the width of each rectangle would be 2
#help-4
plucky pewter
stark wedge
f(1) isnt the lowest value of f on [1,3]
plucky pewter
f(1) isnt the lowest value of f on [1,3]
oh so i need to choose the lowest value?
why so?
stark wedge
N_3 is the lower darboux sum right
plucky pewter
yes
i started with f(-3) and then f(-1), so two in between, and so i though f(1) would be correct, cause it is also two squares in between -1 and 1
stark wedge
yeah but f(1) > f(anything else in [1, 3])...
on the interval [1,3] x=1 is the maximum point... but you want the minimum for the lower sum...
plucky pewter
on the interval [1,3] x=1 is the _maximum_ point... but you want the _minimum_ f...
ohh i see
well then x=3 would be correct
but what about Ø_3
the maximum point on the interval [-3, 3] would be x=0
but what about the two other points
cause i need the area of 3 rectangles
vale dockBOT
@plucky pewter Has your question been resolved?
plucky pewter
<@&286206848099549185>
vale dockBOT
@plucky pewter Has your question been resolved?
distant galleon
but what about the two other points
Pretty sure they told you, at least implicitly, no? You want the maximum values of f on [-3, -1], [-1, 1], and [1, 3]. Use those to define your rectangles and add their areas.
Your rectangles should be like this: https://www.geogebra.org/calculator/d7wkanz4
vale dockBOT
@plucky pewter Has your question been resolved?
long mortar
How do differential operators form vector fields?
vale dockBOT
How do differential operators form vector fields?
long mortar
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Available help channel!
pine prairie
@hazy pivot so uh
vale dockBOT
<@321479019134713857> so uh
hazy pivot
Lmao
hazy pivot
I have somehow never heard of complexification of field extensions
What exactly are you trying to understand tensor products for
Cuz context would change a lot here
pine prairie
Ok wait
hazy pivot
As a heads up I have taken sleep meds so I might disappear randomly
But I hope someone else can help you at that point
hazy pivot
He is doing tensor products here
God I don't know how to make commutative diagrams in latex
But essentially, V ⊗_ℝ ℂ is the space that
Turns ℝ-bilinear maps from V × C to any space
Into ℝ-linear maps to that space
The way you generate the space is a bit weird
hazy pivot
Yup
hazy pivot
Yup
pine prairie
So then this map let’s call it T, does this
T: ℝ x ℂ -> Z, with T(a, b) = z
And T is bilinear in ℝ
hazy pivot
Yes
pine prairie
Now consider the vector space named ℝ otimesF ℂ
There exists a unique isomorphism between elements in here, and any ℝ x ℂ ℝ-bilinear maps
hazy pivot
otimes ℝ
hazy pivot
There exists a unique isomorphism between elements in here, and any ℝ x ℂ ℝ-bili...
NO
Okay have you done any category theory
pine prairie
Only the very slightest
hazy pivot
Ah then it won't help here
Have you done universal properties
In abstract algebra perhaps
pine prairie
Not really
hazy pivot
Interesting
pine prairie
I got stuck in that chapter of aluffi’s algebra book
hazy pivot
Tensor products are a bit hard to motivate without thay
And you aren't even doing tensor products, you're doing smth beyond
hazy pivot
There exists a unique isomorphism between elements in here, and any ℝ x ℂ ℝ-bili...
Hold on Lemme latex smth
idle void
I have somehow never heard of complexification of field extensions
this isn't what I meant. What I was saying is complexification generalises from being smth specific to the field extension C/R to any field extension L/K where we call it extension of scalars
hazy pivot
$BiLin_\mathbb{F}(V \times W, X) \cong Lin_\mathbb{F}(V \otimes W, X)$
God that was annoying to type out
pine prairie
What does \equiv do here
hazy pivot
What the fuck is the isomorphism symbol
idle void
\cong
hazy pivot
Ah
idle void
$\cong \simeq$
rocky lotusBOT
lance lance
idle void
one of those two
rocky lotusBOT
Xavier 🌺
hazy pivot
Thanks
pine prairie
Isomorphic as vector spaces?
hazy pivot
As sets
For every bilinear map, you get a linear map
Tensor products turn multilinear maps into linear maps
pine prairie
Is this unique?
hazy pivot
this isn't what I meant. What I was saying is complexification generalises from ...
Interesting
idle void
I think you get a canonical isomorphism as vector spaces but its 4:30 am
hazy pivot
Is this unique?
Yes it's a bijection
hazy pivot
I think you get a canonical isomorphism as vector spaces but its 4:30 am
The first isn't a vector space is it
pine prairie
Aren’t bilinear maps just (2, 0) tensors
hazy pivot
I have no idea what that notation means
pine prairie
But this is bilinear over the same vector space
idle void
Like the sum of bi linear maps is bi linear, as is a scalar multiple
pine prairie
I think bilinear maps form a vector space
idle void
and you should get a natural vector space isomorphism between those two spaces
pine prairie
There exists a unique isomorphism between elements in here, and any ℝ x ℂ ℝ-bili...
So what’s wrong with this
vale dockBOT
pine prairie
I can’t rn
hazy pivot
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Available help channel!
latent panther
CN someone pls help me
honest stone
Hi, can you please close this channel?
merry crystal
.close another channel in use
fierce echo
I decided to propose myself this question for practice, as seen I use the complex definition of sin to simplify the integral. This later results in a function with imaginary numbers, I know that there is a way to write this in terms of real functions but I cant seem to find it yet. (I know that my derivation may jump steps so feel free to ask for any intermediate steps) Thank you ahead of time.
cosmic lichen
Hi
fierce echo
Hi?
vale dockBOT
@fierce echo Has your question been resolved?
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@fierce echo Has your question been resolved?
forest rune
Yall, I need help with solving the worlds coordinates
fierce echo
wdym by that
fair coyote
vale dockBOT
idle spear
hi
idle spear
can anyone helps olve
Let A be a finite set of points in the plane, no three of which are collinear. Assume there exist two triangles, each with vertices among six distinct points of A, whose intersection forms a hexagon that contains no points of A either in its interior or on its boundary. Prove that A contains a convex hexagon whose interior is free of points from A
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real brook
where does this factor 2pi come from? this is from the fourier transform. the function on the left side already has dirac delta properties. why do we introduce that factor in that case?
echo spear
where does this factor 2pi come from? this is from the fourier transform. the fu...
if you were to integrate the left side you'd get 2pi not 1
real brook
if you were to integrate the left side you'd get 2pi not 1
how
isnt the (e^{i(\omega-\omega_0)x}dx) function with only a spike at (\omega=\omega_0) whose integral is infinity
rocky lotusBOT
sstac
echo spear
how
i mean like if you "integrate both sides" with respect to w
,, \int_{-\infty}^{\infty} (2 \pi \delta(\omega - \omega_0)) = 2\pi = \int_{-\infty}^{\infty} \qty(\int_{-\infty}^{\infty} e^{i(\omega - \omega_0)x} \dd{x} ) \dd{w}
rocky lotusBOT
kizzyyy
real brook
Hmmm
and why is this (\int_{-\infty}^{\infty} \qty(\int_{-\infty}^{\infty} e^{i(\omega - \omega_0)x} \dd{x} ) \dd{w} ) 2 pi?
rocky lotusBOT
sstac
real brook
I mean if you have any reference that would be fine too i dont want you do the hard work for me
echo spear
and why is this \(\int_{-\infty}^{\infty} \qty(\int_{-\infty}^{\infty} e^{i(\ome...
uhhh u can relate it to the gaussian integral
,, \int_{-\infty}^{\infty} e^{-ax^2 + bx} \dd{x} = \sqrt{\frac \pi a} \cdot e^{\frac{b^2}{4a}}
rocky lotusBOT
kizzyyy
echo spear
where b = i(w - w_0) and well a is a constant of your choice (whatever damping factor you like)
echo spear
i mean the whole idea isn't for you to solve the
left thing
it's just for you to know that the left thing
when integrated wrt to w doesn't even match the right thing
without a normalization factor
which happens to be 2pi here
sa long as you intuit that it isn't 1
echo spear
I dont even know where should i start grasping that
uhhh do we agree that the "inner" thing is just the following:
$\int_{-t}^{t} e^{i(\omega-\omega_0)x} \dd{x} = \frac{e^{i(\omega - \omega_0)t} - e^{-i(\omega - \omega_0)t}}{i(\omega - \omega_0)}$
rocky lotusBOT
kizzyyy
real brook
we do
echo spear
which is just 2 sin((w - w_0)t)/(w - w_0)?
using the exponential definition
which you should've seen in like precalc ig
real brook
i knw that
echo spear
okay then your last bit
is just relating this to the dirchlet integral
maybe this one makes more sense?
and you're done
echo spear
real brook
i was actually wandering around the solution with the dirichlet but for some reason didnt apply the second integration to see why the factor of 2 pi has to be there
Thanks once again you the best!
.close
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copper mauve
Okay so my calc1 professors today explained, given a sequence a(n) where n belongs in N where a(n) = (1-n)/n, to prove a(n) converges in a(n) = 2. now i did not understand the definition of limit of sequence very well. he explained it as "for each epsilon greater than 0, it exists an M where n>M (why?) so that the modulus (why?) of a(n) minus the limit (which I assume it's 2 in the proof, but why minus?) is less than epsilon" ?? what's going on here? can someone provide a better explanation as to why for example the limit is being subtracted? I can't envision it.
thanks
chrome beacon
Okay so my calc1 professors today explained, given a sequence a(n) where n belon...
right okay
let's look at something simple here like 1/n as n -> inf
notionally, the idea is that "as n gets bigger, 1/n gets closer to 0" but like... we need to specify that 1/n gets really really close to 0
so how do we actually phrase that? what we want is more like: "1/n gets as close to 0 as you'd like, given a big enough n"
copper mauve
right okay
let's look at something simple here like 1/n as n -> inf
notionally,...
so far so good
chrome beacon
we don't just want it to get that close once though, we want it to get that close and stay there
copper mauve
right ofc
chrome beacon
i've sometimes seen them explained like a two player game. The challenger picks an epsilon, which creates a box or a target around L
Then the defender will choose an N, which can be whatever they want but has to be some number, where everything after that N stays in the box. So if N is, say, 1000, then for every sequence element after the 1000th, it's inside of that target
to answer your specific questions,
it exists an M where n>M (why?)
more precisely: there exists an M where for every n > M (this is the "get in and stay in" part)
so that the modulus (why?)
it's fine if the sequence bounces above and below the limit, but it needs to be constrained to a box around the target
why minus?
what we're saying is that | a(n) - 2 | < epsilon. This means that a(n) is within epsilon of 2 -- it's within the box that the challenger drew around the target. That's true for all n > M, meaning the sequence gets in the box and stays in the box
does that make sense?
here's a visual -- see how the sequence gets within epsilon of 0, starting at M
ebon glade
maybe it's fruitful to say this more explicitly: |x-y| is the distance between x and y. so |a(n)-2| is the distance between a(n) and 2
(also, your sequence doesn't actually converge to 2, so something went wrong there)
vale dockBOT
@copper mauve Has your question been resolved?
midnight fractal
Hatsune
mental root
Alright so I sent this picture to my teacher and he told me that I should add a negative sign with force and normal reaction force below the diagram so -F= mgsin theta and -R= mgcos theta, can someone explain why??
verbal badger
Firstly it looks like we're ignoring friction?
verbal badger
To answer your question. the gravity isn't impeding the applied force, so they should be added
It's not like the force F is "pulling the box up". F is pushing it down, and gravity (mgsin(theta)) is pulling it down
mental root
Wait nvm im so dumb
verbal badger
So the total force along the x component is F + mgsin(theta)
verbal badger
Its cause it's acting in the opposite direction
you mean same direction right
mental root
No
We're talking about the angle below
Its in the opposite direction of the forces above
verbal badger
What do you mean by the angle is in the opposite direction of the forces?
The two downward forces are both pushing the box down, right?
vale dockBOT
verbal badger
chatgpt is wrong. it takes F as friction, while you take F as the dowards force
mental root
Bruh😭
I don't get this
I understand one point and it dosent make sense to the other
copper mauve
does that make sense?
I'll read it more carefully at home, but so far it makes more sense with the M problem, everything else I'll see
tyvm
verbal badger
.reopen
vale dockBOT
✅ Original question: #help-4 message
verbal badger
Draw your FBD and label your coordiante axes
Fx = F + mgsin(theta), since the force from "Force" and gravity is in the same direction (down the slope)
Fy = R - mgcos(theta), since the normal force is opposite to the gravity (on the y-axis, pushing into the slope)
Since we have equilibrium, Fx = Fy = 0
So F = -mgsin(theta) while R = mgcos(theta)
mental root
Normal force remains positive?
verbal badger
The term "positive" and "negative" is arbitrary, anything can be positive, as long as the opposite direction is negative
If we say "upwards is positive", then yes, normal force is positive while the y component of gravity is negative
If we say "downwards is positive", then normal force is negative while the y component of gravity is negative
The important part isn't "which one is positive", but rather they are in the opposite direction
Contrarily the applied force and x component of gravity are in the same direction
mental root
Ohh
Okay
I kind of understand now
Someone sent me this
Wait
Negatives cancel out
verbal badger
You can't interpret "negatives" without defining a coordiante axes. Define your coordinate axes on your drawing first
mental root
But can't you already tell theyre in the negative axis?
verbal badger
How can I tell that when I don't know which way is negative?
is negative down the slope or up the slope?
is it into the slope or out of the slope
mental root
Isn't the angle in the 3rd coordinate? Isn't that taken negative
verbal badger
Do you know how to draw a free body diagram?
verbal badger
Kinda, but you're missing the arrows
it should look like this
With Fa in the other direction of course
(unless it is actually up- which needs to be specified in the problem)
verbal badger
It should be stated in the problem
Is the force pulling the box up the slope or pushing it down the slope?
verbal badger
Do you see the direction of the arrow on f?
mental root
WAIT
Cause they're equal forces in opposite directions😭
I highlighted that aswell
In the book
verbal badger
Yeah, so the force on the x direction (assuming downhill is positive) is mgsin(theta) - F
Force on the y direction (assuming up outside the slope is positive is R - mgcos(theta)
verbal badger
And since the mass is "resting on the plane", the net force is zero, meaning the force on each direction is 0
So mgsin(theta) - F = 0 and R - mgcos(theta) = 0
mental root
Yeah exactly
But here you gotta figure out the relashionship between angle of repose and friction
But you're correct
That helped
verbal badger
well you can just do mgsin(theta) - F = R -mgcos(theta) and solve for theta
mental root
Yeah but exam requirements are different so I gotta stick to that
Even tho you js told me there's a short way out
But I gotta follow this pattern
Anyways that's more knowledge for me
Thanks
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wooden ocean
I'm working on discrete math and I'm not sure how to prove the set questions here...??
https://media.discordapp.net/attachments/409596215697866773/1424772689255727241/image.png?ex=68e52a78&is=68e3d8f8&hm=ee3286c299d851b508b6b51b615aaef596e856f75eea531fd06b34ad5cc48139&=&format=webp&quality=lossless&width=1103&height=282
wooden ocean
safe fulcrum
can you draw the left-hand side of 2a on a Venn diagram?
start with the case where B is not a subset of A
viscid spade
\B U B is kinda cancelling but you have to be careful how it is cancelling
odd jackal
Try analysing the logical forms to start
Let $x\in (A \setminus B) \cup B$. Then $x \in (A \setminus B) \lor x \in B$. Then $(x \in A \land x \notin B) \lor x \in B$
rocky lotusBOT
wai
odd jackal
Use ths to start
wooden ocean
alright, thanks!
odd jackal
alright, thanks!
realise that if this is A then x \in A, and then convert that inot a logical form
wooden ocean
okay, thank you!
safe fulcrum
Try analysing the logical forms to start
omg your logic learning paid off
wooden ocean
I understood using the logical forms, but I'm not sure how to get to proving the subset?
odd jackal
I understood using the logical forms, but I'm not sure how to get to proving the...
Okay, lemme try explaining
What does it mean logically for $(A \setminus B) \cup B = A$
rocky lotusBOT
wai
odd jackal
omg your logic learning paid off
Having to help juniors does that lol
wooden ocean
I got to {x | ( x ∈ A ^ x ∉ B ) v x ∈ B}
but I'm not sure what to do with that from there
odd jackal
I got to {x | ( x ∈ A ^ x ∉ B ) v x ∈ B}
expand this
$(x \in A \land x \notin B)\lor (x \in B)$
rocky lotusBOT
wai
wooden ocean
so, is that... (x ∈ A v x ∈ B) ^ (x ∉ B v x ∈ B)
rocky lotusBOT
wai
wooden ocean
right
odd jackal
so you have $(x \in A \lor x \in B)$
rocky lotusBOT
wai
wooden ocean
that makes sense
odd jackal
Now we analyse the logical form of $B \subseteq A$
rocky lotusBOT
wai
rocky lotusBOT
wai
wooden ocean
oh dear. where is it?
odd jackal
didn't you miss thus
wooden ocean
ooh... where would that have gone
wooden ocean
oh... so, how do I do it for the right?
odd jackal
$(x \in A \lor x \in B) \iff x \in A$
rocky lotusBOT
wai
odd jackal
this is what the entire thing simplifes to
wooden ocean
oh, okay!
my notes don't really explain how to get the logical form of the subset relation so I wasn't able to get that
odd jackal
so $[(x \in A \lor x \in B) \implies x \in A] \land [x \in A \implies (x \in A \lor x \in B)]$
rocky lotusBOT
wai
rocky lotusBOT
wai
wooden ocean
that would be... ¬A v B?
odd jackal
yes!
now use that here
$[\neg(x \in A \lor x \in B) \lor x \in A] \land [ (x \notin A) \lor (x \in A \lor x \in B)]$
rocky lotusBOT
wai
odd jackal
now simplify this
wooden ocean
got it! I'll do that now
odd jackal
This is painful, sorry :(
wooden ocean
alas, such is life ^^;; this is really helping me understand though
odd jackal
ping me when you're done, I'll be working on my own stuff in the meanwhile
wooden ocean
alright, thank you!
hazy pivot
Proving this logically feels.. weird tbh
odd jackal
Proving this logically feels.. weird tbh
The reason I chose that is that there are a bunch of set operations at play here
odd jackal
Proving this logically feels.. weird tbh
wrong?
hazy pivot
I'm not saying it's wrong I'm just trying to see if there's a better way
hazy pivot
I'm not doing Venn diagrams lmfao
A ∖ B is just A ∩ B'
(A ∩ B') ∪ B = (A ∪ B) ∩ (B' ∪ B)
The second term is the entire set so the intersection is just A ∪ B
wooden ocean
the course I'm doing this for is based on logical operations so I do have to prove it that way
hazy pivot
Yeah doing this logically is just tedious af
hazy pivot
the course I'm doing this for is based on logical operations so I do have to pro...
That is unfortunate
Have fun
wooden ocean
^^;
wooden ocean
I think I'm getting somewhere
right now, I have:
[ (x ∉ A ^ x ∈ B) v x ∈ A ] ^ [ x ∉ A v x ∈ A v x ∈ B ]
and in the second part, there's another tautology, right?
odd jackal
Uh, do you know to type in LaTeX?
wooden ocean
I'll try ^^;;
odd jackal
and in the second part, there's another tautology, right?
$(x \notin A \lor x \in A)$ is one , yes
rocky lotusBOT
wai
wooden ocean
right!
$[(x \notin A \land x \notin B) \lor x \in A] \land [(x \notin A \lor x \in A \lor x \in B)]$
rocky lotusBOT
Quill
odd jackal
nice
wooden ocean
so, does the whole second part in square brackets cut out?
odd jackal
no, x \in B surives
which is very important as you'll soon see :)
Just simplifiy the left , and you should be done :D
( hope you don't mind me using emoticons)
odd jackal
Once agin, ping me when you're done
vale dockBOT
@wooden ocean Has your question been resolved?
rocky lotusBOT
Quill
rocky lotusBOT
Quill
wooden ocean
that B is a subset of A... since if an element is present in B, it must be in A, but not necessarily vice versa
thank you so much!!
odd jackal
that B is a subset of A... since if an element is present in B, it must be in A,...
YES!
odd jackal
thank you so much!!
no problem
vale dockBOT
odd jackal
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✅ Original question: #help-4 message
odd jackal
@wooden ocean
do you know how to do the opposite direction now?
because you haven't technically finished the first one
wooden ocean
ah?
odd jackal
What we have shown is $[(A \setminus B) \cup B =A] \implies B \subseteq A$
rocky lotusBOT
wai
wooden ocean
for the opposite direction... I would need to rewrite it so I get $(x \in A \land x \notin B) \lor x \in B \iff x \in A$ from $B \implies A$ ?
rocky lotusBOT
Quill
odd jackal
yea
wait
You need to now show $B \subseteq A \implies [ ( A \setminus B) \cup B]=A$
rocky lotusBOT
wai
rocky lotusBOT
Quill
wooden ocean
I'm not sure how to proceed
odd jackal
Okay, so you want to proceed like this :
\
You know $B \subseteq A$.
\Using this show $[(A \setminus B) \cup B]=A$
rocky lotusBOT
wai
wooden ocean
how do I go about doing that? :0
hazy pivot
Well what does it mean for x to be in the LHS
wooden ocean
I'm... not sure
hazy pivot
What does it mean for x to be in a union
wooden ocean
it can be in either part of the sections that are part of the union
hazy pivot
Break down $x \in (A \setminus B) \cup B$
rocky lotusBOT
Xavier 🌺
wooden ocean
x is an element in the union between A \ B (the part of A that doesn't contain B) and B itself
wooden ocean
right
hazy pivot
Now analyse the cases individually
wooden ocean
so like, x in A, A \ B, and B?
odd jackal
how do I go about doing that? :0
Let $t \in A$. Then show $t \in [ ( A \setminus B) \cup B)$
rocky lotusBOT
wai
odd jackal
can I show ot using a venn diagram?
depends on your instructor
wooden ocean
ahh, I see
I'll email my professor to check if it's allowed, then
thank you so much!
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sudden dirge
vale dockBOT
sudden dirge
stuck on this question
not sure how to approach it
we could substitute but that doesn't really get us far
snow zealot
Put Y in P, then you will get an ineqality relation. Solve for X
sudden dirge
Put Y in P, then you will get an ineqality relation. Solve for X
yeah
now i just get
P((x - 2)(x + 6) <= 0)
so do i just P(X < -6) + P(X > 2)
vale dockBOT
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earnest ridge
Could someone walk me through solving 1 and 2 please?
vale dockBOT
Could someone walk me through solving 1 and 2 please?
valid perch
topaz hawk
are calculators not allowed?
candid socket
Could someone walk me through solving 1 and 2 please?
if calculator arent allowed, you should try to use the triangles
hazy pivot
Ehh both of those are standard values
vale dockBOT
@earnest ridge Has your question been resolved?
tiny torrent
does every cauchy sequence converge?
vale dockBOT
does every cauchy sequence converge?
tiny torrent
class notes
problem im working on
I just dont see why the problem is given if every cauchy sequence converges
I think maybe becaue it's simpler to prove than proving every cauchy sequence converges?
unless every cauchy sequence doesnt converge which is what im wondering now
warped totem
tiny torrent
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shrewd furnace
hi im taking statistics and am stumped by this question. i am not supposed to calculate the answer but I dont know where to find the answer on the table
shrewd furnace
here are my tables!
proud kestrel
hi im taking statistics and am stumped by this question. i am not supposed to ca...
which answer
shrewd furnace
I am supposed to find the percent of the data that is more than 2 movies
proud kestrel
I am supposed to find the percent of the data that is more than 2 movies
like numbers of movies watch >= 2?
shrewd furnace
yeah
proud kestrel
here are my tables!
its not on this table
shrewd furnace
ok yeah i thought so
shrewd furnace
im supposed to give a certain cell location to cite what the answer is
proud kestrel
im supposed to give a certain cell location to cite what the answer is
are u allowed to edit it
shrewd furnace
im not supposed to add anymore functions and formulas
shrewd furnace
but wouldnt that be up to 2 movies?
proud kestrel
j6 is up to 2 movies
shrewd furnace
im supposed to find the percentage of more than 2 movies
proud kestrel
1-j6 is everything greater than that
shrewd furnace
so the percentage excluding J4,5,6
proud kestrel
huh
shrewd furnace
I already had a question where I had to find the percentage for up to 2 movies, the 35%. Im trying to give the location of the cell that tells me the percentage excluding 2 or less movies
proud kestrel
1 minus J6
the answer is .65 dawg
unless you can find a cell that says .65 the answer is to use J6
shrewd furnace
i know but im not supposed to calculate anything, just read the tables so im confused :(
i'll just go with j6 since it really doesn't seem possible what the question is asking
thank you for the quick response!
tidal swift
any movie recommendations
!occupied, sorry. and perhaps a better question for #math-discussion.
vale dockBOT
any movie recommendations
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).
dawn quest
!occupied, sorry. and perhaps a better question for <#359052581022203914>.
euh.. no thank you ?
i meant to post this here
tidal swift
either way, this channel is occupied by another helpee atm
tidal swift
grab an available help channel if you want to ask your own question
dawn quest
okk !!!! thank you
shrewd furnace
.close
vale dockBOT
dawn quest
grab an available help channel if you want to ask your own question
i did !
tidal swift
good
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drowsy atlas
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drowsy atlas
can someone explain what I did wrong
The question is
the 2 arrows I drew are equations of 2 planes. I’m asked to find the vector parametric equation of the intersection
I don’t get what i did wrong
this is the answer
restive aurora
Can you post the original question
sharp knot
It is possible for your parametric form of the plane to "look" a little different. However, your point doesn't seem to satisfy both equations for the planes. I think you made a sign error when solving for z in terms of x.
drowsy atlas
ah
drowsy atlas
It is possible for your parametric form of the plane to "look" a little differen...
i ended up getting
-4
sharp knot
That looks right. But you can check for yourself by plugging the point you get back into the equations of the planes and checking it works
drowsy atlas
oh rlly
sharp knot
Also, your answer looking different just means your 't' is different.
sharp knot
yep
drowsy atlas
Also, your answer looking different just means your 't' is different.
oh
lmaoooooooo
okok
thanks
can you help me with another problem?
sharp knot
sure
drowsy atlas
sharp knot
Ok, it looks like you have the equation of the line, looks good
drowsy atlas
Ok, it looks like you have the equation of the line, looks good
is that right?
sharp knot
Yes, they gave you the direction vector, and used the point they gave you. So for t=0 you know the point is on the line.
Now, what is the value of z when you are in the xy plane?
drowsy atlas
Now, what is the value of z when you are in the xy plane?
0
sharp knot
Yes. What is the z component of the line you found?
sharp knot
Well, you don't want t =0 necessarily.
What is supposed to be 0 in the xy plane again?
sharp knot
yes
sharp knot
no problem
drowsy atlas
do you think it's possible for a question to ask me to reflect a vector along a line that is not y = x?
like smth like y=5x
sharp knot
I think so.
drowsy atlas
would the reflection matrix just be
0 5
5 0
sharp knot
hmm... I don't think so
I assume you haven't studied linear algebra? Might be slightly tough with the tools you have to work with
drowsy atlas
I assume you haven't studied linear algebra? Might be slightly tough with the to...
im doing lin alg lol
this is lin alg
sharp knot
multiplying by 5 just "stretches" things. You want to change the angle
drowsy atlas
yikes
that sounds complicated
cuz i only know the 2 matrices for clockwise and counterclockwise rotation
sharp knot
Draw a picture and think about what happens to your basis vectors
drowsy atlas
the vector equation of a line
to get it into a matrix
i can just like
write out the xyz equations?
sharp knot
I don't follow.
vale dockBOT
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mystic bramble
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mystic bramble
i know that the answer is -2x^4 - 11x^3 + 6x^2 + 47x - 40, but i’m having trouble on the flow of equation.
gray spear
Alright whats your thought process?
restive aurora
Do you know about multiplying like
(x-2)(x-1) = x^2 - 2x - x + 2 = x^2 - 3x + 2
This is just like that but with more terms
restive aurora
i know that the answer is -2x^4 - 11x^3 + 6x^2 + 47x - 40, but i’m having troubl...
If this is the answer, I think it's supposed to be times
mystic bramble
Oh really
restive aurora
And that - is supposed to be a *
green hamlet
Don’t think I understand what it’s asking me😭
vale dockBOT
Don’t think I understand what it’s asking me😭
wraith heart
do you see these definitions of m and M?
green hamlet
Yes
wraith heart
they're numbers that depend on f, a, and b
can you identify f(x), a, and b from here?
green hamlet
f(x)=5tan(3x) and b pi/9 and a pi/12
green hamlet
uhhhh not off the top of my head 😭😭
wraith heart
there are at least two ways. 1 is to recall your trig and figure it out by plotting or take derivatives and show f(x) is increasing on [a, b]. 2. is to do a u-sub with u = 3x and do 1. but more easily
green hamlet
ahhhhh okay
wraith heart
,w plot 5tan(3x) for pi/12 < x < pi/9
rocky lotusBOT
wraith heart
,w plot 5tan(x) for pi/4 < x < pi/3
yea same graph so you should be able to find m and M now.
vale dockBOT
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grizzled isle
I am supposed to solve for x and y, but the 1x4 - 1x3 = 1x3 part is confusing me. How would I get started.
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Available help channel!
olive grove
how do i solve this i got no idea where to start
vale dockBOT
how do i solve this i got no idea where to start
olive grove
ping me if someone comes thanks
umbral isle
Are derivatives used?
umbral isle
how do i solve this i got no idea where to start
Uh i see what you were doing, why did you cross it out
olive grove
i got. no idea
i sat this exam like a few weeks ago
let me think about this
yup i still have no idea why i did that
😭
if i set them equal to each other that means i can find a c value where they both exist?
does that work
olive grove
if i set them equal to each other that means i can find a c value where they bot...
value for constant c*
umbral isle
if i set them equal to each other that means i can find a c value where they bot...
If theyre tangent then there is exactly 1 point where they meet, meaning the cubic function you get from f(x)=y has only 1 real value for x ( i think)
stark wedge
you want the eq 0.1x^2-2x+c = -0.8x+4 to have exactly one solution
stark wedge
If theyre tangent then there is exactly 1 point where they meet, meaning the cub...
why cubic
oh shit it is cubic
nevermind that
stark wedge
ignore me
stark wedge
as in ignore the one solution stuff
olive grove
ok
stark wedge
i had misread the question
olive grove
ohhh ok
umbral isle
Oh ye ye it can have 1 sol and stilll not be tangent
olive grove
equation to the tangent of the curve means u take like the gradient of one spot and draw a linear line?
one coordinate
i remember what it looks like just not how to describe it
like this right?
olive grove
If theyre tangent then there is exactly 1 point where they meet, meaning the cub...
but idk how it will only have one real value for x
😭
umbral isle
Oh ye ye it can have 1 sol and stilll not be tangent
Ye ignore everything i said
olive grove
so this is tangent right
umbral isle
Think so
ionic cape
what do i do
does it work if u differentiate the function and equate to the tangent
olive grove
does it work if u differentiate the function and equate to the tangent
how do i check if it works
what do i gotta do
ionic cape
how do i check if it works
just try it
olive grove
i got
ionic cape
dyk how to differentiate
olive grove
0.3x^2 - 2 = -0.8x + 4
ionic cape
okay
olive grove
wait oopss
ionic cape
c shouldnt
olive grove
there
ionic cape
then youll get a x value, the corresponding y is y=-0.8x+4
substitute y and x into the function and youll probably get c
ionic cape
okay wait
olive grove
ight
olive grove
ok so y = -0.8x + 4
ionic cape
yuh
olive grove
y = -0.8(10/3) + 4
y = 4/3
y = -0.8(6) + 4
y = -0.8
now i use these and use the equation to find both c values?
olive grove
0.1(6)^3 - 2(6) + c = -0.8
c = 8.8
0.1(4/3)^3 - 2(4/3) + c = -0.8
c = -3.23 (rounded 2 dp)
idk gng
is this right
olive grove
Conquest is already here
hello
craggy girder
Conquest is already here
conquest is the op
olive grove
its chill gng
craggy girder
can you give me a recap of what you did?
craggy girder
i aint reading allat 💀
craggy girder
ionic cape
can you give me a recap of what you did?
we cant equate tangent and og graph function right>?
i think
olive grove
can you give me a recap of what you did?
derive function, set equal to tangent, solve for x values, find y values from x values, then solve for c with new x and y values
olive grove
got 2 answers for c cuz 2 x values
ionic cape
we can equate the gradient of the tangent line to f'(x) to find the x values
okay thanks
craggy girder
derive function, set equal to tangent, solve for x values, find y values from x...
that doesnt seem right
ionic cape
mb
olive grove
all good
lets jus do the right way
someone tell me the righ tone
😭
and why it works
olive grove
we can equate the gradient of the tangent line to f'(x) to find the x values
why does this work
craggy girder
think of it this way, the tangent and the graph have the same slope at their point of contact
hence we equate their slopes
merry crystal
moving further to find c values
recall that f(2) = -0.8(2)+4
and
f(-2) = -0.8(-2)+4
Due to point of intersection
ionic cape
thats what we did earlier
olive grove
thats what we did earlier
we did the first derive we jus didnt derive the tangent right
ionic cape
moving further to find c values
recall that f(2) = -0.8(2)+4
and
f(-2) = -0.8(...
howd you get x=2?
olive grove
did u solve for x values
no we didnt derive the tangent thats where we messed up gotta do it from the top twin
ionic cape
no the tangent is alr derived
right
derivation of the function = gradient = tangent?
oh
craggy girder
you need the slope of the tangent
olive grove
no right if we were to derive it we would just get the coefficient of x as our answer
ionic cape
OH
craggy girder
for that you need to derivate
merry crystal
we just use the slope
sacred jewel
Hm for tangency slopes are equal so 0.3x² - 2 = -0.8 giving x = ±2
craggy girder
also dont say derive, say derivate
umbral isle
Something went wrong🗣️ 🔥
merry crystal
wtf is up with wa
olive grove
0.3x^2 - 2 = -0.8
0.3x^2 - 1.2 = 0
ionic cape
we did the first derive we jus didnt derive the tangent right
okay i hope thats the only issue
merry crystal
yes
olive grove
i seeeee
now we can go to ur quick step
moving further to find c values
recall that f(2) = -0.8(2)+4
and
f(-2) = -0.8(-2)+4
Due to point of intersection
ionic cape
also dont say derive, say derivate
is there a reason for this btw
craggy girder
they mean different things
olive grove
also dont say derive, say derivate
o yea i didnt read this why do we do that
olive grove
they mean different things
OH what
none of my teachers ever corrected me are we serious
thanks gng
merry crystal
anw gang lock in
craggy girder
its hard to explain what it means lol
buts its diff
olive grove
anw gang lock in
oh true twin
yeah so
i can use these x values to find the y value
from either function right?
since we set them equal to eaach other
ionic cape
two y values
olive grove
ye i get that part but can i only use the tangent equation or can i use the original cubic function too?
merry crystal
both
sacred jewel
Yes so by substituting in f(x) = 0.1x³ - 2x + c and y = -0.8x + 4 gives c = 2.4 or 5.6
olive grove
tuff
merry crystal
the tangent line intersects with the cubic function at x=2 and x=-2
merry crystal
it is like this curve
olive grove
y = -0.8(2)+4
y = 2.4
y = -0.8(-2)+4
y = 5.6
now i can solve for c with each y value using the original cubic
olive grove
now i can solve for c with each y value using the original cubic
x and y value i mean
ionic cape
real
olive grove
0.1(2)^3 - 2(2) + c = 2.4
c = 5.6
0.1(-2)^3-2(-2)+c=2.4
c = -0.8
olive grove
Yes so by substituting in f(x) = 0.1x³ - 2x + c and y = -0.8x + 4 gives c = 2.4 ...
i got one of them the same but like the other one i got -0.8 twin
merry crystal
,w calc
rocky lotusBOT
Requested by leftover5270
rocky lotusBOT
Result:
3.2
,calc 2.4-3.2
rocky lotusBOT
Result:
-0.8
gotchu twin
ionic cape
0.1(2)^3 - 2(2) + c = 2.4
c = 5.6
0.1(-2)^3-2(-2)+c=2.4
c = -0.8
no y=5.6 when x=-2
rocky lotusBOT
Result:
2.4
,calc 5.6-3.2
rocky lotusBOT
Result:
2.4
true
ionic cape
olive grove
i am NOT getting this in the test but atleast i know how to do it now
olive grove
thanks gng
merry crystal
lock in
olive grove
thank you all of you
im not gonna ping everyone its a lot of effort
i hope you have beautiful days
or nights
thanks guys
ionic cape
no problem brotato chip
olive grove
.close
vale dockBOT
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north scarab
what are reciprocal functions?
vale dockBOT
what are reciprocal functions?
deep cedar
What is ts
stark wedge
"reciprocal functions" are not really a rigidly defined class
rather you should look at these 3 specific integration formulas that they give you
stark wedge
the "small adjustment" it mentions is the absolute value bars you slap on the stuff inside the logarithms.
so that for $\int \frac{\dd{x}}{x}$ instead of writing $\ln(x) + C$ you write $\ln|x| + C$.
rocky lotusBOT
Ann
north scarab
but wasnt that always the case? previosuly in the calculus of logs, they did not use absolute value of the argument
stark wedge
... "the calculus of logs"?
north scarab
yes
calculus = differentiation right?
or is calculus the umbrella term for differentiation and integration
hot tide
or is calculus the umbrella term for differentiation and integration
this
and well more stuff but those are the core components
stark wedge
or is calculus the umbrella term for differentiation and integration
it is the umbrella term
pallid oasis
calculus(in the context of highschool math) would probably mean that, but there are other meanings in math for it as well (maybe with a prefix added)
north scarab
it is the umbrella term
wow Im suprised i never knew until now
what have I done wrong
wait ill open a new ticket
.close
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nimble pier
h
nimble pier
i tried so hard to think how to answer the (ii) question and cant even figure out how to start. please can anyonehelp
circular measure
candid bolt
its helpful to label the intersection points first
candid bolt
its helpful to label the intersection points first
like label where the circle intersects with the stage
and then try to break the intersection area into some basic shapes
nimble pier
this is the area wanted
how do i even start when the only given information for the spotlight circle is just its radius
no angle
candid bolt
how do i even start when the only given information for the spotlight circle is ...
ok did you label the points?
vale dockBOT
@nimble pier Has your question been resolved?
candid bolt
i think you got the idea
so thats a sector + (sector-the triangle bit)
you know how to calculate the sector areas right
candid bolt
unless theres an easier way you should use the cosine law
candid bolt
<@&268886789983436800>
candid bolt
i know the angle OTP but
bro when will you label the intersection points
nimble pier
i know the angle OTP but
but not the rest to find the area of the first sector
candid bolt
what intersection
of the small circle iwth the stage
candid bolt
idk what you
re pointing to with the red splot
but i mean the ones the circle at T makes
nimble pier
omg
nimble pier
unless theres an easier way you should use the cosine law
i got it
vale dockBOT
@nimble pier Has your question been resolved?
prisma flint
Hello!
Can someone please explain to me how I get from the first term to the second term here?
small beacon
Hello!
Can someone please explain to me how I get from the first term to the sec...
x₁,₂ = -p/2 ± √((p/2)² - q)
prisma flint
I know the pq formula, i dont know how they got the term into a from so I can apply the formula
@small beacon
rocky lotusBOT
Ann
