i did C and its wrong
#help-17
hushed pewter
Yeah. It's a bad problem
I sympathize with you, it's so arbitrary
I saw A and C, but answer disagrees with C.
languid dune
F seems a bit far
hushed pewter
Bring this problem up to your teacher. Be sure to use the word "bullshit" a few times
hushed pewter
It's a bad problem
hushed pewter
As a self diagnosed genius, I will assure you that this problem is not worth the effort.
hushed pewter
there can be more than one answer
languid dune
bro that makes ti worse lmao
languid dune
ye im with that too
hushed pewter
F is a maybe, but I think no
vocal sleetBOT
@languid dune Has your question been resolved?
languid dune
Does it at least say the answer?
Nope
sly stag
I have a metric tensor
1 0
0 r^2
which just describes the rate of change of the relative coordinate from polar coordinates to cartessian coordinates right?
So my line element equation would be
ds^2 = 1 * dr^2 + r^2 * dθ^2
Now i simply want to find the length from point r = 1, θ = 0 and r = 2, θ = pi / 2. How would i do that?
vocal sleetBOT
I have a metric tensor
1 0
0 r^2
which just describes the rate of change of the ...
@sly stag Has your question been resolved?
sly stag
<@&286206848099549185>
vocal sleetBOT
@sly stag Has your question been resolved?
vocal sleetBOT
@sly stag Has your question been resolved?
vocal sleetBOT
@sly stag Has your question been resolved?
vocal sleetBOT
@sly stag Has your question been resolved?
timber orchid
this is higher level stuff i think (tensors), maybe there's a another dedicated channel to this stuff?
vocal sleetBOT
@sly stag Has your question been resolved?
flat quartz
I have a metric tensor
1 0
0 r^2
which just describes the rate of change of the ...
I don't know anything about tensors at all but this sounds like a pythagoras theorem problem to me lol
torpid skiff
how can i show that something is a point of inflection using diffrentiation
fervent sparrow
how can i show that something is a point of inflection using diffrentiation
also point of inflections generally apply to functions with a degree higher than 2
so if i take a degree 3 for example, theres gonna be like 2 concavities formed by 3 x-intercepts
ykwim?
fervent sparrow
the x value you get from f"(x)=0 shows you the point at which the concavity changes
torpid skiff
so i just diffrentiate 2 times then show it = 0
fervent sparrow
so i just diffrentiate 2 times then show it = 0
correct terminology is "Solve for x when second derivative of function is 0" but yeah you understood
torpid skiff
correct terminology is "Solve for x when second derivative of function is 0" but...
thanks very uch
fervent sparrow
it wont work for quadratics cuz second derivative becomes a constant n stuff sooo yea
equating it to 0 wont make sense
torpid skiff
it wont work for quadratics cuz second derivative becomes a constant n stuff soo...
yeye this is a ^3
fervent sparrow
yeye this is a ^3
ok you'll definitely get an x
fervent sparrow
np
wary mantle
"If $f$ is injective and $g$ is surjective, then $g \circ f$ is bijective."
wary mantle
Why?
f is injective, sure
g is surjective, sure?
But not really
What about 0? It should be R_0^+, no?
This is just like what we did before with @median crane
wary mantle
its all positive real numbers, and 0 is not positive
I'm saying we have x -> x^2
And for x = 0, we'll have 0
So why does it say R -> R^+
Shouldn't it say R -> R_0^+
patent onyx
true
wary mantle
Though this is written by a professor so maybe not?
patent onyx
your claim is correct
g(0)=0 not a real positive
the professor is wrong on the codomain
magic wasp
R^+ does include 0
It's somewhat ambiguous but most of the time R_*^+ is used to exclude 0
vocal sleetBOT
wary mantle
R^+ does include 0
Oh
magic wasp
The non-ambiguous notation is R_{>=0}
vocal sleetBOT
Available help channel!
young cosmos
How can this rule exist?
vocal sleetBOT
How can this rule exist?
pale perch
could you show the actual rule as it was presented to you
median crane
How can this rule exist?
I think you got the rule wrong. Should be if lim g(x) ≠ 0 then lim of f/g = limf/lim g
visual anvil
yo
dire token
vocal sleetBOT
@visual anvil Has your question been resolved?
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@visual anvil Has your question been resolved?
visual anvil
.close
untold comet
Please help!
vocal sleetBOT
Please help!
untold comet
I haven't leared this yet so I'm not sure what to do
river kettle
Just plot the points first
untold comet
That's the thing idk how
river kettle
Wdym
Just look at the table
At x=-5 you plot a point 7 units above
(-5,7)
And do that for the rest
vocal sleetBOT
@untold comet Has your question been resolved?
drifting jackal
Please don't troll in help channels
vocal sleetBOT
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).
tidal dock
depends on how you define 1 and +
1 apple and another apple make 2 apples together 🤯🤯🤯🤯🤯
crude arrow
Please don't troll in help channels
is it a troll tho to prove that 1+1 = 2
you need a lot
crude arrow
Principia Mathematica took over 1000 pages to prove that 1+1=2
tidal dock
yep
drifting jackal
no problem lmao
I love this one
tidal dock
wonderful
tidal dock
I love this one
@vast shale here you go
waxen portal
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red orbit
I know this relates to trigonometry and would require the use of sin, cos, and tan, but am stuck on how to solve the problem.
vocal sleetBOT
I know this relates to trigonometry and would require the use of sin, cos, and t...
@red orbit Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
fiery crest
(yy')'=5/2(y')^2
vocal sleetBOT
(yy')'=5/2(y')^2
fiery crest
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
haughty warren
vocal sleetBOT
haughty warren
Could somebody please tell me where I'm going wrong
The partial fractions I get don't make sense
fleet ember
A/(x+1) + B/(x+1)² + Cx+D/(x²+1)
= (A(x+1)(x²+1)+B(x²+1)+(Cx+D)(x+1)²)/(x+1)²(x²+1)
hearty dragon
marble kettle
can someone explain?
b/a gives a rational int and the other one shows the relationship between the two numbers and is either true or false
but i still dont understand how that affects these
somber badger
serene cloud
they are all right except the b is 0
i mean a
b divided by a and a can never be 0
marble kettle
oh and i missed one earlier
wait so can there be decimals or they have to be integers?
floral pike
🤔 you can do 0/9, but is 9|0 a true statement or a false statement? Technically, 9 divides 0 zero times
marble kettle
🤔 you can do 0/9, but is 9|0 a true statement or a false statement? Technically...
i have no clue
serene cloud
the denominator (in this case is a) can never be 0, i dont really know why but its a rule in calculus or sth. It can be understand by you cannot divide anything by 0
marble kettle
the denominator (in this case is a) can never be 0, i dont really know why but i...
ah i see so the first term can never be 0
vast shale
🤔 you can do 0/9, but is 9|0 a true statement or a false statement? Technically...
i dont think so
vast shale
since that would imply that there is a number that can be multiplied by 0 to be 9
marble kettle
i meant b|a
serene cloud
but 0/9 is right
serene cloud
since that would imply that there is a number that can be multiplied by 0 to be ...
exactly
marble kettle
its not 0/9 its 0|9
vast shale
yes 0|9 is right
vast shale
yes
vocal sleetBOT
@marble kettle Has your question been resolved?
magic wasp
Wow I think you're all confused
0|a is never right (except if a=0, in some contexts)
$n | m \iff \exists k : kn = m$
twin meteorBOT
Nel
vocal sleetBOT
@marble kettle Has your question been resolved?
marble kettle
<@705255763098075218>
sorry i did not see your message
marble kettle
Can you find a k such that k*0 = 7?
no
i didnt even know what to google to try and find the answer
lol
like to understand the concept
vocal sleetBOT
vocal sleetBOT
Available help channel!
visual anvil
anyone good with spherical coordinantes to cartesian transformation
visual anvil
given the surface of a spherical coordinates: ρ^2 = sec (2φ) where 0 <= φ <= pi/4 express
this surface in Cartesian coordinates and state what type of surface it is.
vocal sleetBOT
@visual anvil Has your question been resolved?
vocal sleetBOT
Available help channel!
fiery bear
can someone help me with the LDE
vocal sleetBOT
can someone help me with the LDE
fiery bear
i have the final answer but its slightly diferent from what the textbook has
this is the textbook solution
These are the roots I’m getting
I dont understand why I cant do this , to get alpha and beta
I thought I could simplify it like that but is it wrong?
nvm I was confusing my self
i kept misclking in my calcualtor... divided whole thing by 3 and realized i didnt need to sepearte cuz theres no imaginary
thanks anyways
.close
torn tree
vocal sleetBOT
torn tree
This is what I have so far, but I feel like I've gone off track.
hard atlas
it might be easier to define a homomorphism Q[x]->Q[sqrtp] and then use the isomorphism theorem
(in general when you see a factor ring in situations like this, the first idea should most of the time be "iso theorem")
torn tree
(in general when you see a factor ring in situations like this, the first idea s...
alr I'll try that out
hard atlas
I'm curious, whats part (1) of the problem?
torn tree
I'm curious, whats part (1) of the problem?
hard atlas
ok
torn tree
It looks deceptively simple, since it's something I could have completed 2 months ago. I feel like there's a catch or something
hard atlas
with iso theorem its not that hard. assuming of course you had that 2 months ago
torn tree
with iso theorem its not that hard. assuming of course you had that 2 months ago
nah the first part of the problem I mean
hard atlas
oh that
well you only need to find inverses
and you already know how to find those in R. so you can find them there first and show that they are actually already in Q[sqrtp]
vocal sleetBOT
@torn tree Has your question been resolved?
torn tree
it might be easier to define a homomorphism Q[x]->Q[sqrtp] and then use the isom...
I'm trying to find the right function but I'm missing it
This is what I tried
Is writing f as (something) + (something)*sqrtp the right approach or do I need to try something else?
hard atlas
the notation Q[x]->Q[sqrtp] already suggest that we should replace x by sqrtp
in other words, the evaluation homomorphism
torn tree
the notation Q[x]->Q[sqrtp] already suggest that we should replace x by sqrtp
I find the notation weird. Is this fine or does it not make sense?
vocal sleetBOT
@torn tree Has your question been resolved?
flat quartz
How to integrate this?
vocal sleetBOT
@flat quartz Has your question been resolved?
flat quartz
No
unborn wind
! status
vocal sleetBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
I tried cosx=u
There is x at the beginnin
1+cos² = u
I thought ain't even worth trying it will give sin*cos etc
Step 1 probably
twin meteorBOT
grizzled halo
are you sure there aren't bounds?
tribal moss
$\int_{0}^{\pi}\frac{xsinx}{1+cos^{2}x}dx=\left[ x=\pi-y \right]
=-\int_{\pi}^{0}\frac{\left( \pi-y \right)\sin\left( \pi-y \right)}{1+\cos^{2}\left( \pi-y \right)}dy=\int_{0}^{\pi}\frac{\left( \pi-y \right)\sin\left( y \right)}{1+\cos^{2}y}dy=\pi\int_{0}^{\pi}\frac{\sin\left( y \right)}{1+\cos^{2}y}-\int_{0}^{\pi}\frac{y\sin\left( y \right)}{1+\cos^{2}y}dy\\<=>\\2\int_{0}^{\pi}\frac{xsinx}{1+cos^{2}x}dx=\pi\int_{0}^{\pi}\frac{sinx}{1+cos^{2}x}dx=\left[ t=cosx \right]=\pi\int_{1}^{-1}\frac{-dt}{1+t^{2}}=\pi\left( \frac{\pi}{4}+\frac{\pi}{4} \right)=\frac{\pi^{2}]}{2}\<=>\\\int_{0}^{\pi}\frac{xsinx}{1+cos^{2}x}dx=\frac{\pi^{2}}{4}$
twin meteorBOT
Joanna Angel
copper pebble
vocal sleetBOT
copper pebble
not sure how to begin
vocal sleetBOT
@copper pebble Has your question been resolved?
flat whale
How did you show that
flat whale
i made the polynomial
Show your work
copper pebble
Show your work
i took the determinant of the matrix by expanding from column 1, which got me:
lambda * (lambda * lambda - 1 * 0) = lambda^3
but i write lambda as z normally
so now we have a polynomial, which can be written as:
(lambda-0)(lambda-0)(lambda-0)
which means the multiplicity of 0 is 3
not sure how to progress here since we don't know the value of lambda
flat whale
flat whale
This shows the solutions for double root. Try to generalize it to a triple root
https://tutorial.math.lamar.edu/Classes/DE/RepeatedEigenvalues.aspx
vocal sleetBOT
@copper pebble Has your question been resolved?
copper pebble
This shows the solutions for double root. Try to generalize it to a triple root
...
We get a triple root yea
For lambda
🙂
copper pebble
<@&286206848099549185>
copper pebble
Just need help with the question
I got triple root for lambda
not sure what to do now
copper pebble
hi
jolly roost
@copper pebble Professional assistance. <@&286206848099549185>
<@&286206848099549185>
<@&286206848099549185>
copper pebble
@flat whale
copper pebble
<@608728365268205642> Professional assistance. <@&286206848099549185>
I think maybe most helpers cant solve a qustion of this difficulty
its quite difficult
copper pebble
yes?
jolly roost
Friend request
flat whale
bernie.madoff
stop spamming
flat whale
We get a triple root yea
did you read the double root solution?
copper pebble
did you read the double root solution?
I don’t get some of the notation
copper pebble
<@&286206848099549185>
copper pebble
can you just ask a question
I just wanted a list of steps to solve it
That’s about it
flat whale
I just wanted a list of steps to solve it
it's described in the link above
flat whale
This shows the solutions for double root. Try to generalize it to a triple root
...
step 1: figure out the solution for double root
step 2: figure out the solution for triple root
copper pebble
I found the triple root
I just want it in a dumbed down way
Because I don’t understand all the notation in your article
flat whale
and be specific
.
flat whale
$\eta$ is a variable
twin meteorBOT
riemann
flat whale
like x, or y
$\vec{x}$ is notation for a vector. in three dimensions, $\vec{x} = (x_1, x_2, x_3)$
twin meteorBOT
riemann
copper pebble
flat whale
In this case, your equation can be given as
$\vec{f}' = A \vec{f}$
twin meteorBOT
riemann
copper pebble
Does this look like my exercise?
flat whale
Does this look like my exercise?
your exercise is 3 dimensions
flat whale
this is 2 dimensions
copper pebble
With Eigenvalues on the diagonal
flat whale
to your problem in 3 dimensions, you should understand 2 dimensions first
copper pebble
this is the solution for the 2d case
right
i still don't understand why we have n ->
and then p ->
what are these variables for
flat whale
and then p ->
i don't understand your questions. they're all explained in the link
copper pebble
I solved it now
Basically just assuming that f_3(t) = 0 and f_2(t) = 0 while f_1(t) = e^lambda*t
Then assuming that f_3(t) = 0 and f_2(t) = e^lambda*t and then calculating f_3(t)
then doing it again but where f_3(t) = e^lambda*t
.close
zinc quail
What's the direct translation of the limes superior using propositional calculus? (for sequences)
vocal sleetBOT
What's the direct translation of the limes superior using propositional calculus...
vernal wigeon
Limit inferior and limit superior
zinc quail
only superior, inferior is trivial if I know the other
after fiddling a bit, this is how I'd translate it
most sites like wikipedia etc. I stumbled upon offer no direct translation this way but I have to use it for proofs
hard atlas
the sequence doesnt have to be smaller than the limsup
zinc quail
the sequence doesnt have to be smaller than the limsup
hm is it not correct given n_0 e N?
hard atlas
no
take any converging sequence. then limsup is the limit. but we know it doesnt have to hold then
zinc quail
so the first expression is correct I presume? but how would I rewrite the second for the equivalence to hold
hard atlas
well you could say the standard "and for all s such that there exists a partial sequence converging to s, you have s<=r"
zinc quail
hm yeah although I'm not sure that helps me with the proof for the criteria such as the root criterion
hard atlas
well you could also just write it as the limit of the supremums
and then unpack all those definitions
zinc quail
I'd have to express something like "if that limit isn't the limit of a_n, then the second statement holds"
ah yeah actually I could directly translate that
@hard atlas probably not a work of art, but it'd be in the form I could use for multiple proofs :3
I think it must be exclusive right, if the lim sup is not the limit, then there must exist an n_0 such that the last statement is true
in turn achieving equivalence
hard atlas
no
the converging sequence was just an example
imagine two converging sequence and alternate between them
the limsup will be the bigger of the two limits
zinc quail
but how does that make the expression false
lim(a_n) = r would then be False
hm nvm right they still wouldn't have to be below
ugh so I need an additional variable for an environment
Ok, so now it either converges to r OR a subsequence converges to r and all values must be within the upper-bound epsilon-environment from n_0 onwards
@hard atlas sry for ping, but I hope it's correct now
vocal sleetBOT
@zinc quail Has your question been resolved?
vast shale
who can help me review slopes?
vocal sleetBOT
who can help me review slopes?
vast shale
.closee
mental falcon
vast shale
.close
left talon
mighty vapor
can anyone confirm if i got this correct?
vocal sleetBOT
can anyone confirm if i got this correct?
@mighty vapor Has your question been resolved?
mighty vapor
.close
snow dune
vocal sleetBOT
snow dune
Im not sure what the trick is for solving this one
sweet birch
well you have a total of N items in the list (find N)
so the number you're looking for is the Nth item
how many elements will start with 1? will this reach the Nth number?
snow dune
well you have a total of N items in the list (find N)
so the number you're looki...
Im not sure this is what is meant by the question
Lets say for example i have an sorted list of 1000 numbers
Then i am looking for the 501'th number
sweet birch
oh sorry! yes, I was looking at the last number of the smallest part
so yes, you'd be looking for the N+1th number
where N is the total ways you can organise the numbers 12345
snow dune
where N is the total ways you can organise the numbers 12345
also the total number of items is just 5!, which is 120
so i am looking for the 61'th number
but im not quite sure how to determine the 61'th number
sweet birch
yep - and, I am sure there is a "smart" way to do this but I'm afraid I'm not too sure, you can also work out which bucket it falls in - if it's in 1xxxx or in 2xxxx or 3xxxx or 4xxxxx or 5xxxx
once you find it's in the bucket axxxx, you can then work out which abxxx it's in
and so on
frank cosmos
need holp?
snow dune
need holp?
yup
snow dune
just so it's not far up
yeah so the progress so far is that there are 120 numbers in total, and im looking for the 59'th biggest aka. the 61'th smallest
snow dune
i think its 61
what is 61?
snow dune
of all the numbers
yeah thats what i said
frank cosmos
ok i see
snow dune
the 59'th biggest and the 61'th smallest are the same
sweet birch
how many numbers will start with 1XXXX?
snow dune
4!?
frank cosmos
the 59'th biggest and the 61'th smallest are the same
what is the 59th biggest
sweet birch
...no, it's 4!.
frank cosmos
oh right
sweet birch
please stop spreading misinfo.
frank cosmos
lol i didnt see the !
snow dune
yeah that man is confusing 🤷
sweet birch
well 3xxxx starts at 2*4! and ends at 3*4!-1
frank cosmos
well, if 1xxxx has 4! then 2xxxx and 3xxxx and 4xxxx and 5xxxx should have 4! too
frank cosmos
yeahj
sweet birch
you can work out how far into 3xxxx it is
and then repeat this for finding the next x
snow dune
yeah i think i can just do it manually from here on
sweet birch
the longer form is that the number will be a(4!) + b(3!) + c(2!) + d(1!) = 61
sweet birch
knowing each of a-d is >0, it's just finding the largest possible value
frank cosmos
@snow dune wanna close this or
snow dune
.close
sweet birch
the last one as in, M)?
oh hang on sorry I misread the Q
no my fault
well you can divide the cube root of 2x^2 into two parts, (2)^1/3 and (x^2)^1/3 right
as you already did for taking the x outside the root
and if you have something like $\frac{a}{bx}$ you can instead make $\frac{a}{b} * \frac{1}{x}$
twin meteorBOT
PrettyPrincessKitty FS
sweet birch
i.e. you can take your numerator - just constant number terms - and the part of your denominator with just constant number terms and combine them into one big numerator
and you'll get $\frac{(a/b)}{x}$
twin meteorBOT
PrettyPrincessKitty FS
sweet birch
simplifying only needs to get rid of those yucky root(x) terms, the rest are constants you can combine
no
also root3(4) = root3(2*2) = root3(2)*root3(2)
it's all about simplifying that root3(2x^5) (which you've done!) but also simplifying it a bit more by using the numerator
that seems to be the bit we can't get rid of out of the denominatotr
so yep 🙂
I didn't check them because it looked like you had got them down haha
steel zephyr
hi can someone help me with these problems for calc 2? i solved it but i think i messed up somewhere along the way. i will attach screenshots
vocal sleetBOT
hi can someone help me with these problems for calc 2? i solved it but i think i...
pallid forge
opening another channel with the same question does not speed up the process of people answering it
steel zephyr
i wasnt sure i thought you had left
my bad
this is my first time using this server
pallid forge
even if i had, there were people probably looking at it trying to help you before you closed it
no worries
someone will help eventually, i promise
pallid forge
i'm just not as well-versed in this math as i used to be, but i can find arithmetic mistakes when i see them
steel zephyr
thats alright thank you for trying. hopefully someone can come and take a look at my problems soon! :-)
vocal sleetBOT
@steel zephyr Has your question been resolved?
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@steel zephyr Has your question been resolved?
vocal sleetBOT
steel zephyr
.reopen
vocal sleetBOT
✅
rocky olive
In the first picture i think the (n+1) should be at the denominator because n!/(n+1)!=1/(n+1)
vocal sleetBOT
@steel zephyr Has your question been resolved?
vocal sleetBOT
@steel zephyr Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
vocal sleetBOT
regal parrot
.close
rugged fjord
$$
rugged fjord
<@&286206848099549185>
vocal sleetBOT
@rugged fjord Has your question been resolved?
rough barn
Let
$\mathbf{A}=\begin{bmatrix}1&0&0\6&1&0\9&8&1\end{bmatrix}
\begin{bmatrix}1&2&3&4\0&1&2&3\0&0&1&2\end{bmatrix}$
How would one determine the bases for the four subspaces of A without multiplying these matrices (namely the column and row spaces of A)? This was an assignment on my course last week and the solution started out by writing the 2 matrices and B and C, then showing we can write $A=[Bc_1, Bc_2, Bc_3, Bc_4]$ and stated that the first three columns now are LI since they are linear combinations of LI column vectors of B. The solution is hard for me to understand so im looking for any alternative explanations, im not able to find any similar problems online either
vocal sleetBOT
Let
$\mathbf{A}=\begin{bmatrix}1&0&0\\6&1&0\\9&8&1\end{bmatrix}
\begin{bmatrix}1...
twin meteorBOT
NTK
vocal sleetBOT
@rough barn Has your question been resolved?
vocal sleetBOT
@rough barn Has your question been resolved?
river wagon
**NTK**
Are you saying you want to find the column space of A?
Oh, nvm you said it
row and col, right
rough barn
yes, technically i need to find C(A), C(A^T), N(A), and N(A^T) but if i can figure out how to work the col and row i can try to work nullspaces on my own
river wagon
Okay, so the main claim is that row(A)=row(C) and col(A)=col(C)
rough barn
the intuition i have for C(A) is that if we started multiplying we'd see that we end up with linear combinations of the first matrix, so probably C(A) is that?
rough barn
yes, C(A) means the column space of A, and C(A^T) means the row space of A
river wagon
the intuition i have for C(A) is that if we started multiplying we'd see that we...
This is a great intuition. You also need to prove that the resulting vectors are linearly independent.
But that is because the map X->BX is bijective, so it must preserve dimension.
Oh, I wrote it wrong earlier. I meant col(A) = col(B)
rough barn
well for the first matrix its inversible so that should be proof enough that they are LI anyway, but is this enough to say that C(A)=span((1,6,9),(0,1,8),(0,0,1))
and i suppose for the row space you could denote again $A=BC$ and taking the transpose $(BC)^T=C^TB^T=A^T$ and follow similar logic
twin meteorBOT
NTK
river wagon
Of course you can. However, C^T is not invertible.
rough barn
if you look at the rows of C, notably the zeros, it should be visible that the vectors are LI and the solution i have just stated as such so i think for independence thats enough proof
river wagon
Your thoughts are very correct. To formalize them, perhaps you want to use the definitions of row- and column spaces.
Together wit the fact that both B and C^T have left inverses.
rough barn
sure... how would you work out N(A)? here B is invertible, so Bx=0, so we can look at Cx=0 and find the solution from there, but i was wondering if theres any alternatives there
river wagon
I don't think so. After all, finding N(C) is quite quick.
rough barn
alright, i think thats good enough thinking about A being formed of linear combinations of B or C so thanks for your help
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cedar kernel
multiplied lhs and rhs with 5-tv
cedar kernel
left hand side and right hand side of the equal to sign...
brazen scroll
How do i find the mapping matrix?
vocal sleetBOT
How do i find the mapping matrix?
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vast shale
Ida has a package of ice cream, which she puts on a plate. The ice cream is in the shape of a rectangle. She cuts ice cream so that the length of the rectangle first decreases by 20% and then the width decreases by 20%. What percentage of the ice cream is left on the barrel now?
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Ida has a package of ice cream, which she puts on a plate. The ice cream is in t...
vast shale
How do I solve it without drawing it up?
I solved it by drawing but I don’t think I’ll get points for it
merry python
,rcw
twin meteorBOT
vast shale
Wait it’s just the top one
The one on the lower half of the page is another question 😅
merry python
The idea is to express the length and breadth of the smaller rectangle in terms of the length and breadth of the larger rectangle
assume length of larger rectangle to be 'l' and breadth of the same to be 'b'
vast shale
Mhm
merry python
Now, 20% of l is decreased.
i.e. length of smaller rectangle is basically l-(20/100)l
a similar approach would be applied for the breadth
merry python
so what is your answer?
vast shale
80/100
merry python
width of smaller rectangle would be b-(20/100)b
merry python
read it again
vast shale
It decreases to
merry python
yes
vast shale
Ok what now
merry python
find area of both the rectangles
merry python
vast shale
😭
merry python
original rectangle and the smaller rectangle
merry python
percentage of the ice cream left =((area of small rect.)/(area of large rect.))*100
vast shale
?
merry python
area of large rectangle would be l*b
and that of smaller would be 0.64*l*b
sure their ratios would be 1:0.64
vast shale
The answer is 64 %
merry python
yes
merry python
kind of
merry python
are you sure 'bout that
vast shale
No
merry python
wait let me think of one
vast shale
Hhhhh
merry python
a rectangle has dimensions 30*20. Its length is halved. From the new rectangle formed, its length is decreased by (100/3)%. Find percentage of area reduced. Given Hint:||length>breadth at all times||
merry python
Ida has a package of ice cream, which she puts on a plate. The ice cream is in t...
Also did you just had a test with this question on it and messed it up?
merry python
oh well
merry python
are you sure?
vast shale
IDK
merry python
It would be advisable to read the hint
vast shale
I already know that
merry python
and clearly see what the question asks for
merry python
yes
vast shale
And that represents
merry python
the new ||name it||
vast shale
Length 👍👍👍👍👍👍😄
merry python
no
merry python
well 15<20
merry python
20 would become the new length of the rectangle
vast shale
You are going to make a shelter for a dog. The enclosure must be shaped like a rectangle and must stand against a house wall. You have 10 meters of fence. We let the short side of the rectangle be x meters. One long side must lie next to the house wall (without a fence).
A) Show that the area A (in square meters of the air space is given by A = 10x - 2x^2
B) How long are the sides of the rectangle when the air space has an area of 12m^2?
C) Investigate whether the shelter space can have an area of 15m^2
An object is composed of a cylinder and a cone as shown in the figure.
The radius of both the cylinder and the cone is r. The cone has height h. The cylinder is three times as tall as the cone.
A) Find the volume V of the object expressed in terms of r and h
B) Find r expressed in terms of V and h
A) Show that the division (2x^3 + 5x^2 - x - 6) : (x+2) goes up without performing the division
B) Solve the equation 2x^3 + 5x^2 - x -6 = 0
C) Factor the expression 2x^3 + 5x^2 - x -6
D) Subtract the fraction (2x^3+5x^2-x-6)/(2x+3)
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You are going to make a shelter for a dog. The enclosure must be shaped like a r...
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twin quail
How do i prove Triangle Inequality for this term?
vocal sleetBOT
How do i prove Triangle Inequality for this term?
twin quail
Been sittin on it for a very long time and ivenot moved forward at all
nice troll, if any1 canhelp id appreciate^^
twin quail
Im supposed to check whether that term is a metric
ive proven its symmetric and its always positive
but im stuck on proving triangle equality
dull bear
Easiest way imo would probably be to show that it’s induced by an inner product
Then all norms induced by inner products satisfy the triangle inequality
twin quail
Could u ELI5? we just got introduced into this topic and its alot all at once
twin quail
Then all norms induced by inner products satisfy the triangle inequality
this phrase
twin quail
are x1 y1 x2 y2 coordimates?
also, yes. and its calcualting the distance of (x1,x2) to (y1,y2) i believe
dull bear
this phrase
Basically you have norms on vector spaces, which satisfy similar properties to metrics (and any norm can be used to create a metric)
<@&268886789983436800>
Anyways, not sure whether you’ve seen them before, but similarly there are inner products on vector spaces (and any inner product can be used to create a norm)
For inner products, the norms they create have to satisfy the triangle inequality for norms because of Cauchy Schwartz
So it might be a bit less pain showing that you can create an inner product that would end up forming this metric
(You can do it without it, but if I recall it’s a bit more work to do)
twin quail
I think without is probably what im supposed to be doing
visual coyote
i mean i would probably do it by supposing a point z
of coordinates (x1,y2)
and assuming x1/=/y1 and x2/=/y2; proving that xyz is a right triangle
then using pythagoras to find the distance
vocal sleetBOT
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twin quail
Can anyone help/walk me throught his please^^
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hard wadi
I can’t figure out how to do #14
vocal sleetBOT
I can’t figure out how to do #14
hard wadi
Comes from chapter 5.3 of Kreyszig’s advanced engineering mathematics 7th ed
I’ve tried finding a series that I can use in place of the right hand side but I’ve had no luck
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hard wadi
<@&286206848099549185>
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flat whale
I’ve tried finding a series that I can use in place of the right hand side but I...
Write the right side as a binomial expansion or Taylor series and you'll see it only has even powers of u
tribal sapphire
how does one do this?
vocal sleetBOT
how does one do this?
tribal moss
.reopen
$\log_{16}\frac{1}{128}=x\Leftrightarrow 16^{x}=\frac{1}{128}\Leftrightarrow 2^{4x}=2^{-7}\\\Leftrightarrow 4x=-7\Leftrightarrow x=-\frac{7}{4}\\\log_{16}\frac{1}{128}=-\frac{7}{4}$
vocal sleetBOT
$\log_{16}\frac{1}{128}=x\Leftrightarrow 16^{x}=\frac{1}{128}\Leftrightarrow 2^{...
twin meteorBOT
Joanna Angel
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sinful forge
vocal sleetBOT
twin meteorBOT
chlamydia
grizzled halo
as represented by the single red line there that's supposed to be a minus
jagged cargo
How did he get 2b=-6
merging 2 statements by subtracting them
the a gets canceled out, $b - (-b) = b + b = 2b$, and $-1 - 5 = -6$
twin meteorBOT
FungusDesu
vocal sleetBOT
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vast shale
vocal sleetBOT
vast shale
Can't proceed really
merry python
are you able to find the bounds of the range
merry python
That didn't helped
show your diagram. you must've inyerpreted it wrong
vast shale
Minimum angle 15°, maximum angle 75° but there is an interval 53° between 15° and 75° , which is not allowed for successful shot
This what written in answer
merry python
can you now find the minimum and maximum range?
vast shale
merry python
no
vast shale
Not really
merry python
convert it to sin(2x)
merry python
well then there must be some misinterpretation or if not then the answer is wrong
oh wait
are you aware of the fact that complementary angles have the same range
@vast shale
vast shale
Yes
merry python
so theta=15 and theta=75 would have the same projections
merry python
well you just concluded that minimum angle would be 15 and max would be 75
the only thing left is to prove 53 does not work
merry python
but there seems some issue with that point
vast shale
18.5 and 71.5 will be inside 15 and 75 so it's done
merry python
the answer says 53 won't work
vast shale
Yea
vast shale
Yeah lol
merry python
since they are complimentary
vast shale
I got a conclusion
Answer will be 15°to 18.5°
And 71.5°to 75°
Even 45 30 60 non gonna work
Including 53
They just didn't wrote answer correctly
What do you say
@merry python
I applied those angles to check answer
vocal sleetBOT
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flat minnow
vocal sleetBOT
flat minnow
yes
-35
year 10
really?
💀
nah lol
thanks
arent these just with factors
damn
.close
placid gust
Good afternoon, colleagues. I'm struggling with specific formula. I have mathematical formulas, which I need to calculate and based on it my question is:
Does anyone know any related to it good analogues for getting calculated steps with explanations?
In Wolfram Alpha and Symbolab, I'm getting the issue as:
No Steps: Steps are currently not supported for this problem - Symbolab
or simply no results related to it.
To clarify:
I'm not asking about 'How to do it/How easy is it', I'm asking:
'What resources can be used for it and why it would be helpful for my use case.'
P.S. If you don't know, at all, this topic and how to help, please, ignore it and don't waste my time on empty talk.
Thank you in advance for your help.
vocal sleetBOT
Good afternoon, colleagues. I'm struggling with specific formula. I have mathema...
@placid gust Has your question been resolved?
vocal sleetBOT
@placid gust Has your question been resolved?
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@placid gust Has your question been resolved?
cyan talon
this operation you're showing is called convolution
What resources can be used for itso you're looking for tools than can compute it for you ? just to be sure what you wanthelpful for my use case, what's your use case ? maybe it's important to know
@placid gust
sharp chasm
placid gust
1. `What resources can be used for it` so you're looking for tools than can comp...
- I‘m looking for a tool which helps to understand how should I calculate it correctly. I‘ll compare it with my theory stuff. I need to understand the principle of calculating it.
-
Under „use case“ I mean this specific formula, @cyan talon
-
I've been given a fairly tight deadline, so I want to speed up my approach to research. My vision of this is to start with an example of a calculation, and then, supported by theory, solve something similar freely.
vocal sleetBOT
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@placid gust Has your question been resolved?
frail mortar
Btw close it if you're done
wicked sonnet
Btw close it if you're done
Why're you after closing help channels?
umbral pawn
.close
umbral pawn
Nothing
vocal sleetBOT
@placid gust Has your question been resolved?
placid gust
Btw close it if you're done
Hello, buddy. I didn't solve it. I'll close it if I don't receive the answer from @cyan talon , at least, today. I'm struggling with it, for this reason, my question is still on hold.
cyan talon
@placid gust I didn't see your ping from yesterday, discord doesn't help very much
- I'm not aware of a tool which would explain you in detail how convolutions are computed, like say wolfram (or another symbolic math tool) understood your query and could tell you the steps, it prolly would just say
ok we have to compute the convolution .... the result is ....with no inbetween. There's a lot of resources explaining convolution though, it's not a completely niche thing, it shows up in quite a few places. (signal processing, probability at least) - ok I thought you had a specific application of that formula in mind already, that's what
use casesounds like to me - I can show you a typical example of a calculation which involves convolutions (with probability), I'll wait for you to come back if you wish to see it
placid gust
<@392731461276532746> I didn't see your ping from yesterday, discord doesn't hel...
Yes, I'm here, please, write me your thoughts👍
rapid swift
btw you can use some integral transform or the discrete version of it if you want a "tool" for it
for suitable transforms, the convolution becomes an elementwise multiplication and an inverse transform
if you simply want to check your work on it, there are things like numpy.convolve that will compute it for you
but other than that, just follow the mathematical formula I guess
cyan talon
Yes, I'm here, please, write me your thoughts👍
here's a very basic example, let's say I throw two dice (one has 10 sides, from 1 to 10, the other has 12 sides, 1 to 12, the sides on each die show up with equal probability 1/no. of sides).
Now I throw these two dice and I look at the sum of the two numbers I get : are you able to compute the probability that the sum of the two dice is, for example, 14 ?
uncut fossil
onyx flax
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fossil python
what am i supposed to even do here, how do i start approaching this question
fossil python
is this trig sub?
woeful cloak
You can either:
- Evaluate the integral and solve for c
or - Do it geometrically, by showing what kind of area the integral is representing
of course, I advise against the first approach since the equation that yo uare going to solve is not very pretty
and yes, you can use trig sub here
empty linden
im so confused
vocal sleetBOT
im so confused
empty linden
This is a log chapter so were supposed to use logs. But I dont know what to do for question a
livid horizon
This is a log chapter so were supposed to use logs. But I dont know what to do f...
Initial mass is 5g
t is 150 years
And half life is 1620 years
Just put in those values
empty linden
Just put in those values
yeah but
isnt M(t) the half life?
And I have to find the remaining mass
Maybe i should say M(t) = (P_f-Pt)^t/h then plug it in to find P_f? which is the final mass
livid horizon
isnt M(t) the half life?
M(t) is mass at time t
empty linden
oh
livid horizon
Nice
empty linden
and for b, i should just use logs to find out t, right?
then rearrange to isolate t
empty linden
alright, thanks
livid horizon
Np
vocal sleetBOT
@empty linden Has your question been resolved?
livid horizon
Over here, it should've been n-1 instead of n in the first line
Oh no mb
It's correct
But
2000= 40*10^n
So 10^n = 50
So n= log 50
That's like 1.69
vocal sleetBOT
empty linden
.reopen
vocal sleetBOT
✅
empty linden
But
2000= 40*10^n
So 10^n = 50
So n= log 50
oh
yeah i forgot about the log outside the 2000/40
livid horizon
Ye
livid horizon
.
lyric relic
np
livid horizon
Ok
empty linden
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unreal lynx
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