uh
#help-27
viscid wagon
I have just one more question
I got 81k3y - 81k2y2 -36k2 - 36ky +36y2 +16 = 0
My teacher went through a similar question and in that question we were able to find some roots and factorise the equation
viscid wagon
I got 81k3y - 81k2y2 -36k2 - 36ky +36y2 +16 = 0
But it doesn't seem like I can easily find roots for this (the equation itself might be wrong)
devout snowBOT
@viscid wagon Has your question been resolved?
devout snowBOT
@viscid wagon Has your question been resolved?
devout snowBOT
@viscid wagon Has your question been resolved?
distant helm
smells like there's vieta's formula here
I think I can suppose x + y + z = a, then find xy + yz + xz and xyz based on a and k?
devout snowBOT
@viscid wagon Has your question been resolved?
brittle anvil
Hello everyone! I’m a new learner, and I only know the basics taught in school. Any advice on how to improve? 😊
viscid wagon
I think I can suppose x + y + z = a, then find xy + yz + xz and xyz based on a a...
Yeah I did do that sort of
bleak arrow
is the following true?
we have integral(sqrt(a^2-x^2) dx), we can set sqrt(a^2-x^2) = acos(theta)
bleak arrow
so the integral becomes int(acos(theta)*acos(theta))dtheta
wispy oyster
we set x = acos(theta) generally
bleak arrow
I know but what about sqrt(a^2-x^2), doesn't it simplify to acos(theta) when i set x = asin(theta)
the professor showed that we can set sqrt(a^2-x^2) to a*cos(theta)
wispy oyster
if we let x = acos(θ)
we have that:
dx / dθ = -asin(θ)
dx = -asin(θ) dθ
so we have that:
∫sqrt(a^2-x^2) dx => -∫sqrt(a^2-a^2cos^2(θ)) sin(θ)dθ
so we have:
-a∫sqrt(1-cos^2(θ)) sinθ dθ
which gives us:
-a∫cosθsinθ dθ
you can solve this using double angle
bleak arrow
nvm i verified that it is actually true, sqrt(a^2-a^2*sin^2(theta)) is just a times sqrt(1-sin^2(theta)) which is just a times sqrt(cos^2(theta)) = acos(theta)
i set x = asin(theta)
it turned out to be true
wispy oyster
both x=asin(θ) and x = acos(θ) work as valid substitutions in the case of sqrt(a^2-x^2)
bleak arrow
yes but it simplifies ur work if u directly set sqrt(a^2-x^2) as acos(theta), just plug in asin(theta) in place of x and ull get this result (as proof)
and for sqrt(x^2-a^2), it's equal to atan(theta), and for sqrt(x^2+a^2), it's equal to asec(theta)
devout snowBOT
@bleak arrow Has your question been resolved?
karmic radish
Once u convert to a linear scale why re we not multiplying I0 on the rhs
north mountain
!nogpt
devout snowBOT
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
devout snowBOT
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flat fjord
Hello i need to show that a system is inconsistent in matlab:
the lead in the assignment is that a system Ax=b is inconsistant if and only if rank A < rank (Ab) where the column of b is part of the matrix
stone stump
and whats the problem with that?
flat fjord
aaah
i know what i did wrong
i should take b apart and add each corrisponding element to each row in the matrix
matlab syntax
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winged hearth
Guys is this correct?
drifting mauve
Guys is this correct?
uhm, the first limit from left hand side should be 6 not 5?
winged hearth
yeha man that 's what i thought
but some p[eople told me i should use the bottom one
winged hearth
ok
keen cloud
it will be 5. It is the left hand limit.
winter patrol
x < 1
indicates values less than 1, which is what you're considering for the left hand side limit
keen cloud
less than 1.
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lucid mason
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faint gorge
do you really have to use the first principles?
lucid mason
do you really have to use the first principles?
I dont know what that means LOL
Why wont it work this way
Im just trying to do it the way the teacher showed
faint gorge
I dont know what that means LOL
oh i mean the h-limit formula basically
lucid mason
well ya
faint gorge
what happend to the 2+h-2/3
lucid mason
i just didnt continue
faint gorge
oh
faint gorge
hmm not really
faint gorge
should i just continue
yes
lucid mason
okayokay LOL
faint gorge
the terms should cancel out nicely
lucid mason
ohh woah
i got the right answer yay
i got scared first bc i thought it wont cancel
bc the fractions looked weird
but thank u LOL
.close
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vocal oar
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vocal oar
I have found a basis for W1, W2
I have proved W1, W2 are both subspaces of V
I found W1+W2 to be the following
How would I find a basis for this?
My wild guess is that the basis is a set of 5 matrixes, one matrix for each coefficient -- but idk i have a gut feeling im wrong
radiant dune
You can tell by observing that you have enough degree of freedom to create all 2x2 matrices by using W1+W2
radiant dune
My wild guess is that the basis is a set of 5 matrixes, one matrix for each coef...
If you try to do that, youll notice that they are not linearly independent
So you'll have to remove one
radiant dune
Yep
scenic barn
devout snowBOT
lethal pollen
Convert m to a power of b
fossil locust
Or by change of base rule, raise both sides to the power of log b
lethal pollen
$m=b^{\log_b{m}}$
woven radishBOT
denzio321
lethal pollen
Ye
lethal pollen
Yea
lethal pollen
Uh no
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spring oasis
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strange arch
Given S & T, show that W e R^4 with ... exists?
woven radishBOT
938c2cc0dcc05f2b68c4287040cfcf71
spring oasis
Given S & T, show that W e R^4 with ... exists?
did you found dim W
topaz crag
You need to find
W = <x1,x2>
Cause dim S+T = 3
So dim W must be 2 or 1 using the first 2 conditions
the third condition tells you that W must contain a vector not in S, so that vector must be in T cause W is in S+T
the 4th condition tells you that W must contain a vector not in T, so that vector must be in S cause W is in S+T
So that leads us to dim W = 2
and W = <x1,x2> such as :
spring oasis
So that leads us to dim W = 2
and W = <x1,x2> such as :
x1 in S perp n S + T
spring oasis
So that leads us to dim W = 2
and W = <x1,x2> such as :
x2 in T perp n S+T
topaz crag
x1 in S perp n S + T
x1 in S perp n T
spring oasis
no
strange arch
x1 in S perp n S + T
topaz crag
Sure
strange arch
is that what you applied shakigras
topaz crag
is that what you applied shakigras
No
spring oasis
S perp n S + T
topaz crag
S perp n S + T
Why ??
topaz crag
is that what you applied shakigras
I just used the conditions as stated
strange arch
I just used the conditions as stated
ah misunderstood yop
topaz crag
there are vectors that are in S + T that are not in S nor T
Yes but we're looking to make things easier.
strange arch
there are vectors that are in S + T that are not in S nor T
you can also start with the intersections with S+T and reduce afterwards
@spring oasis How far are you in determining the two vectors? :]
spring oasis
spring oasis
<@1187916384341078070> How far are you in determining the two vectors? :]
idk bro, I'm tripping hard
spring oasis
Yes but we're looking to make things easier.
is Sn Tperp empty?
,w nullspace {{4,1,0,-1},{1,0,1,0}}
woven radishBOT
spring oasis
ok I see my error now
S = <(-1,4,1,0),(0,1,0,1)>
SnTperp is empty or no
, w nullspace {{-1,1,0,0},{4,0,1,1}}
woven radishBOT
spring oasis
T perp = <(-1,-1,4,0),(-1,-1,0,4)>
,w det {{-1,-1,4,0},{-1,-1,0,4},{-1,4,1,0},{0,1,0,1}}
woven radishBOT
spring oasis
they literally don't intersect bro lmao
devout snowBOT
@spring oasis Has your question been resolved?
devout snowBOT
@spring oasis Has your question been resolved?
spring oasis
,w rank {{-1,-1,4,0},{-1,-1,0,4},{-1,4,1,0},{0,1,0,1}}
woven radishBOT
spring oasis
,w rref {{4,1,0,-1,0},{1,0,1,0,0}}
woven radishBOT
spring oasis
x1 + x3 = 0
x2 - 4x3 - x4 = 0
x1 = -x3
x2 = 4x3 + x4
(x1,x2,x3,x4) = (-x3, 4x3 + x4, x3, x4)
x3(-1,4,1,0) + x4(0,1,0,1)
S = <(-1,4,1,0), (0,1,0,1)>
spring oasis
,w nullspace {{-1,1,0,0},{4,0,1,1}}
woven radishBOT
spring oasis
x(-1,-1,4,0) + y(-1,-1,0,4)
Tperp = <(-1,-1,4,0), (-1,-1,0,4)>
,w rank {{1,1,-4,0},{0,0,-1,1},{-1,-1,4,0},{-1,-1,0,4}}
woven radishBOT
woven radishBOT
spring oasis
,w (1,1,-4,0) * (4,0,1,1)
woven radishBOT
spring oasis
,w (0,0,-1,1) * (-1,1,0,0)
woven radishBOT
spring oasis
,w (0,0,-1,1) * (4,0,1,1)
woven radishBOT
spring oasis
,w (4,1,0,-1) * (-1,4,1,0)
woven radishBOT
spring oasis
,w (4,1,0,-1) * (0,1,0,1)
woven radishBOT
spring oasis
,w (1,0,1,0) * (-1,4,1,0)
woven radishBOT
spring oasis
,w (1,0,1,0) * (0,1,0,1)
woven radishBOT
spring oasis
,w rank {{4,1,0,-1},{1,0,1,0}}
woven radishBOT
spring oasis
,w rank {{-1,5,1,1},{0,1,0,1},{-1,1,0,0}}
woven radishBOT
spring oasis
,w rref {{-1,5,1,1},{0,1,0,1},{-1,1,0,0},{1,1,-4,0},{0,0,-1,1},{4,1,0,-1},{0,0,-1,1}}^T
woven radishBOT
spring oasis
,w nullspace {{4,1,0,-1},{1,0,1,0}}
woven radishBOT
spring oasis
,w rank {{-1,1,0,0},{4,0,1,1},{4,1,0,-1},{1,0,1,0}}
woven radishBOT
spring oasis
,w rank {{1,1,-4,0},{0,0,-1,1},{-1,4,1,0},{0,1,0,1}}
woven radishBOT
spring oasis
<@&286206848099549185>
dapper tiger
I'll think about it in around 1h if you have time to wait and nobody comes before
spring oasis
ty
iron kindle
mystic scarab
And take breaks sometimes (at least in my opinion)
Also you should do things by hand, not calling Wolframalpha everytime, because 1) I don't think you'll have that in the exam and 2) you fill the chat and make it quite messy, as we can't follow your steps
dapper tiger
(They're right)
So, the idea of Shaki was good
S+T is dim 3 so W is dim 1 or 2
It would be one in the case of a vector which is in S+T, orth S and orth T
So well, there is a problem as you can see
So you want to find a vector in orth S and one in orth T
devout snowBOT
@spring oasis Has your question been resolved?
viral lynx
devout snowBOT
viral lynx
x^2 - 3z - 4 factorizes to (x-4)(x+1)
A(x-4) + B(x+1)
Ax - 4A + Bx + B
(A + B)x - 4A + B
midnight echo
There's an easier way.
viral lynx
Ok well first I want to see what I did wrong
A + B = 2
-4A + B = -8
A = (2 - B)
-4(2 - B) + B = -8
-8 - B + B = -8
So -8 = -8 or B = B?
How can I solve with this...
Omg
I see haha
+4B
Alright
viral lynx
There's an easier way.
Whats the easier way?
midnight echo
2x-8 factorizes into 2(x-4), cancel that out with the (x-4) in the denominator and you won't have to do pfd.
midnight echo
So -8 = -8 or B = B?
I mean this shows that anyway, your B term becomes 0.
You get 5B = 0, B = 0
which reduces it into 2/(x+1)
viral lynx
2(x - 4)/(x-4)(x+1) -> 2/(x+1)
Yeah thats a neat trick
Idk if I would spot that in an exam 😅
But I will try to look out for it next time!
midnight echo
Yeah no harm done with pfd, the B term ends up dropping anyway
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lament cradle
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lament cradle
what do the brackets mean
frozen aurora
<@&268886789983436800>
frozen aurora
what do the brackets mean
if they had $A \cap B \cup C$ instead, you could've interpreted it as $(A\cap B) \cup C$
woven radishBOT
artemetra
frozen aurora
which isn't the same thing
lament cradle
Is A n B u C what i have here?
frozen aurora
so it's just to clarify that you need to do B u C first
lament cradle
frozen aurora
Is A n B u C what i have here?
i don't think so A n B u C is kinda ambiguous
lament cradle
o
frozen aurora
you have A n (B u C)
so you first do B u C
and then take the intersection of that result with A
it's just like regular algebra
lament cradle
so it's just to clarify that you need to do B u C first
wait
so its like
A intersection with B and C?
devout snowBOT
@lament cradle Has your question been resolved?
restive river
curious about something
devout snowBOT
curious about something
restive river
if i did an problem in a different way then it was in the solution key
but still got the same result somehow
and im 100% sure i have no mistakes
does it count like a solve
solid osprey
yeah?
restive river
oh
solid osprey
aa long as you followed the instructions
restive river
i had none
solid osprey
ok
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frigid scaffold
I watched 3blue1browns video of matrix multiplication, and wonder how and what it means to multiply two matrixes of diffirent sizes (3x2 matrix with 2x2). Why is that possible when the 2x2 is missing the third dimension?
devout snowBOT
I watched 3blue1browns video of matrix multiplication, and wonder how and what i...
jaunty mantle
I watched 3blue1browns video of matrix multiplication, and wonder how and what i...
The 3x2 matrix transforms ℝ³ into ℝ² in a linear fashion
A mxn matrix is a (linear) map from ℝ^m to ℝ^n
Or maybe it’s the other way round, only one of them works
I always forget which is which but that doesn’t change the reasoning
No it’s the wrong way around, 3x2 matrices transform ℝ² vectors into ℝ³ vectors
frigid scaffold
oh i think i might have a slight grasp
jaunty mantle
But matrix operation goes from right to left not left to right like normal operations
If A and B are matrices and x is a vector
Then ABx means first apply B to x, then apply A to the result
frigid scaffold
so because the 3x2 matrix has more rows than columns, there cant be a pivot in each row
so the "vectors" are linearly dependent
therefore they dont fully span 3d space?
jaunty mantle
The row vectors yeah
No
The row vectors can’t be linearly independent because they have dimension 2 (there’s 2 columns) but there’s 3 of them (there’s 3 rows)
jaunty mantle
so the "vectors" are linearly dependent
This statement
jaunty mantle
therefore they dont fully span 3d space?
And this conclusion
Is not correct
The first does not imply the second
if A is a 3x2 matrix and B is a 2x2 matrix, and x is a vector in ℝ²
Then ABx means first apply B to x, this result is an ℝ² vector, “Bx ∈ ℝ²”
Now apply A to this ℝ² vector called Bx
A sends ℝ² vectors to ℝ³ vectors in a linear fashion
That’s good because Bx is an ℝ² vector so I can feed it into A
frigid scaffold
Yeah i dont really see how R^2 can be transformed into R^3
jaunty mantle
ℝ² is a plane
frigid scaffold
i imagine a 2x2 matrix as being where i_hat and j_hat land
jaunty mantle
Full rank matrices will just flip this plane around in ℝ³ it’s still a plane
frigid scaffold
but there is no k_hat
jaunty mantle
It’s still a plane but the plane is in ℝ³
frigid scaffold
oh
jaunty mantle
It’s still a plane but the plane is in ℝ³
But this 3x2 matrix needs to be rank 2 for this to be true
If it’s rank 1 it’ll turn a plane into a line in ℝ³ (through the origin)
frigid scaffold
so the matrix that is the output of the 3x2 times 2x2 multiplication is a plane in R^3?
ah
jaunty mantle
so the matrix that is the output of the 3x2 times 2x2 multiplication is a plane ...
Depends on the rank of these matrices
The first 2x2 matrix (the one on the right) could be rank 1 and your plane immediately collapses into a line
Then the 3x2 matrix can’t turn a line into a plane
So it’ll at most turn it into a line in ℝ³
And at the least it’ll be a point at the origin
frigid scaffold
ok
but if the 3x2 has the highest possible rank, and so does the 2x2, the output is at most rank 2?
jaunty mantle
Yes
frigid scaffold
ok i feel like it all makes a lot more sense now!
Chatgpt couldnt really understand what i was asking
so thank you very much for helping me understand
.close
feral bobcat
devout snowBOT
feral bobcat
can someone help me understand how these are solved
i am confused by the different radii
so like when i find the cirumference
what raduis do I use?
this is more math than physics btw
devout snowBOT
@feral bobcat Has your question been resolved?
cerulean badge
I'm going to start crying.
devout snowBOT
I'm going to start crying.
valid vector
I'm going to start crying.
Firstly, (try) to solve for theta, or get it in terms of sine and cosine.
cerulean badge
Okay but I don't even understand what the question wants from me 😭
distant helm
it wants you to suffer by confusing yourselves with the variables /j
valid vector
Okay but I don't even understand what the question wants from me 😭
They want you to show that the tangent of the solutions added together is equal to 2ac/(a^2-c^2).
Let me see if I can solve this.
distant helm
you can bring the equation back to a very familiar form:
Msinx+Ncosy=P
cerulean badge
WHO IS SHE AND WHAT ARE THEY TEACHING ME IN SHOOL 😭
Dawg I'm bout to give up, what kind of tomfoolery is my school doing they give us these basic ass questions and give us difficult ass questions and expect us to ACE
wheat pawn
You got an equation.
It has two solutions for theta.
They call the first solution alpha. They call the second solution beta.
You're asked to prove that the sum of the solutions is the thing at the end
distant helm
can you solve?
(it may probably go nowhere yet but try doing some experiments, your goal is make tan(alpha) and tan(beta) appear)
cerulean badge
You got an equation.
It has two solutions for theta.
They call the first solutio...
Okay they're the solutions of THETA. the question has so many damn variables, I didn't know what to solve
wheat pawn
okay, no. Theta is the variable
a, b and c are parameters
cerulean badge
The first bit makes sense but I still don't get the last part
wheat pawn
the difference being that variable is what you do not know, and parameters it what you assume known, even if it's not explicitly given
cerulean badge
Okay
Okay wait lemme try now one sec
...
Why are you squaring it tho :((
Dawg, I'm stupid, you gotta explain this to me like I'm 5
distant helm
yeah no that aint got any better
cerulean badge
This is how far I can solve I ligit got no clue what to do after that
distant helm
so what im trying to do is using this formula
distant helm
this tells me that i need tan(a) + tan(b) and tan(a)tan(b)
it's SUM and PRODUCT, and it reminds me of Vieta's formula
cerulean badge
Okay okay
I forgot bout that formula
Wait, lemme use my head one sec
Okay see, I have the solution for this question
But the solution is so
Confusing
distant helm
ok i just solved it
it's pretty hard for you to understand but i'll try my best to make you understand
cerulean badge
Yes please
distant helm
this tells me that i need tan(a) + tan(b) and tan(a)tan(b)
it's SUM and PRODUCT,...
let's start from the bottom first
so, i want Vieta's formula, which is normally seen from quadratic
so, the idea is to turn the given equation into a quadratic, with our unknown being tan(theta)
cerulean badge
Ahhh okay
distant helm
so, start from this, square both sides
(its the only way to make a quadratic appear)
cerulean badge
Okay okay
distant helm
Then expand: $a^{2}\sin^{2}\theta-2ac\sin\theta\cos\theta+c^{2}\cos^{2}\theta=b^2$
woven radishBOT
TargetVN
distant helm
this is pure algebra so i hope u get it
distant helm
hm?
cerulean badge
I have this tho, how am I supposed to complete the square
Oh wait
Do I like add c²cos²
On both sides
😭
Sorry no
I meant a²sin²
distant helm
:/
cerulean badge
dw
your mistake is very common but now you know
Common mistakes are not an option when I'm preparing for entrances for math hons
cerulean badge
Okay so I expanded the equation (finally, after much trial)
distant helm
alr
now, the question is how the hell can we make "tan" appear
You probably know this: $1+\tan^{2}\theta=\frac{1}{\cos^2\theta} \text{ and }1+\cot^{2}\theta=\frac{1}{\sin^2\theta}$
woven radishBOT
TargetVN
distant helm
alr, flip them to obtain cos^2 and sin^2
valid vector
I got the answer.
Or at least, I proved it.
@cerulean badge Try putting sec in terms of tan
cerulean badge
I got this
distant helm
niceeee
cerulean badge
Shit, I spilt coffee on my notebook
valid vector
I got this
Good job.
valid vector
let it dry for a sec
sec (secant) reference??
distant helm
k, only that sin*cos left
cerulean badge
Yes
distant helm
but we can still find it by exploiting the identities we just used
$\cos^{2}\theta=\frac{1}{1+\tan^2\theta} \text{ and } \sin^{2}\theta=\frac{\tan^2\theta}{1+\tan^2\theta}\newline
\Rightarrow \sin^2\theta\cos^2\theta=\frac{\tan^2\theta}{\left( 1+\tan^2\theta \right)^2}\newline
\Rightarrow \sin\theta\cos\theta=\frac{\tan\theta}{1+\tan^2\theta}$
woven radishBOT
TargetVN
cerulean badge
Okay but
Oh wait nvm got jt
Am I in the right direction
@distant helm my G
Please
Help
distant helm
oh no wonder
cerulean badge
Can I show my way?
Please
valid vector
distant helm
multiple route but overall still ended up with that quadratic 
restive river
.
distant helm
4th one is vieta's formula
cerulean badge
Oh no wait
Yeah yeah I got it mb
Okay
Wow
That was a lot less complicated
Ty
Anyways, chat, I'm cooked
I ain't never getting into that math hons program 🙏
But I might pass 11th
.close
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Available help channel!
warm locust
devout snowBOT
warm locust
why couldnt you just expand this then seperate the variables
i know how you should do it
but why cant you do the way i said
quaint citrus
dT/(200k - kT) = dt ?
winter torrent
i think that's probably exactly how i'd do it
quaint citrus
is that what ur talking about
warm locust
typically you should just divide through by the 200-theta
and keep the k on the other side with dt
warm locust
really?
quaint citrus
why not
warm locust
but you would end up with a different answer no?
quaint citrus
eh the constant might change a bit but its still correct
warm locust
ah right
quaint citrus
why dont u try it out for yourself
valid vector
$\int\frac{d\theta}{200-\theta}=\int kdt$
woven radishBOT
mathisfun
quaint citrus
in any question
as long as you separate properly yes
valid vector
**mathisfun**
$\ln|\theta-200|=-kt+C\ \theta-200=Ae^{-kt}\ \theta=200+Ae^{-kt}$
woven radishBOT
mathisfun
warm locust
i get this
but if you expanded
the original and then solved the DE you wouldnt end up with that
valid vector
the original and then solved the DE you wouldnt end up with that
Yeah, this is an alternate method.
quaint citrus
the original and then solved the DE you wouldnt end up with that
try it and show what u get
valid vector
**mathisfun**
Try it this way.
quaint citrus
Try it this way.
but the point is that he wants to see if it works out the other way
valid vector
but the point is that he wants to see if it works out the other way
Oh, I thought he meant something else.
Sorry.
warm locust
I got sqrt400t + A ( A being a constant)
warm locust
not what was required
quaint citrus
lemme try rq hold on
i got
after integration:
$\frac 1k \ln |kT - 200k| = -t + C$
woven radishBOT
woven radishBOT
quaint citrus
which, if u pull the e^kC out and divide by k, that is "A" in the answer
warm locust
you moved both terms on the left hand side and integrated right?
quaint citrus
$\int \frac {dy}{kT - 200k} = \int - dt$
woven radishBOT
quaint citrus
thats what i integrated
warm locust
Ok got it. Sorry for asking too many questions but suppose you just left the 200k on the dt side
Is that correct?
quaint citrus
wdym by that
quaint citrus
dT/dt + kT = 200k
this. ?
warm locust
yeah ish but move the dt to the 200k side
quaint citrus
then you would get
warm locust
could you do it that way?
quaint citrus
dT + kT(dt) = 200k(dt)
quaint citrus
yeah ish but move the dt to the 200k side
define 'move'
quaint citrus
maybe just write it out on paper and send a picture
by 'move' u meant multiply, which u can 'do', but u cant integrate after that
so no, it doesnt work
quaint citrus
im not understanding what occurred from line 2 to line 3
can you explain what you did
warm locust
Does it need to be multiplied to integrate?
quaint citrus
yes
warm locust
I wasnt aware
quaint citrus
ya misread ur message
warm locust
So the differential needs to be attached to the term you are integrating
quaint citrus
correct
warm locust
And by adding its not "attached"
quaint citrus
correct
warm locust
Im still a bit confused to why not
valid vector
No, you still will have d(theta)+kthetadt=200kdt
valid vector
i dont get this d(theta)+kthetadt
$\frac{d\theta}{dt}+k\theta=200k$
woven radishBOT
mathisfun
valid vector
This is what you proposed correct?
valid vector
**mathisfun**
So then $d\theta+k\theta dt=200kdt$
woven radishBOT
mathisfun
valid vector
Which obviously is NOT a good form for this
warm locust
🤦♂️
dont know what i was thinking
Thank you @valid vector and @quaint citrus
Damn that is so annoying
valid vector
dont know what i was thinking
It's fine. You get better at math this way.
warm locust
It's fine. You get better at math this way.
100%
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scenic barn
HI
scenic barn
THis is my table of values
ignore the x/y it is just x
i need to make a quadurtatic equation of it
and i can do it
but when i put it into desmos these values are true
like it is x is 7 and y is 15 not 24
the equation i got was $-\frac{49}{36}\left(x-6\right)\left(x-18\right)$
woven radishBOT
Slimy
winter patrol
how did you get the -49/36
winter patrol
also who said this was quadratic
scenic barn
then solve for a
scenic barn
also who said this was quadratic
that the whole point of my assigment
i mean what else would you do
keen cloud
it will be -40/27 not -40/36
scenic barn
how?
winter patrol
what were t he exact instructions
keen cloud
the quadratic will be y = a(x-6)(x-18)
Now put x = 9 and equate with 40.
scenic barn
why
keen cloud
at x=9 y is 40 isn't it??
scenic barn
yeah
keen cloud
from here you can find a
keen cloud
If you notice, the vertex is being formed at x=12.
winter patrol
you can approximate/model it with a quadratic,
there isn't one that'd pass through all the points
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hearty sparrow
hello, i am a high school junior taking statistics and probability at a university. i have completed four problems and provided answers and i was wondering if some could check to see if the following are correct.
devout snowBOT
hello, i am a high school junior taking statistics and probability at a universi...
hearty sparrow
here are the questions and answers:
hearty sparrow
can some1 help me
this is occupied
summer barn
mb
hearty sparrow
hearty sparrow
<@&286206848099549185> Can someone please verify to see if my answers are correct.
devout snowBOT
@hearty sparrow Has your question been resolved?
hearty sparrow
<@&286206848099549185> Can someone please verify to see if my answers are correc...
<@&286206848099549185>
supple knot
oh is this a test?
hearty sparrow
oh is this a test?
No, homework
supple knot
why is it dated today lol
hearty sparrow
why is it dated today lol
Homework assignment of today
hearty sparrow
oh is this a test?
University tests are typically 20 q's
@supple knot have u taken prob/stats in college
hearty sparrow
can someone please verify
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quartz flower
devout snowBOT
quartz flower
I require help
delicate pawn
you have two equations
x + y = 6 and 30x + 15y = 150
reduce the second one to 6x + 3y = 30
plot those two lines
get three points satisying each equation to plot them
restive river
So basically you have to do a system
low sentinel
reduce the second one to 6x + 3y = 30
note that this is done by division by 5
not magic
delicate pawn
note that this is done by division by 5
+1
quartz flower
um im very bad at math and dont even know how to plot with that answer yu give me
delicate pawn
its a system of linear equations, youre plotting them to find the space between them which could have solutions
say x+y=6, the first equation. it means that x could be 1 if y is 5, 2 if 4 and so on
restive river
um im very bad at math and dont even know how to plot with that answer yu give m...
You have to resolve the following system:
{x + y = 30
{30x + 15y = 150
restive river
You combine the two lines then find x and y
low sentinel
plot the points (1,5), (2,4), (3,3) accordingly
work for this please
delicate pawn
work for this please
its in the message i sent beforehand
quartz flower
plot the points (1,5), (2,4), (3,3) accordingly
it does not allow me to plot 3,3
low sentinel
get three points satisying each equation to plot them
only need 2
3 is for reliability on paper
delicate pawn
it does not allow me to plot 3,3
you'll notice that 3,3 is already on this line
delicate pawn
3 is for reliability on paper
+1
always worked these out on paper myself, hence the 3. 2 is fine here
quartz flower
you'll notice that 3,3 is already on this line
yeah, ok so what next
delicate pawn
yeah, ok so what next
do the second equation now
6x + 3y = 30
if x is 1, then what will y be?
and if y is 1 then what will x be? plot those two points
quartz flower
if x is 1, then what will y be?
um 4?
delicate pawn
6(1) + 3(y) = 30
3(y) = 30 - 6 = 24
y = 24/3 = 8
y is 8 is x is 1
so (1,8) is one of the points
quartz flower
so something like this?
valid vector
so something like this?
No.
quartz flower
yea thats what i thought im so cooked
valid vector
There should be 2 lines, not a vertical line.
quartz flower
ok so remove the vertical line
delicate pawn
so something like this?
now do the next point, assuming y is 1
doesnt divinde properly, so look for another solution for 6x + 3y = 30
valid vector
Let us denote x as the bottles of soda, and y as the bottles of juice
Then 30x+15y=150 (since there are 30 grams of sugar per bottle and 15 grams of sugar per juice) and x+y=6 (she bought a total of 6 bottles).
Does this make sense?
@quartz flower
quartz flower
Let us denote x as the bottles of soda, and y as the bottles of juice
Then 30x+1...
um somewhat what does the 150 represent?
and where did yu get the x+y=6
valid vector
um somewhat what does the 150 represent?
The total grams of sugar in the bottles of soda and juice you bought.
valid vector
and where did yu get the x+y=6
Read the context.
delicate pawn
and where did yu get the x+y=6
bottles of juice + soda have to be 6
delicate pawn
okay for the second line, plot 0,10 and see what you get
quartz flower
delicate pawn
since 6(0) + 3(y) = 30
y = 10 if x is 0
delicate pawn
and add 1, 8 to the second line as well
quartz flower
this is correct right?
delicate pawn
think it through
valid vector
this is correct right?
How did you get this?
quartz flower
and add 1, 8 to the second line as well
i can not graph a line within a line it just removes the first line i put it done
valid vector
Where is your other line?
quartz flower
How did you get this?
um this 30x+15y=150
quartz flower
Where is your other line?
0,10
valid vector
um this 30x+15y=150
No, like, show your work.
quartz flower
um i kinda just thought how many bottles of soda would get me to 150 and its 5 then i was like but what about the juices so i just said 4 bottles of soda
and two juices
valid vector
Eh, okay.
quartz flower
That's a point?
ig im just plotting what im told its confusing
valid vector
It's right.
valid vector
No clue,
low sentinel
this is correct right?
yes
quartz flower
oh ok thats good
i need both parts correct
or i just get it incorrect
i got it
thanks
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bitter mantle
I am wondering why this answer for this question here
devout snowBOT
I am wondering why this answer for this question here
past moat
this is pre-uni?? 😭
bitter mantle
Okay as if you can explain why then
I am supposed to be taking Theory of Computation being next class
winter torrent
what's R^2?
winter torrent
okay, what does that mean?
bitter mantle
Your the math expert
winter torrent
(x, y) is in R^2 iff .....?
bitter mantle
Is lke (2,3) to (3.4)
winter torrent
okay and what about R*?
bitter mantle
All possible combinations that are transitive
winter torrent
i like the idea of using 'next to each other on the number line' as R
so what's an example of an ordered pair in R*, and why?
bitter mantle
I been usinmg chatgpt to explain this to me as well
@supple knot can you explain it then
ANybody
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restive river
hi Ik this is like a very vague question but idk how to set up the problem
restive river
restive river
omg hi 🙏
restive river
uhh y=3 x^(1/4)?
faint gorge
yes and y = 3
restive river
Idk what else 😭
faint gorge
that are the functions
restive river
Oh that’s it
restive river
Shell
restive river
0,1?
faint gorge
yes!
faint gorge
not quiet
woven radishBOT
faint gorge
the radius is basically the distance from the axis of revolution to the function, so we can simply say x
r(x) = x
h denotes the height
restive river
Is the height 3
faint gorge
restive river
oh-
faint gorge
any ideas what h(x) could be
faint gorge
then the arrow would go all the way down until the x-axis
restive river
Wait is it 1 then
faint gorge
h is a height difference
it's not constant as you can see
h begins great at x = 0, and becomes smaller and eventually 0 at x = 1
any ideas now?
restive river
i rlly dunno sorry 😭😭
faint gorge
h is a height *difference*
ok so do you agree that y = 3 is the maximal height
at all
restive river
Yes
faint gorge
what remains now if you take away a part from it, say 3x^(1/4)
the green height part
from the orange
restive river
Would it just be equal to r1
restive river
oh my god i did something right for once 😮
faint gorge
because then what remains is well
whats between y = 3 and y = 3x^(1/4)
the purple
i think you got that part
r(x) = x
h(x) = 3-3x^(1/4)
restive river
yea i get that
restive river
that makes so much sense now that’s crazy 🤯
restive river
thanks for being patient btw 😭🙏
faint gorge
no problem!
restive river
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restive river
how do i solve this like i am so stuck on ts
devout snowBOT
how do i solve this like i am so stuck on ts
junior flax
What is -2/5 divided by 1/2
past moat
how do i solve this like i am so stuck on ts
i would recommend if u have a pen and paper
restive river
i would recommend if u have a pen and paper
i do
past moat
write it in a form thats easier to look at
junior flax
We can rewrite it as -((2/5)/(1/2))
past moat
yep^^^^
past moat
okay
past moat
what answer did u get
restive river
-4/5
restive river
thx
past moat
np
restive river
nope just what the question says
past moat
fraction means write -4/5
restive river
i have more questions if ur willing to help me
restive river
alright wait
past moat
this isnt ur exam right? 💀
past moat
its obvious 😭
past moat
fine
restive river
ts one next
junior flax
ts one next
I recommend box method
restive river
I recommend box method
box method looks to hard for me
past moat
i recommend name 3x^5 name it u
junior flax
box method looks to hard for me
It’s just multiplication, you got it bro
past moat
and name y^3 name it p
restive river
so (x^5)^2 will give u x^10
i dont understand how u did this
restive river
It’s just multiplication, you got it bro
hell nah bro the teacher said this will be the hardest course ever
junior flax
i dont understand how u did this
Exponent rule
past moat
hell nah bro the teacher said this will be the hardest course ever
dont trust her
she lying fr
scaring u fr
junior flax
hell nah bro the teacher said this will be the hardest course ever
You’re teacher’s capping
past moat
yeah im still confused
is it a timed exam?