But it is possible for $A<0$ if $L-\frac{\epsilon}{2} < 0$
#help-26
pearl pulsar
thorny flameBOT
Jesses
pearl pulsar
Also, sorry if it is unclear but $A_n = \frac{x_N}{(L-\frac{\epsilon}{2})^N}$
thorny flameBOT
Jesses
topaz sinewBOT
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pearl pulsar
<@&286206848099549185>
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surreal gazelle
I actually needed help creating a related rates problem,
I am supposed to create an extremely difficult Original related rate problem but i can not think of ideas, or what can make it extremely difficult while being original
assistance please
topaz sinewBOT
I actually needed help creating a related rates problem,
I am supposed to crea...
@surreal gazelle Has your question been resolved?
sweet shard
I actually needed help creating a related rates problem,
I am supposed to crea...
Why are you supposed to create them
surreal gazelle
what do you mean
topaz sinewBOT
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surreal gazelle
<@&286206848099549185>
vernal matrix
This is probably better in somewhere like #math-discussion as these channels are more for helping you work on problems you have, rather than creating them (you might also get more attention there too!)
lunar salmon
can anyone help?
topaz sinewBOT
can anyone help?
topaz sinewBOT
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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.
acoustic pecan
never figured out how you guys do that so quickly
lunar salmon
Please only use the <@&286206848099549185> ping **once** if your question has no...
my bad gang
🙊
<@&286206848099549185>
hey fellas?
can anyone help
topaz sinewBOT
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lunar salmon
<@&286206848099549185>
topaz sinewBOT
@lunar salmon Has your question been resolved?
topaz sinewBOT
@lunar salmon Has your question been resolved?
lean tulip
can anyone help?
(b,c) (c,d) and (c,c) i think
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cursive thorn
5x = +-7 would be correct, you can divide by 5 if you want
halcyon ember
yeah i just realized
halcyon ember
5x = +-7 would be correct, you can divide by 5 if you want
thanks anyways 😅
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keen harness
topaz sinewBOT
keen harness
Can someone help me
I'm stucked at number 2
I'm not sure if I just multiply it or what
vocal escarp
Yes you can
Thats the answer
As for the 2nd answer penguin shaved ice is gonna cook
broken niche
You cooked enough
vocal escarp
It's a sequence
vocal escarp
Possibly
Like i said penguin shaved ice gonna cook
Wait yea its 180
I just realized we were missing the 5th box as well
Good job cooking
keen harness
Ohh it's alr I have already done the question 3
But last question if u dont mind
For the 4th question I'll say I use a constant number right?(sorry if this is a dumb question)
topaz sinewBOT
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wary lotus
In an 8 by 8 square ABCD, the point M is located in the middle the BC side. The point N is located in the AC side so that its equidistant to the point M and point D. Find the length of AN
topaz sinewBOT
In an 8 by 8 square ABCD, the point M is located in the middle the BC side. The ...
wary lotus
My teacher told me that i should use pythagoras theorem for this one but idk
dusky rune
My teacher told me that i should use pythagoras theorem for this one but idk
figure out which one's a, b, and c.
cobalt dawn
yep
so basically you apply pythagoras theorem on the two triangles and you get a system
wary lotus
cobalt dawn
instead of adding them try equating them since both are equal to x^2 and you dont need x
wary lotus
16+y^2-16y+64=64+y^2
and y is 1
the hard part was getting the formula right
thanks for the help
.close
polar veldt
topaz sinewBOT
polar veldt
is the maturity value the 325k?
topaz sinewBOT
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gusty meadow
topaz sinewBOT
loud oasis
the chain rule applies here
topaz sinewBOT
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autumn condor
I need help with this
topaz sinewBOT
I need help with this
autumn condor
I was absent when this was discussed, and my classmates are too confused to explain, please help 😭
what's the leading term?
lime hollow
I was absent when this was discussed, and my classmates are too confused to expl...
https://www.youtube.com/watch?v=a5x4lwnvHM0
Try watching this
arctic charm
topaz sinewBOT
arctic charm
i am really confused on this
topaz sinewBOT
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lament sage
arctic charm
what do u mean
true minnow
i am really confused on this
!status
topaz sinewBOT
i am really confused on this
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
Your diagram shows x and z
Try to express the cost through x and z
Then, try to express z with L and D (given values), so you end up with a function in x for which you will find the minima
topaz sinewBOT
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neon iron
How do I calculate variance from this data?
topaz sinewBOT
How do I calculate variance from this data?
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ember dune
Simple question: If I have a linear transformation given by a 3x3 matrix and I want to calculate it's eigenvalues, will they be the same if I triangulate the matrix with gaussian elimination and calculate the triangulated matrix's eigenvalues?
topaz sinewBOT
Simple question: If I have a linear transformation given by a 3x3 matrix and I w...
ember dune
The goal is to try to have an easy determinant to calculate
either by cofactor expansion on a row/colum with ceros or a triangular matrix
dreamy drum
Simple question: If I have a linear transformation given by a 3x3 matrix and I w...
They can be the same if you’re careful but some operations that you often do in Gaussian elimination leads to them being changed
If you want ‘easy’ calculations you may find it easier to use the method from Axler’s book
ember dune
what do you mean careful?
knotty ledge
Row operations do not in general preserve eigenvalues
shut obsidian
Regarding the construction of $\mathbb Q$ out of $\mathbb Z$: \[5pt]
So for $A = \mathbb Z \times \mathbb N$ we have the equivalence relation [R \coloneqq {\big((n, m), (n', m')\big) \in A \times A \mid nm' = n'm}.]
If $K((n, m), R)$ is the function that maps the equivalence class of $(n, m)$ w.r.t. $R$ to it, then we define $\frac n m \coloneqq K((n, m), R)$. \[5pt] Now, we have that [B \coloneqq {(n, m) \in A \mid \gcd(n, m) = 1}] is a system of representatives of the equivalence classes and so the equivalence classes are the rational numbers. \[10pt] My questions are \begin{enumerate} \item Why does $B$ being a system of representatives imply the equivalence classes are $\mathbb Q$?\end{enumerate}
topaz sinewBOT
Regarding the construction of $\mathbb Q$ out of $\mathbb Z$: \\[5pt]
So for $A ...
knotty ledge
Well what is your definition of Q before this one
shut obsidian
shut obsidian
Well what is your definition of Q before this one
Uh, there is none?
This is the construction of Q
Well, n/m I guess
n in Z, m in N
knotty ledge
Right so your question doesn't quite make sense
But if we just go with a naive definition of "fractions", then it's because of the fact all fractions can be reduced until n and m are coprime
shut obsidian
(congrats on mod, btw)
shut obsidian
But if we just go with a naive definition of "fractions", then it's because of t...
Ah, so we'd need the fact that fractions can be reduced to n and m coprime, and are equivalent to 2n/2m, 3n/3m, ...
Then the system of representatives B is Q
knotty ledge
Essentially
shut obsidian
But if we just go with a naive definition of "fractions", then it's because of t...
Well, they say the equivalence classes are Q.
But the equivalence classes are the same/can be represented as the system of representatives so we can also say that the system of representatives is Q, right?
(I mean B with the system of representatives)
knotty ledge
I still don't know what you mean by Q if B is you constructing Q and you don't have a prior definition of Q
shut obsidian
But then like what does n/m mean lol?
Well, we know division, right?
That's taken as an axiom, I guess
So it's just n/m
Or is there still a problem?
knotty ledge
Do we? We're constructing Q lol, before Q we had no division in N or Z
shut obsidian
Oh
knotty ledge
It's like a semicircular question if that makes sense
Show this thing we've constructed (Q) is Q
shut obsidian
Show this thing we've constructed (Q) is Q
It's a little weird how my lecture notes wrote it.
They define B like I did above and then say "B is a system of representatives of the equivalence classes, thus, the equivalence classes correspond to the rational numbers. This way, we get a mathematically correct construction: we define Q := K(A, R)"
knotty ledge
Yeah its weird they would say correspond to rational numbers, and then in the next line define the rational numbers lol
But I think you can just get by by viewing rational numbers as sort of the naive high school definition
Without thinking too much what that actually is lol (because it really is just this construction)
shut obsidian
Yeah its weird they would say correspond to rational numbers, and then in the ne...
Yeah, they have some sort of imagination of what Q is already but want to rigorously construct it
knotty ledge
Yeah thats it
Obviously people were using these things before this construction so
I'm just being a bit pedantic
shut obsidian
So on a second read, I guess after all it's not that weird of a wording, since we know Q already and this is just a construction of it, that's like introducing the Peano axioms and then saying that we get N with them
That'd be a bit circular too
knotty ledge
Sure but like what is N before the construction
So like you say you have to have some kind of pseudo definition of things beforehand
shut obsidian
Yeah
knotty ledge
And then construct rigorously the thing that captures that pseudo definition
shut obsidian
And then construct rigorously the thing that captures that pseudo definition
Yeah, I think that's what my lecture notes were doing here. Does that seem weird?
knotty ledge
A little bit, but I'm not sure of a way around it, and pedagogically it makes sense
Like they can't pretend we don't already "know" what fractions are and how they behave
novel echo
what is your question
pure frigate
My question is how do you solve for r1 and r2?
Those are the given values 90v 3a 30 ohms
For the 1 resistor
topaz sinewBOT
pure frigate
K
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humble schooner
Hello. So, I'm trying to solve a geometry problem involving vectors in the plane. Here's the question:
Let ABC be a triangle. Construct the points E, F, and G defined by:
EA = AB + AC
FA = 2/3 FB
GC = 2GB
@humble schooner Has your question been resolved?
hallow hollow
My problem is pretty easy with a calc but I have to solve it no calc. How do I solve:
8cos(2x)=1?
topaz sinewBOT
My problem is pretty easy with a calc but I have to solve it no calc. How do I s...
hallow hollow
I know what to do after I find the value of 2x
cos(2x)=1/8
2x = arccos(1/8)
but from there idk
also i'm working in radians
torpid matrix
My problem is pretty easy with a calc but I have to solve it no calc. How do I s...
im pretty sure the solutions arent rational
cant do better than x = arccos(1/8)/2
torpid matrix
well it will take you an infinite amount of time to solve then
torpid matrix
plug it into a calculator
hallow hollow
9pi/20 radians right?
topaz sinewBOT
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hallow hollow
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hallow hollow
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hallow hollow
sorry
noble laurel
<@&268886789983436800>
vapid lichen
@hallow hollow stop spamming commands
hallow hollow
ok
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shut obsidian
Represent $z = -4$ in polar coordinates.
topaz sinewBOT
Represent $z = -4$ in polar coordinates.
noble laurel
well
if your complex number has no imaginary part
you can think of it as having no height on the complex plane
noble laurel
it's either an angle then of 0 or pi (or pi*k) yes
knotty ledge
how did you get 16?
shut obsidian
Oh, 4, sry
shut obsidian
it's either an angle then of 0 or pi (or pi*k) yes
Are you saying that it doesn't matter whether we use 0 or pi?
cinder moat
sweet shard
do you know properties of a pmf?
plug that f(x) in to all of them to get restrictions on k
cinder moat
do you know properties of a pmf?
It's sum should be 1 ,
And each f(x) should be between 0 and 1 ?
cinder moat
plug that f(x) in to all of them to get restrictions on k
x goes to infinity so I'd assume that wouldn't work?
sweet shard
sorry i'm getting confused with density functions
should be enough to show f(x) >= 0 AND sum f(x) = 1 and not necessary to show f(x) <= 1
cinder moat
here's acouple worked examples
https://www.ncl.ac.uk/webtemplate/ask-assets/exte...
None of them have x going to infinity
I feel like I'm missing something ;-;
cinder moat
Yes, that's what I'm talking about
sweet shard
Yes, that's what I'm talking about
it doesn't matter
are you familiar with infinite series?
have you taken calculus yet?
cinder moat
Kinda, if we solve the sum of the series it would give (1-k)/1-k , I don't really know where to go from there
cinder moat
have you taken calculus yet?
Yes
sweet shard
None of them have x going to infinity
I feel like I'm missing something ;-;
then why does this bother you
just follow the definitions of PMF you were taught
cinder moat
That's what i did.
The sum has to equal 1
Sum of the series is (k-1)/k-1 which is just 1 , so 1=1. Doesn't get us anywhere I'd assume
f(x) has to be non negative
So (1-k)k^x ≥ 0
K^x ≥0 , k≥0
1-k ≥ 0 , k≤1
So 1 ≥ k ≥ 0 would be correct?
cinder moat
well can k=0 or k=1 ?
Yes
Oh wait
It can't be 1 since you'd be dividing by 0 in the series?
sweet shard
just plug in k=1 to f(x)
cinder moat
It gives 0
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mortal island
how do you tell 'x prime' apart from 'x differentiated' using their notations??
chilly walrus
does it just depend on the context??
yes
mortal island
damn, real
chilly walrus
yea
quite unfortunate
but like, if it's a function then 99.9% chance it's derivative
but prime is often denote "something related but not the same" yk
chilly walrus
np
mortal island
.close
topaz sinewBOT
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junior nimbus
Find $\frac{d}{dx}, x^2y^2+5xy=14$
topaz sinewBOT
Find $\frac{d}{dx}, x^2y^2+5xy=14$
thorny flameBOT
junior nimbus
I'm not sure why this answer is wrong
i did every step correctly
but its supposed to turn out to -y/x
sonic dawn
you forgot about the 5 in 5 d/dx xy
glossy fable
You lost me in the 5th step
civic granite
is someone able to dummify this prompt for me? i need to prove that the local error is of the third order and the global error is of the 2nd order, but honestly am lost with how to go about it. (this isn't the midpoint rule, just method)
Suppose for the integral $T_{[a, b]}(f)=\int_{a}^{b} f(x), dx$
we approximate it with the midpoint_method for the mesh ${ x_n}{n=0}^{N}$
where $x_n = a+n\delta x, \quad \delta x = \frac{b-a}{N}$
is given by $A{[a, b]}(f) = \delta x \sum_{n=0}^{N-1} f(x_{n+1/2})$
where $x_{n+1/2} = \frac{1}{2}(x_n + x_{n+1}) = x_n + \frac{\delta x}{2} = x_{n+1} - \frac{\delta x}{2}$
Note: $T_1(x; x_{n+1/2}) = f(x_{n+1/2}) + f'(x_{n+1/2})(x-x_{n+1/2})$
topaz sinewBOT
is someone able to dummify this prompt for me? i need to prove that the local er...
thorny flameBOT
MIA
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
topaz sinewBOT
@civic granite Has your question been resolved?
topaz sinewBOT
@civic granite Has your question been resolved?
glad crater
use Taylor's theorem to expand f(x) around the midpoint of each subinterval and show how the remainder term is related to the third derivative
I suppose the local error for each subinterval will involve the third derivative of f evaluated at some point within the subinterval.
topaz sinewBOT
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vale furnace
I suppose the local error for each subinterval will involve the third derivative...
R u using gpt
glad crater
R u using gpt
no,
glad crater
R u using gpt
are u jealous>?
vale furnace
Nah easy stuff
glad crater
Nah easy stuff
ok bro
eternal osprey
need help with this one
topaz sinewBOT
need help with this one
eternal osprey
teacher wants me to prove how CAF and CFB are right angles
and for b im just stupid
neon iron
F?
where is F
b is accurate because if you draw a line from O to B youll see those triangles are the same
and both are isosceles
which makes the angle the same
vernal matrix
Are you defining F to be the midpoint of AB?
vernal matrix
Well if you extend the line segment CO and can show it passes through F
Might maybe be easier to do it the other way around: let F be the point where if you "extended" CO out, you'd meet AB, then prove that F has to be the midpoint
Doing that allows you to immediately deduce that CAF and CFB would be right angles by a circle theorem
eternal osprey
well what i did was i said that <OCD is equal to 90 degrees, o being the center. If they are parallel BAC and ACD would be the same as they are alternate angles
eternal osprey
tru
topaz sinewBOT
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eternal osprey
i got the first one dont know how to do second one
<@&286206848099549185> need some help
topaz sinewBOT
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eternal osprey
heloo
topaz sinewBOT
@eternal osprey Has your question been resolved?
trim karma
hi there？
jovial raven
Hi everyone, my textbook is defining [-1, 3) as an infinite interval, I can't wrap my head around this, this feels wrong, how can this be an infinite set?
A=[-1, 3] and B=[3, 4], then it defines A-B=[-1, 3) and calls it an infinite interval, and A INTERSECTION B={3} which calls it finite.
topaz sinewBOT
Hi everyone, my textbook is defining [-1, 3) as an infinite interval, I can't wr...
noble laurel
Okay so as for the first part
There are infinitely many real numbers inside the interval [-1, 3)
For example, 1/2 is in it
And 1/3, 1/4, 1/5, 1/6, etc…
long stirrup
[-1, 3] and [3, 4] are both also infiinite
noble laurel
As you can see we can get as many numbers as we like inside this interval, an infinite amount
noble laurel
[-1, 3] and [3, 4] are both also infiinite
Their intersection however is finite
They share only one value
Being 3
Does this clear up your confusion?
jovial raven
very much, now I understand, thank you @long stirrup and @noble laurel for your help.
noble laurel
No problem
jovial raven
Hello everyone, Is it possible to prove the infiniteness of [0, 1] from this set?
noble laurel
Hello everyone, Is it possible to prove the infiniteness of [0, 1] from this set...
That question doesn’t make any sense
Other than that every element of that set is in [0,1]
And that set has infinite elements
jovial raven
I apologize for my bad English, my text book is using this set to prove that [0, 1] is an infinite set, which confirms it is, thank you Austin.
is there a way to close the question when it gets answered, using the bot maybe?
topaz sinewBOT
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stone folio
topaz sinewBOT
stone folio
I dont even know how to start
eternal spoke
u sub
stone folio
what should i sub?
eternal spoke
Wait
eternal spoke
Yeah trig sub
stone folio
kinda
green fog
word
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neon iron
3x^3+2x^2-5x+1 what are the coeffecients of the polynomial
topaz sinewBOT
3x^3+2x^2-5x+1 what are the coeffecients of the polynomial
foggy bronze
The Number with sign with varible part are coeffeciants of Polynomial
neon iron
what ?
foggy bronze
whats variable above?
foggy bronze
im tryna solve the one above b
See ,
neon iron
c?
neon iron
oh
foggy bronze
Coefficients of Polynomial is The Numbers(with sign) That are with variable(x , y etc)
neon iron
is it 3,2 and -5
foggy bronze
yup
foggy bronze
hmm
neon iron
thx
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limpid plinth
How do o further simplify this
topaz sinewBOT
How do o further simplify this
true minnow
How do o further simplify this
,rotate
warm sentinel
god help us
thorny flameBOT
warm sentinel
the issue is that youve written tanx as sinx/tanx
its sinx/cosx
otherwise its an easy proof
thorny flameBOT
musava_ribica
true minnow
also, express $\cot(x)$ as $\dfrac{\cos x}{\sin x}$ , so all you have is sin and tan
thorny flameBOT
musava_ribica
limpid plinth
also, express $\cot(x)$ as $\dfrac{\cos x}{\sin x}$ , so all you have is sin and...
How would ik which one to ise
At what time
warm sentinel
its just about feeling
true minnow
its just about feeling
Not really. It's better to express everything in the lowest number of functions possible
warm sentinel
but ofcourse cotx=/tanx
true minnow
the elementary trig functions are cos and sin
warm sentinel
Not really. It's better to express everything in the lowest number of functions ...
i know but sometimes for proof based trig questions we need to use the identities like sec^2(x)
so there is an element of just practicing till you get the hang of things
limpid plinth
Ehat would i do after this
silk owl
Ehat would i do after this
Take LCM of LHS and see how it goes
topaz sinewBOT
@limpid plinth Has your question been resolved?
true minnow
Ehat would i do after this
,rotate
thorny flameBOT
true minnow
Start eliminating fractions, for example multiplying by sinx and cosx
woven hatch
hi
topaz sinewBOT
@woven hatch Has your question been resolved?
hearty anvil
this is dumb
topaz sinewBOT
this is dumb
neon iron
this is dumb
!status
topaz sinewBOT
this is dumb
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
3
neon iron
show their solution
long stirrup
it's wrong
hearty anvil
how
hearty anvil
says who
hearty anvil
do they show solution?
no
hearty anvil
i just said they dont show it
neon iron
oof
long stirrup
yeah pi/2 is up
neon iron
ok
long stirrup
1 is not a direction
hearty anvil
1 is not a direction
in the polar coordinate system they use a magnitude which means how far it is from the origin and an angle for the direction of the magnitude
hearty anvil
"be up" is not something that i can know the definition of
long stirrup
↑
neon iron
🆙
long stirrup
on the y axis but not down
hearty anvil
i cant tell if he is trolling
magic cedar
complex plane cos(theta) is x coord and sin(theta) is y coord... find theta with cos(theta)=0 and sin(theta)=-1
assuming unit modulus ofc
hearty anvil
complex plane cos(theta) is x coord and sin(theta) is y coord... find theta with...
i dont know what that means
or how its relevant
magic cedar
so, somewhere you musst have read about how to convert from rectangular to polar?
what is the formula for r and theta in terms of rectangular coords?
hearty anvil
r = sqrt(x^2 + y^2), theta = arctan(y/x)
magic cedar
yep so your r=1 is correct... y/x = is -infinity, so what is arctan of -infinity?
magic cedar
well technically yeah but what is arctan(x) when x approaches -infinity?
magic cedar
yep
hearty anvil
but why did you just randomly choose -inf
magic cedar
not randomly, arctan of (y/x) y is -1 and x = 0 so that's -inifinity... loosely speaking
i don't like using the arctan formula tho, alternatively you can say cos theta is 0 and sin theta is -1, then you don't have to worry about infinity.. and you get -pi/2
hearty anvil
magic cedar
you need to find theta where tan is 1
magic cedar
says the auto grader 😄
magic cedar
which symbol?
hearty anvil
the E
hearty anvil
i dont know what its asking
magic cedar
It wants you to find out how the polar coordinates change if the sign on the y coord is flipped (in rectangular coord system).
hearty anvil
how
magic cedar
so think about what happens to r and theta if the sign is changed on y... - what happens to r = sqrt(x^2 + y^2) and theta = arctan(y/x)?
hearty anvil
you have pi /12 = arctan (y/x), so now you need the changed angle arctan(-y/x)
how
i dont know what the changed angle means
magic cedar
theta would be a different angle
I mean this
hearty anvil
how do i know what angle it would be
magic cedar
you know that arctan(y/x) is pi/12 right?
hearty anvil
yes
magic cedar
and now sign on y has changed.. so your new theta is arctan (-y/x), Correct?
hearty anvil
yes
magic cedar
ok so what is arctan(-y/x) if you know arctan(y/x)?
or in general what is arctan(-A) in terms of arctan(A)
magic cedar
yes but in terms of radians
hearty anvil
rad(-arctan(A))
magic cedar
if i remember -arctan(A) should be pi+arctan(A)?
hearty anvil
why
magic cedar
a property of the tan function - if you see the plot, you can try to imagine where a particular point on arctan x goes if you flip the sign. It should be a reflection on the x-axis which means the angle changed by pi. As far as I remember 😄
magic cedar
lol.. it's not that bad.. if you look at the plots and do enough practice it's easy peasy
the theta is pi/12 so they probably want you to put in pi+pi/12 = 13pi/12 assuming i'm right about -arctan being pi+theta 😛
hearty anvil
hearty anvil
hearty anvil
it auto evaluates it
magic cedar
hmm, then I don't remember my trig 😦 I'll have to pass sorry
hearty anvil
:C
magic cedar
ugh you had it and I messed it up.. arctan(-x) = -arctan(x) so pi/12 goes to -pi/12, but you need it in the set [0,2pi], so it should be 2pi-pi/12? I think 😄
magic cedar
but I'm out coz my trig is dodgy 😂
hearty anvil
does this mean its (r, pi/12) because the 2 negatives cancel
magic cedar
unfortunately no, because arctan is funky and will only give you conversions in quadrant I and IV (when x is positive). Think about where the point moves to in rectangular coords if the x and y both flip signs and then think what happnes to theta.
topaz sinewBOT
@hearty anvil Has your question been resolved?
hearty anvil
unfortunately no, because arctan is funky and will only give you conversions in ...
If they both flip signs tan(a/b) = tan(-a/-b) nothing happens
magic cedar
yep true about arctan but what happens in rectangular coords?
hearty anvil
Moves from q1 to q3
magic cedar
yep so what happens to theta (angle with x axis)
magic cedar
forget about the calculation... visually how do you think theta (which is the angle with x-axis) will change if the point moves from 1st to 3rd quad
hearty anvil
Add pi
magic cedar
yep
and that's because tan(pi+theta) is the same as tan theta, so the tan calc will give you correct results only in quads 1 and 4...
so I guess the lesson is don't just rely on the calc...
hearty anvil
How do I find the answer then
hearty anvil
But I don’t understand it
magic cedar
you went from 1st quad to 3rd quad, so you added pi to theta... the tan calc remained the same because tan(pi + theta) = tan (theta)
hearty anvil
Oh
magic cedar
So, basically, if you know your x coord is -ve you need to be careful with the arctan/tan function... Imo it is better to think visually about what is happening in the rectangular coords (like if something is moving from one quadrant to another, etc) and only then do the calculation. Don't rely only on the calculation.
hearty anvil
Good to know
topaz sinewBOT
@hearty anvil Has your question been resolved?
hearty anvil
oh pi - pi/12
magic cedar
yeah, do you have these concepts in the book or course you are using?
hearty anvil
no we dont have a book
magic cedar
coz they should be talking about reflections and rotations
magic cedar
okie - some practice on this will help using an online tutorial or exercises
ok so you are still in the same quad so no reflection/rotation going on but y and x are switched so the new arctan calc should be?
magic cedar
yeah and we know arctan(y/x) is pi/12 so arctan (x/y) =
hearty anvil
12/pi
magic cedar
is it pi/2 - pi/12
this might be right because I looked up and apparently arctan(1/x) = pi/2 - arctan(x)
hearty anvil
yay
magic cedar
again it can be deduced geometrically by switching the y and x coords in rectangular coord system
hearty anvil
not even close
magic cedar
uh oh 😂
hearty anvil
magic cedar
yikes
magic cedar
i suggest you close this help session and post this problem again in a new session so someone with better trig knowledge can help 😂
magic cedar
.close
hearty anvil
.close
late crypt
topaz sinewBOT
late crypt
Why would any of these result 1 with division
sweet shard
Why would any of these result 1 with division
Do you know Taylor series
late crypt
Do you know Taylor series
Yes
sweet shard
Apply that to your terms
late crypt
Apply that to your terms
How to understand when it needs to be used?
sweet shard
When you see this
late crypt
.close
teal grove
Is this right? And what’s the end behavior
teal grove
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
topaz sinewBOT
knotty ledge
c,s,t?
radiant tapir
I mean you can use whatever you want for a substitution
it would probably be good to stay away from theta, alpha, beta to avoid confusion but really you can do anything
a, b, c, etc
neon iron
topaz sinewBOT
neon iron
idk what to do
pastel salmon
use de Morgan law to last task
neon iron
use de Morgan law to last task
.94?
sonic dawn
de morgan works but also there’s nothing stopping you from just directly computing it
pastel salmon
didactically, it is typical to use the complement of a sum, i.e. it is about de Morgan
neon iron
laymans terms
pastel salmon
its not .94
do you remember de Morgan Laws?
neon iron
AUB = A^c intersect B^c
sonic dawn
close but no
pastel salmon
you missed complement on union
neon iron
complement of union is intersection
pastel salmon
complement of unuion is intersecion of complements
the words, union and intersection can be repalced too, it is dual law too
neon iron
i still dont know what your talking about
pastel salmon
but you wrote almsot well, you wrote AUB = A^c intersect B^c, but it is not true, you have to write (AUB)^c = A^c intersect B^c, using yoru symbols
neon iron
okay but how do I do the problem
pastel salmon
and then, when you write out your probability according to this formula, use the probability of the opposite event
pzl show me here, how your probability looks, due to formula i wrote for you
neon iron
wrong
pastel salmon
0.94 is wrong sure
neon iron
0.06
pastel salmon
yes!
fluid gate
How did you get 0.06?
neon iron
and then, when you write out your probability according to this formula, use the...
^
(AUB)^c
fluid gate
I think the reason why it’s incorrect is because A and B are mutually exclusive but their complements are not
Like you can have event A AND B not occur at the same time
neon iron
A + B = AUB
fluid gate
Idk why they said 0.94 is right for the union
neon iron
0.945
fluid gate
0.945 rounded is not 0.94
neon iron
theres a 5 on the end
that ones right why are we talking about it
if you could help with the wrong one
pastel salmon
mutually exclusive means A ∩ B = ∅, hence P(A∅B) = P(A) + P(B)
neon iron
topaz sinewBOT
@neon iron Has your question been resolved?
gritty matrix
topaz sinewBOT
gritty matrix
what do I do
wooden osprey
topaz sinewBOT
@gritty matrix Has your question been resolved?
topaz sinewBOT
@gritty matrix Has your question been resolved?
topaz sinewBOT
@gritty matrix Has your question been resolved?
gritty matrix
<@&286206848099549185>
pastel salmon
as you can easily notice , the function is trinomail a quadratic fucntion
so the graph is a parabola opens down, but that is not hard, plz try to think
topaz sinewBOT
@gritty matrix Has your question been resolved?
hallow terrace
topaz sinewBOT
simple orchid
I can't read a single word
simple orchid
Do you need help or not
topaz sinewBOT
@hallow terrace Has your question been resolved?
elder wharf
topaz sinewBOT
@hallow terrace Has your question been resolved?
hallow terrace
hi
hallow terrace
Idk use perhaps split them into smaller triangles you never know
idk what u mean
but ok
amber dove
Look at it
She makes a triable
Base 2
Height 1.6
Find the angle
Apply it to the larger triangle
amber dove
Do you know what
hallow terrace
im failing math omf
amber dove
Trigonometry is
hallow terrace
no
amber dove
What grade u in
hallow terrace
or sum
amber dove
?
hallow terrace
8
amber dove
Ok so Pythagorean theorem states when u have a right angle triangle
amber dove
Do you inow what a right angle triangle is
hallow terrace
uh
im not learning that
im leaening ratios rn
and i have a test
n a science test td
amber dove
U could if you wanna do it that way
Say
If she’s 1.6 tall
And she’s 2 meters away
It’s a ratio of 1.6:2
hallow terrace
ohh
hallow terrace
so
amber dove
X=4
hallow terrace
OH
amber dove
1.6 times 4 gets u ur ratio answer
amber dove
Basically means
The rate of something
Unit can become
Any
Form of measurement
Ykw I mean
It could become cm
Mm
Meters
Literally
hallow terrace
uh
amber dove
A unit is one of something
hallow terrace
idkk
hallow terrace
oh
amber dove
Ur not assigning a distinct system to it
hallow terrace
soo
amber dove
Just leaving it as one of something
hallow terrace
howndo we know yhe unit tate
eate
so
like for example
is if like
uh
1 pizza/1 bite
idk
im tired
gn
amber dove
Okay
topaz sinewBOT
@hallow terrace Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
Available help channel!
versed widget
topaz sinewBOT
jade thunder
!1channel
topaz sinewBOT
Please stick to your channel.
jade thunder
!noclopen
topaz sinewBOT
Please don't repeatedly close and claim a new channel with the exact same question. This erases all previous progress made towards your problem and is confusing for helpers, making it more difficult to help you. Please be patient, even if your channel has not received much attention.
jade thunder
Just wait
versed widget
it wanst that
i just put the wrong picture
so to avoid confusing i closed it to make a new one
topaz sinewBOT
@versed widget Has your question been resolved?
versed widget
<@&286206848099549185>
topaz sinewBOT
@versed widget Has your question been resolved?
odd sigil
can someone help me to prove this ?
neon iron
can someone help me to prove this ?
this help channel is taken
topaz sinewBOT
@versed widget Has your question been resolved?
gray mantle
trying to find y intercept... what did i do wrong?
topaz sinewBOT
trying to find y intercept... what did i do wrong?
cunning yarrow
in your working out
you have 5y =
it should just be y=
the 5y came from nowhere lol
storm kraken
hello
ruby tree
Try sketching x^4-8x^3+16x^2 and then move the graph down by 2
topaz sinewBOT
@storm kraken Has your question been resolved?
light jay
having issues with some basic calc 2 stuff
topaz sinewBOT
having issues with some basic calc 2 stuff
light jay
I know how to find the sum of a harmonic series but I cant find a formula on something to help me with the one on the left, and for the one on the right both root test and ratio test are being weird for me to come to any reasonable conclusion
not sure how to manipulate (n+1)^2 to get something I can cancel
light jay
I know the answer for the one on the left but I don't know if there is some way for me to solve it besides knowing that its supposed to be e^whatever the top constant is
wary tulip
that is all there is to it
wary tulip
what have you done to find interval of convergence in the past?
oh ic you said root test and ratio test already
light jay
having weird time with the algebra for some reason
wary tulip
that should work
light jay
can I turn (n+1)^2 into som ehting that can cancel with n^2
wary tulip
"turn into" idk what to say to that
wary tulip
turn into and cancel aren't really the right words
wary tulip
$\lim_{n\to\infty} \frac{(4x+1)n^2}{(n+1)^2}$
thorny flameBOT
layla
light jay
oh
n^2 is dominant term or whatever its called on the bottom right
so I can just ignore the 2n + 1 after I foil the bottom
wary tulip
sure
light jay
ok cool thanks
for some reason I couldnt realize this earlier XD, appreciate the help
.close
serene lodge
topaz sinewBOT
serene lodge
Assuming that set A is {1,2,...,n} how can I find the cardinality of this?
I used the example to let n=2 but the only possible combinations are {1} and {2}, would the cardinality of that be 2 or 1 (because I don't know if you can use it both ways round)
serene lodge
ohhh
So that makes it 8?
Assuming you can do it both ways round?
2^{A}={{\emptyset},{1},{2},{1,2}}
acoustic tangle
I have counted 9
(e, e)
(e, {1})
(e, {2})
(e, {1, 2})
({1}, e)
({2}, e)
({1, 2}, e)
({1}, {2})
({2}, {1})
"e" is the empty set
acoustic tangle
I think a good start would be to count the amount of (S, T) with cardinality of S fixed, say it's i
How many T are there such that (S, T) is in the defined set given |S| = i?
acoustic tangle
And T is still up to n?
Yes, but you can come up with a better upper bound for |T|
Remember that since S and T are disjoint, you can't have |S| + |T| > n
Or you can think of it as T being a subset A\S (which has n - i elements)
serene lodge
Sorry I'm really confused as to what you're asking me here?
acoustic tangle
Let's say the cardinality of S is fixed, name it i; S and T have to be disjoint subsets of A, so T is a subset os A\S, right?
acoustic tangle
And A\S has n - i elements, so 0 <= |T| <= n - i
serene lodge
Or max
acoustic tangle
so cardinality of T is n-i?
No, it may be lower than that
serene lodge
Yeah
acoustic tangle
Right