Here's the exact
#help-17
honest flame
olive stag
proof of this
olive stag
ok
olive stag
square it to the half?
olive stag
ok
honest flame
Squaring on both sides
olive stag
x=y^2
honest flame
yeah
so
The power
Gets cancelled
When multiplied with 2
In power
@olive stag got it?
olive stag
yes
honest flame
yeah
We basically get same answer
okay so
229.7
Let's focus on powers only
what we have is square root is writen as 1/2
And it's actually squared (given in question)
1/2×2
olive stag
the root and square cancel
honest flame
Is basically 1
olive stag
ok so can you tell me what calculus is now
olive stag
i dont need it for homework i want to know
honest flame
Well for an instance
We could say it's the topic which deals with study of functions and limits including differentiation,integration,etc.. as their primary types classifying into various subjects
olive stag
ok
honest flame
it's the basic thing.
jagged cargo
calculus is studying of how functions behave
honest flame
calculus is studying of how functions behave
yeah it's part.
olive stag
i use prime fator tree for this?
loud walrus
?
honest flame
Oh you meant finding another roots
olive stag
i use prime factor tree tofind y
honest flame
i use prime factor tree tofind y
That isn't required tbh
olive stag
y= cube root of -343
honest flame
y= cube root of -343
-343=(-7)³
Cube root=1/3
Cancel 3
We get -7
I think any of those prime factor you were talking about isn't required
frozen belfry
Its called a calculator
olive stag
Its called *a calculator*
say that to the non calculator exam
frozen belfry
say that to the *non calculator* exam
oh
olive stag
yes
honest flame
now
olive stag
x=y^2
olive stag
root of x = y
olive stag
how do i find cube root of -343
loud walrus
root of x = y
That is only true due to the previous manipulation
In general that is false
honest flame
how do i find cube root of -343
343 is cube of 7
frozen belfry
how do i find cube root of -343
First find the cube root of 343 then multiply it by i
honest flame
In general that is false
We just assumed it.
honest flame
First find the cube root of 343 then multiply it by i
that's insane lmao
olive stag
yeah thats why math is fun it is so flexible
viscid bane
how do i find cube root of -343
without calculators the only way is to use prime factorization
loud walrus
We just assumed it.
I know u know, im just telling him he might have not realized
honest flame
why do we need some complex number here
honest flame
I know u know, im just telling him he might have not realized
fr
olive stag
I know u know, im just telling him he might have not realized
thanks, but im not that clueless
honest flame
thanks, but im not that clueless
how do u proof a square root is 1/2?
Bro literally
loud walrus
thanks, but im not that clueless
So you are aware what is sqrt(x^2) in general?
honest flame
So you are aware what is sqrt(x^2) in general?
No his doubt is
Prove the square root
Why 1/2 considered square root
olive stag
343 is cube of 7
how??
loud walrus
No his doubt is
I am answering ti him cause he said he is not clueless about what I am saying
honest flame
I am answering ti him cause he said he is not clueless about what I am saying
bro I'm getting dumber
honest flame
so i need to memorise all roots?
Yeah till 20 is enough ig
loud walrus
You can know if a number is divisible by 7 taking all digits except last one and rest last one multiplied by 2
For example 343
34 - 2(4) = 28
28 is divisible by 7
So 343 too
loud walrus
Yes
honest flame
so cube root -343 is 7
-7
viscid bane
its -7
honest flame
-×-×-=-
loud walrus
If the number is big, you have to find out, if it is small it would be better you know them
The same you know 8 * 9 = 72
frozen belfry
Most likely if you’re gonna get an exam with cube roots, it will probably be like 3-15
honest flame
If the number is big, you have to find out, if it is small it would be better yo...
fr
honest flame
Most likely if you’re gonna get an exam with cube roots, it will probably be lik...
Around 20 is enough
Unless it's an advanced calculus sum
olive stag
You can know if a number is divisible by 7 taking all digits except last one and...
you said 34 - 2(4) but thats 34 - 8 not 34 * 2
honest flame
What grade are you in @olive stag
loud walrus
you said 34 - 2(4) but thats 34 - 8 not 34 * 2
I made a typo
olive stag
What grade are you in <@1058352869721514074>
why
loud walrus
34 - 2(3)
olive stag
im not dumb i can do trigonometry
honest flame
im not dumb i can do trigonometry
It's not abt dumb
honest flame
I asked the grade that's it.🙏
honest flame
9th grade huh
loud walrus
I will give you another example
olive stag
9 next term
olive stag
?
honest flame
-_-
loud walrus
2975
olive stag
no
loud walrus
297 - 10 = 287
olive stag
i not american
honest flame
That's okay
olive stag
297 - 10 = 287
ok
frozen belfry
and i dont say grade i say year
You’re 8 years old?
loud walrus
28 - 14 = 14
frozen belfry
14 is divisible by 7
Obviously
loud walrus
So 2975 too
frozen belfry
So 2975 too
What are you getting at
loud walrus
The opposite lol
loud walrus
What are you getting at
I am answering to renvrs question he made
olive stag
28 - 14 = 14
so i get all digits other than last and takeaway but 10
olive stag
so 2975 we do 297 * 10 because 5*2=10
no 297 - 10
which is 287
and 287 is a multiple of 7
lets see 3142
314 - 4
310
7 doesent go into 310 so 310 isnt divisble by 7
frozen belfry
7 doesent go into 310 so 310 isnt divisble by 7
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boreal wren
this is a graph of a function. it's area is given 1 unit. and we have to find value of h
vocal sleetBOT
this is a graph of a function. it's area is given 1 unit. and we have to find va...
boreal wren
coordinates are (1,h) (2,2h) and (3,3h)
if I treat it as 3 different functions, and calculate area under curve with integration by applying 3 individual limits to each 3 linear functions, 0 to 1, 1 to 2, 2 to 3.
.
but if I treat it as a single function and apply 0 to 3 limit on each integral
.
answer in both cases is same
I want to know why
here is a clear graph if someone likes this one
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bitter pilot
<@&286206848099549185>
They cannot be equal unless your sketch is wrong, as you can see the yellow area is missing out on parts from the green
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undone aurora
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undone aurora
Why would they use the equal variance method for this question?
why would they assume equal variances for this question?
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undone aurora
<@&286206848099549185>
undone aurora
wait a min im so slow I could have used the unequal var method and it would have given the same soln
because S_1^2 + S_2^2 / 2 = (3.92^2 + 3.98^2) /2= 31.2068/2 = 15.6034
🤦
boreal wren
They cannot be equal unless your sketch is wrong, as you can see the yellow area...
I said if I take those three functions and apply their corresponding limits 0 to 1, 1 to 2, and 2 to 3 respectively, it gives the same answer as when I apply 0 to 3 on all three functions. I didn't take the whole function which you mentioned in green area. I took same yellow three functions.
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cinder frost
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fair flame
I'm a bit confused on how to go about answering this as I've kind of contradicted myself.
vocal sleetBOT
I'm a bit confused on how to go about answering this as I've kind of contradicte...
fair flame
So Initially I decided that the answer cannot be b or e because when you make y=0 you get x-values which insinuates that there are intersections with the x axis.
Then I made x=0 and I got a y-intercept of 1. However, from the graphs none of them have that
Yes like this
dull quest
Nah sorry i didnt see the sin x inside the cosine
fair flame
Ah ok
mellow void
Then I made x=0 and I got a y-intercept of 1. However, from the graphs none of ...
in fact, b, c, and e all have this point (0,1)
fair flame
I would disagree with C having that point
fair flame
Yeah that's whats really confused me though because there has to be an intersection with the x-axis from the results of making y=0
b and e do not intersect with the x-axis
fair flame
So when you make y=0 you get x = 90 (pi/2 in radians) which connotes that there are intersections with the x-axis right ?
mellow void
that's wrong
suppose cos(sin x) = 0
this implies that the input of cos must be pi/2 or -pi/2 (or its friends of the form pi/2 + kpi)
the input, however, being sin x
taking the easier of these, we have sin x = pi/2 or sin x = -pi/2
does such an x exist now?
fair flame
OHHHHHHHHHHHHHHHHHHHHHHHHHH
How silly of me yes you are completely right
I made the mistake of thinking the inverse of cos0 is 1 when it's 90
That makes alot more sense now
So it must be b or e
fair flame
One second sorry I'm having a little think
I mean on basic observation I'm noticing that one has alot more x-values in the given range than the other one. I'd probably start investigating what the x-values at the max/min are. For example, b seems to have about 3 in the range whereas, e seems to only have one. Does that make sense ? Am I moving alone the right track ?
mellow void
I think you are, but you probably don't mean to say x-values; they're defined on the same domain [0, 2pi] so they have the same number of x-values
b has more bumps than e, if that's what you wanted
fair flame
b has more bumps than e, if that's what you wanted
Yeah that's what I meant
mellow void
the places where a function attains a 'peak' are usually called local maxima, and 'valleys' local minima
I'd say b has 3 local maxima and 2 local minima, and e 2 max and 1 min
you would learn these terms in a calculus class, but I don't think this is calculus?
in that case it's a bonus fact lol
fair flame
I'm thinking that to find the values of the 'bumps' we could do cos(sinx) =1 and input an x value that gives us 1 and use this value to determine what the other x-values are ??
mellow void
sounds solid
fair flame
So if you let x=0 you get cos(sin0) which is cos(0) which gives us 1
Which means that x=0 is for our first bump. To find the second bump I like to use the law of cosx=cos(360-x) though I know some people use the unit circle or something. So if I did that that would mean our second x-value for our second bump is 360 ?
Doing it in degrees anyway
But that doesn't really work given the range is 2 pie...
mellow void
I'd argue that you could be skipping a bump, i.e. we don't know if we can anticipate bumps between 0 and 360 or not
fair flame
I'm kind of lost then... do you have any idea on how you would go about doing this ?
mellow void
I'm thinking that to find the values of the 'bumps' we could do cos(sinx) =1 and...
it's probably cleaner to assume that x satisfies cos(sin x) = 1 and then determine restrictions on x, rather than picking values of x
so let's assume that x satisfies cos(sin x) = 1
fair flame
Yep
mellow void
we know that cos(y) attains this value of 1 only when y is some integer multiple of 2pi
hence sin x = 2kpi for some k
but of course, 2pi and -2pi are simply too big, they're out of the range of sin
so the integer multiple of 2pi in question is therefore 0
hence x satisfies sin x = 0
fair flame
How can we use this though ?
mellow void
well, when does sin x = 0?
on the unit circle, these points correspond to the extreme left and rightmost points on the circle
in particular, sin x = 0 only if x is an integer multiple of pi (even multiples on the right, odd multiples on the left)
fair flame
Oh so we're trying to find other values other than 0 that satisfy cos(sin x) = 1 ?
fair flame
Those are our bump values right ?
mellow void
right
mellow void
the positive ones in particular
no no, in solving cos(sin x) = 1 and finding three solutions, we learn there are three points that intersect the line y = 1
we could also see that cos(sin 180) is indeed 1, and not less than 1 as we see in e
fair flame
I'd argue though if our bumps have values of 0, 180 (pi) and 360 (2pi) respectively then would this not connote that e is our graph ?
Because the range is 2pie
mellow void
the parity of the bumps matters more than the count of bumps
high-low parity that is
again, we know that cos(sin pi) = 1, so the function must contain the point (pi, 1)
fair flame
Agreed
mellow void
the corresponding point on e is not (pi, 1), it's closer to (pi, 0.5) by a very rough estimation
fair flame
Ah I see I'm only thinking about the maximums (when y=1)
fair flame
Ok I see it now. Having x= 0,180,360 means that there are 3 bumps at the maximums that should be present on the graph. B has this but e only has about 2
mellow void
yup
fair flame
I see that makes so much more sense. I was assuming that all bumps would have the same y-value of 1 which clearly they do not
mellow void
right lol
fair flame
I really liked your thinking back at cos(sinx) = 1 when you had the thinking of sinx=0 which allowed you to find the x-values of 0,180 and 360 that really opended my mind
mellow void
that's good, I'm glad that helped
fair flame
This has been very helpful thanks alot for taking the time to explain this to me it makes so much more sense now. I suppose I'll close the channel as my question has been answered but thanks so much again !
.close
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gilded cedar
hi
wintry sonnet
it has to do with the fact that every number you will get will be a root
gilded cedar
okay but how do i prove it with algebra
gentle thicket
maybe some induction action
but I am not sure if it will work or not
wintry sonnet
is it given that the limit is 3 or do you need to find it
try proving that a_n <= a_n+1 and that a_n+1 <= a_n+2
gentle thicket
I've tried it now, Induction will work here
gentle thicket
try proving that a_n <= a_n+1 and that a_n+1 <= a_n+2
what after that?
gentle thicket
giving it bounds i think
what are your thoughts on Principle of Mathematical Induction?
wintry sonnet
i've never heard of mathematical induction
maybe i know it through a different name
short pilot
Yes
short pilot
Getting bored any idea
short pilot
What?
gentle thicket
@gilded cedar you here?
gentle thicket
No i know that
so what?
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jade vale
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compact fable
for questions 29/30, how are you supposed to find the other solutions? I’m able to find one, but i’m confused on how you find the others
vocal sleetBOT
for questions 29/30, how are you supposed to find the other solutions? I’m able ...
vivid pumice
for questions 29/30, how are you supposed to find the other solutions? I’m able ...
Are you referring to 30?
compact fable
either one
compact fable
radians
vivid pumice
Ok, when you have cos(θ)=x
You have 2 answers,
Answer1 : θ1=arccos(x) + 2πk
Answer 2: θ2= 2π-arccos(x) +2πk or θ2=-arccos(x) +2πk
where k is a regular number
For example, If cos x = 1/2, then x =± π/3
Or x=2π-π/3
You may look at it this way, where cos(θ)=x
You have 2 answers
Now if you look at sin(x), you also have 2 answers
sin(θ)=x
θ1= arcsinx
θ2= π- arcsinx
Got the idea?
compact fable
sorry just saw this now @vivid pumice
how do you know which quadrant
the like reference second angle is
if that makes sense
or does it always differ
vivid pumice
For cos, the second angle is -arccos(x)
compact fable
let’s see.
vivid pumice
vivid pumice
let’s see.
Here.
compact fable
woah
vivid pumice
Got it?
vivid pumice
yes
compact fable
thank you kevin snow
vivid pumice
np
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round merlin
how do i achieve the movement like that
vocal sleetBOT
how do i achieve the movement like that
round merlin
hold on, lemme drop the code i have so far
Angles(math.cos(t) * 0.25, math.rad(angle - 90 + t * 45), math.sin(t) * 0.25)
t its the number that increases over time
angle its a result of function that used to distrubute objects over the circle
right now it looks like the plane is tilting up and down
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vast shale
Could someone explain how this relation is transitive? As far as I know, transitive means if there exists (a,b) and (b,c), then (a,c) must also exist. But in this set no three different elements are connected
vocal sleetBOT
Could someone explain how this relation is transitive? As far as I know, transit...
dusty ice
I'm not sure I understand where your confusion is
what do you mean by "no 3 different elements are connected"
hard atlas
there exist no three elements with (a,b), (b,c) but not (a,c)
rephrased, there is no counterexample to it being transitive
all conditions of the form "if this then that" and "this" never happens then they are true
tho I wanna note that actually (1,2), (2,1) and (1,1)
nothing says that a != c
similarly (2,1), (1,2) and (2,2)
brittle charm
tho I wanna note that actually (1,2), (2,1) and (1,1)
yea that is why empty set is also transitive
vast shale
tho I wanna note that actually (1,2), (2,1) and (1,1)
Ohhhh that makes sense lol, than you very much
vast shale
yea that is why empty set is also transitive
That's useful to know, thank you guys
.close
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brittle charm
That's useful to know, thank you guys
welcome... also symmetric relation does this... if the intial condition (a,b) E R does not arise then you don't have to check for it
therefore empty set is both transitive as well as symmetric
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vast shale
How would we show this is transitive?
vocal sleetBOT
How would we show this is transitive?
tawny nacelle
well, what can you assume? 
in order to prove this relation is transitive, you need to assume some things first
vast shale
in order to prove this relation is transitive, you need to assume some things fi...
Well, all I know is that if (a,b) and (b, c) exist, then (a,c) also exists
vast shale
Yes
I did try this with some numbers as an example and of course it worked with those numbers but I'm not sure how to actually prove it
tawny nacelle
if a R b and b R c, then we immediately know that a - b is divisible by 4, and b - c is divisible by 4
now we need to show that a - c is divisible by 4
any ideas?
mild flower
it might help to translate "is divisible by 4" into something else
vast shale
any ideas?
No 😭
vast shale
it might help to translate "is divisible by 4" into something else
My mind is blank smh
mild flower
do you have a definition for "is divisible"?
vast shale
do you have a definition for "is divisible"?
Well, a modulo c = 0? Idk
brittle charm
I did try this with some numbers as an example and of course it worked with thos...
hmm that works when we have to prove that is NOT transitive... but here this is not the case so you will have to make general statement
tawny nacelle
what divisibility properties do you know of?
vast shale
Wdym by that?
brittle charm
I did try this with some numbers as an example and of course it worked with thos...
try to make equations with the condition to arrive at a R c
tawny nacelle
Wdym by that?
I don't want to give away too much 
oak magnet
A is divisible by b means that b is ? of a
tawny nacelle
I think I'll hand the reins over to others then, because I've gotta head out actually
oak magnet
I have too 💀
mild flower
your modulus definition will work
we know:
a-b is divisible by 4
b-c is divisible by 4
we want to show:
a-c is divisible by 4
translating those into modulus definitions:
we know:
a-b = 0 (mod 4)
b-c = 0 (mod 4)
we want to show
a-c = 0 (mod 4)
continue from here
ocean lynx
think about showing: if x = 0 (mod k) and y = 0 (mod k), then x + y = 0 (mod k)
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@vast shale Has your question been resolved?
vital violet
the midpoint riemann sum = Left riemann sum + right riemann sum divided by 2 right
vocal sleetBOT
the midpoint riemann sum = Left riemann sum + right riemann sum divided by 2 rig...
half imp
No
you have to sample the midpoints from each interval
That's not the same as averaging the endpoints
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surreal spoke
Then find NP by similar triangles
i tried that, it says the answer is 7.7
every time i try to set up the proportion i get 10/13 = 10/NP i don't think im looking at it right
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humble iris
Other than the squeeze theorem what other ways to find a limit without using derivatives?
vocal sleetBOT
Other than the squeeze theorem what other ways to find a limit without using der...
humble iris
Oh yes geometric methods exist but aren't they specific for each limit,
scenic ravine
Yes
humble iris
I am talking abt general algorithms
scenic ravine
Algebric then
humble iris
Can u elaborate on the algebric ones
scenic ravine
series expansions for infinitely differentiable functions
humble iris
Again ur using differentiation here
humble iris
In my specific case I'm trying to find a derivative
scenic ravine
!original
vocal sleetBOT
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.
scenic ravine
so what have you done so far?
humble iris
So I stumbled across this limit
scenic ravine
uh
humble iris
Which I'll have to prove to be 1
twin meteorBOT
🏳🌈f(why am i here )= idk
scenic ravine
yes?
humble iris
Yea
scenic ravine
now what ?
humble iris
U can factor out the e to the x
humble iris
(e^h - 1)/h
humble iris
(e^h - 1)/h
Lim of this as h tends to 0
That's what I need to prove to be equal to 1
twin meteorBOT
🏳🌈f(why am i here )= idk
scenic ravine
?
humble iris
Yea but u already factored out the e^x outside the limit
scenic ravine
you can take ( if you're at scholl), e^h-1/h =1 to be a fact
humble iris
Bruh
scenic ravine
otherwise
humble iris
I am trying to prove that statemebt
twin meteorBOT
🏳🌈f(why am i here )= idk
humble iris
That's using differentiation
scenic ravine
the series expansion,yes
humble iris
U can't use a derivative to calculate a derivative
U r pre supposing d/dx e^x = e^x
So it's circular reasoning
So I need to find the limit without using derivative of e^x
humble iris
Yea I want other methods other than squeeze thm
scenic ravine
https://math.stackexchange.com/questions/2832934/how-to-prove-that-lim-h-to-0-fr...
see this
humble iris
Hey thanks for sharing!
In the top answer soln 1 uses the squeeze thm and sol 2 uses Taylor series
I didn't get the solution 3 tho
Also can u find this limit using some geometric logic
?
scenic ravine
Also can u find this limit using some geometric logic
I don't think so
let me think
I'll have to look at the graph for that
humble iris
I think I just realised something...
scenic ravine
yes?
humble iris
I mean that limit equalling 1 is what defines e
scenic ravine
I'm not too sure, sorry
humble iris
lim h->0 (a^h - 1)/h = ln(a) right?
scenic ravine
yup
scenic ravine
You can explore it, if you have the time
humble iris
I don't 
scenic ravine
Then explore it during your breaks!
scenic ravine
No problem !
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manic lance
why is there a minus at the end?
vocal sleetBOT
why is there a minus at the end?
manic lance
.close
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scenic ravine
why is there a minus at the end?
What is the exponential form of $\frac{1}{t}$?
twin meteorBOT
🏳🌈f(why am i here )= idk
manic lance
What is the exponential form of $\frac{1}{t}$?
yeah i see it now, ty
scenic ravine
You're welcome!
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dense knot
I'm in 8th grade taking Algebra 1 and I am confused with variables that are negative without a prior negative symbol
vocal sleetBOT
I'm in 8th grade taking Algebra 1 and I am confused with variables that are nega...
tawny nacelle
okay, what seems to be the issue?
full ferry
what do you mean?
dense knot
whenever A variable is negative but is not indicated until you figure out the variable
tawny nacelle
so if I gave you 5x = -5, you have issues understanding why x = -1?
even though there's no minus sign there?
dense knot
no I understand that it is -1 but I dont understand how im supposed to know that it is negative in the firstplace
devout kindle
depends upon ques
mellow oyster
i mean the whole point of algebra is that you don't really know what the value of the variable is, you figure it out by rearranging
livid prairie
no I understand that it is -1 but I dont understand how im supposed to know that...
when you or the teacher decides what the variable should be
mellow oyster
you could intuitively know that the solution is negative since you know that the product of a positive and an unknown is negative
tawny nacelle
i mean the whole point of algebra is that you don't really know what the value o...
no, the point of algebra is to be as abstract as possible to obfuscate the point
anyways, what neil said is correct @dense knot
(ignore my silly joke)
mellow oyster
you also don't even need to guess
we know exactly how to solve equations like these
algebraically
mellow oyster
we know exactly how to solve equations like these
an initial guess doesn't really help you
livid prairie
that equation that was deleted has infinitely many solutions
livid prairie
an initial guess doesn't really help you
except for approximation
velvet zephyr
it's easy to solve linear equations. just follow the steps.
subtraction/ addition first then division/multiplication then other things
mellow oyster
and even then linear algebra tells us exactly how to solve for all solutions to every family of those kinds of equations
dense knot
7r+5 = -6-2(-8 -r)
mellow oyster
yeah for this you don't need a guess, you can exactly solve this for r
velvet zephyr
7r + 5 = -6 +16 + 2r
5r = 5
r = 1
livid prairie
7r + 5 = -6 +16 + 2r
5r = 5
r = 1
btw just providing the solution is discouraged here (you didn't do anything wrong in this case though, just telling you)
velvet zephyr
my advice is that you should eliminate negative signs (where possible) to make it more peaceful
dense knot
I already finished the paper I just got that wrong and it confused me alot
velvet zephyr
btw just providing the solution is discouraged here (you didn't do anything wron...
ok
Neil got 4 upvotes
Speedy delete got 2
Meolve got 1
geometric progression
dense knot
I think I get it now tho
livid prairie
Neil got 4 upvotes
Speedy delete got 2
Meolve got 1
geometric progression
and this matters why?
velvet zephyr
Idk
doesn't matter but take this info
ok
dense knot
how do I unclaim this chat
velvet zephyr
I think I get it now tho
Don't worry lil bro I am in 9th and was also kind of suffering in 8th but now it's soooo easy
do .close
dense knot
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dusty cypress
Anyone know how to make a PDA accepting 0^2n 1^n 0^m 1^2m s.t. n, m >= 0?
scenic ravine
PDA?
humble patrol
Anyone know how to make a PDA accepting 0^2n 1^n 0^m 1^2m s.t. n, m >= 0?
what is this expression?
dusty cypress
001, 011, etc.
dusty cypress
No, they are strings
the exponents are the amount of characters
1^0 is the empty string
humble patrol
but this is supposed to be math help right?
humble patrol
Is cs not math?
uh, not at its finest point?
livid prairie
but this is supposed to be math help right?
you're allowed to do math related cs questions here
inner osprey
but this is supposed to be math help right?
people have been known to ask non-math questions in this server. nobody really complains
dusty cypress
anyway this pda is annoying me
inner osprey
physics? yeah many people who study math also study physics so go ahead. cs? same deal, why not
dusty cypress
if anyone knows about them and can help lmk
humble patrol
you're allowed to do math related cs questions here
yeah, untill you understand what does the question mean
dusty cypress
0^2n 1^n 0^m 1^2m s.t. n, m >= 0
humble patrol
if anyone knows about them and can help lmk
welp, new topic to know about ig
dusty cypress
@blissful sentinel are you smart enough to do this haha
livid prairie
can you elaborate on what you want the pda to accept
livid prairie
He's really good
yeah
dusty cypress
can you elaborate on what you want the pda to accept
0^2n 1^n 0^m 1^2m s.t. n, m >= 0
0101 is not accepted
001 is accepted
011 is accepted
01 is not
livid prairie
what are s and t
blissful sentinel
livid prairie
0^(2n) 1^n 0^m 1^(2m)
livid prairie
what are s and t
dusty cypress
I don't see s and t
livid prairie
oh you mean string terminator
humble patrol
oh, its the automata theory, now it makes sense why its math related
livid prairie
so a pda is just a fsm with a stack right lol
livid prairie
ok
so in the internal state you need to include 2 bits, first one indicates whether it's on n or m, and second one indicates whether its on 0 or 1
and then for zeros you push 2 values on the stack, and for ones you pop one off
stack underflow is validation faliure
stack is reset when switching from state 01 to state 10
i am not an expert, this is the the first time i've used pda's
@dusty cypress does this look like it will work
livid prairie
sorry, i don't really understand this kind of state diagram
humble patrol
so, from whatever I have researched till now, for you to make a PDA, you need transition functions, namely 4 as you have 4 strings, they would be made as per the super script you entered there
as for the examples I saw till now, as per that, for the first string for the 'stack', if you have one 0, you out add 2 to the stack, if you have one 0 for the next string you pop out from the stack, and so on
does this seem right? Its quick research so it may be wrong
vocal sleetBOT
@dusty cypress Has your question been resolved?
humble patrol
ok, I got a grasp of it, so suppose a input string, if when reading the first state, say q0, it reads a 0, it pushes 2 zeros in the stack, else transfers to the next state when a 1 is encountered, and then like wise works as per the strcture of the transitions
and, you can create a representation of that, as:
$$
(S_1, 0, NULL) \rightarrow (S_1, 00)
$$
twin meteorBOT
Greydawn Dewer
humble patrol
**Greydawn Dewer**
Now I guess I am done, a lot of new things
karmic tundra
how to solve further on even if i multiplied nd entered its showing as wrong ans
dull bear
What did you get? 
dull bear
how to solve further on even if i multiplied nd entered its showing as wrong ans
Also is this (the dy/dx expression) what you got from a circle? 
karmic tundra
Also is this (the dy/dx expression) what you got from a circle? <a:thonk2:112384...
one sec i will send the first part of the question
dull bear
Cool cool, thought so 
karmic tundra
Cool cool, thought so <:catGiggle:668948717772079128>
smartt
dull bear
What did you get? <:catThink:519997422194393108>
In your expression you should find x^2 + y^2 appearing, right?
karmic tundra
In your expression you should find x^2 + y^2 appearing, right?
yess
dull bear
how far did you get with simplifying it?
karmic tundra
only this much
karmic tundra
<:SCgoodjob2:750436894915166321> how far did you get with simplifying it?
should i apply uv rule?
dull bear
see in the numerator, if you factor out a negative, it becomes -(x^2 + y^2)
karmic tundra
<:happyCat:536371654251511828> see in the numerator, if you factor out a negativ...
yess
dull bear
Replace that x^2 + y^2 with 25
dull bear
-25/y^3 but yep
karmic tundra
its showing as wrong
ohh nvm nvm they to express in x nd y terms
thnk u tho
.close
vocal sleetBOT
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hidden kelp
I know this is going to be bleak to look through, but I cannot for the life of me figure out why I pick up an extra negative sign at the end. The answer should not have it 😭
vocal sleetBOT
I know this is going to be bleak to look through, but I cannot for the life of m...
hidden kelp
In the first step, I used the addition formula for tan but flipped it to get cot
bitter pilot
maybe there is typo along those lines
,w Re(pi/3 * cot(ipi/3+pi/3)-pi/3cot(ipi/3+2pi/3))
hidden kelp
I've been looking through this for like 2 days. Taking breaks to hopefully find it, but no luck :despair:
bitter pilot
2 days
twin meteorBOT
hidden kelp
yeah there
bitter pilot
typed cos haha
hidden kelp
you made a typo 
bitter pilot
what formula is that in the 2nd line for cot
hidden kelp
bruv
hidden kelp
In the first step, I used the addition formula for tan but flipped it to get cot
Your lack of reading turned me Br*tish
bitter pilot
BRUH
hidden kelp
did I do a stupid?
bitter pilot
well you took 2 days give me like 5 min
hidden kelp
It wasn't 2 full days
bitter pilot
whats 3rd line for formula
bitter pilot
ok
hidden kelp
,w tan(ix)
twin meteorBOT
hidden kelp
ok I didn't do a stupid there, good
bitter pilot
,w (itanh(pi/3) + sqrt(3)) * (itanh(pi/3) - sqrt(3))
twin meteorBOT
bitter pilot
burh
hidden kelp
burh
hidden kelp
yeah that would give me a negative that cancels out the extra I have I imagine
bitter pilot
I imagine too
bitter pilot
always
hidden kelp
Yeah it flips everything around and gives me the right trig identity
Btw Adonis, this came from an integral, do you wanna check it out? 
bitter pilot
nah i havent eaten all day, i dont think i will handle it
hidden kelp
Yeah I think I'm better off handing it over to kheeri
anyways, thanks for the help :D
.solved
neat anvil
Hi
neat anvil
So i want the value of (Ea)
You can consider it as (x)
rare swift
So i want the value of (Ea)
You can consider it as (x)
Use a calculator
neat anvil
It's not mine bro 😭🙏
analog python
Hi
bitter pilot
So i want the value of (Ea)
You can consider it as (x)
,rccw
twin meteorBOT
analog python
I am Dr. Oppenheimer
rare swift
I am Dr. Oppenheimer
Hi
neat anvil
Sorry lil bro
bitter pilot
Sorry lil bro
np less bro
rare swift
Is it base 10 or base e
bitter pilot
Just divide by whats on the right side
twin meteorBOT
neat anvil
Where is the x?
twin meteorBOT
bitter pilot
same shit
rare swift
That's what I said use a calculator
bitter pilot
ok
vocal sleetBOT
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vocal sleetBOT
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faint wind
Never seen this question worded like this before and have no idea where to start. I had to look up the answer to the first one btw so an explanation would be helpful
vocal sleetBOT
Never seen this question worded like this before and have no idea where to start...
@faint wind Has your question been resolved?
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@faint wind Has your question been resolved?
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toxic oracle
Sup folks. Does this notation look correct?
We define the distance between a vector $\mathbf{t}$ and a lattice $\Lambda$ as the distance between $\mathbf{t}$ and the closest vector in $\Lambda$:
$$\text{dist}(\mathbf{t}, \Lambda) = \text{min}\left{||\mathbf{t}-\mathbf{v}||, \mathbf{v} \in \Lambda\right}$$
twin meteorBOT
Trapture
vast shale
Looks good to me. I'd have used inf instead so I don't have to think whether the minimum actually exists 😂
toxic oracle
It should, generally, right? 😅
I'll just use ìnf tho, thanks 😄
median sun
Hi, I am studying suprema. I am working on this exercise and I think I am making it more complicated than it is. I am not sure if finding the interval where the equation is negative is sufficient to find the supremum. I say this because that interval belongs to the set. Then, the supremum is the maximum and there would be no need to prove more. However, I don't know if I am skipping steps, like proving that it is at least an upper bound. I appreciate any suggestions and help in advance :')
( A = {x \in \mathbb{R} : x^2 + x - 1 < 0} )
\begin{itemize}
\item Does $\sup (A)$ exist?
\item If it exists, what is its value?
\end{itemize}
Let's use the formula:
[ x^2 + x - 1 = 0 \quad , \quad a = 1 \quad , \quad b = 1 \quad , \quad c = -1 ]
[ \Rightarrow \sqrt{b^2 - 4ac} = \sqrt{1^2 - 4(1)(-1)} = \sqrt{5} > 0 , , , 2 , \text{roots} , \in , \mathbb{R} ]
[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]
[ x_1 = \frac{-1 + \sqrt{5}}{2} \quad , \quad x_2 = \frac{-1 - \sqrt{5}}{2} ]
Since the parabola opens upwards, it means that it will be negative in the interval of the roots, therefore
[ x \in \mathbb{R} \Rightarrow \left( \frac{-1 - \sqrt{5}}{2}, \frac{-1 + \sqrt{5}}{2} \right) ]
Then $\sup (A) = \frac{-1 + \sqrt{5}}{2}$
vocal sleetBOT
Hi, I am studying suprema. I am working on this exercise and I think I am making...
twin meteorBOT
Mαя
vocal sleetBOT
@median sun Has your question been resolved?
vast shale
As long as the set is non-empty and has an upper bound, then it has a supremum in R, this is the defining property of real numbers.
To find the supremum, we guess the least upper bound M, and show that M - \epsilon is not an upper bound for all \epsilon > 0. Writing this all out formally is annoying though.
median sun
Oh, then the first step that I have to do is show that is non-empty? how can I do that?
hybrid flicker
Oh, then the first step that I have to do is show that is non-empty? how can I d...
if you wanna show that a set is non empty, find some random number, any number, that's in the set
if you wanna show that the supremum EXISTS, it's enough to show "non-empty + upper-bounded"
if you wanna find the supremum, showing A = (-phi, 1/phi) is not a bad idea either, it's what I would have done
because then the supremum is in front of your eyes
Btw showing a value is a supremum can be done in multiple ways
after showing such a value is an upper bound, you can either do the "-epsilon" way
or find a sequence in A that converges to it
or show that it's the LEAST of the upper bounds
meaning find the set of upper bounds
(in that case it's [1/phi, +inf))
it's clear that 1/phi is the smallest
thus the LEAST upper bound
median sun
okay, mm I'm a little confused with the part to show that is a upper bound, because, I have that x^2 + x - 1 < 0, and the definition of a upper bound is: exist a real number c, such that for all x who belongs to the set A, x <= c, so I don't know how to write the inequality that I have to prove, this x^2 + x - 1 < -1 + sqrt(5) / 2, or this x^2 + x - 1 < 0
hybrid flicker
okay, mm I'm a little confused with the part to show that is a upper bound, beca...
no you have to show that if x^2+x-1 < 0 then x <= (-1+sqrt(5))/2
L is an upper bound if:
For all x that BELONG to A, x <= L
so for all x such that x^2+x-1 < 0, x <= (-1+sqrt(5))/2
that's the definition of an upper bound
hybrid flicker
**Mαя**
I thought you already showed A = (-phi, 1/phi)
so I'm not sure how this is a problem
vocal sleetBOT
median sun
.reopen
vocal sleetBOT
✅
median sun
so I'm not sure how this is a problem
Ah I apologize :'( I'm new in this topic, and I'm confused, with the part the upper bound, and I don't uderstand what are you trying to say me with the A = (-phi, 1/phi), sorry for being slow :c
hybrid flicker
Ah I apologize :'( I'm new in this topic, and I'm confused, with the part the up...
A is equal to this set
median sun
so for all x such that x^2+x-1 < 0, x <= (-1+sqrt(5))/2
I don't understand if 0 is the upper bound or just a condition of the set
hybrid flicker
I don't understand if 0 is the upper bound or just a condition of the set
A = {x | x^2+x-1 < 0}
that's the condition for being in the set A
hybrid flicker
And it translates to A = this set
hybrid flicker
A = {x | x^2+x-1 < 0}
this
median sun
okay
hybrid flicker
it doesn't take long to see that this set is non-empty and upper-bounded
so it has a supremum
which is (-1+sqrt(5))/2
median sun
it doesn't take long to see that this set is non-empty and upper-bounded
aah I feel that is a stupid question, but, how can you see with a first look that is upper-bounded, it just because it's a interval?
hybrid flicker
(x,y) is the interval of all values > x and < y
so all values are < y
if that doesn't scream "y is an upper-bound" Idk what else
median sun
Btw showing a value is a supremum can be done in multiple ways
then, I have to the part to show that -1 + sqrt(5) / 2 is the supremum using the method that fits more?
hybrid flicker
then, I have to the part to show that -1 + sqrt(5) / 2 is the supremum using the...
yep
here it's pretty straight forward because -1 + sqrt(5) / 2 is the "y" in (x,y)
median sun
they doesn't have to be in the set
hybrid flicker
yep
the supremum is the "least upper bound"
we've shown the "upper bound" part
now we have to show "least"
so we have to show there can't be a smaller upper bound than -1 + sqrt(5) / 2
median sun
get it :D
hybrid flicker
so "-epsilon" way for example
median sun
do you refer to: ∀ ε > 0, ∃ a = a_x ∈ A, s - ε < a <= s, where s is a upper bound of the set A
hybrid flicker
where s is the "supposed supremum"
median sun
yes
I think that I can continue alone, really really thank you so much, you help me a lot <<33
.close
waxen hawk
this is a question about mathematical term
vocal sleetBOT
this is a question about mathematical term
vocal sleetBOT
tawny nacelle
vocal sleetBOT
Available help channel!
midnight axle
An isosceles triangle with vertex angle 2α is inscribed in a circle with radius 1 (see figure below).
By letting α vary in time, the perimeter L of this triangle also changes.
Between t = 0s and t = 9s the increase in angle α per unit time is constant. Furthermore, we know that
t = 0s the angle α = π/12 and that at t = 9s the angle α = π/3.
vocal sleetBOT
An isosceles triangle with vertex angle 2α is inscribed in a circle with radius ...
midnight axle
Determine the decrease in circumference per unit time at t = 6s.
I first calculated the angle Alpha at t=6s (simple linear functions) it's Pi/4
This means at t=6 the top angle is Pi/2 (Right angle isosceles triangle) Ik the angles are PI/2, Pi/4 and Pi/4 but I have no side length, tried cosine rule, Pythagoras, cord length formula, Trigonometric formulas in right angle triangle I can never figure out a side length (no calculators allowed on exam, otherwise the cord lenght forula would work)
All ways I tried result into 1=1
(You get roughly 8 mins per question on this exam)
<@&286206848099549185>
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midnight axle
<@&286206848099549185>
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rancid kestrel
Wth is this
vocal sleetBOT
Wth is this
jagged cargo
do you know what this is?
rancid kestrel
Yeah but I don’t know how to solve it..
I come back to 116
Ik angle=1/2 arc
Yeah
Wait how
116 and FD
Idk dude :((
When you say arc BD which one do you mean?? BFD or BCD
Or is it a straight line through the circle from D to B
No idk how
Can’t I just say BC is 116?
And FD is 62
The sides look like they’d be the same
Oh okay
62?
120?
No okay
I did 89*2 = 178
178-116=62
BFD 62+116?
and then for 120 I did 360-116-62-62
So
116+120 = 236
236/2
? = 118
Thank you so much
Like draw the circle and start labeling it when I find the arcs and angles?
vocal sleetBOT
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vocal sleetBOT
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bleak whale
vocal sleetBOT
bleak whale
Whats the base point here supposed to mean?
Like, do I sub it in for 0 and 1 to find all base points of this
Wouldn't the only base point be (0, -3) ??
jagged cargo
what the hell is base point
lament linden
First time i heard of base point
mental falcon
i don't think base point is a term that i've seen defined everywhere, can't even find it on google. sounds like your teacher making crap up. i'd probably put down for an answer "do you mean y intercept?" then work with that. then ask your teacher what they mean by a base point
and ask them to show you a definition in the book
(possibly a mistranslation if this was written in another language originally)
scenic ravine
,w base point
twin meteorBOT
scenic ravine
vocal sleetBOT
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full ferry
"A dice that has its sides marked with 1 - 6, is thrown. Find how many throws on average it takes to land on each of its sides at least once"