im not crazy then!
#help-19
manic ibex
manic ibex
thank you for your help!
manic ibex
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wanton bison
I was actually referring to [ \log_{b^n}(x) = \frac{1}{n} \log_b(x) ]
clever fjordBOT
bacc the sigmašš¤
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wispy turtle
Hey! Iām really confused how to go about this question, like I honestly donāt really know where to start and I would love some help on how to approach this.
odd edgeBOT
Hey! Iām really confused how to go about this question, like I honestly donāt re...
brittle beacon
You know how to reduce matrices to RREF using row operations, right? (Considering weāve done that before 
)
brittle beacon
Cool, and you know that carrying out a row operation is the same as multiplying by a certain matrix, right?
wispy turtle
Yes, I kind of understand that concept
brittle beacon
Cool, so bearing in mind each operation you carry out is the same as multiplying by a certain matrix, do you know what those matrices look like for each type of operation?
Say if you wanted to take the second row of the original and add the first row to it, what would the matrix that does that look like?
wispy turtle
Hereās my work for the RREF and
wispy turtle
Say if you wanted to take the second row of the original and add the first row t...
As for this
Im not too sure, I guess would it just be the result of that operation? š
Or would it be
Like an elementary matrix
brittle beacon
Like an elementary matrix
Yes, an elementary matrix, exactly those!
wispy turtle
Iām not too sure what they are supposed to look like to be honest I just know the idea that every row operation is like multiplying with an elementary matrix š
brittle beacon
Awwww, fair enough 
Well, there are two ways to do it, one way you might like-
Actually, would I even explain myself well 
wispy turtle
I will try to understand !!
brittle beacon
Anyways, we know that U should be 3x3, right? (by the fact it's invertible, so needs to be square, and that we intend to left multiply A by it, and A has three rows, so U needs three columns)
brittle beacon
Cool, so anyways, the idea is that as left multiplying by elementary matrices corresponds to carrying out row operations, what I'm gonna do is take your RREF matrix, and augment it with the 3 x 3 identity matrix, so
Like
[
\begin{pmatrix}
1 & 0 & 5 & 5 & 1 &\bigm| & 1 & 0 & 0 \
0 & 1 & 2 & 1 & 1 &\bigm| & 0 & 1 & 0 \
0 & 0 & 0 & 0 & 0 &\bigm| & 0 & 0 & 1 \
\end{pmatrix}
]
clever fjordBOT
@brittle beacon
wispy turtle
Okay that makes sense
brittle beacon
Now, if I do the row operations you did in reverse, I would get the original matrix A back on the left, but then I'll have a new matrix on the right hand side
But, the matrix that'll be on the right will actually be U 
as before, each row operation corresponds to multiplying by a certain elementary matrix, and so we'd be multiplying R by an elementary matrix, but also the identity
So slowly by slowly, we'll build up the matrix U as we do the row operations backwards 
if any of that is clear?
wispy turtle
<@788085606483361802>
Like you want me to do the steps I did but backwards and apply them to both the augmented matrix and identity matrix here ?
brittle beacon
Yep 
wispy turtle
Like my last step was to do r3+r2 when I was getting that rref but now Iāll do that first?
And then whatever I get as the 3x3 matrix is U?
brittle beacon
<@788085606483361802>
Yep, basically do all the row operations but doing them backwards, as your last step was adding row 2 to row 3, now you want to subtract row 2 from row 3 here
(this way also has the benefit of not making you have to find the elementary matrices forms, but I'll try and dig for one of those)
wispy turtle
Ahh I see and if I did R1 -3r2 does that mean Iād do r1+3r2 instead?
brittle beacon
Ahh I see and if I did R1 -3r2 does that mean Iād do r1+3r2 instead?
Yep if you divided a row by some non zero scalar, multiply by that scalar instead and all 
brittle beacon
Yep, that should be U, now 
,w [[1, 3, 0], [-1, 0, 0], [3, 8, 1]] *[[1, 0, 5, 5, 1], [0, 1, 2, 1, 1], [0, 0, 0, 0, 0]]
clever fjordBOT
brittle beacon
It works 
wispy turtle
Yes ! Thank you so much :))
So any time I want to approach a problem like this I just
Do the opposite operations and backwards
After finding the RREF form and putting a square identity next to it
Ofc the square identityās size would be dependent on how many rows the rref has
brittle beacon
Yep, pretty much!
If instead they gave you the matrix A, with RREF matrix R, and they said to find the matrix U such that UA = R, then you could just augment the matrix A to begin with by the identity, and carry out row operations until the A gets RREFed, you won't need to go backwards and would find U instantly in that case
wispy turtle
So like youāre saying say they gave you
A = [1 3 11 8 4]
[-1 0 -5 -5 -1]
[3 8 31 23 11]
And
R = [1 0 5 5 1]
[0 1 2 1 1]
[0 0 0 0 0]
Then Iād just do
[1 3 11 8 4 | 1 0 0]
[-1 0 -5 -5 -1 | 0 1 0]
[3 8 31 23 11 | 0 0 1]
And do row operations
To get rref then Iād get U
Just want to be clear in case I get a question like that on the exam
brittle beacon
Yep, if they asked the question in the opposite way, they just give you A, and tell you to find the RREF matrix R, and the matrix R such that UA = R, then you'd do it just like that, keep going until the left hand side is in RREF, and then take that as R, and take the right as U
Argh, wording 
wispy turtle
Okay that makes so much sense thank you so much, have a great day/night ! š
brittle beacon
You too 
oh yeah, also-
These are the elementary matrices and how they should look like
Just in case you were curious on their form 
flat mortar
odd edgeBOT
flat mortar
i dont understand this
forest sky
which part don't you understand?
forest sky
it's a constant multiplied by some function
flat mortar
oh i get tit
so the first deravtive is 5x^4 -4ex^4x right
then times 4
ok i think i get it now
can you help me with one more?
odd edgeBOT
No need to ask āCan I askā¦?ā or āDoes anyone know aboutā¦?āāitās faster for everyone if you just ask your question! See https://dontasktoask.com/
odd edgeBOT
@flat mortar Has your question been resolved?
signal rampart
this was wrong. Im a bit confused as to why
odd edgeBOT
this was wrong. Im a bit confused as to why
mystic saffron
this was wrong. Im a bit confused as to why
Try differentiating ln(xy) again
signal rampart
Try differentiating ln(xy) again
I differentiated lnxy by doing 1/(xy) times dydx but my teacher told me that was wrong
mystic saffron
Did you use the log rule or chain rule
Log would be ln x + ln y
Which gives 1/x + 1/y * dy/dx
signal rampart
Honestly in general i do not understand chain rule
like i understand what it means for āa function to be inside a functionā but it seems arbitrary as to when that applies to differentiating
does it only apply when something is to the power of something??
signal rampart
Did you use the log rule or chain rule
but i thought the derivation of lnx was 1/x
why does this not apply
mystic saffron
The derivative of ln x is 1/x
But
The derivative of ln u for any u
Is uā/u
The derivative of the inner function over the inner function
signal rampart
my friend told me this is correct but i dont understand what she means by āthis is bc of chain rule!ā
signal rampart
The derivative of ln u for any u
why is this?
ocean torrent
why is this?
Because u is a substituted function, whereas x is 1 variable
differential of ln(f(x)) = f'(x)/f(x)
it's actually the exact same thing for ln(x)
if f(x) = x, then f'(x)/f(x) = 1/x
Differentiation of ln(x) = 1/x because it's the differential of what's inside the ln, which is just 1, divided by the actual function inside the ln, which is x
If you make u = x^2, then if you differentiate ln(u), it should make sense that it's not gonna be 1/u
Because if you substitute it back out, you're saying that the differential of ln(x^2) = 1/x^2, but it would actually be 2x/x^2, which is 2/x
odd edgeBOT
@signal rampart Has your question been resolved?
signal rampart
Because u is a substituted function, whereas x is 1 variable
differential of ln...
im sorry, i dont know what you mean by substituted function or variable
well i know what those words mean on their own but i dont understand the connection from those to here
odd edgeBOT
@signal rampart Has your question been resolved?
odd edgeBOT
@signal rampart Has your question been resolved?
odd edgeBOT
@signal rampart Has your question been resolved?
fallow wagon
Any tips to find the roots of this equation? I tried isolating the exponential functiom and using logs but it just becomes a mess
odd edgeBOT
@fallow wagon Has your question been resolved?
polar creek
do you need to find the answer analytically?
fallow wagon
do you need to find the answer analytically?
i need a value for x
i need to prove that the equation has 4 real roots
polar creek
well you could always use numerical methods lol
fallow wagon
well you could always use numerical methods lol
how?
polar creek
any one of them works, look for the bissection method
but tbf i think there's something wrong with your solution
mainly on step (4)
the log one
fallow wagon
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odd edgeBOT
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past temple
I need help with this
odd edgeBOT
I need help with this
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@past temple Has your question been resolved?
past temple
.close
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whole hazel
Help me understand pls
odd edgeBOT
Help me understand pls
umbral wadi
Help me understand pls
Wow very hard question
whole hazel
I understand we must use the formula, but why can't I use my method?
unborn dragon
I understand we must use the formula, but why can't I use my method?
what's your method?
whole hazel
what's your method?
unborn dragon
that's right too
but using the difference of cubes formula gives you the answer in a single step
whole hazel
that's right too
I didn't get the right answer though, miscalculation?
unborn dragon
wait
whole hazel
Why not?
unborn dragon
(x+y)(x+y)(x-y) ā xĀ³ - yĀ³
whole hazel
Oh shit
unborn dragon
xĀ³ - yĀ³ = (x-y)(xĀ²+xy+yĀ²)
use this formula
and it cancels out the denominator
whole hazel
xĀ³ - yĀ³ = (x-y)(xĀ²+xy+yĀ²)
I understand this formula must be used but, can I get even more barebones, yfm?
unborn dragon
I understand this formula must be used but, can I get even more barebones, yfm?
it's a prove sum
whole hazel
Like I don't wanna remember that, I'd rather do the bare bones shit n build up
unborn dragon
bro doesn't want to remember formulas šš
whole hazel
(x+y)(x+y)(x-y) ā xĀ³ - yĀ³
My understanding was this:
I did (x+y)(x^2-y^2) and I though "Oh difference of squares", so I went deeper and said (x+y)(x+y)(x-y)
nocturne brook
Like I don't wanna remember that, I'd rather do the bare bones shit n build up
you might be able to do polynomial long division
broken leaf
yo Bryan can u help me jf my answer correct, LAST that's my last request
unborn dragon
yo Bryan can u help me jf my answer correct, LAST that's my last request
sure
whole hazel
It makes sense w/ distributivity, but I don't trust myself to remember it type shit so I'd rather go all da way to step 1
whole hazel
My understanding was this:
I did (x+y)(x^2-y^2) and I though "Oh difference of ...
Can you point out the flaw in my thinking?
Ok I hear ya, I'll do that
I feel you
Imma do that, ty
whole hazel
Can you point out the flaw in my thinking?
But can you answer this last Q for me please?
I was trynna go deeper
Like go from cube to square to everything one
yfm
Nah, just stupid
Yes exactly
It doesn't go down to ^1 ey?
It still a cube type shi?
Yk what ima continue w/ the exercises and see if I can fill in the gaps myself, if not I'll hyu
Thank you for the help + time though bro, I appreciate it
.solved
odd edgeBOT
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limber cove
this graph is wrong, right?
odd edgeBOT
this graph is wrong, right?
limber cove
it should be f(x) against x
the piecewise function graphed is f(x) not y. Also, dy/dx wont exist if y looked like that, its not differentiable
also
y(0) = 0
loud yoke
hi guys i am new here
limber cove
wrong chat brev
odd edgeBOT
@limber cove Has your question been resolved?
limber cove
it should be f(x) against x
right?
odd edgeBOT
@limber cove Has your question been resolved?
odd edgeBOT
@limber cove Has your question been resolved?
odd edgeBOT
@limber cove Has your question been resolved?
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Available help channel!
mystic saffron
is this doable without using series
odd edgeBOT
is this doable without using series
clever fjordBOT
quasi sparrow
nope i was wrong
odd edgeBOT
@mystic saffron Has your question been resolved?
mystic saffron
<@&286206848099549185>
cold sleet
<@&286206848099549185>
What question
mystic saffron
is this doable without using series
this
cold sleet
Uhm
cold sleet
like variation of params
Alright so there is no need to apply variation of parameters, as it doesnāt suit this problem
mystic saffron
alr
cold sleet
No problem
odd edgeBOT
@mystic saffron Has your question been resolved?
white dagger
Can anyone help me with a question about data analyze
elder cliff
cant be 100% sure but B seems like better option
elder cliff
yep sure b
odd edgeBOT
@white dagger Has your question been resolved?
white dagger
It was A š, but I got it right
obsidian robin
Help
sterile blaze
what is fg?
strong sentinel
f(g(x))
mystic saffron
How i find
mystic saffron
How i find
its 2/3
odd edgeBOT
@obsidian robin Has your question been resolved?
mystic saffron
pls help is the first answer choice right thats what i chose but idk
mystic saffron
only have one try left
green elm
no
mystic saffron
dang
green elm
!nosols
odd edgeBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
lament turtle
it's over lmao
mystic saffron
right
@mystic saffron
wtf @mystic saffron don't you even know zeroes of polynomial
idec ab math twin
@mystic saffron yes y = x . (x-4)
tyy
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Available help channel!
mystic saffron
for LDU factorization of a matrix
odd edgeBOT
for LDU factorization of a matrix
nocturne belfry
i saw that
mystic saffron
mb :(
mystic saffron
https://www.youtube.com/watch?v=jQMlwCNJQUc
oh yea is it okay if you explain to me the purpose of LU decomposition?
because wouldnt you solve the system finding U anyways?
nocturne belfry
These decompositions usually have nice properties that tend to crop up later
a lot of them are nice for inverse problems
so usually you can assume they're useful by virtue of being named
mystic saffron
so its not for solving for the x vector right
nocturne belfry
I think it has applications for solving linear systems, yea
I just know of the inverse application off the top of my head
mystic saffron
like the linear system application isnt the important thing
but its mostly for the inverse application
nocturne belfry
but its mostly for the inverse application
mostly isnt something I would say
nocturne belfry
They are just tools I mean is a hammer mainly useful because it can hit nails
in a intro linear algebra course, yea you're probably interested in the systems
but maybe inverse too idk 
nocturne belfry
but if you are looking at an inverse problem, that isn't going to matter to you
etc etc
nocturne belfry
you can just create D from either, IIRC
so it can kind of depend on the class and what definition youre using
nocturne belfry
,w LUDecomposition[ { {2, 4}, {4, 11} } ]
clever fjordBOT
nocturne belfry
i guess we have to do some work 
well, this is better left to you, maybe
you can leave it like that
i'll tex it for you
mystic saffron
so i have [ {1, 0}, {2, 1} } ] [ {2, 0}, {0, 3} ] [ {1, 2}, {0, 1} ]
nocturne belfry
$L = \mqty( 1 & 0 \ 2 & 1 )$ and $D = \mqty( 2 & 0 \ 0 & 3 )$ and $U = \mqty( 1 & 2 \ 0 & 1 )$
clever fjordBOT
jan Niku
mystic saffron
thats the right answer right?
nocturne belfry
yea
nocturne belfry
imma do the second matrix rq, is it okay if you double check my work
on the first
I have something you can try
assume that X is symmetric
so say like
$X = \mqty( \uparrow & N \ N & \downarrow )$
clever fjordBOT
jan Niku
$X = \mqty( \uparrow & N \\ N & \downarrow )$
jan Niku
and we say $L = \mqty(1&0\\ \ell & 1 )$ and $U = \mqty( 1&u\\0&1)$
jan Niku
oh, and $D = \mqty( D_1 & 0 \\ 0 & D_2)$
nocturne belfry
multiply it out
$X = \mqty( \uparrow & N \ N & \downarrow ) = \mqty(1&0\ \ell & 1 ) \mqty( D_1 & 0 \ 0 & D_2) \mqty( 1&u\0&1)$
clever fjordBOT
jan Niku
nocturne belfry
we dont have to go too crazy
$LDU = \mqty( D_1 & D_1 U \ \ell D_1 & \ell D_1 U + D_2 ) = \mqty( \uparrow & N \ N & \downarrow )$
clever fjordBOT
jan Niku
$LDU = \mqty( D_1 & D_1 U \\ \ell D_1 & \ell D_1 U + D_2 ) = \mqty( \uparrow & N \\ N & \downarrow )$
nocturne belfry
what do you notice
mystic saffron
$L = \mqty( 1 & 0 & 0 \ \ 4 & 1 & 0 \ \ 0 & 1 & 1 )$ and $D = \mqty( 1 & 0 & 0 \ \ 0 & -4 & 0 \ \ 0 & 0 & 4)$ and $U = \mqty( 1 & 4 & 0 \ \ 0 & 1 & -1 \ \ 0 & 0 & 1 )$
pain
clever fjordBOT
depresso
mystic saffron
lmfao
mystic saffron
what do you notice
is l D1 = D1 U ?
nocturne belfry
yea
nocturne belfry
is l D1 = D1 U ?
and whats D1 
mystic saffron
first entry
nocturne belfry
yea
mystic saffron
which is 1
nocturne belfry
no
nocturne belfry
no
$LDU = \mqty( D_1 & D_1 U \ \ell D_1 & \ell D_1 U + D_2 ) = \mqty( X_1 & N \ N & X_2 )$
clever fjordBOT
jan Niku
$LDU = \mqty( D_1 & D_1 U \\ \ell D_1 & \ell D_1 U + D_2 ) = \mqty( X_1 & N \\ N & X_2 )$
mystic saffron
oh X1
mystic saffron
x1*U
nocturne belfry
alright
which is equal to what
we can just start reading stuff off, is what i mean
and assembling results
if you try to do it all in your head you might get a little mixed up
but its very straightforward
clever fjordBOT
jan Niku
nocturne belfry
then what do we know abbout L and U
mystic saffron
wait how does x1 * U get to N
nocturne belfry
wait how does x1 * U get to N
we get 4 equations from a 2x2 matrix equality
each entry-wise
nocturne belfry
$LDU = \mqty( D_1 & u D_1 \ \ell D_1 & \ell u D_1 + D_2 ) = \mqty( X_1 & N \ N & X_2 )$
clever fjordBOT
jan Niku
nocturne belfry
so, yea, you can just sit and read off everything
but, the important part
u = l
so what do we know about L and U?
mystic saffron
is the answer that L and U just flipped along the diagonal?
mystic saffron
transposed ?
nocturne belfry
yea, so L^T = U
mystic saffron
and U^T=L
nocturne belfry
yea
mystic saffron
is this for any m x m matrix
nocturne belfry
you feel comfortable using symbolab?
mystic saffron
oh wait this is only the case for LDU not LU right
nocturne belfry
oh wait this is only the case for LDU not LU right
we could always try ...
i didnt do any crazy math
mystic saffron
you feel comfortable using symbolab?
yea
nocturne belfry
$X = \mqty( X_1 & N \ N & X_2 ) = \mqty( \ell _1 & 0 \ \ell _2 & \ell _3 ) \mqty( u_1 & u_2 \ 0 & u_3)$
clever fjordBOT
jan Niku
nocturne belfry
now, we want symbolab
or, maybe you want to do the 3x3 case for LDU
see if it holds true
we definitely want symbolab
mystic saffron
hmm how do i input this
nocturne belfry
$\mqty( X_1 & N \ N & X_2 ) = \mqty( \ell _1 u _1 & \ell _1 u_2 \ \ell _2 u _1 & \ell _2 u_2 + \ell _3 u _3 )$
clever fjordBOT
jan Niku
nocturne belfry
maybe not so easy
nocturne belfry
I don't think youre allowed to use it
odd edgeBOT
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haughty granite
The equation used here is much larger than the actual question being asked, sorry in advance. I'm not in a place where I can edit LaTeX easily.
However it provides an example of my question. There are various uses of summation and product where the variable D is used in the bounds. Is there any way to inverse this, as in, if I were to write the inverse of this equation in terms of D?
This is my first time doing this, so sorry if I did something incorrect. Please tell me if I did.
Also how do you edit LaTeX in a chat? Sorry
quasi sparrow
The equation used here is much larger than the actual question being asked, sorr...
Can't answer anything if you don't define variables
haughty granite
Got it so put simply
$y=\sum^x_{n=0}(f(n))\Define in terms of x.$
Is there any way to invert this, like as x= instead of y=?
clever fjordBOT
Qwertious
quasi sparrow
Not generally no
haughty granite
So there's basically no way to get the inverse of a calculus equation? I need it to be like x^2 and sqrt(x), where you provide the output for the equation and you receive the input
quasi sparrow
**Qwertious**
There's zero calculus here
What is "it" that you need to be x^2 or sqrt x
haughty granite
I'm just referring to the fact that they are inverse, where if f(x) = x^2, then f(2) = 4. Whereas the opposite is true of g(x) = sqrt(x), f(4) = 2.
I figured there had to be something like that for summation and product. The reason I need it is for a code snippet I am making, and I just need to be able to provide the outputs of the equation and get the inputs back.
odd edgeBOT
@haughty granite Has your question been resolved?
quasi sparrow
I'm just referring to the fact that they are inverse, where if f(x) = x^2, then ...
Yes inverting functions like x^2 are easy
quasi sparrow
**Qwertious**
Inverting functions like 1 + 1^2 + ... + (x-1)^2 + x^2 is harder
So unless you provide a very simple f(n), it's unlikely to find an inverse of y
,w sum of first n^2
E.g. when f(n) is n, n^2, n^3, it's doable
haughty granite
What about product? Like $\prod^x_{y=0}(z)$?
clever fjordBOT
Qwertious
haughty granite
Even without simplification, there's no way to write
$a=\prod^x_{y=0}(z)$, in terms of x
?
clever fjordBOT
Qwertious
quasi sparrow
Even without simplification, there's no way to write
haughty granite
I see that, but I haven't found how it relates to products
Or in what way it could be used to construct an inverse
It seems to only take one input where products take three, and doing some quick research haven't found anything about their connections with products
Or I'm an idiot, because apparently I am
I just figured out that, yes, the product I showed is very close to the factorial function, but there's a bit of a difference that I need that I don't think the inverse gamma can deal with
Okay I'm sorry for keeping on changing the equation, but I think what I'm really asking for is this:
$a=\prod^x_{y=0}(z-x)$, in terms of x
clever fjordBOT
Qwertious
haughty granite
I don't think inverse gamma can deal with this, but I could be wrong
I'm going to close this for now but I know more about what I need now, thank you for your help
.close
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dapper raptor
Given 3 points, A, B, C
odd edgeBOT
Given 3 points, A, B, C
dapper raptor
What does it mean by altitude through B in the triangle ABC
is it a line passing through B, that is perpendicular to AC?
pale atlas
is it a line passing through B, that is perpendicular to AC?
The altitude of a triangle is the perpendicular line segment that extends from a vertex of the triangle to the side opposite that vertex
dapper raptor
so is B the vertex?
I get the concept, it's just the wording that I'm not so sure about
rancid leaf
yes, b is the vertex in this case
pale atlas
I get the concept, it's just the wording that I'm not so sure about
Yes from B to AC perpendicular line
dapper raptor
ah fair enough, thanks!
rancid leaf
is it a line passing through B, that is perpendicular to AC?
this is half correct, it's not just passing through, it's ending at b
so yeah :]
dapper raptor
wait, why do they say "through" then?
rancid leaf
hmm, ur right about the wording on that one, usually the altitudes are contained within the triangle though afaik? lemme look up the definition for you rq...sorry if i was misleading š
dapper raptor
Nah, that's fine hahaha
It's the test that are usually confusing
I thought I got away with english after choosing maths degree lol
pale atlas
hmm, ur right about the wording on that one, usually the altitudes are contained...
If the figure is extending it can be through as well, important point is it will be perpendicular to AC
rancid leaf
okay, they're not always contained, but often appear so, just go with the wording on this one
rancid leaf
If the figure is extending it can be through as well, important point is it will...
thank you for the correction!!
pale atlas
thank you for the correction!!
Also altitude is height of triangle so it will not pass through AC
But I can't see the figure for their question
dapper raptor
yeah, fair enough
there was no figure, it was just words
I'm just looking to find the length of that altitude
so I'll probs use projection
pale atlas
there was no figure, it was just words
-Thunder```alrighty, good luck!!
muted scaffold
How can u definitively know this has more than 1 solution without using like desmos
tacit haven
if a < b and g(a) < 0 but g(b) > 0 or g(a) > 0 but g(b) < 0 then theres a solution in [a, b]
sweet cloud
How can u definitively know this has more than 1 solution without using like des...
!1c
odd edgeBOT
How can u definitively know this has more than 1 solution without using like des...
Please stick to your channel.
tacit haven
for example g(1) < 0 but g(10) is definetly > 0 so there exists a solution in (1, 10)
but g(-2.5) > 0 so theres a solution in (-2.5, 1)
so we now know theres atleast 2 real solutions
tacit haven
if a < b and g(a) < 0 but g(b) > 0 or g(a) > 0 but g(b) < 0 then theres a solut...
a way to intuitively prove this is that if we have a point a < 0 and b >0 then there must be a line connecting those 2 points, thus passing through y = 0
@muted scaffold
sweet cloud
The function has to be continuous too
tacit haven
well yeah but g(x) is obviously continuous
sweet cloud
well yeah but g(x) is obviously continuous
I meant that they should know this for other problems
tacit haven
oh okay
austere nebula
can the number be negative?
muted scaffold
for example g(1) < 0 but g(10) is definetly > 0 so there exists a solution in (1...
Oh ok thanks
Thats
A nice method
sweet cloud
How can u definitively know this has more than 1 solution without using like des...
You could just put g(x) = 3 , you'll have three solutions which means it's not injective
tacit haven
oh yeah i completely forgot
sweet cloud
Your method is good too, it'll definitely be useful in the future for him
odd edgeBOT
@muted scaffold Has your question been resolved?
boreal musk
Help me spot the mistake I made in this problemā¦. Itās from binomial distribution
odd edgeBOT
Help me spot the mistake I made in this problemā¦. Itās from binomial distributio...
boreal musk
P is supposed to be 1/3
sinful pike
are you allowed to use a calculator or do you have to do it by hand?
unborn dragon
Help me spot the mistake I made in this problemā¦. Itās from binomial distributio...
isn't it (1-p)Ā²?
the third step from the bottom
boreal musk
are you allowed to use a calculator or do you have to do it by hand?
Calculators allowed āŗļø
sinful pike
Calculators allowed āŗļø
highly recommend doing 2nd -> dist -> binompdf then
if you have a ti 83 or 84
boreal musk
Only simple calculators my guyā¦ā¦ š„²š„²
sinful pike
oh
unborn dragon
Only simple calculators my guyā¦ā¦ š„²š„²
you're ignroing me
š
here's your mistake
unborn dragon
Help me spot the mistake I made in this problemā¦. Itās from binomial distributio...
boreal musk
you're ignroing me
Nah broā¦ I cancelled 2 from LHS
unborn dragon
it's (1-p)Ā² on lhs and (1-p)ā“ on rhs
you're cancelling out the entire term
so it's (1-p)Ā²
boreal musk
Yes
boreal musk
Ooooh so 1+p^2
unborn dragon
consider it (1-p)Ā² and here's your answer
boreal musk
Thanks bro
unborn dragon
it's jsut a minor mistake
unborn dragon
Thanks bro
you're welcome š«
boreal musk
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dapper raptor
evaluating LHS and RHS limits
odd edgeBOT
evaluating LHS and RHS limits
dapper raptor
How do we normally go about doing this?
weary pelican
when x -> 1 from the left, then f(x) = (x-4)/|(x-1)(x-2)|, and it could help knowing the sign of what's inside the absolute value
weary pelican
to find the limit of f(x) when x approaches 1 from the left hand side
you have to find what f(x) is equal to when x is close to 1, but not equal to it
AND x is on the left of 1
(if we're looking for the LHS limit)
dapper raptor
if it's very close to 1, both LHS and RHS would just go to infinity
oh wait, it would be negative infinity since numerator would be -
weary pelican
yes that's one way to do it
since the denominator always goes to positive 0
and the numerator is negative
LHS and RHS both go to -infinity
dapper raptor
can you give an example of when the LHS and RHS limit is not the same? I'm not familiar with one
weary pelican
1/x
elfin bear
he made a mistake?
odd edgeBOT
he made a mistake?
elfin bear
i only know it can be < or <=
mystic saffron
he made a mistake?
dim W is not a set and neither is dim U
weary pelican
he made a mistake?
yes it's either $W\subseteq U$ or $dim(W) \leq dim(U)$
clever fjordBOT
rafilou is not not born in 2003
weary pelican
one implying the other
odd edgeBOT
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raven nebula
how can i express this in terms of x?
odd edgeBOT
how can i express this in terms of x?
@raven nebula Has your question been resolved?
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raven nebula
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wanton bison
how can i express this in terms of x?
Do you need help
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mystic saffron
.help
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Type .help <command name> for more info on a command.
mystic saffron
.help rational equation
odd edgeBOT
No command called "rational" found.
steady valley
GUYS GUYS GUYS
odd edgeBOT
GUYS GUYS GUYS
steady valley
VERY IMPORTATNTNTNTNT
im SO GODDAMN CLOSE
volumetic flow rate is -0.098175m cubed per second
average velocity is 12.5 meters per second
reyrolds number is 1250000
YESSSSSSSSSSSSS
GUYSSSS
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@steady valley Has your question been resolved?
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proven harbor
how can i express this in terms of x?
You can say that xĀ² + yĀ² = 32Ā²
Then substitute x or y and differentiate
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spark saffron
am i right in thinking that for $$s = {x|x = 1/n ,n=1,2,3...}$$ the limit set is empty? because there are always many real between the elements of s so there will be a deleted neighbourhood that contains non of the values of S, only members of R not in S
clever fjordBOT
lewis_f04
spark saffron
i guess that the point im confused about is 0; 0 has elements of S that get arbitrarily close to it. however, there are elements between 0 and these arbitrarily small points in S that are between them and not in s. Can limit points contain in their neighbourhood an element that isnt in S?
odd edgeBOT
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spark saffron
<@&286206848099549185>
mystic saffron
yessir
whats your questions
hmm
i dont think the limit set is empty
since as x āā 1/n gets closer and closer to 0
spark saffron
since as x āā 1/n gets closer and closer to 0
if x is in the limit set, the neigbourhood of x can contain elements not in S?
mystic saffron
if x is in the limit set, the neigbourhood of x can contain elements not in S?
yes
spark saffron
yes
ok, so because the elements in S get close to 0, the is an element of S in 0s epsilon neighbourhood, and regardless of wether there is an element in this neighbourhood that isnt in S, 0 is still a limit point?
mystic saffron
exactly
spark saffron
perfect thank you so much!!
mystic saffron
very nice
mystic saffron
perfect thank you so much!!
np
odd edgeBOT
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whole ledge
Ace Machine Works estimates that the probability its
lathe tool is properly adjusted is 0.8. When the lathe
is properly adjusted, there is a 0.9 probability that
the parts produced pass inspection. If the lathe is out
of adjustment, however, the probability of a good
part being produced is only 0.2. A part randomly
chosen is inspected and found to be acceptable. At
this point, what is the posterior probability that the
lathe tool is properly adjusted?
whole ledge
nvm
warped glacier
.close
lunar fable
i need help with basic maths, where does 1560 come from?
quasi sparrow
,calc 30 * 52
clever fjordBOT
Result:
1560
they put the two fractions over a common denominator
nimble blaze
the radical should also be longer to make it clear what its covering
odd edgeBOT
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bronze shell
Can somebody help me with finding m so that f(x) can exist
dapper canyon
@mystic saffron can help
bronze shell
I know that whatever is under the radical needs to not be negative
cursive arrow
I know that whatever is under the radical needs to not be negative
it says already that f: [0, +inf) so you do not really need to work on that
bronze shell
the fact that f is defined on the interval [0,+inf) means that x is positive but the equation can still be negative for some values that m can take
patent idol
Someone help , what do i do
odd edgeBOT
Someone help , what do i do
odd edgeBOT
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rancid sundial
I just need someone to solve this and explain because how Iāve solved it so far Iām getting the wrong answer
rancid sundial
My work so far
quasi sparrow
,rotate
clever fjordBOT
quasi sparrow
if you just need an answer plug it into a system of equations solver online
coral palm
on the right most 20x + 15y + 35z the addition is wrong
coral palm
and the minus -23 * -21 is not 231
where did you get the -80 above -231 from
odd edgeBOT
@rancid sundial Has your question been resolved?
mystic saffron
Related Rates Problems:
odd edgeBOT
Related Rates Problems:
mystic saffron
a pebble is dropped into a pond and the ripples form concentric circles. the radius of the outermost ripple is changing at 1 ft/s. at what rate is the area changing when the radius is equal to 4
is the answer to this one just 8pi ft/s?
odd edgeBOT
@mystic saffron Has your question been resolved?
dire kite
Hi!
dire kite
I'm a little confused with how to draw vector diagrams
Ignore the scribblings over it
From the question, if the wind is blowing due east, why doesn't the arrow start on the positive x axis?
Why does it start on the negative x axis?
odd edgeBOT
@dire kite Has your question been resolved?
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@dire kite Has your question been resolved?
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@dire kite Has your question been resolved?
mystic saffron
mystic saffron
I closed the last one
dense sonnet
are you expected to use L'Hopitals?
upper sphinx
what if we multiply by the conjugate then use the property that lim x-->0 (1-cosx)/x=0
didn't work it out, just my first thought
mystic saffron
what if we multiply by the conjugate then use the property that lim x-->0 (1-cos...
idk this
I haven't learned that property
what can I do?
elfin zodiac
Hint: 1-cosx=2sin^2(x/2)
mystic saffron
Hint: 1-cosx=2sin^2(x/2)
?
elfin zodiac
$\lim_{{x \to 0}} \frac{2 \sin^2 \left( \frac{x}{2} \right)}{x^2 \left( \sqrt{\cos x} + 1 \right)}$
clever fjordBOT
Samuel
elfin zodiac
Are you here already?
mystic saffron
yeah
elfin zodiac
Ok now we separate in 2 products
First 2/(sqrtcosx+1)
Multiplied (sin(x/2))^2/x^2
Correct?
mystic saffron
mm yeah,so 1?
elfin zodiac
Wait
We have x^2 in the denominator
Not (x/2)^2
We need to add this in the numerator and denominator and rearrange
upper sphinx
i got an answer working it that way, not sure if it is right
mystic saffron
We need to add this in the numerator and denominator and rearrange
why?
they need to be equal
elfin zodiac
Multiplied
mystic saffron
ye
elfin zodiac
So u have the first one
mystic saffron
1
mystic saffron
1/4
elfin zodiac
That is the final answer yes
odd edgeBOT
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thin void
this is stats: how do i solve the first question, usuign the graph: The Wall Street Journal reported some interesting statistics on the job market.
One statistic is that 40% of all workers say they would change jobs for "slightly higher
pay." In addition, 88% of companies say that there is a shortage of qualified job
candidates. Suppose 16 workers are randomly selected and asked if they would
change jobs for slightly higher pay. What is the probability that nine or more say yes?
What is the probability that three, four, five, or six say yes? If 13 companies are
contacted, what is the probability that exactly 10 say there is a shortage of qualified
job candidates? What is the probability that all of the companies say there is a
shortage of qualified job candidates? What is the expected number of companies that
would say there is a shortage of qualified job candidates?
thin void
thats the grapgh
this si the question, i need helpsolving the first question attatched
odd edgeBOT
@thin void Has your question been resolved?
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@thin void Has your question been resolved?
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steel spire
yeah using chatgpt for math is whack don't use it if possible
tacit haven
just saying, you shouldnt use chat gpt cause it may get some stuff wrong
steel spire
you know the quadratic formula @supple bluff ?
cool, so the roots are symmetrical on either side of the vertex right
so the +-sqrt(...) stuff is really telling you where from the vertex -b/2a that the two roots are, if that makes sense
so if you know the quadratic formula, you basically know the x value of the vertex.
only other thing you need is the y value for vertex form, so you can just get that by plugging in that x value f(-b/2a) to get it
that make sense? In the end it's f(x) = a(x+b/2a)^2 +f(-b/2a)
try to work through an example or two here and I'll help
odd edgeBOT
Available help channel!
slender saffron
odd edgeBOT
meager juniper
Without knowing more about the function, -1 is a good guess for the average.
forest sky
-1 is the average if we can assume it's sinusoidal
slender saffron
yeah it is, thanks
amber schooner
midpoint between the max and min
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@slender saffron Has your question been resolved?
tight spear
how can i solve this question using long division: (x^4 - 15x^3 + 2x^2 + 12x - 10) Ć· (x^2 - 4)
tight spear
im just confused cauce when im doing it i have to subtract -4x^2 from -15x^3 or im doing something wrong
mental ridge
im just confused cauce when im doing it i have to subtract -4x^2 from -15x^3 or ...
Yep
Whats the issue
odd edgeBOT
@tight spear Has your question been resolved?
gentle valve
How to integrate Ae^(-a2xĀ²) from -ā to +ā where A and a are constant
gentle valve
It is from chemistry stuff.
golden marten
you could have a look at how that's solved, I believe it's a special case called the gaussian integral or something
I can't think of an elementary way to solve it but I've only gone partially through calc 1 and 2
gentle valve
I heard e^(-2xĀ²) integrated from -Ī± to +Ī± is ā(Ļ/2)
gentle valve
How to integrate Ae^(-a2xĀ²) from -ā to +ā where A and a are constant
But this one has an extra a
gentle valve
I heard e^(-2xĀ²) integrated from -Ī± to +Ī± is ā(Ļ/2)
Does it go with the 2 in the denominator?
golden marten
Does it go with the 2 in the denominator?
I think it's /a
gentle valve
I think it's /a
Outside of the root?
golden marten
inside the root
gentle valve
It makes a bit of sense to me.
gentle valve
I heard e^(-2xĀ²) integrated from -Ī± to +Ī± is ā(Ļ/2)
Is there a page with derivation of this?
golden marten
Is there a page with derivation of this?
not sure if this is exactly what you're asking
this should show the derivation of a similar kind of integral
and I assume you can apply the same concepts over
otherwise you could search up the exact integral yourself
odd edgeBOT
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tardy horizon
y/y+2 is it possible to decompose this fraction
odd edgeBOT
y/y+2 is it possible to decompose this fraction
forest sky
decompose how?
tardy horizon
like split the fraction
bitter folio
Wdym
tardy horizon
huh
bitter folio
Like 1-2/y+2
forest sky
y = (y + 2) - 2
tardy horizon
how did u arrive at that value
forest sky
because (y + 2) is the denominator, and adding then subtracting the same number doesn't change anything
tardy horizon
so basically (y/y+2) - (y/y+2)?
forest sky
,, \frac y{y+2} = \frac{(y + 2) - 2}{y + 2} = \frac{y+2}{y+2} - \frac 2{y+2}
clever fjordBOT
cloud
tardy horizon
ah so its something like fake numerator smth (idk if that's the right term)
shell cypress
i got a permutation question its easy but my dumbass cant
shell cypress
forest sky
,rccw
clever fjordBOT
shell cypress
its the total no of ways which is 6 factorial minus 5 factorial right when i consider2 ns as 1 letter
but i get 600 as answer which is not in the option
anyone??
shrewd laurel
Can someone please help me with my math work.
odd edgeBOT
@shell cypress Has your question been resolved?
shell cypress
<@1268965460452315186> Has your question been resolved?
No
jovial isle
40
static totem
@shell cypressthey mean 100
shell cypress
How can you guys explain
static totem
because there's 3 A and 2 N, so you get your 600 permutations have 6 repeats of each
and they want to count them once
shell cypress
Answer given is 40 but idk how u get to that
So when there's repetition I divide right?
Ya I forgot
jovial isle
Step 1: Total Permutations of "BANANA"
The word "BANANA" consists of 6 letters where the letters are not all distinct:
B: 1
A: 3
N: 2
The total number of permutations is given by the formula:
Total permutations=p (n!/p1! * p2! ...*pk!)
Where n is the total number of letters, and p1! p2! ...pk! are the frequencies of the distinct letters.
shell cypress
so this is how u get it right
static totem
oh okay divide by 12
jovial isle
so this is how u get it right
yes
shell cypress
thx a lot
ya i am on a grind i will prob ask more questions later cause the text i am using dont have a solution to the problems
static totem
what's 6*5*4 i don't get it
shell cypress
that 6factorial divided by 3 factorial and the 3factorial in 6factorial gets cancelled
so all left is 6 multiplied by 5 and 4
static totem
okay yeah makes sense
shell cypress
sohow do i close the channel
static totem
type .close
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mystic saffron
I need help with doing this question
odd edgeBOT
I need help with doing this question
mystic saffron
I get how to evaluate
but with the method I am using
it doesnt give me staright forward awnsers
.close
odd edgeBOT
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muted scaffold
how do you do this
odd edgeBOT
how do you do this
wanton bison
What I do is write down what's 5 mod 40, 5Ā² mod 40 etc
56 can be written in factors like 56 = 8 Ć 7
Or 56 = 14 Ć 4
muted scaffold
5^(8) * 5^(7) mod 40 or smthn
Idk how this helps though
warped glacier
how do you do this
well 5^56 is clearly 0 mod 5
now find what 5^56 is mod 4, that should also be easy
so then it must be either 1 mod 8 or 5 mod 8
writing 5^56 = 25^28, you can figure out what it is mod 8
then just combine the two congruences
for instance, you have 5k where k is an integer cause 0 mod 5
muted scaffold
well 5^56 is clearly 0 mod 5
how is 5^56 0 mod 5
warped glacier
how is 5^56 0 mod 5
...........
rotund hawk
muted scaffold
Ok idk how that helps answer the question š
warped glacier
Ok idk how that helps answer the question š
you need to revise basic basic properties of modular arithmetic
if you don't know that if you have $5^{56} \pmod 4$
cause $5 \equiv 1 \pmod 4, 5^{56} \pmod 4 = 1^{56} \pmod 4$
clever fjordBOT
higher's secret twin brother
warped glacier
how is 5^56 0 mod 5
or it might be that you're not aware of the Chinese remainder theorem then
odd edgeBOT
@muted scaffold Has your question been resolved?
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@muted scaffold Has your question been resolved?
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@muted scaffold Has your question been resolved?
static totem
what bacc said is by far fastest in this case
5 25 125 625 3125
mod 40
5 25 5 25 5
so the even powers are all 25, so the answer is 25
just a very fortunate case
narrow crypt
Proof of lamiās theorem
odd edgeBOT
Proof of lamiās theorem
sweet cloak
Thatās really impressive
sweet cloak
donāt worry k im here for you brother
narrow crypt
What should I do
How do I manipulate the parallel lines
Or get the angles of the three vertices of triangles in term of alpha, beta, and gamma
sweet cloak
Idk
narrow crypt
š
sweet cloak
@narrow crypt
What if he wanted to find the work done for just one slice? How would this change?
narrow crypt
One slice?
One slice is just one dy
U donāt have to integrate thatās all
Itāll just approach zero
sweet cloak
U donāt have to integrate thatās all
Hold up so you mean like this
narrow crypt
Can u help me prove lamiās theorem plz
narrow crypt
Hold up so you mean like this
How do u define āone sliceā
Like what is the depth of one slice
sweet cloak
Like what is the depth of one slice
Idk man
oh I guess it would just be delta y and then I donāt specify
sweet cloak
So you would say itās this
narrow crypt
M = density x volume
If 1000 is the density of ur liquid
And width x length = 2
Then thatās correct
sweet cloak
Ok love you
narrow crypt
Can u help me prove lamiās theorem
narrow crypt
<@&286206848099549185>
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faint charm
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faint charm
Hello I got 3 on math test
thanks very much for all your helps šš»
hardest exam in college 
lyric dust
š«” welp lets hope this doesnt go south too quickly
supple shuttle
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