me to understand?
Like 0 clue where to even begin this
marsh citrusBOT
@gentle owl Has your question been resolved?
marsh citrusBOT
@gentle owl Has your question been resolved?
light crown
having trouble integrating after i substiute w
marsh citrusBOT
having trouble integrating after i substiute w
wraith elm
trig sub?
w = 7 sin theta
dw = 7 cos theta (dtheta)
so then its (98 * 7 cos theta d theta)/(7 sin theta)^2 * sqrt(49-(7sintheta)^2))
you can simplify the radical into 7 cos theta
and then cross out with the top and then 98/49 = 2
light crown
i managed to reduce to 2 intgrl 1/sin^2 theta
light crown
and yea i used trig sub
wraith elm
do you know integral of csc^2theta
wraith elm
yeah
u can usub to prove it
but its helpful to just memorize unless u need to profve it for somethign
marsh citrusBOT
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modest scarab
In the formula
P (X = k) = ( nk ) ⋅ p^k ⋅ (1 – p)^n – k, (nk) means n! / k! * (n - k)!
Why can ( nk ) be used to calclulate how many paths there are for k, I understood why the other stuff makes sense just not the ( nk )
modest scarab
ohhhhh
I wondered where this help channel was, It was just closees so I thought none was created
.close
marsh citrusBOT
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still temple
There are 100 patients in a hospital. Some (an even number) are one-legged but wearing shoes. One-half of the remainder are barefooted. How many shoes are being worn?
marsh citrusBOT
There are 100 patients in a hospital. Some (an even number) are one-legged but w...
still temple
umm
Ig the remainder the question says are all those except one-legged + wearing shoes?
cunning oak
well the remainder could be wearing one shoe also
still temple
wait I got 100
bruh
it's 100 shoes?
is it really 100 and why do they mention even number? It shouldn't make a difference, right?
weary thistle
Because if it’s odd then there is odd number of two leg patients remaining and half of that would be a decimal
still temple
x + 2 . (100-x)/2 is 100 regardless of x being odd or even though but yea
weary thistle
It is it’s just the example wouldn’t make sense if the number of one legs wasn’t even
marsh citrusBOT
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robust mountain
could someone verify if i have done these correctly ? particuloarly part ii and iv
marsh citrusBOT
could someone verify if i have done these correctly ? particuloarly part ii and ...
robust mountain
marsh citrusBOT
@robust mountain Has your question been resolved?
abstract hull
`perimeter of triangle is 10m if one side is 4m what are the other 2 sides of the triangle for its maximum area
marsh citrusBOT
`perimeter of triangle is 10m if one side is 4m what are the other 2 sides of th...
@abstract hull Has your question been resolved?
abstract hull
<@&286206848099549185>
crystal lagoon
`perimeter of triangle is 10m if one side is 4m what are the other 2 sides of th...
Is this a calc problem or?
Because we know that equilateral triangles have the most area per perimeter, followed by isosceles
Unless I'm wrong on the isosceles one then it's just both 3/3
abstract hull
Is this a calc problem or?
you have to make a function and derive it
crystal lagoon
you have to make a function and derive it
I'm not sure if you know it but I'd just use heron's formula then
x+y=6 then do simultaneous with heron's formula
marsh citrusBOT
@abstract hull Has your question been resolved?
fickle shell
