like this? $(n^{1/n}(1 - n^{-1/n}))^n = n \cdot (1 - n^{-1/n})^n$
#help-17
misty goblet
twin meteorBOT
p1za
but maybe this isn't helpful
twin meteorBOT
misty goblet
yeah im not sure if the binomial theorem is the right move
flat whale
,w plot (n^(1/n)-1)^n
twin meteorBOT
flat whale
Not sure if 1/n even bounds it from above
misty goblet
the hint was to use the squeeze theorem, power laws, and the fact that $\sqrt[n]{n} = 1$
twin meteorBOT
p1za
misty goblet
the limit*
flat whale
did you prove n^(1/n) is decreasing after some N
misty goblet
no we did not prove that
@flat whale did you have an approach in mind?
i also had another unrelated problem, I had to prove that the set $M = {\sqrt{2} + q: q \in Q}$ is dense in R
twin meteorBOT
p1za
misty goblet
Knowing that Q is dense in R, my idea was to pick any two $a, b \in R, a < b$, show that there is a $a - \sqrt{2} < q < b - \sqrt{2}$ and then "shift" this by $\sqrt{2}$ to get $a < q + \sqrt{2} < b$ is this ok?
twin meteorBOT
p1za
misty goblet
problem 1
hoary umbra
for the question on the limit you can use that a^(oo) if 0<=a<1 is 0
misty goblet
hmm i dont think im allowed to use that
<@&286206848099549185> i would appreciate input/hints on either problem
vocal sleetBOT
@misty goblet Has your question been resolved?
novel smelt
<@&286206848099549185> i would appreciate input/hints on either problem
I think the bottom bun could just be 0, as for 1/n being on top, i think its true but im working on showing it...
novel smelt
**p1za**
and if we can assume Q is dense in R, that's a good way to do it as far as I can tell
its how i would do it
novel smelt
<@&286206848099549185> i would appreciate input/hints on either problem
oh i think top bun could be C^x for some 0<C<1, lemme know what you think of that
vocal sleetBOT
@misty goblet Has your question been resolved?
misty goblet
oh i think top bun could be C^x for some 0<C<1, lemme know what you think of tha...
hmm ig sure but i still have to prove its >= from some N
nocturne spade
Do you know L'Hôptial's theorem?
misty goblet
nope didnt do that yet
nocturne spade
In that case you will need to sophisticated estimates.
flat whale
You could show that after some N, |n^(1/n) - 1| is less than 1 so that when it's raised to the nth power that goes to 0
vocal sleetBOT
@misty goblet Has your question been resolved?
ashen steppe
Hey, im really lost about how to do these. I understand that the first one is supposed to use the stars and bars theorem but i dont know why i cant do 5^20 and i just dont know how to do b and c (i sent the question earlier but had an emergency and had to go, sorry if the ones who answered earlier see this)
vocal sleetBOT
Hey, im really lost about how to do these. I understand that the first one is su...
vocal sleetBOT
@ashen steppe Has your question been resolved?
ashen steppe
<@&286206848099549185>, could you help please
novel smelt
Hey, im really lost about how to do these. I understand that the first one is su...
i don't see why the first uses stars and bars, 4a seems to be looking for an ordered set with replacement?
ashen steppe
should i contact my teacher and ask him if its a mistake then?
novel smelt
should i contact my teacher and ask him if its a mistake then?
no i somehow mixed it up in my head, stars and bars is the exact method for ordered with replacement
ashen steppe
no i somehow mixed it up in my head, stars and bars is the exact method for orde...
ah okay
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@ashen steppe Has your question been resolved?
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@ashen steppe Has your question been resolved?
weak jay
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weak jay
This picture doesn't it show it but I've tried so many different ways to solve this. And this is just my recent attempt. Does this mean there are no solutions?
sudden compass
Its a system of 4 equations, should be solvable
weak jay
I'm not sure how to go about it, I've tried everything that makes sense
I either can't solve it or with trying certain things I get such a restricted domain it doesn't really feel like a solution.
sudden compass
Hmm
weak jay
Have any ideas?
sudden compass
Yes got one
Notice that a+d=0 (divide both sides of 2 and 4 by ac and bd respectively)
Similarly we derive b+c=0
From there use equations of consistency should give you a contradiction
sudden compass
The equations 2 and 4 of the list
Uhh multiply both lhs and rhs of equation 2 and 4, that's what I mean
weak jay
Yes I don't get how that gives you a+d=0
sudden compass
Yes I don't get how that gives you a+d=0
y+z = a, y+z=-d..
vocal sleetBOT
sudden compass
Those are the equations you get
Oh f right mb
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kind light
help channels are opened for when you ask a question btw
if you want to help someone, go to their channel and help them ig
@signal goblet do you mind if i close the channels?
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gritty shard
Is this proof ok?
vocal sleetBOT
Is this proof ok?
gritty shard
daring needle
Looks good
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neat ore
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toxic trout
hi can i have help
vocal sleetBOT
hi can i have help
toxic trout
<@&286206848099549185>
explain how e^x and Ln(x) are reverse functions
@vocal sleet
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toxic trout
.reopen
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red flower
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mighty nacelle
!status
vocal sleetBOT
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
I used u=ln(x+1)
Then substituted and got 0.111
However I get a different answer when I bring the 2 back using logarithmic property and substituting for u=ln(x+1) to get 2lnu rather than just substituting for u to get u²
quiet echo
does it mean $\int_0^1\frac{(\ln(x+1))^2}{x+1}dx$?
twin meteorBOT
;(
quiet echo
However I get a different answer when I bring the 2 back using logarithmic prop...
because they would be different expressions.
red flower
because they would be different expressions.
How it would be the same thing just done in a different way
Isn't it
quiet echo
How it would be the same thing just done in a different way
no, they're completely different expression.
$(\ln(x+1))^2\neq\ln((x+1)^2)$
twin meteorBOT
;(
quiet echo
you're squaring the WHOLE ln, as opposed to squaring just the argument
red flower
The expression is ln((x+1)²)
red flower
The expression is ln((x+1)²)
And by using the property it would make it right?
<@&286206848099549185>
<@&286206848099549185>
mental egret
!original
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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.
tardy cliff
And by using the property it would make it right?
how did you do your u sub?
is the square meant to be in or outside the function?
because the answer would be different
tardy cliff
you cant use the power property if the square was for the function itself and not the thing inside
red flower
is the square meant to be in or outside the function?
On the (x+1)² only
tardy cliff
On the (x+1)² only
so you can use logarithmic property
red flower
so you can use logarithmic property
Yes but it gives a different answer that's what's confusing me
tardy cliff
int(2ln(x+1)/(x+1)dx)
tardy cliff
Yes but it gives a different answer that's what's confusing me
where does it give different answer?
twin meteorBOT
tardy cliff
he subbed it wrong i assume
red flower
;( told you before to sub u = ln(1 + x)
I did this
mental egret
What'd you get?
red flower
Try both methods trust me they don't different answers
red flower
What'd you get?
0.111 without log property
mental egret
,w int_0^1 (ln ((1+x)^2))/(1 + x)
tardy cliff
Try both methods trust me they don't different answers
can you please show the work and what you did in each step so we can tell you where it couldve went wrong?
tardy cliff
yes so the exponent was wrong
twin meteorBOT
red flower
And with the property i got 0.480
mental egret
Both expressions are different, see
tardy cliff
And with the property i got 0.480
yes and the question is a bit silly there
is it like a homework assignment or smth?
where you could complain about it
red flower
Both expressions are different, see
How
red flower
is it like a homework assignment or smth?
Yes
tardy cliff
How
so
to understand why its different you need to know why ln(x^2)= 2ln basically why the log property works
mental egret
$\ln[(1+x)^2] = 2 \ln (1+x) \neq [\ln (1 + x)]^2$
twin meteorBOT
Arya
red flower
one is ln(x+1)+ln(x+1) and the other is ln(x+1)*ln(x+1)
Yes
red flower
**Arya**
But I had the middle one(2ln(x+1)) the I used used u as ln(x+1) so it became 2u
And when I integrated it just became u² and I used the limits and got 0.480
tardy cliff
But I had the middle one(2ln(x+1)) the I used used u as ln(x+1) so it became 2u
yes that is applicable only if the square was in the ln function
tardy cliff
And when I integrated it just became u² and I used the limits and got 0.480
exactly
that is correct only if the square was inside
if its $\ln^2(1+x)$ then its not 2u its gonna be u^2$ which means a different answer
twin meteorBOT
keb abs
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
vocal sleetBOT
@red flower Has your question been resolved?
bleak prawn
vocal sleetBOT
bleak prawn
Im not really sure how to solve this one, the square root is kinda messing things up for me
u = sqrt(x) + 1
vocal sleetBOT
Show your work, and if possible, explain where you are stuck.
bleak prawn
If you give me a moment I will 😇
u = sqrt(x) + 1
du = 1/2sqrt(x) dx
If I sub in u for sqrt(x) + 1 the du = 1/2sqrt(x) dx still remains, so im left with 2sqrt(x)/u^4
mighty nacelle
u-1
bleak prawn
I have a u AND an x
mighty nacelle
think about it
nocturne spade
u = sqrt(x) + 1
^
nocturne spade
If I sub in u for sqrt(x) + 1 the du = 1/2sqrt(x) dx still remains, so im left w...
here
bleak prawn
Ohhhh
mighty nacelle
how can we write sqrt(x) in terms of u?
nocturne spade
put the relation of x.
bleak prawn
So sub in u-1 for sqrt(x) into 2sqrt(x)/u^4 to get 2(u - 1)/u^4 ?
And then I can integrate right?
zinc quail
si if you adapted the boundaries
bleak prawn
si if you adapted the boundaries
What do you mean by adapted the boundaries sry
bleak prawn
So sub in u-1 for sqrt(x) into 2sqrt(x)/u^4 to get 2(u - 1)/u^4 ?
But this is the correct method, right?
zinc quail
What do you mean by adapted the boundaries sry
when you change the integration variable you also need to change the interval over which the integral is determined
zinc quail
But this is the correct method, right?
yoppa
vocal sleetBOT
zinc quail
what do you have as boundaries? :D
bleak prawn
what do you have as boundaries? `:D`
1 and 0?
zinc quail
but that's only true if the integration variable is x :v
vocal sleetBOT
✅
bleak prawn
Oke 1 moment
zinc quail
that's why I mentioned it, otherwise you'r done
bleak prawn
I will think
zinc quail
when u(x) = something with x
then the boundaries a and b become u(a) and u(b), which is the rule you need
bleak prawn
Oh really?
zinc quail
sure
bleak prawn
So it becomes sqrt(x) + 1 and 0?
zinc quail
you can verify it with a simpler integral yourself afterwards
bleak prawn
instead of 1 and 0?
zinc quail
then wish thee good luck
zinc quail
np
bleak prawn
.close
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solemn spear
The answer key says it's C
vocal sleetBOT
The answer key says it's C
desert hornet
The primitives in both branches must give the same value at x=0
Since a primitive is continuous
desert hornet
also your method of solving integral e^(-x) is unnecessary, you can just substitute u=-x
exotic ravine
also your method of solving integral e^(-x) is unnecessary, you can just substit...
yeah i was wondering what was done there,
OP integral of e^kx = e^kx / k
just remember this
solemn spear
ok
desert hornet
OP integral of e^kx = e^kx / k
This isn't a good thing to remember
solemn spear
but why is D wrong tho?
desert hornet
A better thing to remember is that if $\int f(x)\dd{x}=F(x)+C$ then $\int f(ax+b)\dd{x}=\frac1{a}F(ax+b)+C$
twin meteorBOT
kheerii
desert hornet
but why is D wrong tho?
Because it's not continuous at 0
solemn spear
even if c was right couldn't c_2 just be c_1 + 2
desert hornet
even if c was right couldn't c_2 just be c_1 + 2
Yes, but D says that c1 and c2 can be anything
It doesn't restrict c2 to be equal to c1+2
exotic ravine
this.
desert hornet
Technically you need to take thr limits as x tend to 0 from the right and from the left respectively
But these are continuous functions so yes you can just plug in x=0
solemn spear
Alr thx for the help
turbid snow
i need help
vocal sleetBOT
i need help
turbid snow
how do u express 15e^(-2t) in phasor format A<phi
vocal sleetBOT
@turbid snow Has your question been resolved?
turbid snow
ok
spiral turtle
If it is supposed to be 15e^(-2it) instead, then your complex amplitude is just 15
Phi is 0
turbid snow
how do u simplify this set of differential equations into ONE equation?
15e^(-2t)-i1-2d(i1-i2)/dt=0|
2d(i1-i2)/dt-2i2=0
i wanna solve for i2
vocal sleetBOT
@turbid snow Has your question been resolved?
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@turbid snow Has your question been resolved?
vocal sleetBOT
@turbid snow Has your question been resolved?
knotty lynx
how do u simplify this set of differential equations into ONE equation?
```
15e^...
Take the second equation and rearrange to find an expression for i1. Note that this expression will only be in terms of i2 and di2/dt
Find di1/dt using your expression for i1 (just differentiate the expression) and substitute both di1/dt and i1 into the first equation.
Now, i1 will be eliminated in the first equation
dense hamlet
helppp
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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
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quiet tusk
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quiet tusk
yo guys how do i start doing this?
novel smelt
yo guys how do i start doing this?
can you think of a real number that can't be expressed by 1/xy for some x,y in the reals?
quiet tusk
yeah 1/0?
hybrid flicker
1/0 isn't a real number
novel smelt
1/0 isn't a real number, but yeah you seem to have identified 0 as being missing
quiet tusk
so means everything except for 0 can be the range?
hybrid flicker
so means everything except for 0 can be the range?
so it's kind of a hasty conclusion
the reason why 0 can't be in the range
is because if 0 = 1/(xy) for some x,y
then 0*xy = 1
mental egret
Again, -inf and inf are a concept, not numbers
to write range is (0, inf) doesn't imply the function does not have infinity in it's range. It just means, for each number in range of f(x) there's a bigger number that is also in the range of f(x)
quiet tusk
ohh i see
mental egret
Anyways, so how'd you describe the range of f(x, y) = 1/xy ?
in set notation form :o
quiet tusk
i guess the 3rd choice
xd
-inf to above zero union with zero to inf
is that right?
novel smelt
is that right?
we are bound by oath to not directly answer, what matters is that you can feel confident in your answer
hybrid flicker
we are bound by oath to not directly answer, what matters is that you can feel c...
uh
that's kinda bs
you can confirm if they are right
hybrid flicker
is that right?
and you are
even though not written in math notation like this is hard to truly pinpoint what you mean
quiet tusk
we are bound by oath to not directly answer, what matters is that you can feel c...
oh hahh thats interesting
novel smelt
uh
i was overstating the point a little, I did say earlier that the answer was reasonable. ill tone it down though
hybrid flicker
i was overstating the point a little, I did say earlier that the answer was reas...
you are completely allowed to confirm to someone they are right
vocal sleetBOT
hybrid flicker
if you're purposefully evasive like this, they may start to go in the wrong direction again and be counterproductive
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Available help channel!
hybrid flicker
notice that it's different from handing out an answer they previously didn't have
vocal sleetBOT
notice that it's different from handing out an answer they previously didn't hav...
mental egret
!status
vocal sleetBOT
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
Show your work, and if possible, explain where you are stuck.
mental egret
hybrid flicker
did this start a channel for me bruh
mild flower
it's really about what's best for the student. i've done problems directly in front of them before because it's more useful than playing 20 questions
hybrid flicker
didn't notice
novel smelt
notice that it's different from handing out an answer they previously didn't hav...
i do tell people they are right, and its definitely different from giving away stuff. i shouldn't have been misleading by being over the top like that. i agree with your point about evasiveness
novel smelt
it's really about what's best for the student. i've done problems directly in fr...
could we discuss this a little in pedagogy or general or something? 
vocal sleetBOT
@hybrid flicker Has your question been resolved?
lusty prism
.reopen
gentle oriole
What's the difference between range and codomain?
vocal sleetBOT
What's the difference between range and codomain?
gentle oriole
This book as well as Google says that the codomain is the set of all possible values of Y
And range is the actual output of f(x)
But isn't the actual output of f(x) the codomain?
Or is the codomain something else that'd arbitrarily defined
heavy yoke
codomain is the set of all outputs that f(x) might give, even if it only actually outputs some of them
gentle oriole
codomain is the set of all outputs that f(x) might give, even if it only actuall...
How does that work
heavy yoke
for example, it is usually convenient to set the codomain of a function to be "all real numbers", because it definitely outputs real numbers, but it's often difficult to find out exactly which real numbers it does and doesn't output
gentle oriole
for example, it is usually convenient to set the codomain of a function to be "a...
Aha so you're saying the codomain is arbitrarily defined?
heavy yoke
the domain and codomain are part of the definition of a function, so you have to specify them up front. but usually it is not convenient to find the range of the function, so it is more useful to just specify the codomain as a set which you know the range will be a subset of
gentle oriole
the domain and codomain are part of the definition of a function, so you have to...
Ohhh ok
So let's say f(x) = x^2 for x>0
gentle oriole
So let's say f(x) = x^2 for x>0
This would be a function with a domain restriction of x>0
How would I specify the codomain
heavy yoke
the usual notation is f: (domain) -> (codomain)
gentle oriole
the usual notation is f: (domain) -> (codomain)
Ohhh
heavy yoke
How would I specify the codomain
first you have to choose what the codomain should be (there are a couple of obvious ones in this example)
gentle oriole
So f: R^3 -> R^2 smth like that?
heavy yoke
that's a function with domain R^3 and codomain R^2
gentle oriole
Aha
I actually rarely see codomains used at my level
Usually just work with domain and range
What happens if f(x) can somehow output a value outside the codomain
gentle oriole
So let's say f(x) = x^2 for x>0
So this for example, if I defined my codomain to be y>10
lilac pebble
then the function is improperly defined
gentle oriole
then the function is improperly defined
Ooo ok
Alright I think that's everything
Ty for the help
.close
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wicked tundra
If the equation ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 represent two straight lines which intersect each other then show that the point of intersection is [ ( hf - bg / ab - h^2) , (gh - af / ab - h^2) ]
vocal sleetBOT
If the equation ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 represent two straight li...
wicked tundra
I have no idea how to prove this
Can somenoe tell me how to begin with this question?
vocal sleetBOT
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wicked tundra
<@&286206848099549185> IS it hard or smt 😂
mild flower
complete the square
atomic jasper
fill in and show that its indeed 0
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bitter pilot
hi i need help
vocal sleetBOT
hi i need help
twin meteorBOT
anti-algebraist 𝔸dωn𝓲²s
bitter pilot
i feel it's wrong
hard atlas
why should a-b have an inverse
flat whale
half group is the official term
hard atlas
if you dont know, what do you do?
vocal sleetBOT
@bitter pilot Has your question been resolved?
signal pendant
you should have some intuition regarding this because ||it is false in the case one of the rings you have worked with for your whole life now||
bitter pilot
i am blacking out
hard atlas
what rings do you know
signal pendant
look at examples
have you tried this
bitter pilot
yea and i am blacking out i have no idea
signal pendant
you dont know a single example of a ring?
bitter pilot
Only thing that comes in mind was if a ring R is not a field then (R, *) is a semi-group, implying that there exists no multiplicative inverses. So no units.
hard atlas
dont be abstract currently
what actual rings do you know
you should be able to list at least a few
hard atlas
sorry aber du kannst mir doch nicht erzählen dass du kein beispiel von nem ring kennst
signal pendant
Only thing that comes in mind was if a ring R is not a field then (R, *) is a se...
(also this implication is not true)
gloomy cedar
heloo
bitter pilot
R is real numbers here ?
I meant real numbers, but I think R = Z_4 should work because then R_E = Z_4* with {0}.
If I now take the sum 1+3 = 4 is not unit anymore..
cyan talon
1+3 is 0 in Z_4 tho
hard atlas
1+3=4=0 in R_E
bitter pilot
1+1 then
signal pendant
Why do you think of complicated examples first...
bitter pilot
I can't think of any cause I don't memorize stuff
hard atlas
the first ring in your mind should always be Z
signal pendant
I can't think of any cause I don't memorize stuff
Neither do i
hard atlas
its the ring
bitter pilot
the problem with Z was I couldn't think of units
as easy as with Z_n because I just take Z_n*
signal pendant
Just go by the definition
bitter pilot
i forgot -1 and 1 were trivial ones
signal pendant
They are the only ones
hard atlas
some of the rings you should know are: Z, Z_n, Q, R, C, polynomial ring over a ring or field, ring of square matrices over some ring/field, Z[sqrt(3)] or similar
and I think you need a break
signal pendant
as easy as with Z_n because I just take Z_n*
Determining which elements in Zn are units is far harder than determining which in Z are units, btw
Which contradicts your point about memorizing stuff but anyways
twin meteorBOT
anti-algebraist 𝔸dωn𝓲²s
hard atlas
associativity is inherited, yes
signal pendant
Oh this is a different question altogether
bitter pilot
I want to check if (R_E, *) is a commutative semi-group. That means when I multiply the elements they must satisfy the associativity property, and also commutativity. But they basically do because they are elements of R as well that is commutative ring. So since every element of R satisfies these, then a sample of elements must as well?
bitter pilot
In my notes it says: Let M be a non-empty set with some operation θ. If for all x,y,z in M (xθy)θz = xθ(yθz) then the operation is associative and such operation structure (M,θ) is called a semi-group.
signal pendant
And how is an operation defined
bitter pilot
It says: Let M be a set and θ : M x M -> M a map. Then θ is an inner map on M and the pair (M, θ) is called operation structure.
signal pendant
So how do you know * is a map R_ExR_E -> R_E
bitter pilot
I guess this map has to be well defined
signal pendant
All you know is that * is a map RxR->R
In other words, you need to check that R_E is closed under *
bitter pilot
hmm okay
bitter pilot
In other words, you need to check that R_E is closed under *
Let $a,b \in \mathbf{R}_E$. Then there are $x,y \in \mathbf{R}$ such that [ ax = xa = 1 \text{ and } by = yb = 1. ]
So $ab = ab \cdot ax \cdot by = a^2x \cdot b^2y = 1 \cdot 1.\$
I proved previously that $a$ is a unit if and only if $a^n$ is a unit for all $n\in \mathbb{N}.$
twin meteorBOT
anti-algebraist 𝔸dωn𝓲²s
signal pendant
Yes
bitter pilot
I don't know what's the matter with me
signal pendant
It looks like you are abstracting very quickly
Why are you learning groups rings and more general structures all at once 
bitter pilot
I thought that was normal in a course as Algebra
But then I have heard stories like one could be occupied just with group theory one semester
twin meteorBOT
anti-algebraist 𝔸dωn𝓲²s
vocal sleetBOT
hot pine
That math is actually a bit scary
bitter pilot
That math is actually a bit scary
It's not I am just a moron
hot pine
It's not I am just a moron
I don’t even know the symbols, no wonder you find math hard 😭😭😭
bitter pilot
I don’t even know the symbols, no wonder you find math hard 😭😭😭
it's just symbols
hot pine
it's just symbols
I am quite sure we normie call them abstraction 😭
bitter pilot
If I had to review what happened the past 2 hours - horrible how moronic i am
hot pine
If I had to review what happened the past 2 hours - horrible how moronic i am
What happened?
bitter pilot
i struggled with something
hot pine
I heard group theory is very very advanced though and rings or halo or something
I am actually quite curious of those studies but don’t know where to start I have very little knowledge base
Only thing I know about algebra is different type of diagonalization and how to do Cayley Hamilton theorem to expand polynomial
bitter pilot
I started with relations and binary operations maybe that's a good start, but you might ask in #math-discussion or #book-recommendations
hot pine
How hard is it? If I may ask
Those books are quite expensive so I am a bit scared if I would give up
bitter pilot
I don't think I can give an objective answer
Only thing I can say is, you really have to internalize the basics
which I think you are good at
hot pine
I will try to print a pirate book to see if I would like it
You won’t believe how much I spent on those stupid cal and analysis book
bitter pilot
or read some stuff on wikipedia
hot pine
Wikipedia doesn’t help much as it doesn’t dive to the deepest depths..
I have a good study hobby that I read different textbooks of the same subject that I then try to rephrase it myself
Which is a bit money consuming especially these days books are crazily expensive
hot pine
Goldbach’s conjecture also phrased in easy terms but profoundly complicated
bitter pilot
1+1 is indeed the most complicated thng
hot pine
"The math is a bit scary" the math I do:
Like most know how zeta function is defined but to prove the questions related to its roots it becomes profoundly more complicated
I just feel like I study math more than I do in economics theory which I admit I should focus even only for the sake of final
bitter pilot
Study the intersection: finance math
hot pine
Study the intersection: finance math
That study is even cringier believe me
bitter pilot
ikr that's why I chose Algebra
hot pine
People become dumb when they study something they feel what makes them intellectually better, financial math makes them even more
Econ students… I don’t want to describe what I was like during year 1
bitter pilot
EconEmma
hot pine
Basically believe that I would be rich for the study.. cringe enough but if people are still like this for year 2 then it’s really bad
And those false beliefs over my studies cause me so many mistakes, don’t know why I would chose classics or and some others
Should’ve focused more on stem
bitter pilot
isn't economics stem kinda
hot pine
isn't economics stem kinda
Like depends, and if you counts financial mathematics or quantitative analysis or these type of studies. What I am studying is considered humanities rather than science
So basically i studied the theories, like Adam smith, cringe thing again
bitter pilot
I see
hot pine
I really regret of this study choice and kinda stuck with it bcs if I really want to go to other study then only math is possible since I am filled up with humanities subjects and even my math isn’t sufficient probably
Like i wouldn’t naive enough to think math is only about calculus and advanced calculus (real analysis)
hot pine
If I really want to transfer to math, maybe I have to do a couple of other studies
Yes like finals, I just have to take finals.. I can pass calculus1, 2, 3 , linear algebra, analysis and the other studies I probably will fuck up
bitter pilot
You know calculus?
bitter pilot
So what's the derivative of x
hot pine
1
hot pine
My name is exposed fuck
bitter pilot
Green's Theorem
hot pine
My name so childish 😭
bitter pilot
I didn't see a name lol
hot pine
Can’t imagine they name me like that
bitter pilot
I didn't see a name
hot pine
Great
bitter pilot
I just saw Green's Theorem and Integral symbol
hot pine
I just saw Green's Theorem and Integral symbol
Name free version
People see my name they often laugh so 😭
hot pine
I just saw Green's Theorem and Integral symbol
Best calculus I know
vocal sleetBOT
Available help channel!
sacred anvil
vocal sleetBOT
sacred anvil
.close
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glad comet
What is the difference between a line with a 0° angle and a line with a 180° angle? How can we tell them apart visually?
vocal sleetBOT
What is the difference between a line with a 0° angle and a line with a 180° ang...
flat whale
Line or ray?
glad comet
Ray
flat whale
Ray of 0deg goes in positive x direction. Ray of 180 deg goes in negative x direction
vocal sleetBOT
@glad comet Has your question been resolved?
vocal sleetBOT
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agile mica
Is there a way to cancel out the square root before doing the integral?
strong grove
Is there a way to cancel out the square root before doing the integral?
u mean so that the integral becomes
$$\int_{-1}^1 (1+4x^2) \dd x$$ ?
twin meteorBOT
JustToPro
agile mica
u mean so that the integral becomes
$$\int_{-1}^1 (1+4x^2) \dd x$$ ?
yes basically just any way to simplify it
strong grove
no u cant do that , but a nice way to solve this would be trig sub
velvet karma
agile mica
no u cant do that , but a nice way to solve this would be trig sub
would that be the most clean way of doing it because I cant recall if I have ever really gone into trig sub before
or maybe I have just forgotten it
strong grove
would that be the most clean way of doing it because I cant recall if I have eve...
yeah
strong grove
or maybe I have just forgotten it
this thing!!!!!
agile mica
dont remember this but does seem useful thanks
Im guessing a^2 is just 1 in this case then
strong grove
Im guessing a^2 is just 1 in this case then
yes
agile mica
so would it be a plain tan or does the coefficient 4 change anything?
oh wait
does this mean replace the whole (1+4x^2) for just tan
or plug tan in for the x
strong grove
no
u have 4x^2 , which means ur "x^2" is actually (2x)^2
so 2x = (1)tantheta :d
or the other way would be factor out 4
$$\sqrt{(4)(\frac14 + x^2)}$$
$$2 \sqrt{((\frac12)^2 + x^2)}$$
twin meteorBOT
JustToPro
agile mica
and then couldnt you take out the ^2 to make
$$2 \sqrt{((\frac12) + x)^2}$$
twin meteorBOT
icey
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
twin meteorBOT
icey
strong grove
nvm that would mess it up i think
no thats all good
but u cant take out the ^2 like that
$$\sqrt{a^2 + b^2} \neq \sqrt{a^2} + \sqrt{b^2}$$
twin meteorBOT
JustToPro
strong grove
**JustToPro**
recall the image i send , now from here ur $$"a" = \frac12$$ and ur
twin meteorBOT
JustToPro
strong grove
$x$ stays the same
twin meteorBOT
JustToPro
agile mica
so how would I rewrite my integral, that would help me understand it more
strong grove
$$x = \frac12 \tan \theta$$
differentiate this with resect to theta (common substitution thing)
$$\frac{\dd x}{\dd \theta} = \frac12 \sec^2 \theta$$
$$\dd x = \frac12 \sec^2 \theta \dd \theta$$
integral becomes
$$\int\sqrt{ (1+4x^2)} \dd x = \int2 \sqrt{(\frac12)^2 + (\frac12 \tan \theta)^2} \frac12 \sec^2 \theta \dd \theta$$
fixed
twin meteorBOT
JustToPro
strong grove
easy , im a genius
agile mica
jesus we didnt do anything near this in class 😭
agile mica
im in calc 2 rn
strong grove
that doesnt tell me what u have studied till now
agile mica
uhhh
agile mica
Just started
strong grove
done with u sub?
strong grove
can u check if u wrote the problem correctly?
agile mica
well Im doing arc lengths and my function was
$1-x^2$
twin meteorBOT
icey
strong grove
damn
agile mica
so i found the derivative
and then squared it
and plugged it into the formula
i got 4x^2
for the derivative squared
strong grove
is it 1-x^2 or sqrt or smthing
strong grove
hmm
agile mica
its cut off but yes 1-x^2 only
strong grove
well ur derivative is correct and everything seems correct
solving without trig sub will be VERY tricky and difficult
agile mica
maybe im supposed to use a calculator?
it told me to on other problems
but not this one so i didnt
but we never did trig sub to solve any of these in class at the same time so im not sure
strong grove
but we never did trig sub to solve any of these in class at the same time so im ...
are there other problems with "x^2" term in the function
if possible , can u screen shot the entire exercise :d
agile mica
strong grove
i cant figure out a way other than trig sub , maybe im just dumb 
agile mica
I asked chagpt and it mentioned trig sub and hyperbolic sub, both of which I dont think Ive used so those might be the only ways
strong grove
I asked chagpt and it mentioned trig sub and hyperbolic sub, both of which I don...
yeah i got nothing
agile mica
😭
well thank you for your help I might just use a calculator for now and ask my teacher later
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
karmic crane
vocal sleetBOT
karmic crane
I kind of had the right idea. Im just wondering why the $3(x-x')$ chain of equalities is necessary. Since $3x$ and $3x'$ both equal $w-v$ cant we just then equate $3x=3x'$ or am i missing something
twin meteorBOT
Luca M
hushed pewter
I kind of had the right idea. Im just wondering why the $3(x-x')$ chain of equal...
You could do that, yes. It would lead you same way tp 3x-3x'=0
vocal sleetBOT
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Available help channel!
untold arrow
A fruit distributor purchased peaches and apples from a mountainous orchard. The purchasing price of peaches is $10 per pound, and apples cost $4 per pound. Their selling prices are $25 per pound for peaches and $12 per pound for apples. The distributor made a profit of $40,000 in this transaction. It is known that the distributor purchased more than 500 pounds of each fruit, and the weights are integers. What is the distributor's minimum investment?
A. $20,000
B. $21,260
C. $21,300
D. $21,280
vocal sleetBOT
A fruit distributor purchased peaches and apples from a mountainous orchard. The...
untold arrow
,w plot 15x+8y=40000, x+0y=500, 0x+y=500
twin meteorBOT
untold arrow
My question is, with so many integer points in this area, how can I quickly determine which one is the correct one?
serene needle
You're asked minimum
livid bane
You're asked minimum
So do we need to take the x and y values at the middle of the line
?
grizzled vault
A fruit distributor purchased peaches and apples from a mountainous orchard. The...
what class is this for?
btw x,y = 500 doesn't work
untold arrow
Why?
untold arrow
I couldn't draw inequality so i wrote =
grizzled vault
,w 15x + 8y = 4000 when x = 500 and y = 500
twin meteorBOT
grizzled vault
I couldn't draw inequality so i wrote =
what class is this for?
grizzled vault
have u done calculus?
grizzled vault
uhhh idk how you do it with algebra
if you're allowed a calculator then yeah
or like maybe looks like a linear programming exercise
you have to minimize 10x + 4y under the constraints:
x,y > 500 and 15x + 8y = 40000
and you get that the minimum of 10x + 4y = 21250 or smth
serene needle
,w plot x>500, y>500, 5x+8y=40000
grizzled vault
So I'm wondering
to minimize investment, you could fix x = 500 or something
because x is "expensive"
then obtain a value for y
untold arrow
,w plot x>500, y>500, 5x+8y=40000
Yh i already plotted above
grizzled vault
and then plug that into 10x + 4y yeah
twin meteorBOT
grizzled vault
,w solve for y in 15x + 8y = 40000 when x = 500
twin meteorBOT
grizzled vault
,calc 10*500 + 4 * (8125/2)
twin meteorBOT
Result:
21250
grizzled vault
untold arrow
So it's like, B?
grizzled vault
yeah
untold arrow
,calc 10*500 + 4 * (8125/2)
In this case, x is 500 and y is 4062?
grizzled vault
In this case, x is 500 and y is 4062?
smth like that
your task is to minimize 10x + 4y
this is the investment for some (x,y)
it makes sense for you to minimize x and maximize y instead right?
we're doing this heuristically and not super rigorously
so yeah we minimize x by setting x = 500
and solve for y under the constraint 15x + 8y = 40000
we get the corresponding y and then we just compute 10x + 4y
vocal sleetBOT
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Available help channel!
tawdry pollen
help please, i have no idea
vocal sleetBOT
help please, i have no idea
rough patrol
you did the hardest one already lol
the second one
is done by simply reflecting it over that line
oh wait nvm
thats the answer to part C there
okay so part (a)(ii) is called a dialation
draw the lines between corresponding verticies
and they should all intersect in the same place
vocal sleetBOT
Available help channel!
gritty axle
f(x) is continuous on [0,1]
vocal sleetBOT
f(x) is continuous on [0,1]
quiet echo
f(x) is continuous on [0,1]
!status
vocal sleetBOT
f(x) is continuous on [0,1]
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
graceful canopy
f(x) is continuous on [0,1]
consider the floor(nx)/n to be a step function
it jumps by 1/n. also consider the riemann sums
vocal sleetBOT
@gritty axle Has your question been resolved?
vocal sleetBOT
@gritty axle Has your question been resolved?
tardy peak
vocal sleetBOT
tardy peak
i think only the second answer is correct
but i saw the answer it said the third answer is also correct
but isnt the probability cannpt be more than 1?
vocal sleetBOT
@tardy peak Has your question been resolved?
bitter pilot
but isnt the probability cannpt be more than 1?
the integral of f_y on R has to equal 1
f_Y has to be non-negative, generally speaking
bitter pilot
Also yea 3rd is correct
X ~ U(0,1) then Y ~ U(0,1) too here P(Y ≤ y) = P(X³ ≤ y) = P(X ≤ cbrt(y))
twin meteorBOT
anti-algebraist 𝔸dωn𝓲²s
tardy peak
but why is the 3rd one is correct
bitter pilot
because your f_Y is wrong
tardy peak
what am i missing?
bitter pilot
showing your work
tardy peak
fY(y) = 1/(3y^(2/3)) the function i found was this
bitter pilot
yes
tardy peak
can density be more than 1
tardy peak
where can i see that one
bitter pilot
it is not the probability function
tardy peak
Then what function is this?
bitter pilot
2nd
That's what you call P(X ≤ x)
that gives the probability of some random variable X
bitter pilot
what exactly is it?
tardy peak
What what exactly is it?
tardy peak
All of them
Nothing makes sense suddenly
The random variable X follows continous uniform distribution on the interval [0, 1] means. X might be any number between 0 and 1 inclusive and all of them will have same probability isnt it?
I think i understood the problem wrong
nova cedar
The random variable X follows continous uniform distribution on the interval [0,...
thats basically the idea, every number in the range [0, 1] is equally likely to be picked for X, but here's the tricky part: when we talk about continuos distributions, we have to be a bit careful about 'probability' for a single number
tardy peak
So does that mean the probability can be more than 1 in continuous distribution?
nova cedar
thats basically the idea, every number in the range [0, 1] is equally likely to ...
imagine you're mesauring someone's height, let's say we're looking at adult heights in meters. Can someone be exactly 1.750000000 meters tall? In reality, our measurements are never iniftely precise
bitter pilot
So does that mean the probability can be more than 1 in continuous distribution?
no
look at the definitions
nova cedar
So does that mean the probability can be more than 1 in continuous distribution?
no, no probability itself can never be more than 1 ( or 100%), wheter it's a continuos or discrete distribution, probability awals represents a fraction of the total possibillities, and the total probability of everthing happening is aways 1
tardy peak
Ok then why fY(0.1)=1.547?
nova cedar
Ok then why fY(0.1)=1.547?
this number is not a probability, it's a density value
bitter pilot
the probability is the integral of the density function or area under the density function
tardy peak
Then doesnt that mean the probability will be 0 for certain x?
nova cedar
yes, for a continuos distribution, the probability of x being exatly equal to any single specific value is indeed considered to be zero
look
tardy peak
Ok then why fY(0.1)=1.547?
Then why
bitter pilot
that is because the integral would have equal bounds
twin meteorBOT
anti-algebraist 𝔸dωn𝓲²s
bitter pilot
Then why
because you calculated that f_Y(y) = 1/3(cbrt(y²))
but that is not your probability function!
tardy peak
So its no more about probability?
bitter pilot
exactly
tardy peak
The question is just about transformationssatz?
bitter pilot
probably
tardy peak
No i see.
bitter pilot
I am beruhigt.
tardy peak
Es ist noch nicht Zeit zu beruhigen
Ich habe mehr Fragen
Ich habe am Freitag eine Prüfung
bitter pilot
und ich am Samstag
bitter pilot
can you translate it
bitter pilot
If e.g. Tom won 7 rounds and Jerry 4 rounds, and for some reason the game stops
and then under these circumstances they are asking how the price should be distributed
or something like that
so that it is fair
tardy peak
Hwo do i even calculate that?
bitter pilot
I am thinking this may have to do with expected value but i am not sure
tardy peak
Expected value for what?
vocal sleetBOT
@tardy peak Has your question been resolved?
bitter pilot
Expected value for what?
I asked another helper and they said this:
Jerry has to win 4 times in a row.
In any other scenario Tom wins.
Jerry has 1/16 = (1/2)^4 chance to win, where as Tom's 1 - (1/2)^4 = 15/16.
Thus 15:1 split
tardy peak
So tom will get the 15/16 of the prize money or jerry will get 15/16?
Someone who has more chance to win will get the more money?
bitter pilot
It's not clear though who is winning currently it could be 7:4 for Tom or Jerry, but that's not the point.
bitter pilot
Someone who has more chance to win will get the more money?
Basically the opposite, you are being rewarded for making a comeback
tardy peak
So the one who only won 4 times will get the most amount of money?
tardy peak
Yes.
bitter pilot
No it should be the other way actually
The one who was leading should get the most
because hypothetically it would be unlikely to make such a comeback
tardy peak
Okay but.
bitter pilot
So since it's more probable that the leading person would have won it would be fair to give them the greater cut, I believe
tardy peak
But the one who have already 7 times won might won next time if its head right?
bitter pilot
Yes
tardy peak
So he will have the 1/2 chance to win
bitter pilot
and that's even more probable then the other person winning 4 times in a row
tardy peak
Then the other will have 1/2 chance to loose
Why are we specifically choosing the person who won only 4 times case?
bitter pilot
here is a tree diagram also from the other helper
bitter pilot
Why are we specifically choosing the person who won only 4 times case?
because otherwise the game is over if the other person wins
tardy peak
So we will think the game will continue until the one who won 4 times wins?
bitter pilot
you are thinking hypothetically how the game would have ended
and you end up with the person who's leading having a chance of 15/16 winning while the other who needs to make a comeback has a chance of 1/16
tardy peak
I see.
tardy peak
No you are not moron.
Better than me. Im crying inside. Shouldve started to prepare earlier
I need explanation for Schätzer
No first bootstrap
I dont understand this graph
vocal sleetBOT
@tardy peak Has your question been resolved?
proven linden
does Angle ? = 130?
vocal sleetBOT
does Angle ? = 130?
proven linden
someone help plsss
atomic jasper
does Angle ? = 130?
no
atomic jasper
consider this
proven linden
how do u know its a tangent tho?
quiet echo
how do u know its a tangent tho?
its touching the circle at only one point for both PR and PQ
proven linden
not drawn to scale
quiet echo
you think they're gonna trick you like that
hollow kite
PQ and PR are tangent lines
proven linden
ic now
quiet echo
but it passes thru
yes
quiet echo
its tangent?
thats the definition
proven linden
if u r given this scenario, where the 2 lines arent tangent, would u still be able to figure out the value of x?
proven linden
thats the definition
.
proven linden
PQ and PR are tangent lines
.
quiet echo
if u r given this scenario, where the 2 lines arent tangent, would u still be ab...
yes
there is a rule for this
let me draw it
proven linden
ik its something with circle theorem, but i wasnt in skl...
proven linden
is that part of circle theorem or congruency/similarity?
quiet echo
is that part of circle theorem or congruency/similarity?
circle theorems yeah
proven linden
circle theorems yeah
what is A with a curve
and B with a curve
like the length of the arc?
proven linden
circle theorems yeah
do u know what this specific rule is called?
quiet echo
what is A with a curve
an arc, the m thing represents measure
quiet echo
also an arc?
yep
proven linden
how cam an arc has a degree?
quiet echo
how cam an arc has a degree?
an arc has a degree because it is the measure of the total circumference
a circle "is" 360 degrees, right?
proven linden
right
quiet echo
(im using "is" very loosely here because it is not very rigorous)
proven linden
as it when u measure from the centre?
as in when the "radius line" rotates from A to B?
and thats 160°?
quiet echo
as in when the "radius line" rotates from A to B?
mhm
quiet echo
and thats 160°?
yep, it "rotates" 160 degrees, so the arc "measure" is 160
heady locust
I suppose this is more of a MATLAB question than anything else... how would I go about inputting something like this in MATLAB? does anyone have guides on how to start understanding the syntax?
vocal sleetBOT
I suppose this is more of a MATLAB question than anything else... how would I go...
atomic jasper
!occupied
vocal sleetBOT
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).
heady locust
I think my question is actually better suited for a discussion channel
I'll leave this
.close
vocal sleetBOT
opal steeple
1 + 2 + 3 + 4 DOES NOT EQUAL -1/12
vocal sleetBOT
Available help channel!
snow schooner
i need help with two step inequalitys
vocal sleetBOT
i need help with two step inequalitys
atomic jasper
!da2a
vocal sleetBOT
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
snow schooner
please help
atomic jasper
just send your question
snow schooner
there is like ten
snow schooner
oak magnet
, rotate
twin meteorBOT
oak magnet
Whats blocking you ?
snow schooner
wdym
oak magnet
How would you solve this ?
atomic jasper
if it was an equality would you know how to solve?
snow schooner
3 - 21 divide 6 i think
snow schooner
if it was an equality would you know how to solve?
shje noty teach it
atomic jasper
consider $6a-3=21$
twin meteorBOT
Bonk
atomic jasper
what is a?
snow schooner
i think it is 4