#help-27
restive river
1.422B
translation is that
i have that system and i have to find the sum of alfa + beta such that the system is compatible undeterminated
iron kindle
restive river
alfa + beta clearly yields me -1 which is inccorect
now
i do think i made a mistake because
the rank between the two matrices shouldnt be equal
if they are equal it means that it is compatible determinated(has finite sets of solutions)
but
so far i know that compatible systems have to have the rank < (number of unknown variables)
in this case there are 3? i think
but i might have lost along the way...
any help or hints will be highly appreciated
final dune
what you want is a system of equations which are consistent but have infinite solutions
final dune
js checking bcz different terminology
restive river
sure no problem
final dune
resolving ur matrix shows me $\alpha = -1$ is correct
woven radishBOT
RadMeerkat62445
final dune
never talk about yourself like that
final dune
we want infinite solution
final dune
yes
final dune
not super sure abt that..
x+y+2z=1,2x+2y+z=-1, x+y-z=beta
add the first and last equations
we get 2x+2y+z=1+beta
we want 1+beta = -1
restive river
no?
final dune
so beta = -2
restive river
i mean i have a test coming on wednesdday but from way easier ones but i do harder ones just to be extra prepared
anyway thank you so much for the help
:>
.close
devout snowBOT
woven radishBOT
meinebow
devout snowBOT
@carmine estuary Has your question been resolved?
north mountain
clearly it is an ideal , u need to show R != J @carmine estuary
consider the polynomial 1 its in R clearly it is, show that it isnt in J, approach is with a contradiction
gleaming horizon
devout snowBOT
tropic skiff
Are you trying to simplify?
gleaming horizon
Yessir
Wait
Ok so here is what i tried but apparently somethings wrong
Its kinda messy too
tropic skiff
I think its correct
olive snow
You can cancel the n+3 since its 1
tribal cairn
1^(n+3) = 1 for starters
tropic skiff
Also perhaps you should raise the entire fraction to the exponent
olive snow
But yeah you got the idea
gleaming horizon
i totally forgit
tropic skiff
I thought the n + 3 in 1^(n + 3) wasnt an exponent :(
olive snow
Yes
tropic skiff
devout snowBOT
tropic skiff
Can someone explain why they did $\hat{p_c} = \frac{10 + 28}{50 + 53} = 0.369$
woven radishBOT
King Leo [Ping For Help]
tropic skiff
gray axle
Can someone explain why they did $\hat{p_c} = \frac{10 + 28}{50 + 53} = 0.369$
I thought you were the one teaching people
@foggy willow
tropic skiff
I thought you were the one teaching people
were
potent venture
what type of formula are you using fo p value
tropic skiff
what type of formula are you using fo p value
I'm honestly not sure
I missed the day when this was taught
Context
potent venture
they are calculating overall proporation with the p^
to find the p value you have to look in the table
woven radishBOT
King Leo [Ping For Help]
tropic skiff
$$\hat{p_c} = \hat{p_b} - \hat{p_a}$$
woven radishBOT
King Leo [Ping For Help]
potent venture
you got 3.45 over here look up P(Z < 3.45)
tropic skiff
**King Leo [Ping For Help]**
mu comes from here
tropic skiff
sigma comes from hree
potent venture
oh yes this is calculating standard error
basically it goes something like this Z = (p1 - p2)/SE
tropic skiff
oh yes this is calculating standard error
basically it goes something like thi...
So is there any problem with my method?
I just hate table-a with a passion
potent venture
and then you use this Z from the normal table
potent venture
So is there any problem with my method?
hahah lemme see
potent venture
I just hate table-a with a passion
i think your method makes sense, but i do not know if it is correct, i would say to try both ways and see if your answers match
tropic skiff
Ok i got smth completely different
potent venture
Ok i got smth completely different
hmm i see
tropic skiff
**King Leo [Ping For Help]**
Can you explain why they did this though
potent venture
ok on second look this won;t work
tropic skiff
Can you explain why
potent venture
Why cant i `normal_cdf(lower: 0, upper: 10^99, mu: _, sigma: _)`
this essentaially becomes 1, probability of X being less than an extremely large number like that one
potent venture
Can you explain why they did this though
you do this when you have two samples, it is called pooled proportions
like you need both of them to represent same proportion to calcuate the standard error
potent venture
**King Leo [Ping For Help]**
so for combined estimate of the proportion you do this, essentially assuming that both groups come from the same population
so you add their successes and divide with total sample to get the combined estimate
tropic skiff
But then how will we know the difference in proportions?
potent venture
Can you explain why
you can look into how cdf works in normal distribution to understand this into more
Yeah the difference in proportions is captured in the numerator of the Z-score formula that we do p1 - p2
you can think of p^ to ensure "fair comparsion" when comparing
tropic skiff
But thetn why do we add here
potent venture
we still use we still use the individual sample proportions p1 and p2 to check the difference
tropic skiff
Then what are we calculating /p\c for
potent venture
But thetn why do we __add__ here
you can think of it like by the Null Hypothesis we are tryna assume whilca calucating p^ is that they come from same group of population, like this is how you get the best estimate by combining both the groups
its like if H0 were true, we get this accurate estimation from adding (since it means there is essentially no differnece b/w two samples, so we can "combine" them)
(like you can think of this in that way )
potent venture
Then what are we calculating `/p\c` for
for the standard error
tropic skiff
you can think of it like by the Null Hypothesis we are tryna assume whilca caluc...
Ok, so since proving the null hypothesis is the first priority, we can assume both true proportions are the same?
potent venture
yup exactly
tropic skiff
yup exactly
Thx, just trying to make usre i understand
potent venture
Thx, just trying to make usre i understand
they were good questions ngl
you seem to really want to understand the topic, its good
tropic skiff
.close
granite anvil
This supposed to be -1
devout snowBOT
This supposed to be -1
granite anvil
But I’m getting 0
storm gyro
,rccw
woven radishBOT
wind mason
This supposed to be -1
Can you elaborate?
granite anvil
wind mason
Then apply the chain rule.
granite anvil
Try using the angle sum formula for sine first.
its sinxcosy+cosxsiny isn't it?
i think thats what i did
wind mason
i think thats what i did
I don’t see that?
granite anvil
I don’t see that?
in like the first step
wind mason
i wrote sinxcosy + cosxsiny = 1
What was the original question?
wind mason
find dy/dx for the function
You can just use chain rule.
wind mason
Also, in your original working, you did dy/dx where you should not have. Can you see it?
granite anvil
Also, in your original working, you did dy/dx where you should not have. Can you...
uh no
i do not
wind mason
i think this is wrong
I wonder why he posted.
granite anvil
siny * dy/dx?
wind mason
siny * dy/dx?
No, when you took the derivative of sin(x), you’re not supposed to add a dy/dx.
Since, you know, chain rule.
granite anvil
where im so confused
wind mason
The first block.
granite anvil
do you mean in the first second, third or fourth bracket
oh
deriv of sinx is cosx
i didn't write dy/dx there
wind mason
Wait a minute, why did you take the derivative of both??
granite anvil
Wait a minute, why did you take the derivative of both??
its f(x)g(x) + f(x)g(x)
i thought we take $f'(x)g(x) + f(x)g'(x)$
woven radishBOT
gamer75431
wind mason
its f(x)g(x) + f(x)g(x)
Gah you know what let’s just go from sin(x+y)=1
granite anvil
ok
heres my next step
$(cosx)(-siny \frac{dy}{dx}) + (-sinx)(cosy\frac{dy}{dx})$
woven radishBOT
gamer75431
granite anvil
then i did
wind mason
@granite anvil I don’t want to be rude, but stop, since I think it will be better if I teach you the other way.
This is more confusing than it needs to be.
So, we have sin(x+y)=1.
granite anvil
$-cosxsiny\frac{dy}{dx} - sinxcosy\frac{dy}{dx} = 0$
woven radishBOT
gamer75431
wind mason
Now if we take the derivative, by chain rule, we get (x+y)’*cos(x+y)=0, right?
granite anvil
ok
wind mason
Are you lagging?
wind mason
Ok.
granite anvil
Now if we take the derivative, by chain rule, we get (x+y)’*cos(x+y)=0, right?
but where is your first term here
theres no sin or cos in front of the (x+y)'
fiery flare
$(\cos x) (-\sin y \frac{dy}{dx}) + (-\sin x)(\cos y \frac{dy}{dx}) = \frac{\sin(x+y)}{\cos(x-y)} \left( \frac{d}{dx} \left( e^{x^2+y^2} \right) \right)$
woven radishBOT
pratikitiki
fiery flare
Use this
granite anvil
someone ban this guy
wind mason
<@&268886789983436800> We have a troll in the house.
granite anvil
no jk
fiery flare
Im literally helping
granite anvil
he is my friend
he is also stuck on the same question lol
we both did the same
question
wind mason
Im literally helping
If you look at your past messages, no.
granite anvil
<@&268886789983436800> can you please unban
fiery flare
what past message?
winter torrent
i did not ban anyone
wind mason
If you want to observer, observe. If you want to ask questions, ask. There is absolutely no need to intervene here with any other purpose.
fiery flare
Yeah cause im helping
winter torrent
nor mute nor delete messages
granite anvil
If you want to observer, observe. If you want to ask questions, ask. There is ab...
Please, continue.
fiery flare
Thanks Hayley
wind mason
If you want to observer, observe. If you want to ask questions, ask. There is ab...
@fiery flare
fiery flare
Comprende amigo 😄
wind mason
The derivative of (x+y) with respect to x.
atomic sparrow
it is a notation for differentiation
wind mason
i've never seen this notation before
It’s Leibniz notation. Usually used as shorthand if you don’t want to write out the whole d/dx thing.
atomic sparrow
woven radishBOT
;(
wind mason
I’ll be right back, someone is calling me.
granite anvil
ok
granite anvil
$1 + y\frac{dy}{dx}$
woven radishBOT
gamer75431
granite anvil
i think
wind mason
Hmm.
You’re on the right track, but that’s not necessarily the case.
Think about the chain rule.
What is the derivative of y^2 with respect to x?
granite anvil
$2y\frac{dy}{dx}$?
woven radishBOT
gamer75431
granite anvil
oh so its $1+ y'\frac{dy}{dx}$
woven radishBOT
gamer75431
wind mason
oh so its $1+ y'\frac{dy}{dx}$
Again, right idea, but this time I think it’s just an abuse of notation problem.
$\dv{x}[y]=y’$
woven radishBOT
;(
wind mason
Yes?
wind mason
I said that earlier.
granite anvil
yeah sorry i didn't quite understand what you meant
wind mason
It’s fine.
granite anvil
anyways thanks for the help
wait also
what was wrong with my notation
how should i have written it
wind mason
You basically have y’*y’. Now, that doesn’t look correct, right?
woven radishBOT
;(
wind mason
Since $\frac{dy}{dx}=\frac{dy}{df}\cdot\frac{df}{dx}$
woven radishBOT
;(
granite anvil
i would write $cosy * derivative of argument$
woven radishBOT
gamer75431
wind mason
Yes.
granite anvil
so why wouldn't i keep the dy/dx there
wind mason
You would.
woven radishBOT
gamer75431
devout snowBOT
@granite anvil Has your question been resolved?
granite anvil
.close
jaunty musk
$cosy \frac{dy}{dx}$ is right then?
The chain rule is used for differentiating when a function is replacing x in your well known functions
devout snowBOT
The chain rule is used for differentiating when a function is replacing x in you...
sharp wagon
lol
jaunty musk
Yup wait a min it will only last a few minutes
And then I am closing it
HELPING SOMEONE WHO CLOSED JUST BEFORE
sharp wagon
lmaoo
jaunty musk
@granite anvil Earlier you were differentiating the function $f(x)=x+y(x)$
woven radishBOT
Epsilia aka Epe
jaunty musk
With respect to x, if you use the chain rule with y even if there is no function inside, you can ... But what is inside y is none other than x, so what you would multiply y'(x) with is $\dv{x}(x)$, which is just ... 1. So it wouldn't really change much
woven radishBOT
Epsilia aka Epe
jaunty musk
What you wrote after $y'$ is $\frac{dy}{dx}$, which is the name of a function, probably varying with respect to x in all generality
woven radishBOT
Epsilia aka Epe
jaunty musk
But it's as if you are differentiating y(y(x)) ...
granite anvil
ohh ok
ill take a look at this later i have to go eat
but thanks
Also I’m confused on how this = -1
Which is the answer
jaunty musk
Well you show me this, and this is a function
Are you supposed to show that if you have sin(x+y)=1, then you have -2cos(x-y)/(cos(x)-sin(x)) = -1 ?
wind mason
We had (x+y)’*cos(x+y)=0, by chain rule, correct?
^
wind mason
Are you supposed to show that if you have sin(x+y)=1, then you have -2cos(x-y)/(...
No, you show dy/dx=-1.
jaunty musk
With y being ?
wind mason
Just an arbitrary variable.
jaunty musk
Then where do these sin and cos come from
I tried to understand what was at the start of the channel but found myself really unsure of what he wanted
wind mason
Then where do these sin and cos come from
Do you know what implicit differentiation is?
jaunty musk
Yes
wind mason
I tried to understand what was at the start of the channel but found myself real...
Implicitly differentiating sin(x+y)=1.
jaunty musk
So that has been asked by the professor ?
wind mason
So that has been asked by the professor ?
I don’t know who the fuck asked, but yeah, that’s the question.
jaunty musk
**gamer75431**
By differentiating y with respect to x that function, you almost get what you wrote here yeah
But I say almost because in the chain rule, there is no changing in the argument of the function which is the most "outside"
If you differentiate u(v(x)) with respect to x for example
The derivative would look like that :
u'(v(x)) • v'(x)
As you can see, the v(x) hasn't changed inside the u, it's just that you are differentiating u with respect to v(x) before multiplying by v'(x), so you treat v(x) as an other x
And then once you have differentiated u, you apply the derivative you found onto v(x)
That's where the notations need to be clear
Between (u(v(x)))' and u'(v(x))
Here, x+y is inside your sine function
So your x+y part is like a function inside your most "outer" function
@granite anvil which is why x+y would stay as x+y inside even after differentiating. Although you would keep y inside, so if you isolate dy/dx, you would get dy/dx with respect to y and x
Which would mean that you would then need to ... Solve a differential equation
fiery flare
Taking this too far. It's a simple undergrad question that can be completed in 5 lines max.
jaunty musk
What would he do about his x+y inside ?
fiery flare
Its the sum identity where sin(x+y) = sinxcosy + sinycosx.
He can then differentiate both using power rule to get sinxcosy + sinycosx as [(sinx)(-sinx)(dy/dx)]+[(cosx)(cosy)] + [(cosx)(cosy)(dy/dx)]+[(-sinx)(siny)]
Equate [(sinx)(-sinx)(dy/dx)]+[(cosx)(cosy)] + [(cosx)(cosy)(dy/dx)]+[(-sinx)(siny)] to 0 which allows him to move the non dy/dx terms to the right.
He will end up with (dy/dy)[(-sinxsiny)+(cosxcosy)] = (-cosxcosy)+(sinxsiny) after factoring out the dy/dx
Then isolate the dy/dx to get: dy/dx = [(-cosxcosy)+(sinxsiny)]/[(-sinxsiny)+(cosxcosy)] = -1
Which gives a final answer of -1.
There, 5 lines.
jaunty musk
It's surprising how they cancel out like that in the end
fiery flare
It's surprising how they cancel out like that in the end
Yeah, it's all a matter of persistence.
jaunty musk
They really test out the resilience of the students like that
Thank you for taking your time to write everything though
fiery flare
No worries.
devout snowBOT
@jaunty musk Has your question been resolved?
jaunty musk
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rugged kraken
.close
scarlet radish
how do you solve x-3=4x?
devout snowBOT
how do you solve x-3=4x?
solid osprey
send x over
devout snowBOT
devout snowBOT
Available help channel!
gritty cairn
how do i integrate
(sinax + cosax)/(sinax-cosax)
gritty cairn
so every time do i have to try to get the derivative of the denominator?
radiant dune
no
gritty cairn
then?
gritty cairn
how do i find out waht to derivate from the problem?
junior flax
how do i find out waht to derivate from the problem?
intuition (that's my best method I know)
gritty cairn
Whats the answer
the answer is sinax+cosax
jaunty dagger
@gritty cairn Going slow, whats the derivative of the denominator
junior flax
what is the flow of this conversation💀
radiant dune
whenever i see fractions in integrals, the first i thing i do is try to see if i the derivative of the denominator is equal to the numerator. If its not, i see if i can make any tweaks to it to make it so
otherwise i try simplifcation
gritty cairn
whenever i see fractions in integrals, the first i thing i do is try to see if i...
okay bro that was helpful
junior flax
whenever i see fractions in integrals, the first i thing i do is try to see if i...
Lowkey i do the oposite of what you do @radiant dune . I just go back to see if theres a u sub if simplification gives me a bunch of unkindly functions and algebra'
junior flax
whenever i see fractions in integrals, the first i thing i do is try to see if i...
this is probably the better strat
gritty cairn
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gritty cairn
.reopen
devout snowBOT
✅
gritty cairn
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devout snowBOT
Available help channel!
marble otter
Hello! 👋 How do I get the first matrix line here, considering that I want to calculate the Deti/detG in the long run? 
devout snowBOT
Hello! 👋 How do I get the first matrix line here, considering that I want to c...
@marble otter Has your question been resolved?
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@marble otter Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
cedar grotto
I want to calculate the ak coefficient for the fourier series for |t| between -pi and pi, is this approach correct? If i add the integrals it evaluates to 0
devout snowBOT
I want to calculate the ak coefficient for the fourier series for |t| between -p...
cedar grotto
devout snowBOT
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valid garden
guys is it ok to ask about chemistry here? but i was jsut wondering if anyone knows how to know if its polar/nonpolar and if what type of IMF
with just looking at the molecule (Not a drawing of it but literally just moelcules) bc our teacher wont let us use periodic table
for example
jsut: Si, Ne, H2O
like that, how can i immediately tell if its polar/nonpolar and its imf
devout snowBOT
guys is it ok to ask about chemistry here? but i was jsut wondering if anyone kn...
strong tiger
what does imf stand for? i forgot...
valid garden
what does imf stand for? i forgot...
intermolecular forces ^^
strong tiger
afaik you have to calculate the dipole moment of the molecule ? not exact but a rough estimate.. if the dipole moment of the molecule is zero then the molecule is non polar and if it is not zero then it is polar
valid garden
afaik you have to calculate the dipole moment of the molecule ? not exact but a ...
okioki i will search htattt, but do u also know how to differentiate the different imf ?
i swear i dont know how 😔
strong tiger
you should try reading that from your chemistry course textbook i bet that will help you
valid garden
you should try reading that from your chemistry course textbook i bet that will ...
oop we dont have that we just have ppts but our teacher didnt teach us that part, but ill try searching more
strong tiger
ahh..
valid garden
im cooked right
strong tiger
not really
valid garden
hmm
strong tiger
you can try searching i would recommend you a youtube channel for it but the ones i studied from were not in english
valid garden
you can try searching i would recommend you a youtube channel for it but the one...
okyoky, did u have to draw the lewis structure ?
or can i just learn without learning the structure
strong tiger
kind of..? like there were 2 ways just memorize it or draw lewis structure to calculate it yourself.. either way you should learn drawing lewis structures its kind of helpful
valid garden
kind of..? like there were 2 ways just memorize it or draw lewis structure to ca...
okayokay my chem exam is in a few hours but im gonna clutch this
thank you!
strong tiger
you got this
smoky nimbus
okayokay my chem exam is in a few hours but im gonna clutch this
Good luck
devout snowBOT
@valid garden Has your question been resolved?
restive river
So let’s say we’re playing roulette.
We’re putting on things that pay 2 to 1.
You’re putting all 8100$ on one spin. Let’s say you have 50% chance to win (in reality it would be around 48)
I’m playing a martingale on steroids.
first spin:100
second:200
third:600
fourth:1800
fifth:5400
(if one of them wins it’s started all over from 100)
Who has more chance of at least doubling their starting money (8100)?
devout snowBOT
@restive river Has your question been resolved?
restive river
<@456226577798135808> Has your question been resolved?
nope
devout snowBOT
@restive river Has your question been resolved?
restive river
<@&286206848099549185>
fiery flare
How many rounds do you get to go in this scenario?
If you can keep going, then there are infinite pathways this hypothetical can take
@restive river
fiery flare
So until you run out, you can keep going?
Wait yeah that makes sense, okay gimme a sec to write this out
restive river
So until you run out, you can keep going?
Until you run out. With the system I described, 5 tries.
100,200,600,1800,5400.
fiery flare
Lmao, the longest and most annoying way for you to double your money would be if you kept winning the 100s, that would have a probability of 4.13x10^-25 chance of occuring.
81 wins in a row with 50% chance of it hitting.
okay let me do that for each win now.
restive river
Until you run out. With the system I described, 5 tries.
100,200,600,1800,5400.
Take into account that it’s not simple “double down” strategy.
So when you win at 100, you profit 100
When you win at 200, you profit (total) 100,
when you win at 600, the clean profit is 300
when you win at 1800, you profited 900
and at 5400 you profit 2700
restive river
Lmao, the longest and most annoying way for you to double your money would be if...
yes
that must be annoying
the first 2 tries
fiery flare
Take into account that it’s not simple “double down” strategy.
So when you win a...
it pays 2:1 as in you put in 200 and what they give back is your original 200 with 100 added?
restive river
it pays 2:1 as in you put in 200 and what they give back is your original 200 wi...
if you put in 200, you profit 200. But you already lost your first bet of 100.
200-100, the clean profit is 100.
fiery flare
Ah got it, thats what you meant.
restive river
yep
fiery flare
Okay. So winning any bet is 1/2. And winning at any part of the bettign results in a profit of 100 (if you win the 600 bet, you get net 300 back to the pot for the next round of betting).
This means we need to find the expected return on profits for each round of betting by seeing how probable it is to get to that point in betting and how much we can get back.
So, for the first bet, we have a 50% chance of winning and $100 as profit, so we do (0.5**100). The second bet, we have a 25% chance of winning (50%50% because 50% for loosing the first bet and 50% for winning the second bet) thus the estimated profit for that would be (0.25100).
restive river
Okay. So winning any bet is 1/2. And winning at any part of the bettign results ...
wait wait
restive river
Okay. So winning any bet is 1/2. And winning at any part of the bettign results ...
what do you mean winning at any part results in 100?
cuz if you win at 5400 it’s 2700 profit for example
fiery flare
cuz if you win at 5400 it’s 2700 profit for example
No yeah, im just building up to that.
So lets get the expected profits as E(P) = (0.5100) + (0.25200) + (0.125300) + (0.0625600) + (0.03125*1200)
restive river
So, for the first bet, we have a 50% chance of winning and $100 as profit, so we...
hmm.. The first bet doesn’t affect the second bet so the second bet is 50% too right?
if we said “winning both the first and the second” that would be 25%
simultaniously
fiery flare
No the first does affect the second, because we need to lose the first to get to the second. Second is depended on the first failing.
restive river
oh yea
fiery flare
if we said “winning both the first and the second” that would be 25%
No losing the first and winning the second are both 50% so we multiply to get the chance of winning the second.
restive river
yea i see it now
fiery flare
Okay so the expected profit is $212.5
So to double our money from the 8100, we do 8100/212.5 which is 38.1
That means we must win 38.1 games in order to double our money
The probability of winning each game is 0.5
And instead of finding the probability of winning each of those games, lets see where we can lose all 5 of those betting scenarios in a row.
Which will allow us to find the probability of winning at least once on each 5 betting rounds.
So we know we'll get money if we win atleast one of those games, and we can see the probability of winning atleast one game by finding the probability of losing all 5.
restive river
That means we must win 38.1 games in order to double our money
we have a 96,875% chance of winning one round right?
so 0,96875^38,1 is our expected chance?
fiery flare
we have a 96,875% chance of winning one round right?
so 0,96875^38,1 is our exp...
Yes!
Thats good, well done.
restive river
thats about 30% wow
restive river
That’s crazy actually 😄
fiery flare
Thats good that you found it out in the end. Well done! 😮
fiery flare
Well, it's regular martingale has around 8% chance.
This is a significant improvement.
fiery flare
Well, it's regular martingale has around 8% chance.
To double, that is.
restive river
Yeah haha
This is the better martingale imo. If you bet big you also win big here
As you’re losing your first few bets you’re actually getting happy not just stressed😂
fiery flare
High risk = high reward yeah.
I wonder if you can increase the bets and get better probabilities
fiery flare
or 1 dollar 😄
Oh god, doubling $8100 with $1 bets is wild.
restive river
that would be
1
2
6
18
54
162
486😭
1458
your house🏡
anyways thanks this was really helpful!
fiery flare
Holy.
Start with 8500. Bets of 100, 400, 1600, 6400. 69.7% chance of doubling.
That's 70%. Wow. That might actually be profitable if you're lucky.
restive river
Start with 8500. Bets of 100, 400, 1600, 6400. 69.7% chance of doubling.
That’s crazy
Can we continue in dm?
fiery flare
Now optimize it using calculus to give you the highest probability of doubling.
Lmao
fiery flare
Can we continue in dm?
Sure
restive river
.close
restive river
Can someone help me do q10,11 and 12
devout snowBOT
Can someone help me do q10,11 and 12
strange arch
Can someone help me do q10,11 and 12
elaborate on where you're stuck and what you've written
vital dagger
To get
AE
Its AF+FE right?
no
why are you doing that when you have a straight path
you are right but you don't know AF and FE yet
restive river
Ohhh wait
AE=3a
AF=3b
Cus its an enlargement of 3
vital dagger
✅
vital dagger
Am I correct
ya
restive river
Then how do I do q11
I dont understand what they r saying
Ac=3×0A those ones
<@&286206848099549185>
strange arch
I dont understand what they r saying
Ac=3×0A those ones
AC is 3 times as long as OA
BD is three times as long as OB
and they represent the vectors of OA as a and OB as b
strange arch
What are they telling me to do in the a) part
if two vectors are parallel, then they're a multiple of each other
if v = 7 * w and v,w are vectors
then v and w are parallel
because v is just some multiple of w
they point in the same direction, just with different lengths
@restive river notice AB = AO + OB
you can split any vector
by taking a different path
restive river
<@456226577798135808> notice AB = AO + OB
Yes
restive river
Yea
strange arch
so AB = AO + OB = 1/3 * CA + 1/3 * BD
restive river
Ok
strange arch
so 1/3 * (CA + BD)
from here you may notice that if you go from C to A
and from A to B
and from B to D
that it's the same path as from C to D
so CA + AB + BD = CD
i.e. CA + BD = CD - AB
thereby 1/3 * (CA + BD) = 1/3 * (CD - AB)
but since we started with AB
we now have AB = 1/3 * (CD - AB)
bring the 1/3 * AB to the other side:
4/3 * AB = 1/3 * CD
and multiply with 3 for clarity:
4 * AB = CD
which tells us CD is just a multiple of AB
so they're parallel
restive river
😭why is the answer long just to prove it is a paraallel
strange arch
hm these "pathmaking" proofs usually take a few steps
but you always have different options
we could start with CD too
CD = CA + AO + OB + BD = 3 * AO + AO + OB + 3 * OB
= 4 * AO + 4 * OB
= 4 * (AO + OB)
= 4 * AB
yeah that's faster
restive river
Oooo okip
strange arch
get comfortable with experimenting like above
replace vectors with others
and slowly work your way towards the vector you want
strange arch
CD = CA + AO + OB + BD = 3 * AO + AO + OB + 3 * OB
are the steps clear?
restive river
Yes
strange arch
kk
restive river
Thank,u very much
strange arch
np and gl with further progress 🦇
devout snowBOT
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hot nova
can someone help me plug this stuff in pls
devout snowBOT
can someone help me plug this stuff in pls
tropic skiff
What is t(44)
hot nova
-10?
hot nova
mower can u stop intruding pls
topaz beacon
!noadvert
devout snowBOT
Please do not advertise your help channel or thread in other parts of the server. There are many people who need help, so advertising can quickly turn into spam.
hot nova
thx ga31
im still so confused king leo on how to write that
wair no im not
44(-10(44))
?
tropic skiff
44(-10(44))
No, just write the number
tropic skiff
If $f^{-1}(x)$ is the inverse of $f(x)$, then $f^{-1}(f(x)) = x$.
woven radishBOT
King Leo [Ping For Help]
hot nova
ok wait should i close this and open a new channel when i need mroe help
hot nova
cuz i think ima need more help..
tropic skiff
!done
devout snowBOT
If you are done with this channel, please mark your problem as solved by typing .close
devout snowBOT
hot nova
.reopen
devout snowBOT
✅
hot nova
mk so i have
leme show u
bruh whyd it do that
but like im confused
cuz wouldnt it turn into
tropic skiff
Which part are you confused about
hot nova
no im dumb ignore this oml i confused myself
tropic skiff
Lol
hot nova
ok wait i
im confused on finding the inverse tho
i have
g(f(x)) = 1/4(4x-3) +3
can i cancel out the 4s?
idk how to solve this i might js be having a brain fart but idk
tropic skiff
can i cancel out the 4s?
Not yet, because you have a ... - 3 in the parentheses
hot nova
so what can i do
wait
theyre inverse ight i js did the math?
?
i divided the 4
is fhat completely wrong
or am i like ok
tropic skiff
Where did this 4 come from
hot nova
IT WAS WRONNGGG i confused myself again
i tried dividing but like
i forgot it was alr.. a fraction
hot nova
does this look right
devout snowBOT
does this look right
hot nova
i forgot to add the f(x) in the top thats why its kinda messy
fiery flare
Yep, looks good.
fiery flare
alright
hot nova
ok im confused now
idk where to go with this
could the x^2 cancel oit the radical
?
tropic skiff
could the x^2 cancel oit the radical
It doesnt cancel
tropic skiff
does this look right
Here, you got h(f(16)) = 14 which should tell you something
hot nova
oh so its not recersable
i mean
OK
ok wait i have another question & ima send my work for it when imm done but ima need u guus to chrck it reallt wuick
am i correct
fiery flare
$$g(h(x)) = (2((sqrt[3]{x})/2))$$
woven radishBOT
pratikitiki
hot nova
how the fuck do i do this
tropic skiff
how the fuck do i do this
f must not have any repeated y-values, because f^-1 must not have any repeated x values (meaning the same x-value of f^-1 leads to two y-vaules)
hot nova
i was not taught this
fiery flare
how the fuck do i do this
bros not even asking politely anymore 💀
hot nova
`f` must not have any repeated `y`-values, because `f^-1` must not have any repe...
em
how do i check for that
woven radishBOT
tropic skiff
,rccw
woven radishBOT
tropic skiff
This graph is your f^-1(x)
tropic skiff
Is this a valid function?
hot nova
umm yes i think so
tropic skiff
umm yes i think so
Why
fiery flare
(it's not)
hot nova
oh..
tropic skiff
i dont know
A function will have only one y-value for any x-value
hot nova
thats awk....
tropic skiff
Have you heard of the vertical line test @hot nova
tropic skiff
umm yes but like briefly
Ok, do you know how to apply that to f^-1
hot nova
js switchin the numbers
tropic skiff
its js switching the x & y right?
❌ Thats for inverses
hot nova
oh
tropic skiff
This is a graph of f^-1. does it pass the vertical line test
hot nova
ummmm
tropic skiff
If you dont know, dont hesitate to tell me
hot nova
not really
fiery flare
If you draw a straight line anywhere on the graph, it should pass through only one point on the function.
Here, it can pass through multiple and has many y-values.
hot nova
can u give me an example for this question so ican like visualzie it
tropic skiff
hot nova
okk thats what i thought
tropic skiff
Multiple intersection points = bad
tropic skiff
so then how would i test the intervals thing
So you need to simply remove parts of the function that cause it to fail the vertical line test
hot nova
if its like veery single one then how do i know which to remove..
fiery flare
oopsies, @tropic skiff you can take over here 😎
tropic skiff
oopsies, <@1214057610857160835> you can take over here 😎
Wdym oopsies
tropic skiff
if its like veery single one then how do i know which to remove..
These are inequalties of x in f(x)
therefore, these are inequalities of y in f^-1(x)
Pick an interval and see if it passes the vertical line test
hot nova
im so sorry but
i have no idea how to do that
like what do i plug in
😭
guys im slow im SORRY
tropic skiff
like what do i plug in
Do you wanna vc so i can show you
tropic skiff
I DONT HAVE THAT FUCKASS QUESTION ANYMORE
💀
tropic skiff
,rotate
woven radishBOT
hot nova
where can we vc
tropic skiff
What range of f^-1 will help pass teh vertical line test
tropic skiff
where can we vc
Dms if its ok with you
hot nova
ok im not talking tho
tropic skiff
ok im not talking tho
Sure
tropic skiff
@hot nova do you see my screen
tropic skiff
!done open a new channel if you need further help
devout snowBOT
If you are done with this channel, please mark your problem as solved by typing .close
hot nova
.close
devout snowBOT
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Available help channel!
quaint apex
devout snowBOT
quaint apex
for a
i got this
but the answer says this
so im a bit confused
what does the semi colon mean in this
iron kindle
$\dv{x} 1=0$
woven radishBOT
Bonk
acoustic leaf
the colon here is just separating the function from its derivative
quaint apex
ohh right okay
iron kindle
a semicolon wouldve been more appropriate
acoustic leaf
because you should not write that the function is "equal" to its derivative
versed garnet
makes sense
devout snowBOT
wind mason
so when i write it should i use : instead of =
Yes, since a function's derivative is not necessarily equal to the function (except for e^x!)
devout snowBOT
Available help channel!
warm compass
Doea this look correct?
devout snowBOT
Doea this look correct?
warm compass
I'm supposed to evaluate this at 0 for the next step
idk how to do that without a calculator
any tips
warm compass
yeah
olive snow
Its not that hard, compute it dw
warm compass
I get 2ln(3)*1^ln(3)
olive snow
Which is ?
warm compass
when I sub 0
warm compass
Which is ?
no idea
fickle solar
when u sub 0, you should get 2ln(1) * (5) * something else
olive snow
1 times smth = smth
warm compass
oh right
fickle solar
im pretty sure the ansewr is just 0
olive snow
when u sub 0, you should get 2ln(1) * (5) * something else
No its inside the ln
The 5
fickle solar
ah i see
warm compass
it'd be like ln(9)
fickle solar
then isn't this just 2ln(5)?
because its (2x + 1)(6x+5) in side the ln
which is just 5 if x = 0
olive snow
because its (2x + 1)(6x+5) in side the ln
Its a 3 not a 5
fickle solar
oh i see
olive snow
it'd be like ln(9)
It will
fickle solar
y then its just ln9
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Available help channel!
jaunty dagger
Would this be a map in f:Q->Q
jaunty dagger
Would this be a map in f:Q->Q
My counter example was (1/-1)
which gives a devide by 0
the thing is (1/-1) = (-1/1)
And the second one does not give a devide by 0
so is this still a valid counter example?
iron kindle
are there any further conditions on p and q?
jaunty dagger
the thing is (1/-1) = (-1/1)
this is throwing me off because both are rational
one gives a rational output (0)
devout snowBOT
@jaunty dagger Has your question been resolved?
north mountain
you know about consistency? @jaunty dagger
if p/q = r/s, then does f(p/q) = f(r/s)?
jaunty dagger
@north mountain Yes I think so if its a map
oh is this not a map because one imput can give 2 outputs
north mountain
pick -1/1 and 1/-1
jaunty dagger
on top of what i showed
devout snowBOT
@jaunty dagger Has your question been resolved?
worthy flicker
devout snowBOT
worthy flicker
i used the dot product equation to get 6x+8y=5 and x^2+y^2=1
and solved the system
but idk what i did wrong
spare crypt
where did 5 come from
worthy flicker
the product of the magnitudes was 10
and the LHS was cos60=1/2
x and y are the vector components of the unit vector
worthy flicker
how would i put the component in vector form
acoustic leaf
i think it wants the full vectors, it's just asking for the vectors with smaller and larger i-component respectively
devout snowBOT
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Available help channel!
jaunty dagger
How would i go abount proving this?
devout snowBOT
How would i go abount proving this?
jaunty dagger
I tried it using a law that allowed me to add the elements, but im not sure if its the proper way or if it even holds
devout snowBOT
@jaunty dagger Has your question been resolved?
idle carbon
How would i write “The intersection of slopes A and B is located at (x, y)” in a formula?
devout snowBOT
How would i write “The intersection of slopes A and B is located at (x, y)” in a...
idle carbon
Example: intersection of f(x)=2.5-(1/2)x and g(x)=(-1)+3x is (1, 2)
<@&286206848099549185>
idle carbon
I want a formula or equation that formulates “the intersection of slope a and b is located at (x, y)”
restive river
There is no such formula :c
idle carbon
Dang
restive river
You have to follow the procedure
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Available help channel!
feral bobcat
devout snowBOT
feral bobcat
picture 3 is constant speed
i do not know how to know which picture is accelerating and which is braking and why
dull loom
i do not know how to know which picture is accelerating and which is braking and...
Everything has inertia, meaning it only moves when a force is acted upon it
So when the truck brakes, the fluid inside of the truck remains moving in the same direction the truck was moving, until it hits the front of the truck
The force that the front of the truck acts on the fluid makes it stop moving, that’s why it doesn’t go thru the vehicle
When the truck is accelerating, the fluid stays still until the force from the back of the truck moves it
So D
feral bobcat
what is the force from the back of the truck
i imagined it is A because the fluid will move behind because acceleration will be negative
and accelerating the fluid will move forward because acceleration is positive
dull loom
It’s just like when you crash into a car while you’re seated without seatbelt
You remain moving forward as you hit the car, (the break in this example) until the windshield stops you
feral bobcat
so it has nothing to do with the direction of acceleration or anything?