and neither does trying random things
#help-17
rapid swift
stuck harness
im gonn atry that for 10 minutes and look at this problem again with a new headspace
rapid swift
and furthermore
you should only do steps that actually make sense to you
writing random stuff like x rad 3 = 6 is not going to help
vocal sleetBOT
@stuck harness Has your question been resolved?
vocal sleetBOT
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patent nymph
How do you prove that in a commutative ring with no zero divisors, the characteristic is either prime or zero? The proofs I could find all assume the ring has identity
vocal sleetBOT
How do you prove that in a commutative ring with no zero divisors, the character...
patent nymph
Please ping when replying
vocal sleetBOT
@patent nymph Has your question been resolved?
patent nymph
This is the part I'm stuck on, what do you do here?
worthy citrus
stop spouting AI nonsense
worthy citrus
How do you prove that in a commutative ring with no zero divisors, the character...
if you have a (finite) commutative ring with no zero divisors it must have unity no?
cyan talon
also how do you even define the characteristic if you don't have a multiplicative identity ?
worthy citrus
How do you prove that in a commutative ring with no zero divisors, the character...
I think a counter example would be the ideal generated by (2) in Z_12? is a comm ring without unity that has characteristic 6? if by characteristic in a non unital ring you mean minimum n such that nk = 0 for all k
patent nymph
I think a counter example would be the ideal generated by (2) in Z_12? is a comm...
It has zero divisors
Can you explain further?
worthy citrus
right yes
worthy citrus
if you have a (finite) commutative ring with no zero divisors it must have unity...
in which case i think this is true
patent nymph
in which case i think this is true
How about the infinite case?
worthy citrus
unsure 
patent nymph
Ok, thanks anyway
vocal sleetBOT
@patent nymph Has your question been resolved?
hard atlas
if you have a (finite) commutative ring with no zero divisors it must have unity...
btw this follows by considering that x->ax is a permutation, so repeatedly applying it necessarily gives you the identity at some point
clever holly
hi
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
obtuse radish
ok so u know what a continuos and discontinuous data group is?
clever holly
ok sir
obtuse radish
they are disjoint
clever holly
they are disjoint
disjoint
?
obtuse radish
their a gap between them
clever holly
their a gap between them
ok
obtuse radish
e.g. 126 to 127
clever holly
ok
obtuse radish
remove the gaps
fill in the gaps
whatever u prefer
think of it a little
unless u got a test tomorrow there shouldnt be any hurry to get the answer
sir
clever holly
118.5-126.5
clever holly
next 127.5-135.5
vocal sleetBOT
@clever holly Has your question been resolved?
slate pond
Question in Linear Algebra, regarding inner product, orthogonality and projections.
The question itself is in the picture, and so is my solution attempt thus far.
I tried working with the expression down below with the given transformation, but it got me pretty much nowhere. I wonder what might I have missed or whehter there's another better way to prove this.
vocal sleetBOT
Question in Linear Algebra, regarding inner product, orthogonality and projectio...
slate pond
Hints are appreciated, not looking for the final answer
cyan talon
well you gotta use the transformation you have at some point
it would be nice if you find the subspace U we're projecting on to begin with
slate pond
Well I tried using it directly e.g. just placing v in it and seeing how it turns out, but the expressions within the new transformed vector don't mean much to me, at least I think they don't
slate pond
it would be nice if you find the subspace U we're projecting on to begin with
Hmm, wouldn't it be just any subspace? I can't assume anything about it
slate pond
Ah, interesting
slate pond
If I'm going to do that, I'm going to need to prove that the transformation is also U-invariant, or that the composition upon itself is itself
cyan talon
yeah T^2 = T
slate pond
Yeah exactly
cyan talon
at least you'd know it's a projection (not orthogonal necessarily)
and then you could check whether it's orthogonal
slate pond
and then you could check whether it's orthogonal
I guess I can do that by finding the basis of U and its orthogonal complement and seeing that T is sending the sum to U?
Which is done directly by finding the image of the transformation etc
cyan talon
that would work
i have an easier idea in mind tho
nice diagram in hand
if p(x) is the orthogonal projection of x
can you say something about p(x) and x-p(x) ?
slate pond
They're orthogonal
cyan talon
yeah
slate pond
So I can just check the dot product of the basis vectors
cyan talon
and you want that to be true for any x
nah just plug in some arbitrary vector v=(x,y,z)
and see that that dot product is indeed 0 whatever the choice of v
slate pond
Oh right that's much more straightforward
cyan talon
(using x as a vector and as a coord is a bit confusing lol)
slate pond
Yeah I got it, it's all good
Rightio, that's done some clarification for me, I'll go ahead and do that rn
Thank you!
.close
true falcon
hello I need to solve 4cos(theta)=2 to know the limits of my integral
true falcon
Is normal that I get an irrational no pi number in that
glossy maple
well you get an angle in radians
true falcon
so, I just put +-cos^-1(1/2) as my limits
glossy maple
and do you know whats cos^-1(1/2)
true falcon
why my calculator doesnt show me that ;-;
glossy maple
in degrees, arccos(1/2) is 60
since cos(60 degrees) = 1/2
you can look at a 30-60-90 right triangle to understand why thats true
vocal sleetBOT
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Available help channel!
mighty dust
Ok if a have two points A and B how would I approach creating a parabola between these two points and are there infinitely many possibilities?
vocal sleetBOT
Ok if a have two points *A* and *B* how would I approach creating a parabola bet...
viral copper
mighty dust
ok well how would create a parabola between the two points with a equation like this ax^2-bx+c
whole oasis
if they're not specific then just make 2x2 system and parametrize
mighty dust
what do you mean by that
whole oasis
(i.e. substitute given points and solve for two of three variables, any)
mighty dust
vocal sleetBOT
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@mighty dust Has your question been resolved?
vocal sleetBOT
@mighty dust Has your question been resolved?
mighty dust
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hybrid fossil
vocal sleetBOT
hybrid fossil
f(z) = conjugate(z) is continuous
so how come it has no antiderivative
when 3.3.4 (a) states there must then be a derivative
or is f(z) = conjugate not continuous?
cobalt crypt
it doesn't claim existence of an antiderivative
it claims equivalence of the 3 statements
cobalt crypt
f(z) = z* fails all 3
vocal sleetBOT
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Available help channel!
eternal glacier
vocal sleetBOT
eternal glacier
for u substitution, do you prefer evaluating for x, or evaluating for u with no back substitution?
outer warren
eval for u
eternal glacier
it's quicker?
outer warren
work is cleaner
outer warren
avoids tedious additional notation to compensate
eternal glacier
yeah
less room for error
OK thanks
@twilit reef you contributing something? i don't follow
outer warren
many do it because they just came from doing indefinite integrals with substitution
English?
rich depot
I don't know how to graph the measurements... and do the said questions followed with it, I tried it a few times a gave up since the points I put down don't match up...
vocal sleetBOT
I don't know how to graph the measurements... and do the said questions followed...
summer spoke
for each object, you have 2 attributes: inches and centimeters. this should tell you what your axes should represent
rich depot
Yeah I've written that down, just don't know what numbers I should go by like: 2's, 3's, etc. To get the correct placements
summer spoke
theres no one correct way to do it. all that matters is that you can fit all the data in a way that looks reasonable
so you can always count how many grid squares you have and compare that to the number of units you need
Ex: if you have 10 grid squares but need to go up to 50 miles, counting by 5s would be appropriate
rich depot
I know how to count the squares. What I don't get is the numbers they gave me to put on the graph...they are decimals so when I try to get the slope, it comes out to be .363....
summer spoke
that is a reasonable conversion rate from centimeters to inches
seems like youre on the right track
rich depot
How would you get the y-intercept if the straight line wouldn't start from the 0?
summer spoke
well intuitively 0cm = 0in so the line should intercept the y axis very close to 0
but there will probably be a little error with your data
in that case if you know the slope of your line and one arbitrary point that it passes through (call it (x, y)), you can backtrack
y=SLOPE*x + YINTERCEPT
from the equation for a line
solve for the intercept
rich depot
Hm, I think I got it now, thanks for your help!
summer spoke
np
rich depot
.close
tame stone
vocal sleetBOT
tame stone
Its apparently 3x??
Idk how Im missing an x here
oh wait
Ig I could take the integral of y'' and y' and 3
but then the xs cancel each other out
already I guess you have to plug A into yp when there is no yp present in original equation
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vocal sleetBOT
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Available help channel!
obtuse nest
Hey math legends, would like your help about math notations.
So let say I have a undirected graph with 3 vertices A, B, and C. And I like to define a set of edges, where vertex A is not connected(lone vertex), like when only B, and C are connected, or non of them are connected (a null graph), now I don't know how to define the set using the math notations, any thoughts? Thanks
vocal sleetBOT
Hey math legends, would like your help about math notations.
So let say I have a...
summer spoke
Call the graph G, the set of vertices V, the set of edges E. So G = (V, E)
A common notation for an undirected edge between vertices u and v is (u, v)
so you could say V = {A, B, C} and E = {(B, C)}
alternatively, you could say $E = \emptyset$
twin meteorBOT
srhoosteen
paper depot
question: why do you need Notations™️ for this and why would a picture or verbal description not suffice
obtuse nest
so you could say V = {A, B, C} and E = {(B, C)}
Great, so how may I define it using set/graph notations, as for instance assuming Graph G has n vertices, so I cannot come up with exact E={(B,C)}, also mind E={} works too, as a null graph.
paper depot
are you solving a graph theory problem right now?
summer spoke
I think simply using words will suffice a lot of the time when it comes to these sorts of things (e.g. "Node A has no neighbors", or "there are no edges")
if its hard for you to come up with the notation, odds are the notation would be hard for anyone to read
obtuse nest
are you solving a graph theory problem right now?
graph+set theory. I'm trying to solve a problem using inclusion-exclusion principle. As given Graph G, with vertices ABC. I'm trying to find sets Ea, Eb, and Ec where vertices A,B, and C are not connected to any other vertices(lone). Like for Ea it's {(B,C)|, and {}. But I like to define it using set/graph notations, like I don't know, maybe something like "for a set where non of defined edges are connected to vertex A" maybe
paper depot
...
as for instance assuming Graph G has n vertices, so I cannot come up with exact E={(B,C)}
what's this supposed to mean then
also can you please show the PROBLEM ITSELF exactly as it's stated? cause i'm confused
obtuse nest
what's _this_ supposed to mean then
For simplicity, example comes with 3 vertices, so it's easy to find those edge sets where in each one a specific vertex come isolated/lone. But what if we consider size of vertices as n, not 3, what now
obtuse nest
also can you please show the PROBLEM ITSELF exactly as it's stated? cause i'm _c...
Im sorry, okay let say we have 3 cities(like vertices A,B, and C), and we like to build roads between them somehow non of them become isolated/lone(at-least connected to one). Now using inclusion-exclusion principle, finding how many(the count) possible ways we could set up those edges between those vertices.
I know I have to find Ea, Eb, and Ec edge sets, which each one includes edge-sets that make a specific vertex isolated, like Ea = { {(B,C)} , {} }, just need to know how to define those sets using set/graph notations
paper depot
so your problem reads as follows:
How many ways are there to connect 3 cities with a road network such that no city is isolated?
did i get that right? yes or no
obtuse nest
Yes
obtuse nest
did you perhaps also want to do this for _n_ cities rather than just 3?
Probably yes, but I'm thinking if we stick with connected graphs only. so yes
paper depot
... ???
"but I'm thinking if we stick with connected graphs only" does not make any sense to me as a sentence
obtuse nest
I know it's bad, but I also asked some AI/gpt out there, and it suggested something like following
{ S ⊆ E : A ∉ S and for all (u, v) ∈ S, neither u nor v is A }
paper depot
DO NOT USE CHATGPT FOR MATH.
especially not with the phrasings you've been using, which are hard even for a HUMAN to understand, let alone a chatbot.
i mean ok like
obtuse nest
# DO NOT USE CHATGPT FOR MATH.
I'm sorry.
paper depot
heres the thing with "notations"
i think youre overly attached to the idea that math is about manipulating symbols on a page
when it... isnt
what you've got here is a counting problem
so you should care less about how to formally write down the things you're counting
and more about how to count them
obtuse nest
Yes I understand, and I'm sorry for confusing you. Guess I'm going to practice more, and study more counting problems in detail then.
Really appreciate your time, math bless you.
.close
sudden hill
help
paper depot
wdym by "possible"?
do you mean "Does there exist at least one x such that this is true?"
or "Is this true for all x?"
sudden hill
no like am i allowed to do this
paper depot
so that means your question is "Is this true for all x?"
the answer is no, it is not
paper depot
sudden hill
this is the question im doing
paper depot
yes, i understand.
i was expressing my frustration at the fact that you said something related-ish but only tangentially
you overabstracted
anyway have you made any progress on this so far?
lyric fossil
(it does not)
paper depot
expand the fraction? as in break it into the sum of two fractions?
sudden hill
mb seperate
paper depot
yeah, no, that doesn't help.
have you considered that
a. cos(3pi/2) is an easily calculable/recallable value
b. cos(3pi/2 + h) may be expanded with the angle sum formula cos(x+y) = cos(x)cos(y) - sin(x)sin(y)?
paper depot
yes
or if you can arrive at cos(3pi/2 + h) = sin(h) by other means you can do that too
sudden hill
or if you can arrive at cos(3pi/2 + h) = sin(h) by other means you can do that t...
2 ez👍
i got it thanks
.close
distant ridge
How do i find the maximum value of sin^4(x)+cos^4(x)
vocal sleetBOT
How do i find the maximum value of sin^4(x)+cos^4(x)
dusk python
you could think about the nature of sin and cos
they are periodic, and always between -1 and 1
outer warren
you could consider
a^2 + b^2 = (a+b)^2 - 2ab
distant ridge
you could consider
a^2 + b^2 = (a+b)^2 - 2ab
tried that but im stuck at
1-sin2x cosxsinx
idk how to move forward from here
outer warren
seems you did something that went against you
distant ridge
Most likely yeah
outer warren
forget the double angle identnties
distant ridge
ok
outer warren
for the max, you'd want to be subtracting the least non-negative value if possible
(which is 0)
distant ridge
for the max, you'd want to be subtracting the least non-negative value if possib...
okay
outer warren
and are there values of x where
sin^2(x)cos^2(x) is 0?
distant ridge
so that will basically give me -1
wait that sounds wrong lol
no wait
it gives me 1
my bad
ohk it makes sense
thanks a lot for your help
vocal sleetBOT
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vocal sleetBOT
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Available help channel!
rustic pilot
vocal sleetBOT
rustic pilot
dont know how to approach
vocal sleetBOT
@rustic pilot Has your question been resolved?
vocal sleetBOT
@rustic pilot Has your question been resolved?
royal grotto
2^3.7
royal grotto
Just wanna see how you guys think this situation
paper depot
what's the goal
royal grotto
To think like you do
urban edge
At this point, i cant calculate it, so i put it in the calculator
What are you looking for here?
urban edge
i cant calculate it
royal grotto
Yeah I also know that but book says 12.996..
urban edge
So why cant you use a calculator?
royal grotto
And I get 13.6
vast shale
There are approximation techniques
royal grotto
I did use calculator
vast shale
But yet again they are just approximations
royal grotto
But yet again they are just approximations
How would you do this
urban edge
What class are you in? Jw so i can find the best one to explain
royal grotto
University
urban edge
The class
royal grotto
I think I’m doing it wrong basically thinking that I could do 8*1.7
I wonder what way is best to think
hybrid fossil
Then I thought 8*1.7 but I get wrong numbers
thats not really how exponentiation works
youre trying to linearly interpolate between 8 and 16 by doing that
which is not a bad approach for an approximation
but its only an approximation
royal grotto
How would you do it
cursive matrix
in my head i did 2^(3+0.7) = 2^3 * 2^0.7 which is approximately 8 * sqrt(2) which is aproximately 8*1.5 which is aproximately 12
hybrid fossil
i would just do a taylor series of 2^x
taylor series is probably a bit too advanced tho
royal grotto
in my head i did 2^(3+0.7) = 2^3 * 2^0.7 which is approximately 8 * sqrt(2) whic...
Wow thank you
cursive matrix
in my head i did 2^(3+0.7) = 2^3 * 2^0.7 which is approximately 8 * sqrt(2) whic...
but there are a lot better methods if you take the time, if you are just thinking about how to do it in head this is one way i guess
urban edge
I still dont understand why approximate though
hybrid fossil
^
urban edge
taylor series is probably a bit too advanced tho
Also you need to approximate ln2
vast shale
Yeah u can like Taylor it and manually calculate up to 5 terms or something
But again
Why LOL
hybrid fossil
Also you need to approximate ln2
ln(2) = 0. funny number = 0.69
urban edge
Yeah u can like Taylor it and manually calculate up to 5 terms or something
But then you need to calculate 3.7^5/120
half imp
so 2^0.7 is a out 1.1^5
half imp
which is 1.61051
hybrid fossil
you could also do lagrange interpolation
half imp
so 8*1.61051 ≈ 12.88...
hybrid fossil
$2^{3.7} = 2^3 \cdot 2^{0.7} = 8 \cdot 2^{0.5} \cdot 2^{0.2} \approx 8 \sqrt{2} \sqrt{\sqrt{2}} \approx 8 \cdot 1.4 \cdot 1.2 = 13.44$
twin meteorBOT
heavy0201
royal grotto
$2^{3.7} = 2^3 \cdot 2^{0.7} = 8 \cdot 2^{0.5} \cdot 2^{0.2} \approx 8 \sqrt{2} ...
You got too into this 😆
hybrid fossil
hahah yeah
urban edge
To be honest, any approximations for exponents either involve natural log or another unwieldy exponent
Still dont know what class youre in
half imp
doing e^anything by hand is very nasty
royal grotto
Still dont know what class youre in
Wym by class
urban edge
Like calc 1 or smthn
royal grotto
I have no clue
hybrid fossil
doing e^anything by hand is very nasty
e^anything isnt that bad
urban edge
I have no clue
Ok thats fine
hybrid fossil
its the easiest exponent
glad python
e^real is bad by hand
half imp
2^x = 1 + xln(2) + x^2ln(4)/2 + ...?
doing any power series where x isn't <0.05 by hand is probably going to be awful
urban edge
U sure bout that one
hybrid fossil
2^x = 1 + xln(2) + x^2ln^2(2)/2 + ...
half imp
ah right
vocal sleetBOT
hybrid fossil
you also have to factor accuracy
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Available help channel!
royal grotto
Sqrt(2)^6
full arch
because they followed what you suggested
by removing 2 out of 6 , if i'm interpretting this correctly then you mean to write 6 as 2 * 3 ?
royal grotto
No I meant subtract
rocky rapids
Sqrt(2)^6 = ((2)^1/2)^6
full arch
No I meant subtract
and how would you do that
im sure you could do it that way
lets just say y=sqrt(2)^6
royal grotto
I always that exponent two get rid of sqrt
full arch
I always that exponent two get rid of sqrt
sure thing, thats why its always nice to check if you can write the exponent as a multiple of 2, but we can also try your subtraction shenanigans
royal grotto
sure thing, thats why its always nice to check if you can write the exponent as ...
Thing is it wouldn’t work since I get a diffrent answer
full arch
Sqrt(2)^6 = ((2)^1/2)^6
you should get 8 regardless of how you do it, using rules of indices with this, 'subtracting 2' from the exponent by dividing both sides by (sqrt(2)^2)
full arch
Thing is it wouldn’t work since I get a diffrent answer
posting your work would be useful :P
full arch
im not sure how (sqrt(2))^6 = 2^4,
and under that you have the correct answer?
royal grotto
No under that are diffrent calculations to diffrent questions
royal grotto
The one under is a diffrent question
full arch
the (-27)^(1/3)?
royal grotto
No haha the one above it
full arch
royal grotto
They are different!!’ 😭
royal grotto
Ya
royal grotto
I know but they are diffeent
full arch
Sqrt(2)^6 = ((2)^1/2)^6
this
yes but you should be able to use common sense to apply it to your question
sqrt(a) = a^(1/2)
use that with exp rules
rocky rapids
$\sqrt(2^6) = (2^6)^1/2$
twin meteorBOT
justapresence
full arch
{} around the half
royal grotto
What made you get this
rocky rapids
Supposed to be power of one half
royal grotto
Like what was the thought process
royal grotto
Meaning whatever exponential number it would reduce to half?
Could it also be written as 2^6.5?
royal grotto
Why do I have that and not 6.5
rocky rapids
And you can use power rules to calculate
rocky rapids
When you take the power of a power you dont add the power
royal grotto
Ok hold let me take picture
full arch
neat iron
Curly brackets 😉
lyric fossil
also \cdot instead of *
royal grotto
Wait so. Sqrt(x) = x^0.5 but sqrt(x^6) = x^0.5)^6 ?
full arch
no, sqrt(x^6) = (x^6)^(1/2)
royal grotto
Ugh
rocky rapids
Scroll up to the exponent rules and look at 'power of a power'
royal grotto
Ya I know but I see still as 6.5
rocky rapids
You multiply the powers instead of adding them
royal grotto
Yes but why is it multiply
rocky rapids
Thats the rule when you take a power of a power
royal grotto
I think it’s the product rule or it’s stuck to my head
rocky rapids
If its easier, you can evaluate 2^6 first then take the square root of the answer
full arch
2^a * 2^b = 2^(a+b)
(2^a)^b = 2^(ab)
rocky rapids
For a square root yes
vocal sleetBOT
full arch
Yes but why is it multiply
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Available help channel!
vast shale
Hi I was wondering if I could get some help on this problem. I’m very bad at math so if you could try to please explain this in the most simple way possible I would really appreciate it.
vocal sleetBOT
Hi I was wondering if I could get some help on this problem. I’m very bad at mat...
vast shale
The question I’m trying to anwser is part b.
How do you calculate a confidence interval?
Does someone else maybe know then?
Hello?
undone valve
hi
vast shale
Hi
undone valve
how old are u
vast shale
Why
undone valve
any
glad python
naww
vocal sleetBOT
@vast shale Has your question been resolved?
errant lake
Hi I have a question with this.
vocal sleetBOT
Hi I have a question with this.
errant lake
I thought it was a discriminant question but I'm getting stuck
errant lake
Heres what I have - a= 1, b=x and c=1
so the value of b^2-4ac should be less than 0
so thats b^2 - 4 = something less than 0
paper depot
Heres what I have - a= 1, b=x and c=1
no, b is b, b isn't x
paper depot
so thats b^2 - 4 = something less than 0
b^2 - 4 < 0
vocal sleetBOT
@errant lake Has your question been resolved?
opal venture
vocal sleetBOT
opal venture
trying to figure out the last one
i thought it would have been n(A) = 5 x 4 **x 2 x 1 **x 3 x 2 x 1 but it just equals the same as the second one
the answer has to be 720
paper depot
the answer has to be 720
says who
opal venture
my teacher lmao
paper depot
"teachers on both sides of the pic" is a little vague
you and i would read that as TSSSSST
which is 5! * 2 as you correctly calculated
opal venture
yeah I haven't learned about doing stuff like 5! yet, the teacher wants it in this specific way
<@&286206848099549185> any one else able to help?
vast shale
<@&286206848099549185> any one else able to help?
What is the question?
empty frigate
the students can be arranged in 5! = 5*4*3*2*1 = 120 ways
the teachers can be arranged in 2 ways
there are 3 choices for which two of the three middle slots the teachers are in
120 * 2 * 3 is 720
vocal sleetBOT
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Available help channel!
undone aurora
vocal sleetBOT
undone aurora
so basically for this question
should I explain the claim like the rough work for it
something like this
because I feel like the reader might be confused idk
vocal sleetBOT
@undone aurora Has your question been resolved?
mild flower
generally in proofs like this you wouldn't include your rough work
you would pretend that the formula came to you in a dream or something
vocal sleetBOT
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slate pond
Question in linear algebra. I'm having a bit of trouble in concluding the first point.
I can understand that there is a natural k such that (T-Id)_k = 0, hence it's the minimal polynomial of T-Id, but what can it possibly tell me about the characteristic polynomial of T?
vocal sleetBOT
Question in linear algebra. I'm having a bit of trouble in concluding the first ...
wraith venture
The char-pol of a nilpotent endomorphism is known
Use it to deduce the char-pol of T (||using the definition||)
vocal sleetBOT
@slate pond Has your question been resolved?
slate pond
Oh I see, so it would actually be (x+1)^n where n is the dimension of V
Or I'm saying completely false stuff?
wraith venture
X(T-Id) = x^n
X(T-Id)(lambda) = det(T - Id - lambda Id) = det(T-(lambda+1)Id) = X(T)(lambda+1)
Hence x^n = X(T)(x+1), so X(T)(x) = (x-1)^n
You should expect that since 0 is a eigenvalue of T-Id, so 1 is an eigenvalue of T, so (x-1) is a factor of its charpol
slate pond
Right, precisely, and not only it's a factor, it's the only factor
vocal sleetBOT
astral pebble
can someone help me here?
dy/dx just means a negative slope at the point
but idk how to interpret the squared
vocal sleetBOT
tawdry harness
but idk how to interpret the squared
what do u mean "interpret the squared"
astral pebble
what do u mean "interpret the squared"
like the d^2y/dx^2
tawdry harness
this?
vocal sleetBOT
Available help channel!
vocal sleetBOT
its gotta point B or C I believe
astral pebble
right
tawdry harness
its gotta point B or C I believe
so u've already solved it?
astral pebble
so u've already solved it?
I cant decide which one
because idk how to use the info that second statement is telling me
tawdry harness
because idk how to use the info that second statement is telling me
i dont think the statement that question gave can be useful
and accroding to the graph
tawdry harness
its gotta point B or C I believe
C is wrong
B might be wrong,but it's the most likely to be right
A should be right
tawdry harness
B might be wrong,but it's the most likely to be right
that because u,or the question,dont give me any expression
astral pebble
the question doesnt give one
tawdry harness
and dy/dx has to be negative
but the rate of change of the rate of change doesnt have to be negative too
astral pebble
but if we know dy/dx is negative that means that the slop at the point has to be negative I thought?
tawdry harness
but if we know dy/dx is negative that means that the slop at the point has to be...
yes
but what dy/dx is now wont have any impact on the second derivative
tawdry harness
it says both must be true
who?the answer?
tawdry harness
o sry,i dont mention that 'and'
astral pebble
its ok
tawdry harness
that,B is the only answer to this question
tawdry harness
nothing
astral pebble
I do have another one I am stuck on
Not continuous on B and G right?
B because of the straight up and down
and G because of the split
tawdry harness
Not continuous on B and G right?
continuous?
astral pebble
yes
tawdry harness
not derivable right?
hum,i'd say,even it requests that it should be derivable,B is ALSO qualified
astral pebble
A continuous function is a mathematical function that has no abrupt jumps, holes, or interruptions in its graph. More formally, a function f(x) is continuous at a point x = c if the following conditions are satisfied:
f(c) is defined (the value of the function at x = c exists).
The limit of f(x) as x approaches c exists.
The value of the function at x = c is equal to the limit of f(x) as x approaches c.
tawdry harness
and,accroding to the definition
astral pebble
f(c) would be undefined in B right because of the straight line?
tawdry harness
A continuous function is a mathematical function that has no abrupt jumps, holes...
this,ofc
astral pebble
A vertical line occurs when there is a value of x for which the function is not defined or has an infinite value. This creates a break in the graph and violates the conditions of continuity.
Right?
tawdry harness
f(c) would be undefined in B right because of the straight line?
no,whether a function is defined on a point or not has nothing to do with the tangent line
tawdry harness
yes,ur right
tawdry harness
so B IS continuous
regal slate
B looks continuous
astral pebble
oh shoot
tawdry harness
and D isnt
tawdry harness
yes
regal slate
all differentiable functions are continuous but not all continuous functions are differentiable
astral pebble
how can I determine the second deriv from a single line?
tawdry harness
how can I determine the second deriv from a single line?
what?
'a single line' u mean the original function or?
astral pebble
astral pebble
'a single line' u mean the original function or?
yes
based off each function given, I need to find if its second derivative is positive at the point
regal slate
A vertical line occurs when there is a value of x for which the function is not ...
what you’re confused about is the vertical line being an asymptote, the graph shows a vertical tangent not an asymptote
regal slate
based off each function given, I need to find if its second derivative is positi...
are you familiar with concavity?
astral pebble
are you familiar with concavity?
yes and no
I get the difference
but idk how to apply it in a practical sense here
tawdry harness
A and E
regal slate
the 2nd derivative test tells you whether the function is concave up or down depending on the sign of f’’(a)
tawdry harness
B D G and H are all nondifferentiable at the point x=a
C and F,u can clearly see that their dy/dx are decreasing
regal slate
B D G and H are all nondifferentiable at the point x=a
don’t just give the answers, explain your thought process
else you’re not helping
regal slate
this is as we apporach 6 from the right
this looks right
that’s one half
the first derivative is < 0 on the interval (0,3)
astral pebble
regal slate
what’s your explanation for this^
astral pebble
undefined at x=6
and the hollow circle adds a point of discontinuity
how do I incorperate the last limit?
as we go to infinity y approaches 2?
Im so lost
regal slate
undefined means there’s a VA (vertical asymptote) at x = 6
also because the graph approaches +- infinity approaching x=6 from either side
regal slate
as we go to infinity y approaches 2?
as x goes to infinity, y reaches 2, meaning there’s a horizontal asymptote at y=2
regal slate
this is as we apporach 6 from the right
this is almost correct, the y-value has to be 2
sorry i’m a bit busy rn, can’t give more detailed explanations
astral pebble
I am stull so confused
regal slate
i’ll translate it into plain english:
• f(x) is continuous of the interval (0,6) and (6, inf), this one should be self explanatory
• f(x) is not differentiable on x = 3 meaning the derivative is undefined at x = 3 so there is probably a kink at x = 3
• f’(x) < 0 on (0,3) meaning the function is decreasing on (0,3) i.e. y-value is decreasing-going downwards
• f’’(x) > 0 on (3,6) meaning the function is concave up on that interval
• first limit: as we approach 6 from the left side, the function goes toward positive infinity
• second limit: as we approach 6 from the right side, the function goes toward negative infinity
• third limit: as x heads toward positive infinity, the y-value reaches 2
vocal sleetBOT
@astral pebble Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
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tropic anvil
hello, could someone help solve this problem?
vocal sleetBOT
hello, could someone help solve this problem?
tropic anvil
I was thinking of using monvariants but I didn't succeed in finding a suitable one
dark kiln
um
obtuse radish
u know what neighbouring refers to? do diagonal count?
dark kiln
it doesn't even start spreading
tropic anvil
u know what neighbouring refers to? do diagonal count?
no
dim prairie
hello, could someone help solve this problem?
try starting out with a few squares
try a 4x4 grid
then see if you notice any patterns
obtuse radish
also does the question mean "for any starting combination will all 100 burn"?
since starting positioning seems to be the key
dim prairie
also does the question mean "for any starting combination will all 100 burn"?
obviously
obtuse radish
tropic anvil
try a 4x4 grid
okay I'll try it
dark kiln
it doesn't progress
tropic anvil
it doesn't progress
oh
tropic anvil
that means that the squares that are neighbours to the red square are those in black?
dark kiln
no, i'm assuming diagonals are not neighbours
tropic anvil
then see if you notice any patterns
nope it does not progress
:((
anyways thanks a lot for your help @obtuse radish @dark kiln @dim prairie
dark kiln
this mostly burns
but not entirely
if diagonals are neighbours, then clearly it burns
tropic anvil
okie dokie
vocal sleetBOT
vocal sleetBOT
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burnt gyro
Hello! I was able to solve the equation using a graphing calculator (answers are -4pi/3, -pi/3, 2pi/3, and 5pi/3), but i dont know how I would go about solving it algebraically. How would I do that?
vocal sleetBOT
Hello! I was able to solve the equation using a graphing calculator (answers are...
timber orchid
It's kinda just about knowing the special ratios
burnt gyro
but is there a way to solve it for x values that yield the negative square root of 3?
like how you can solve for the zeroes of a polynomial
can you do that?
burnt gyro
It's kinda just about knowing the special ratios
and if you don't mind, I understand how the ratios are important, but how can they be used to find good x values here?
timber orchid
The original -> sin x = -sqrt(3) cos x
Think abt the special ratios x which make this true
burnt gyro
so is it just finding the number of radians (from -2pi to 2pi) that will put you at (-1/2, 2sqrt(3)/2) on the unit circle?
or (1/2, -2sqrt(3)/2)
that does explain why the answers were all pi apart from each other. I mean, I understand that the tan function has asymptotes that are pi apart from each other so it already makes sense that the answers would be pi apart
dreamy viper
yeah you have to know your unit circle
burnt gyro
but this just gives it another reason
burnt gyro
yeah you have to know your unit circle
i see
I think I get it now
tysm both of you!! enjoy your day!!
.close
granite wing
$300.a$=$b^3$
find the smallest positive natural a value and it's b if a and b is natural.
twin meteorBOT
ajax4074
granite wing
this is translated so it might sound a little weird but let me clarify that it doesn't want b to be positive number as well it just needs to be natural.
i tried replacing the options:
12
15
25
30 and
45
well i have just tried 12
granite wing
but what i want to ask is is there a way to find if a number can be written as another's cube
granite wing
300 = 10^2 * 3
ok
civic pendant
To make it a power of 3 you need one more 10 and two more 3's
granite wing
what do you mean by 'one more'?
im trying to see if 3600 can be written in 'cubic(?)' form by the way
dim grove
a=90, b=30
granite wing
a=90, b=30
well i got the asnwers i cant get there tho you see
civic pendant
You want all powers to be multiplies of 3 to make it a cube
Of all prime factors
you already have 10^2 * 3
granite wing
You want all powers to be multiplies of 3 to make it a cube
ok makes sense
granite wing
no im trying to
civic pendant
$300 \cdot a = 10^2 \cdot 3^1 \cdot a$
twin meteorBOT
cain0196
granite wing
oh yeah
granite wing
The smallest a to complete it to multiplies of 3 is 10^1 * 3^2
is this equation, this?
if so, i got it till here
civic pendant
I mean, for $a=10^1 \cdot 3^2$ you get $300 \cdot a = 10^3 \cdot 3^3$
twin meteorBOT
cain0196
granite wing
i dont see
if i give a, a value then there's no a left
in the equation
am i misunderstanding what you mean by a= 10^1. 3^2 perhaps?
civic pendant
True, $300 \cdot a = 10^2 \cdot 3^1 \cdot a = 10^3 \cdot 3^3$
twin meteorBOT
cain0196
granite wing
oh the 300 was missing i suppose
well,
now it has become 10^2 ?
what was before 10^1
wait nevermind what i said there
but can you explain how the rhs (far right) is equal to 10^2. 3.a ?
bc 10.10 .3.a = 300a = 1000.27 ?
so 27000
you give a = 3^3 then?
civic pendant
no
granite wing
sorry i missed one 0 also
twin meteorBOT
cain0196
granite wing
90
yeah i was calculating didnt see that you've already told
did we give a=90 or figured it out?
civic pendant
Figured it out
granite wing
what are we doing basically
civic pendant
Let's do another one
civic pendant
$50 a = b^5$
twin meteorBOT
cain0196
civic pendant
$50 = 5^2 * 2$
granite wing
2.5.5
twin meteorBOT
cain0196
civic pendant
Now we want all powers to be multiplies of 5
So we want to get $5^5 \cdot 2^5$ for this we need $a=5^3 \cdot 2^4$
twin meteorBOT
cain0196
granite wing
yeah yeah
okay
we had 1, 2 already needed to multiply it by itself 4 more times and same for 5
civic pendant
yes
civic pendant
good
granite wing
third step?
granite wing
oh
twin meteorBOT
cain0196
civic pendant
@granite wing Is that clear?
granite wing
ooh
yes
i just wrote it to see that
so the same for 300
let me try one sec
wait we already did it right?
civic pendant
Yes, maybe I was lazy and wrote 10 instead of 5 * 2
But we did it
You should use primes though!
granite wing
oh i suppose thats why i got 300 hm
granite wing
You should use primes though!
why did we have to use primes again?
did you say that already?
let me check
civic pendant
Otherwise... you can't count on the powers
For instance 300 = 100* 3
And then you may try multiplying by 100^2 * 3^2
which isn't the smallest a
granite wing
hmm
civic pendant
?
granite wing
which isn't the smallest a
well got this
civic pendant
right
granite wing
did we change it later on?
civic pendant
you mean 3* 10^2?
granite wing
you mean 3* 10^2?
but that's still the same
civic pendant
nope
granite wing
10 isnt prime either so i thought we'd have the same case?
civic pendant
10 isn't prime but it gives the right result
Because all it's prime factors are to the power of 1
10 = 2*5
so we can use it
granite wing
oh this is new to me
civic pendant
Don't use 10
granite wing
then i'd use many more numbers?
twin meteorBOT
cain0196
granite wing
is that one of the reasons why we used 10?
civic pendant
we need 3 more 2's, 3 more 5's and 2 more 3's
civic pendant
is that one of the reasons why we used 10?
Umm, we used 10 because I was lazy
It's not the best practice
The best practice is to go with the prime factorization
granite wing
Umm, we used 10 because I was lazy
ahaha thats what you said beforee ok now i understand what you meant
granite wing
The best practice is to go with the prime factorization
all right
why do i get it 10?
ugh
civic pendant
what do you mean?
granite wing
a= 2.5.3^3 right?
granite wing
**cain0196**
by here
civic pendant
3^2
granite wing
(2.5.3)^3= b^3 then?
i still get the wrong answer
im too mathed its 2 am for me
i'll blame that factor
but since i get 30 here
then im missing a ^2 somewhere i suppose
...
civic pendant
2 AM is time to go to bed
hollow thorn
Hello anyone know what's the point of dy/dx = 0 helps for ?
vocal sleetBOT
Hello anyone know what's the point of dy/dx = 0 helps for ?
hollow thorn
I do found my after integrals d²y/dx² is 2x² + c
lyric fossil
helps you remove arbitrary constants
urban edge
Yeah, that helps solve for the +c
lyric fossil
after you integrate again you'll get another constant
each of the conditions fixes 1 of the constants
hollow thorn
So 2x² + c = 0
lyric fossil
no
hollow thorn
Integrals again ?
lyric fossil
just when x = 0
the derivative at x = 0 is 0
so plug in 0 into the derivative and set it equal to 0
shrewd dagger
formally this is an IVP involving second order diffy q's
and you need two initial values to be able to fully solve it
hollow thorn
Ah okay solved it thanks u too
vocal sleetBOT
@hollow thorn Has your question been resolved?
twin meteorBOT
elfin moon
,rotate
twin meteorBOT
elfin moon
Can it be symmetric matrix?
gleaming turtle
Can it be symmetric matrix?
nope as A^t not equal to A
elfin moon
Can cos couldn't digest minus in Matrix?
gleaming turtle
the minus is with the cos, cos would digest the minus of the angle
if thetha was negative then cos(thetha) would the positive
twin meteorBOT
elfin moon
@gleaming turtle
gleaming turtle
vocal sleetBOT
@elfin moon Has your question been resolved?
elfin moon
ohh that is the confusion
-cos thita= cos thita wrong?
cos(-thita)=costhita is correct only
.close
dry forge
vocal sleetBOT
vocal sleetBOT
@dry forge Has your question been resolved?
thin vale
the degree of a differential equation is the degree of the highest order differential in the equation
this equation has first, and second derivatives
so the largest of those, is the second derivative
so it would be a 2nd order equation
vocal sleetBOT
@dry forge Has your question been resolved?
elfin moon
