So, we can easily say that its injective => inversable
#help-17
dull bear
[this is the idea you want though! showing you're always (strictly) positive [/negative] means you're always (strictly) increasing [/decreasing], so injective...]
civic hound
this derivative is ugly as
might wanna retouch it algebrically, but is it correct lmao
dull bear
you can make one tiny simplification for sure 
tidal dock
im stuck AHHHH
wrong factoring
tidal dock
although further on it indeed cancels out lmao
civic hound
what cancels out
i can't figure it out
Well, i mean 4x^3 isn't always positive so i need to solve that equation
how if theres an exponential?
dull bear
Exponentials of real numbers are always positive(!)
civic hound
yes but if 4x^3 is negative the result is negative
dull bear
well you should have $e^{x^4}$ but otherwise fine
twin meteorBOT
@dull bear
civic hound
oh yeah π
dull bear
But basically sure, you have $x^3 \geq 0$ iff $x \geq 0$ (one way you can see that was e.g. divide that by $x^2$)
twin meteorBOT
@dull bear
civic hound
oh yeah
lemme do something i will brb
to prove that this function aint inversable for all x:
should i just say
its only for x>0 so it can tbe that?
Ok solved... omg.
dull bear
Well better would be just to say as per here
dull bear
it's .close
civic hound
.close
vocal sleetBOT
vocal sleetBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
hushed pewter
Is x supposed to be some periodic function of t?
Not my area of study, sadly. Best I recommend is a starting source: https://math.stackexchange.com/questions/661638/period-of-sum-of-sinusoids
vocal sleetBOT
@vast shale Has your question been resolved?
vocal sleetBOT
Available help channel!
tulip lagoon
I have a random question... If A: B = 3:5 and A: C = 4:7, then B: C = ?
I would have guessed 5:7 but apparently thats incorrect.
paper shoal
you need to set up an equation that cancels the As and leaves you with B:C and then plug in the ratios
tulip lagoon
thanks I'll give that a try. I wasn't even sure where to start π what do you mean by plug in the ratios?
paper shoal
$\frac{B}{A} * \frac{A}{C} = \frac{B}{C}$
twin meteorBOT
Panda
paper shoal
so now just put the numbers in for the letters
tulip lagoon
thanks! I now see what you mean by cancel the A, by multiplying the A in the denominator
paper shoal
yup
vocal sleetBOT
@tulip lagoon Has your question been resolved?
vast shale
vocal sleetBOT
vast shale
How would one make an equation for this problem?
vagrant solar
change time into hours
use equation time = distance/speed
time upstream + tomr downstream = time thatβs been converted into hours
so 12/s-3 + 12/(s+3) = converted hours
vast shale
Can I put 5 hours and 20 minutes as a mixed number
vast shale
so 12/s-3 + 12/(s+3) = converted hours
What do I do after that?
I got an quadratic equation
vocal sleetBOT
@vast shale Has your question been resolved?
vast shale
HELP
vast shale
<@&286206848099549185>
vocal sleetBOT
@vast shale Has your question been resolved?
vast shale
<@&286206848099549185>
languid adder
$$\frac{12}{v - 3} + \frac{12}{v + 3} = \frac{16}{3}.$$
twin meteorBOT
Flamey
languid adder
@vast shale
vast shale
Yes
languid adder
Yes
vast shale
**Flamey**
Am I supposed make this a quadratic equation?
vast shale
5 1/3 or 16/3
Yeah I got that
Problem is when I tried multiplying the lcd
And solving for the problem
languid adder
u multiply every term by 3(v-3)(v+3)
to clear the fractions
$$36(v + 3) + 36(v - 3) = 16(v^2 - 9).$$
Expanding the left side gives:
$$36v + 108 + 36v - 108 = 16v^2 - 144.$$
Simplifying the left side gives:
$$72v = 16v^2 - 144.$$
twin meteorBOT
Flamey
languid adder
see
twin meteorBOT
Flamey
languid adder
**Flamey**
Yeah. Dividing this through 16 simplifies the equation:
$$v^2 - 4.5v - 9 = 0.$$
twin meteorBOT
Flamey
languid adder
By substituting A, B, C into the quadratic formula, yes
One of the solutions will be negative, but speed cannot be negative so you discard that
vocal sleetBOT
@vast shale Has your question been resolved?
vast shale
.close
vocal sleetBOT
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fervent geyser
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pallid forge
What is the equation you came up with?
fervent geyser
price for one book is 20x120+1400 + 1.55
so 6000 is that into 6000
which is 3801.55 x 6000
so 22809300
what am i doing wrong
could you please tell me what to do im actually in a bit of a rush it would mean alot if you could tell me before i have to leave in 10mins
pallid forge
alright so
fervent geyser
120x20+1,55x6000+1400
fervent geyser
yeah i had to figure out what type-setting was
same
vocal sleetBOT
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Available help channel!
vocal sleetBOT
placid plank
the x is 3, so it is saying 3.5 = f(3)
pallid forge
the y-value of f'(x) is the slope of f(x)
vocal sleetBOT
@vast shale Has your question been resolved?
vocal sleetBOT
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hot mica
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hot mica
E)
shy trench
scenic ravine
!occupied
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scenic ravine
One way would be to bruteforce it. x=5-2y. Substitute that into equation 2 and solve
stable skiff
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marsh acorn
quick doubt related to vector space
vocal sleetBOT
quick doubt related to **vector space**
marsh acorn
is division of vector possible if no then why?
if square of vector is possible?
if not why?
what about subtraction
river minnow
is division of vector possible if no then why?
You would have multiplication of vectors if that was possible
Wait, there is no division of vectors even mentioned in the options
marsh acorn
You would have multiplication of vectors if that was possible
we do have scaler multiplication
river minnow
v/2 denotes the scalar 1/2 scaling a vector v
marsh acorn
v/2 denotes the scalar 1/2 scaling a vector v
oh so it's like multiplying 1/2 to v
river minnow
Right
marsh acorn
perfect
so we can't multiply or divide vectors like we do to scalers?
am I correct?
river minnow
No
Definition of a vector space does not provide a way of multiplying vectors together to form another vector
One such example though would be the cross product in R^3, but I am pretty sure you can't define division for that
marsh acorn
Definition of a vector space does not provide a way of multiplying vectors toget...
i see, but we can add vectors?
marsh acorn
One such example though would be the cross product in R^3, but I am pretty sure ...
yes but i am very new to vector space so can you pls explain this sir/mam?
river minnow
Forget about that example for now
marsh acorn
Forget about that example for now
oki doki
marsh acorn
And subtract them as well
cool so v1-v2 is possible
river minnow
Yes
marsh acorn
bcz multiplication is not possible then v^n is also not possilbe?
like v square or cube
river minnow
Right
marsh acorn
ohh got it I will note these down, Thank you so muchhh <33
river minnow
They could have also meant v^2 to be the Euclidean norm, but that still wouldn't be a correct answer as v^2 would denote a scalar rather than a vector
They would also need to mention that V is finite-dimensional
river minnow
Dot product with itself
marsh acorn
ohh oki doki understood Thank youu
marsh acorn
Dot product with itself
it can be to the power of n?
river minnow
Only power of 2
river minnow
v^2 will be a scalar, not a vector
And dot product requires vectors as its inputs
I guess that could work only if V = R
marsh acorn
ohh oki doki
I just searched for vector's defination in maths but this is too complex, In mathematics and physics, vector is a term that refers colloquially to some quantities that cannot be expressed by a single number, or to elements of some vector spaces.
river minnow
Vector spaces are more abstract than what non-mathematicians think, yeah
marsh acorn
Vector spaces are more abstract than what non-mathematicians think, yeah
ohh so it's more like an imaginatative thing?
river minnow
Any set where you have sensible addition of elements and scaling could be a vector space
Real functions for example form a vector space over R
spring tapir
Also you can do some basic operations on this vector space, which defines it as a vector space. which is what the question is kind of asking
marsh acorn
Real functions for example form a vector space over R
what does it mean here "vector space over R"? does over here means ^
marsh acorn
Also you can do some basic operations on this vector space, which defines it as ...
oki doki I understood the question and solved it but I am trying to understand fundamentals...
river minnow
what does it mean here "vector space over R"? does over here means ^
It means that it's a vector space with the scalars taken from R
spring tapir
the first one you missed is quite important
marsh acorn
It means that it's a vector space with the scalars taken from R
oki oki thank you, friend, I really appreciate it π
spring tapir
It means that it's a vector space with the scalars taken from R
i think the squared isnt a solution since you would have to take the square root of it right for it to be acceptable?
marsh acorn
the first one you missed is quite important
yes yes I just notice it's more like if we multiply scaler to vector where scaler c belongs to real rumber correct?
river minnow
Yeah I said that v^2 is not a correct answer
spring tapir
yes yes I just notice it's more like if we multiply scaler to vector where scale...
i dont think it really matters where the scaler comes from, as long as its a scaler.
river minnow
i think the squared isnt a solution since you would have to take the square root...
Why square root?
spring tapir
Why square root?
thinking of a norm
river minnow
Square rooting the norm of a vector still gives you a scalar though
marsh acorn
Yeah I said that v^2 is not a correct answer
yes yes I understood it's bcz we can't multiply vectors
marsh acorn
i dont think it really matters where the scaler comes from, as long as its a sca...
ohh oki so the scaler here doesn't have any value π
spring tapir
Square rooting the norm of a vector still gives you a scalar though
makes complete sense.
marsh acorn
Square rooting the norm of a vector still gives you a scalar though
really? we can square root a vector and can't square it?
river minnow
I never said that you can take the square root of a vector
marsh acorn
a genuine doubt
spring tapir
well taking the norm gives you a scaler, im a dummy and wasnt thinking
marsh acorn
I never said that you can take the square root of a vector
ohh oki doki
any good lecture can you suggest on vector space?
river minnow
Not really, I didn't watch lectures to understand vector spaces
But if you want to watch a video about them, 3b1b has a playlist about linear algebra
marsh acorn
But if you want to watch a video about them, 3b1b has a playlist about linear al...
oki dokii I will check them out
Thank you sooo muchh
you guys are bestt <33
marsh acorn
But if you want to watch a video about them, 3b1b has a playlist about linear al...
final ques,
this link?
https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab
spring tapir
i dont think watching videos helps me much sorry
i kind of read my notes and do problems
marsh acorn
i kind of read my notes and do problems
oki dokii, how do make notes?
spring tapir
I go to lectures, I write down everything, I read them and try to understand since I don't understand during lecture most the time.
I then re-write them nicely, and typically try to do the proof on a chalkboard without looking.
river minnow
final ques,
this link?
https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3Miz...
Yeah, I meant that one
And yes reading books is more efficient for math in general
spring tapir
It's an important skill to be able to read from a book and learn. Eventually there won't be any videos left.
marsh acorn
It's an important skill to be able to read from a book and learn. Eventually the...
yes yes I understand I need to learn it.
Thank you guysss I really appreciate your help <33
.close
vocal sleetBOT
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Available help channel!
heavy tusk
Meow
arctic mantle
okay two things @heavy tusk
whenever possible express roots as fractional powers; you've done that with 1/sqrt x but not sqrt x
and yes it's correct
heavy tusk
whenever possible express roots as fractional powers; you've done that with 1/sq...
Okie
arctic mantle
,w factorize derivative of (x^0.5 + x^-0.5)^8
i have no idea what that is
actually, hang on.
heavy tusk
Meow
arctic mantle
,w antiderivative of 8(0.5x^-0.5 -0.5x^-1.5)(x^0.5 + x^-0.5)^7
twin meteorBOT
heavy tusk
Integrals π³
arctic mantle
fax
scenic ravine
Is this correct?
looks right to me
vocal sleetBOT
arctic mantle
Thanks guys!
np
vocal sleetBOT
Available help channel!
heavy tusk
Meow
scenic ravine
I think so
lapis marten
It depends on how much they want you to simplify it
heavy tusk
The worst part is how I can't check on google if its correct or not
heavy tusk
It depends on how much they want you to simplify it
I can simplify it further?
lapis marten
Well, you can multiply 8 and 1/2, but there is also a technique that's a bit more complicated, for 'simplifying' the entire expression
I'm not sure what is expected from you
heavy tusk
Yeah idt my teacher would expect allat
lapis marten
$\left(\sqrt{x} + \frac1{\sqrt{x}}\right)^2 = x + \frac1{x} + 2$, this is a pattern that continues
twin meteorBOT
Jelle
lapis marten
nvm
lapis marten
You are good
heavy tusk
.close
vocal sleetBOT
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Available help channel!
pearl current
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@pearl current Has your question been resolved?
glad thicket
i thought it was related to n
First, you need to calculate L.
Get the $L$ for each sequence.
twin meteorBOT
KOforaf
pearl current
for the first one its 0 right
bronze wharf
Hey
bronze wharf
I need help with cutting off parabolas in desmos
bronze wharf
ye
outer warren
{what you want to keep}
bronze wharf
but im in a bit of a pickle
this is my equation cos i needed to use rotations too
x\sin(w)+y\cos(w)=a_{1}\left(\left(x\cos(w)-y\sin(w)\right)-b_{1}\right)^{2}+c_{1}
bruh
twin meteorBOT
Aβ€Γ
bronze wharf
so, ik this is dumb, but i just searched a yt video and i copied their formula to be able to turn a parabola
on normal parabolas i was able to use {<x<}
but im not quite sure how to do it with my new funky equation
i would be open to elarning how to be able to restrict the domain of this equation orrrrrr learn how to be able to rotate normal quadratic equations
pale perch
ig you could write
{xcos(w)-ysin(w)<A}
bronze wharf
ig you could write
{xcos(w)-ysin(w)<A}
in the same equation box?
dam gtg have dinner brb
pale perch
yeah, that would restrict the shape of it to a regular parabola that ends at x=A
which will be maintained while rotating
bronze wharf
im back
bronze wharf
ig you could write
{xcos(w)-ysin(w)<A}
sick, that works one way
how about the other way?
actually,... i think i can get it
bronze wharf
yeah, that would restrict the shape of it to a regular parabola that ends at x=A
wait, im a bit confused, this does let me choose specific two points on the parabola to be my start and end?
is there a way i could do that?
pale perch
if you want a two end restriction just write
{A<xcos(w)-ysin(w)<B}
the A and B are relative to if w was 0
in practice, anyway
it will be rotating the parabola shape that would be given if A<x<B
bronze wharf
hm, it doesnt seem to work?
or atleasst when making A and B sliders ranging from -150 to 150
actually it works
sorry
just had to reset sliders
ty for the help
safe spindle
vocal sleetBOT
tired gate
You can think of them as two planes, do two planes always intersect?
safe spindle
not always
tired gate
So this matrix won't always have infinite solutions
In what circumstances do planes never intersect? In what circumstances do they intersect?
safe spindle
if 2-4a = 0, then they'll never intersect?
i have no idea what it means if there is infinite solutions tho
safe spindle
So this matrix won't always have infinite solutions
ok wait it doesnt always have infinite solutions, but its impossible to have a unique one right?
crisp spruce
Im sorry if my terminology is incorrect, but I need help in understanding something,
If an Inscribed angle in a circle that's like 'layed' (? idk the term in english) on a diameter in a circle is 90 degrees, why isn't it 45 degrees when layed on a radius?
crisp spruce
this is the drawing, I don't understand how ABO is 36 degress and not 45
lethal rock
this is the drawing, I don't understand how ABO is 36 degress and not 45
You should give some info if AB parallel OC and BOC=36 then OBA=36 cause they are alternate angles
Or if it is given OAB=36 then OBA again=36 cause OA=OB(radius) and angles opposite to equal sides in a triangle are equal
crisp spruce
basically O is the circle ceter, out of it they drawn 4 radiuses, creating 5 equal sections (180/5=36)
I just don't understand the principle
if the rule says an inscribed angle that's layed on a diameter is 90 degrees, why isn't it half of that when its layed on a radius
lethal rock
if the rule says an inscribed angle that's layed on a diameter is 90 degrees, wh...
I dont get what you r saying, r u referring to the theorem that says diameter subtends 90 degrees at the peripheri of the circle?
crisp spruce
yeah
lethal rock
None of the angles here is subtended by the diameter
Lets name the other end of the diameter as M
If CM subtends any angle at circle that would be 90
crisp spruce
Yeah, ok, So if there was a angle that Subtends MO or CO why would it not be 45 degrees
lethal rock
Why would it be 45?
Can you draw and send what u r saying
The theorem that u r referring to says specifically about angles subtended by the ends of diameter
crisp spruce
Yeah let me explain
lethal rock
Ok
crisp spruce
Basically if MKC is 90 degrees because it "sits" on the diamter. why wouldn't MKO be 45 degrees?
lethal rock
It could be and it could not be ,you will have to prove congruency of triangles
Join OK
You will have two triangles
Now vary K along the peripheri
Those triangles will not always be congruent
Whats your logic behind bisecting the angle?
crisp spruce
because the MKC will stay the same no matter the location of K on the peripheri, so why isn't it true for the radius as well?
i mean KM AND KC will vary in size but wouldn't the angle stay the same?
lethal rock
Why
How r u able to conclude that angles are being bisected
They wont be bisected in every cases
They will be bisected when OK will be perpendicular to MC
Alright?
I can go now?
crisp spruce
i just don't understand why, I mean if we continued stretched AO to a diameter, then why wouldn't it OB bisect?
maybe im stupid man, but this doesn't really make sense to me
lethal rock
Umm i dont know whats troubling you
First of all you are being very intutive
You need to have a proof then we can argue
Now if u really want i can give you a proof why it cant be 45 always
But maths doesnt work that way if you are saying something you need to have a proof to back it up
You know what i mean
Anyways if it helps i can give you a proof why it cant be always 45
crisp spruce
Yes please
I mean I donβt understand why is it always 90 when it comes to diameters, but not always 45 when it comes to radius
lethal rock
Join OK and send me
crisp spruce
lethal rock
Lets assume you r right and say okc is 45
But ok=oc
That means ock also 45
Which means koc=90
Now vary k along peripheri, is koc always 90?
It will be 90 in one case only the very symmterical one that you have drawn
Hope it helps
wicked tundra
vocal sleetBOT
wicked tundra
Sry for that huge part
arctic mantle
wth is that
arctic mantle
no--wait, nvm
wicked tundra
but it got all mixed up in my mind
arctic mantle
the genuine hell
scarlet tapir
its easy dude
arctic mantle
f
livid horizon
Sum of angles in a polygon with n sides= 180(n-2) degrees
wicked tundra
never heard of that ok
livid horizon
Ig you can
arctic mantle
and im fairly certain it only works for convex
scarlet tapir
Sum of angles in a polygon with n sides= 180(n-2) degrees
that's the way
scarlet tapir
yep
livid horizon
9 I think
wicked tundra
180*9 = 1620
arctic mantle
wait hang on
wicked tundra
how is it 9
arctic mantle
doesn't it work only for convex?
arctic mantle
how is it 9
n-2
arctic mantle
yep
wicked tundra
how did I count 11
scarlet tapir
x7
wicked tundra
mb
livid horizon
Actually any no of sides work, as long as you have the measure of angles
arctic mantle
7?
arctic mantle
what are we counting hre
livid horizon
,calc 1260/180
twin meteorBOT
Result:
7
signal pendant
doesn't it work only for convex?
Why won't it not work? The proof is just joining all the vertices to one vertex, you get n-2 triangles in joining them, hence (n-2)Ο
wicked tundra
yeah
arctic mantle
i really can't tell which sides ur referring to
arctic mantle
Why won't it not work? The proof is just joining all the vertices to one vertex,...
oh yea i forgot about that
scarlet tapir
41
peak echo
I gotta ask, what subject is this question from? Is there any specialisation here?
livid horizon
doesn't it work only for convex?
In case it is concave you take the reflex angle I think
wicked tundra
I gotta ask, what subject is this question from? Is there any specialisation her...
its a mixed sheet
peak echo
Sorry, it's not helping, but I'm curious as hell
signal pendant
I gotta ask, what subject is this question from? Is there any specialisation her...
Looks like competition math tbh
arctic mantle
Sorry, it's not helping, but I'm curious as hell
me on most questions
peak echo
u want the syllabus
Yeah, that'd be great, thank you, you can DM it to me
wicked tundra
Yeah, that'd be great, thank you, you can DM it to me
cant I send it here?
peak echo
Well yea, sure, that works for me
peak echo
So it's just completely wild
wicked tundra
yeh...
peak echo
Is there any book you're using for this?
wicked tundra
Is there any book you're using for this?
its like
combined syllabus
for 11th grade and 12th grade
so I havent yet studied geometry from 12th grade
so no yet references
from books
peak echo
Okay, so 12th grade geometry, I'll assume that
peak echo
Thanks, that's good to know. My geometry is pretty weak, I want to fill this gap
wicked tundra
well lets get back to the question
peak echo
Didn't it get solved
wicked tundra
Didn't it get solved
no...
the summation of the angles ended up being something 400+
peak echo
Right, 409
peak echo
I'm cookin
wicked tundra
I'm cookin
aght
inner osprey
Consider:
peak echo
I still can't figure it out
peak echo
The angles between the squares is easy, x is tough
peak echo
Lmao
inner osprey
so every triangle i create there is a right triangle
wicked tundra
so every triangle i create there is a right triangle
ik
but the other 2 angles
matter as well
right?
wicked tundra
yeah
inner osprey
well that is what we are trying to solve for
peak echo
I think I got it
wicked tundra
yeah
peak echo
60 in the leftmost triangle
peak echo
You can follow from there
inner osprey
you just move left to right
vocal sleetBOT
peak echo
what i do is i draw perpendicular linesβ¦
This is brilliant
inner osprey
coincidentally i saw very similar to problem for this some weeks ago while working with some studentsβ¦
answer always involves drawing parallel/perpendicular lines
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hollow prism
Show that if G has max degree at most 3, then their vertex/edge connectivities are equal.
vocal sleetBOT
Show that if G has max degree at most 3, then their vertex/edge connectivities a...
hollow prism
I was recommended to do this by vertex connectivity cases if it helps ?
vocal sleetBOT
@hollow prism Has your question been resolved?
hollow prism
<@&286206848099549185>
fresh solstice
oh
hollow prism
question
How can we show that if G has max degree at most 3, then their vertex/edge connectivities are equal?
hollow prism
?
Im doing cases
If vertex connectivity=0, then it's trivial that edge connectivity is 0 right?
Since its already disconnected?
hollow prism
uni
hollow prism
I dont think it matters as long as u know graph theory
hollow prism
Do u agree that vertex connectivity=0 => edge connectivity=0
hollow prism
YEah
vast shale
then
ure right
since
The edge connectivity of a disconnected graph is therefore 0, while that of a connected graph with a graph bridge is 1
vocal sleetBOT
@hollow prism Has your question been resolved?
jolly cedar
how does this
vocal sleetBOT
how does this
jolly cedar
1 ax2+b
flat whale
Like x -> x * c
Do this and solve for c that works
jolly cedar
what does * mean in x*c
flat whale
Multiplication
jolly cedar
how does x=x*c
jolly cedar
I don't understand
u want to transform x to xc?
i solved it without substitution
i dont understand how we can solve it with substitution
flat whale
i solved it without substitution
Show
flat whale
i dont understand how we can solve it with substitution
You substitute x * c for x and solve for c
jolly cedar
nvm i discovered in error in my solution
jolly cedar
You substitute x * c for x and solve for c
i don't understand how you substitute x*c for x
and solve for c
how do you want to solve for c when the functiun doesnt equal a specific number
flat whale
how do you want to solve for c when the functiun doesnt equal a specific number
You just set the fraction with the substitution equal to the result you want and equate coefficient
lilac lava
vocal sleetBOT
lilac lava
Idk how to proceed the solution
vast shale
vocal sleetBOT
tawny pier
The figure shows three externally touching circles and internal angles A, B and C. Based on the figure, find the degree measure of Ξ±.
vocal sleetBOT
The figure shows three externally touching circles and internal angles A, B and ...
@tawny pier Has your question been resolved?
last jolt
@tawny pier are radiuses given?
tawny pier
<@695285164024135800> are radiuses given?
.
tawny pier
Okay, do u see picture?
yep i see it
tawny pier
okayy, so O_1, O_2, O_3 are centres
.
last jolt
so i sum up all of these to 180 degrees (2a, 6a, 20)
Yea
But for full solution, you need to prove that it's really triangle
Or that points O_1, O_2 and touch point are on the same line
tawny pier
Or that points O_1, O_2 and touch point are on the same line
btw why are there two O_2s?
last jolt
Oh, O_3, sorry
tawny pier
so i sum up all of these to 180 degrees (2a, 6a, 20)
so finding a is like this? that's all?
last jolt
Or that points O_1, O_2 and touch point are on the same line
For finding yes, but for full solution this:
velvet cove
vocal sleetBOT
velvet cove
ignore the n=0 at the end of the first line of the question im pretty sure its misprint
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
3
i got D orignally
the answer is C
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onyx thicket
how do I get the VA's for denominator 2e^5x + 3e^3x + 14
vocal sleetBOT
how do I get the VA's for denominator 2e^5x + 3e^3x + 14
hexed needle
how do I get the VA's for denominator 2e^5x + 3e^3x + 14
that expression is a sum of exponentials and positive numbers, so it is always positive
so there are none
vocal sleetBOT
@onyx thicket Has your question been resolved?
somber flame
always positive isnβt really enough
like 1/x when x > 0 always has positive denominator
but still an asymptote
onyx thicket
This is for x > 2 btw
I didnβt send the numerator but should I? Idk if it effects va
somber flame
whatβs the whole question?
somber flame
i donβt think it has any vertical asymptotes
loud walrus
Do you know the definition of Vertical asymptote?
onyx thicket
a line where the function doesn't touch?
loud walrus
what kind of line?
onyx thicket
vertical
loud walrus
what is the domain of your function?
onyx thicket
the top expression when x<=2 and the bottom is x > 2 but idk how to write the domain
This is whole thing
onyx thicket
for the first one I said VA at x = 0
somber flame
again thatβs not enough
somber flame
no
somber flame
f(x) = 1/x with f(0) defined to be 0
somber flame
wdym ?, itβs a perfectly good function with domain R
loud walrus
you're not being rigurous
somber flame
i am
somber flame
that means no vertical asymptotes
this is not rigorous
somber flame
i just gave a counterexample
loud walrus
with a function which denominator
can NEVER be 0
that's not a counter example
it has nothing to do
vocal sleetBOT
onyx thicket
.reopen
vocal sleetBOT
β
onyx thicket
is there a VA at x = 0 cuz of the top one tho?
somber flame
no, there are none
onyx thicket
so what would i do for f(0) cuz thats less than or equal to 2
somber flame
$\lim_{x\to c} f(x)$ exists for every $c\geq 2$
twin meteorBOT
soulgazer
somber flame
because f is continuous on [2,infinity)
or if youβre saying the domain is (2,infinity) maybe better to say itβs continuous and also limits exist on the boundary of its domain (which is just 2)
but thatβs excessive
somber flame
**soulgazer**
for f to have a vertical asymptote this limit would have to be infinity or -infinity on one side of some c
thatβs what vertical asymptote at c means
ashen peak
vocal sleetBOT
ashen peak
Hi i'd like to get help with how to solve this
hexed needle
first, graph it. then let L = ax (no y intercept bc it goes through the origin). you need to find a
hexed needle
also notice that a has to be positive
hexed needle
lemme rephrase that
ashen peak
okok
hexed needle
L(x) = ax
it's a function
that's just a line through the origin with slope a
you could use m if you wanted
I just like a lol
plot that function, and try to find an a value that cuts that region in half
ashen peak
they are asking for slope through
the slope of the line
i would need to use limits right
ashen peak
yeah i understand that part
i understand the concept of it
but idk which formula to use to find it
ashen peak
the goal is to find the slope of the line that cuts the areas in half
hexed needle
what i would do is find the total area under that curve first
ashen peak
so i need to subtract the upper limit by the lower limit
hexed needle
wdym limit?
hexed needle
yes exactly
ashen peak
dx
hexed needle
so find the total area under that quadratic, then half it. you need the area between the curve and that line to be that number
hexed needle
I'm so lost hahah
what did you try?
vocal sleetBOT
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round plover
I have this in some notes I'm reading
vocal sleetBOT
I have this in some notes I'm reading
round plover
but some other notes say that two singular simplices (or more generally, elements of a chain complex) are homologous if they're in the same homology class
vocal sleetBOT
but some other notes say that two singular simplices (or more generally, element...
round plover
i.e., the formal difference between two elements is itself exactly a boundary
is this the same thing, just worded weirdly, or is this some other equivalent characterisation
vocal sleetBOT
@round plover Has your question been resolved?
vocal sleetBOT
@round plover Has your question been resolved?
grand basin
vocal sleetBOT
grand basin
need help
vocal sleetBOT
@grand basin Has your question been resolved?
grand basin
<@&286206848099549185>
distant girder
so if im reading this right, its basically asking if you have regular language L, you can cut every single even-length word in L in half, make it its own language, and have that also be a regular language?
distant girder
hmm
if you have an NFA A that accepts L, you basically just want to see whenever you get to a 'halfway' point, or in other words, if the number of steps needed to go to the end is the same as the number of steps we needed to get to the point where we are.
think of an NFA A', which is A but where the direction every single connection is reversed, and the 'accept' states become the 'begin' states and vice versa. Remove all of the specific transitions and replace them with sigma (any value) transitions, and add an epsilon transition from the start state to all accept states if there's more than 1 accept states (if you do this, then add it to A as well).
Consider what happens when we run these two together, on the same input, and were to freeze it at some point, if NFA A is at some state q after n transitions, and NFA A' is also at that same state q, that means that was some valid path of length n was found from q to the end in the forward NFA (after all, the backwards NFA took it to get there)
so if at any point the two NFAs have the same state, you have a match
now you need some way to formalize this 
i don't remember enough to help
theres a lot of resoruces online about this i think just search 'half closed under regular language'
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waxen hawk
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waxen hawk
Anything wrong?
vocal sleetBOT
Anything wrong?
vocal sleetBOT
merry python
yep, no error
vocal sleetBOT
Available help channel!
hollow compass
vocal sleetBOT
hollow compass
Is my work ok?
void latch
please keep it to a single channel
hollow compass
the bot said the channel would automatically close then I tried closing the other channel 
*manually
I put my solution into wolf ram as well as the problem and its way off lol
is there a reason why u isnt replaced with what we substituted out?
<@&286206848099549185>
vocal sleetBOT
@hollow compass Has your question been resolved?
hollow compass
No
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deep zenith
If $f : X \rightarrow Y$ is a dominant morphism of varieties (defined as integral separated schemes of finite type over a field), is the field extension $K(Y) \rightarrow K(X)$ a finite degree extension?
vocal sleetBOT
If $f : X \rightarrow Y$ is a dominant morphism of varieties (defined as integra...
twin meteorBOT
DavidL1450
If $f : X \rightarrow Y$ is a dominant morphism of varieties (defined as integral separated schemes of finite type over a field), is the field extension $K(Y) \rightarrow K(X)$ a finite degree extension?
vocal sleetBOT
@deep zenith Has your question been resolved?
inland stump
vocal sleetBOT
@inland stump Has your question been resolved?
inland stump
.close
dry cedar
Hey I had a quick question
vocal sleetBOT
Hey I had a quick question
outer warren
no
dry cedar
no?
outer warren
no, as in it isn't correct
outer warren
you committed a sign/order of operations error
what they have there is correct,
but that isn't what you wrote
() around the -2 isn't optional here
outer warren
you're missing () around the -2
dry cedar
Oh alright
If I may ask then
if its something like
5/ (-3/4)^n-1
Would it just be
(-20/3) ^n-1
outer warren
write it out
dry cedar
Im just a bit unsure bc of the x ^y
5x 4^n-1 = 20^n-1 / -3
So thats the same as (20/-3? ) ^n-1
@outer warren sorry for the ping good sire
dry cedar
5/ (-3/4)^n-1
5x (4/-3)^n-1
dry cedar
No that makes sense yeah
outer warren
nor multiply into the exponent like that
outer warren
just leave it as
$$5\times \br{-\frac43}^{n-1}$$
twin meteorBOT
βΞ±ΞΌΞ©βΟβ €
outer warren
multipling BOTH in / out like that is illegal
outer warren
what
outer warren
flipping is fine
dry cedar
Oh ok
So you cannot multiply
eg,
3 x 6^n
yeah that makes sense
so the only way to possibly combine the two is
3 / (1/6)^n ?
wait but i guess you wouldnt do that in the first place or idk im losing myslef a bit
outer warren
3 * 6^n is simpler than 3/ (1/6)^n
dry cedar
Im a bit confused
outer warren
just don't try to forcibly combine things
know when to stop
only do what laws allow you to do
outer warren
and there are things that you "can" do compared to stuff that you should and whether they're helpful
if what was =4
outer warren
have to do what
dry cedar
3/ (1/6)^n = 4
18^n = 4
outer warren
no
outer warren
like siad
just don't try to forcibly combine things
know when to stop
only do what laws allow you to do
dry cedar
No i understand that
outer warren
3 * 6^n can NOT be combined into 18^n period
because there are no laws justifying that
dry cedar
But how come
dry cedar
3 * 6^n is NOT the same as 18^n
Oh ok okok
I understand
now what your getting at
srry
outer warren
instead you can first divide both sides by 3,
then log_6 both sides
dry cedar
But how come
So the only reason they were able to do this