u made a good friend
#help-26
ocean terrace
ornate trellis
Tis why i need a textbook
agile harness
u made a good friend
never heard of it
agile harness
Tis why i need a textbook
did you look at your dms
ocean terrace
me š
ornate trellis
did you look at your dms
uhhh no
agile harness
š¤
ornate trellis
uhh
agile harness
yea
ornate trellis
am i gonan be arrested
ornate trellis
im scared
agile harness
ornate trellis
oh here is a funny lil example
of why i wish i could personalize math courses
nvm
My teacher just gives
weird definitions for things that i think might fuck people up in the future
agile harness
interesting
ornate trellis
interesting
like
pls tell me
what is e?
I would define it as
The number which
has a derivative of itself
but she was telling me it means something about the function being continuous
like how is that a definition
agile harness
has a derivative of itself
false
ornate trellis
e*x
ornate trellis
E^X
ornate trellis
Lemme correct it
number which when rasied to the x power has a derivative of itself
also
agile harness
but she was telling me it means something about the function being continuous
sheās probably talking about continuous interest
ornate trellis
im pretty sure there is something qwith like
agile harness
compound interest
compounded continuously
$e = \lim_{x \to \infty} \left(1+\frac{1}{x}\right)^x$
thorny flameBOT
knief
ornate trellis
but isnt there something that defines it with eulers thing
and one that defines it as like
the value that makes some constant = to 1
agile harness
but isnt there something that defines it with eulers thing
what
a continued fraction?
iām not sure what youāre getting at
ornate trellis
$e^(\pi i)=-1$
agile harness
thatās not the definition of e
thorny flameBOT
ā cj Ī£
agile harness
thatās eulers identity
ornate trellis
thatās not the definition of e
cant you use it to derive one tho?
agile harness
i mean sure but this comes from having already defined e, pi, and i
ornate trellis
wouldnt you only have to define 2 of them?
then solve 4 e
ig it would be backwards
ornate trellis
the value that makes some constant = to 1
do you know what im talking abt here tho
topaz sinewBOT
@ornate trellis Has your question been resolved?
ornate trellis
ln(e) = 1? like iām not sure what you mean
Ok
so itās the the thing with exponential
i watched one of the 3b1b vids a while ago
thatās whatās iām thinking of
and i think he is essentially just describing the concept via constants
2^x= 2^x(c)
and i think what heās saying is what can we swap 2 with to make that c=1
and itās e
warm monolith
maybe you got a bit confused with something
that c is gonna be 1 no matter what it is
wether it's two or e
maybe he was talking about derivatives?
ornate trellis
maybe he was talking about derivatives?
yeah
I thought i mentioned that it has something to do with derivatives of an exponential
so i think itās prettt much the same definition i was giving with a more technical explanation of why
iirc
warm monolith
i would guess he was talking about a the derivative of $a^{cx}=ca^{x}$, in this case that would only happen if a=e
thorny flameBOT
UbuRoi
warm monolith
so.. is your question is what is the definition of e is? i scrolled back a little but i don't get exactly what you're asking :p
ornate trellis
mkay so with the given equation he seems to suggest that as dt->0, the value of it approaches a weird constant. I think the point is heās trying to find what number would make that constant 1
ornate trellis
so.. is your question is what is the definition of e is? i scrolled back a littl...
oh it started with stuff about the unit circle now itās kinda evolved into what the definition of e is
ornate trellis
mkay so with the given equation he seems to suggest that as dt->0, the value of ...
@agile harness
grave hazel
ornate phoenix
is the graph concave up, concave down, convex up, or convex down at f(1) and f(3)? I think its concave up and decreasing at f(1) and concave down and increasing at f(3). If this is correct, would that mean f''(1) < f''(3)?
topaz sinewBOT
is the graph concave up, concave down, convex up, or convex down at f(1) and f(3...
ornate phoenix
wait what
but its decreasing
as x increases y is decreasing
but its still concave up-
does that mean its concave down then?
ornate phoenix
wait does decreasing / increasing matter?
vestal sigil
you said its concave up at f(1), which means f " (1) is +
and its concave down at f(3), which means f " (3) is -
how can you say that something - is > something +
š
ornate phoenix
you said its concave up at f(1), which means f " (1) is +
but is that actually correct
vestal sigil
yes, thats what i told you
what you said is correct
except for the inequality
If this is correct, would that mean f''(1) < f''(3)?
no, its f " (1) > f " (3)
cuz as you said, concave up at x=1, meaning f " (1) +
and concave down at x=3, meaning f " (3) -
ornate phoenix
ok so concave up is when it curves inward but goes up? concave down is when it curves inward and goes down.. etc
vestal sigil
i use another way
concave up when the slope is increasing
concave down when the slope is decreasing
its a better method
ornate phoenix
concave down when the slope is decreasing
then how do I differentiate between concave and convex
vestal sigil
i dont do math, i do engineering, i did not study this deeply
i suggest you wait for somebody else
ornate phoenix
oh ok
vestal sigil
but again, what you said was correct
except for the inequality, you literally said something negative was greater than something positive lol
ornate phoenix
yeah but im just confused because idk what the graph actually is at f(1) and f(3)
at f(1) it seems to be decreasing
and increasing at f(3)
but then again it can be either convex or concave-
topaz sinewBOT
@ornate phoenix Has your question been resolved?
ornate phoenix
The graph is concave down at f(1) and concave up at f(3), meaning f''(1) < f''(3)
is that correct?
topaz sinewBOT
@ornate phoenix Has your question been resolved?
ornate phoenix
how do I close the channel
warped coyote
If i remember correctly, im supposed to kind of remove lg out of both of the equations
topaz sinewBOT
If i remember correctly, im supposed to kind of remove lg out of both of the equ...
warped coyote
but i think i may have fucked up somewhere and im not too sure if i did the logarithms correctly
unreal tinsel
$\log_{0.1}(k) = lg(k)/lg(0.1) = lg(k)/lg(10^{-1}) = lg(k)/(-1) = -lg(k)$
thorny flameBOT
kaue
unreal tinsel
change of base formula
if you sub log base 0.1 with -lg(k) in the beginning it should be easier
warped coyote
if you sub log base 0.1 with -lg(k) in the beginning it should be easier
oke lemme try ah
unreal tinsel
oh you did that sorry didn't see it
unreal tinsel
If i remember correctly, im supposed to kind of remove lg out of both of the equ...
the logs are correct, but you need to solve for a
unreal tinsel
hollon how did you get 4a = ak + kĀ²
you wrote that
warped coyote
well yea then i wasn't sure how to proceed because i need to answer a interms of k
unreal tinsel
If i remember correctly, im supposed to kind of remove lg out of both of the equ...
.
after solving the logs you got 4a = ak + kĀ²
subtract ak
4a - ak = kĀ²
factor a
a(4 - k) = kĀ²
divide by 4 - k
a = kĀ²/(4 - k)
topaz sinewBOT
topaz sinewBOT
Available help channel!
silent frigate
how can i show exactly two pre-image for every image?
topaz sinewBOT
how can i show *exactly* two pre-image for every image?
silent frigate
more specifically, I was trying to prove this by contreadiction
specifically I said: suppose by contradiction that there is at least 3 pre-images for an image
the probelm is, can i just show that 3 unique pre-images are just not possible for an image?
i dont think i can, because at least 3 pre-images is an OR statement. Which is pre-images = 3 or # pre-omages > 3. So even if pre-images = 3 is false, we need to show that # pre-images > 3 is false as well. \
topaz sinewBOT
@silent frigate Has your question been resolved?
vernal matrix
Well, if you canāt have 3, you canāt have more than 3, as your argument could be repeated by taking just 3 of the however many
silent frigate
hmmm. but dont we need to show both parts of the OR statement is false when doing a proof by contradiction?
or shoudl it not be an OR statement?
vernal matrix
Well, the argument youāre likely to end up making can be used by taking just three elements: probably something like āsay you have a1, a2, a3 as three distinct inputs that get sent toā¦ā
silent frigate
Well, the argument youāre likely to end up making can be used by taking just thr...
hmmm
vernal matrix
Anyways, if you had a^2 in the image, you know that a and -a get mapped to a^2: considering that p is a prime and at least 3, would a and -a be the same?
silent frigate
no
vernal matrix
why not?
silent frigate
isnt a in a differnet residue class then -a
vernal matrix
In this case it is, but be careful of why 
e.g. if you chose p as 2, it wouldnāt be true
Similarly if p werenāt prime but was even(!)
topaz sinewBOT
@silent frigate Has your question been resolved?
pseudo pond
Am I doing this right so far?
topaz sinewBOT
Am I doing this right so far?
pseudo pond
Problem 17
Not sure if my setup is correct
If it is how would I go from here
Kinda confused how to continue
Oh I got it right lol just gotta move that out of the brackets
:)
.close
topaz sinewBOT
pseudo pond
.reopen
topaz sinewBOT
ā
pseudo pond
How hard are Definite Integrals to learn?
Iām just curious
Cause I have to learn them by myself I canāt be in class tomorrow
dense crescent
How hard are Definite Integrals to learn?
Depends on ur interest š
loud oasis
you mostly don't actually use the riemann sum definition of the limit. vast majority of calculus class uses FTC to evaluate definite integrals
winter egret
If you know how to evaluate an indefinite integral then definite integrals are basically the same thing
you just have to do a few more computations
pseudo pond
Depends on ur interest š
If you rolling eyes at me again Iām gonna
Thanks
.close
topaz sinewBOT
golden blade
If you rolling eyes at me again Iām gonna
serial killerš
topaz sinewBOT
ā
pseudo pond
Am I doing 18 right
golden blade
Yea but u donāt count
I don't count because I am irrelavant
dense crescent
If you rolling eyes at me again Iām gonna
Tf?
trim ermine
topaz sinewBOT
@pseudo pond Has your question been resolved?
karmic dove
topaz sinewBOT
topaz sinewBOT
@karmic dove Has your question been resolved?
karmic dove
<@&286206848099549185>
topaz sinewBOT
@karmic dove Has your question been resolved?
topaz sinewBOT
@karmic dove Has your question been resolved?
neon iron
Hello I am currently doing this exercice
topaz sinewBOT
Hello I am currently doing this exercice
neon iron
I need help with calculating the lax of Xmin
please don't insult me if im doing something stupid, I dropped out of my master for 1 year due to personal reasons and I just got back and now i feel like im clueless 95% of the time
this is what I tried doing so far but something feels off
topaz sinewBOT
@neon iron Has your question been resolved?
neon iron
law
neon iron
Yes on the first line right
yes :c
neon iron
non mais je fais mes Ć©tudes en france yes
near steeple
en angalis
neon iron
merci :c
neon iron
well idk yet ! i need to calculate the mean and variance of Xmin and then the quadratic risk
idk how to do that yet, I will try and see
je peux te mp ?
near steeple
oui pdp
dawn falcon
Hello I have a question about an exercise the them is Borel Cantelli lemma
dawn falcon
How could I show this result ?
The chapter corresponding is Borel Cantelli lemma
I wish to understand its applications by the end of the day lol
opal vault
the idea is to show that P(limsup{|Xn/cn| > epsilon}) = 0 for every epsilon > 0
dawn falcon
So I need to construct such a sequence c_n ?
opal vault
yes
dawn falcon
So if I write A={limsup [X_n/c_n]>eps}
Well i'll think about why this concludes
Is There a link between limsup of sequences and of events ?
topaz sinewBOT
@dawn falcon Has your question been resolved?
topaz sinewBOT
@dawn falcon Has your question been resolved?
slate plover
topaz sinewBOT
slate plover
how can i find the 116 condition of existence
fervent ferry
Expression under the square root must be $\geq 0$ and denominators must be not equal to zero.
thorny flameBOT
LooseEthics
fervent ferry
First denominator tells us nothing, the second that $x \neq +-4$.
thorny flameBOT
LooseEthics
fervent ferry
Factor the quadratic, it must be greater than or equal to zero, so $x \in <-4, 4>$
thorny flameBOT
LooseEthics
fervent ferry
In the second root the denominator is negative in the interval, so -3x must also be negative, thus $x > 0$.
thorny flameBOT
LooseEthics
fervent ferry
Put all that together and you get $x \in <0, 4)$
thorny flameBOT
LooseEthics
slate plover
thanks
just a question
in the first one doesn't |x|+4 make us simplify the top one since we factorize it in (4-x)(4+x)
topaz sinewBOT
@slate plover Has your question been resolved?
cunning peak
How do I evaluate this limit?
I believe I have to utilize a method involving e and the natural log to manipulate the exponent, but I think Iāve made an error somewhere.
slate valve
How do I evaluate this limit?
I believe I have to utilize a method involving e...
you can make it in the form as (1+1/u)^u
by splitting x/7 into two fractions multiplied together in order to match the reciprocal inside
cunning peak
I donāt follow you here
slate valve
you know (1+1/u)^u as u approaches infinity = e right?
cunning peak
I was under the impression the method was the same / similar to another problem I had that I was able to solve
cunning peak
you know (1+1/u)^u as u approaches infinity = e right?
it doesnāt ring a bell at the moment, no
slate valve
uh
cunning peak
Hereās the one I solved if this helps at all
slate valve
how can you do these questions without that knowledge?
you learnt lāh before definition of e???
slate valve
How do I evaluate this limit?
I believe I have to utilize a method involving e...
oh, the x/7 is outside the ln
not inide
inside
cunning peak
I guess so? Or maybe it was taught to me at one point and Iāve forgotten it
cunning peak
Hereās the one I solved if this helps at all
Does this method make sense?
slate valve
oh, the x/7 is outside the ln
hey
slate valve
š
cunning peak
Got myself stuck again 
actually, would it make more sense to pull the 1/7 out of the limit completely?
im not sure how that would work out with the e involved but thats what i just noticed
slate valve
actually, would it make more sense to pull the 1/7 out of the limit completely?
yeah its more convenient that way
cunning peak
ill try it out
I can get it to 0/0 for LāH to apply but i think now im struggling to get the derivative right on the ln
would it just be 1/[1+(4/x)]? i think i just get 1/1/0 that way
topaz sinewBOT
@cunning peak Has your question been resolved?
chilly pollen
we are trying to prove this using the definition of limits, but we cant find a way to get something like n < M... , how should we approach this?
topaz sinewBOT
we are trying to prove this using the definition of limits, but we cant find a w...
raven sparrow
If you fix M, maybe first look at the equation 1/n - n = M
Can you solve that for n? Once you do, can you see when 1/n - n < M?
arctic hawk
we are trying to prove this using the definition of limits, but we cant find a w...
what's the definition you were given?
chilly pollen
what's the definition you were given?
chilly pollen
Can you solve that for n? Once you do, can you see when 1/n - n < M?
we are working on it
chilly pollen
Can you solve that for n? Once you do, can you see when 1/n - n < M?
n>sqrt(m+1) and n> -1/m
raven sparrow
Hmm not sure this is great if M is very negative
outer salmon
M>0
raven sparrow
Yeah true
outer salmon
I think sqrt may even be a bit too fancy here
If you understand why the expression is going towards -infinity, I think you can find a rather simply choice for n (in terms of M)
chilly pollen
we understand how to algebrically calculate what the limit is, but we aren't able to prove it with the definition, and that is what the excrsize asks us to do.
we get weird results for 1/n -n < -M and we don't know how to move forward
outer salmon
Do you understand in principle how to prove the definition holds for a given expression?
I can give you a hint for what n_0 can be
chilly pollen
Do you understand in principle how to prove the definition holds for a given exp...
we were just substituting our succesion to an in the definition
chilly pollen
I can give you a hint for what n_0 can be
yeah that would probably help us out
outer salmon
Take n_0 = M+1
topaz sinewBOT
@chilly pollen Has your question been resolved?
thorny flameBOT
daniel_zein
neon iron
hi
neon iron
If
I have a triangle
Two angles are given
And the side between them is given too
HOW To find its area?
dense lily
And the side between them is given too
Sine rule to find another side then and Area=Ā½absintheta
Or you can use Heron's formula.
neon iron
mhm
neon iron
Sine rule to find another side then and Area=Ā½absintheta
this is the best
thanks
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
vital vector
Hello, (the question states that these three points are collinear and itās asking to find a and b, the solvingās the part thatās lined with brown, ) someone please help me with this Iām stuck on the last part idk what to do after 8b+4a-60=0.
And if Iāve done anything wrong pls state so , thank you.
((@ me when someone answers))
topaz sinewBOT
Hello, (the question states that these three points are collinear and itās askin...
earnest apex
Hello, (the question states that these three points are collinear and itās askin...
Good morning [?]
earnest apex
Oh so it is morning for you
Lucky guess
Anyways we've been given that (a, 3) (5, -5) and (b, -9) are collinear
vital vector
No itās not
earnest apex
You got one of the conditions
Now do you know* what will be the area of the triangle formed by these three points
vital vector
but collinear means points on one line
vital vector
ye
earnest apex
do you know the formula for the area of triangle formed by three points?
topaz sinewBOT
@vital vector Has your question been resolved?
spark bison
What value of k makes the two functions x/k and x! intercept at exactly one point?
topaz sinewBOT
What value of k makes the two functions x/k and x! intercept at exactly one poin...
spark bison
On Desmos, I got approximately 1.1291738854501417
If there an exact answer though? or is it just impossible?
topaz sinewBOT
@spark bison Has your question been resolved?
neon iron
why does this graph not go in the third quadrant?
topaz sinewBOT
why does this graph not go in the third quadrant?
neon iron
for example, if x = -2, then y = -2, innit?
vernal matrix
,calc (-2)^4.9
thorny flameBOT
Result:
-28.395747408622 + 9.2263376223158i
unreal tinsel
,calc (-2)^4.9
but it should show it, even tho its complex, at point (-2, -2) it is true that (-2)^4.9 = (-2)^4.9
i guess your desmos is prob not configured to allow complex numbers
vernal matrix
but it should show it, even tho its complex, at point (-2, -2) it is true that (...
Well, you "shouldn't" be dealing with complex numbers really
topaz sinewBOT
@neon iron Has your question been resolved?
fathom sequoia
topaz sinewBOT
golden blade
can i just take the aqrt?
yes but i wouldnt
golden blade
just expand
you wanna avoid absolute value equations
taking the square root would lead to
|2x-3| = 4|x|
topaz sinewBOT
@fathom sequoia Has your question been resolved?
shut obsidian
I rewrote the proof in
topaz sinewBOT
I rewrote the proof in
shut obsidian
(ignore the underline)
Does this look fine?
(@gleaming thunder if you can read mathematical German haha - I know you started the LA lecture notes so most likely yes)
shut obsidian
I find the phrasing in the original pretty bad
My lemma 0.7 is this
Yeah it looks fine
.close
topaz sinewBOT
gleaming thunder
Does this look fine?
why is the first direct sum you write true?
shut obsidian
.reopen
topaz sinewBOT
ā
shut obsidian
why is the first direct sum you write true?
By lemma 0.7
(I posted that below the picture)
shut obsidian
So yeah, it should look fine, right?
gleaming thunder
yeah
shut obsidian
Thanks
And the reason it was proven that Im(A - lambda id)^k is invariant under A is so that we can even define this restriction of A
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
plain parrot
How would i prove that composition of functions on the set of bijective functions from some set to itself is not commutative?
topaz sinewBOT
How would i prove that composition of functions on the set of bijective function...
plain parrot
i understand to show that f o g isn't equal to g o f but how would i show that in notation if i cant just use some specific examples (b/c the set is arbitrary)
plain parrot
maybe i misinterpreted the question then
it says Let A be a set. Prove that (Bij(A), o), with Bij(A) being the set of bijective functions f: A -> A and o being composition of functions, is a group that is not commutative.
strange whale
rip question
you're not misinterpreting the question, the question itself is fucked
strange whale
you can show it's a group for any set tho yea
but the non-commutative part is not for all sets
just try and find some A such that it's not commutative
plain parrot
ahh the professor says that presenting one counterexample is sufficient
question wasn't clear that you dont have to prove it for all sets A
strange whale
ahh the professor says that presenting one counterexample is sufficient
well the guy can't write
ĀÆ_(ć)_/ĀÆ
topaz sinewBOT
topaz sinewBOT
Available help channel!
jaunty helm
Would I be able to get calc 1 help in about an hour? (De moivre's, implici diff, area v volume rate of change, etc...)?
topaz sinewBOT
Would I be able to get calc 1 help in about an hour? (De moivre's, implici diff,...
glass maple
Would I be able to get calc 1 help in about an hour? (De moivre's, implici diff,...
for what particular reason
jaunty helm
for what particular reason
Studying
glass maple
why in an hour
jaunty helm
Cos im waiting on help now and deciding if I should go home and have help later
glass maple
just make a ticket then instead of asking for help an hour later
if someone is aroudnto help then they might answer
jaunty helm
Yeah I'm asking bc I hope if someone's here they see it and I'd know they fcan help
topaz sinewBOT
@jaunty helm Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
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open kindle
topaz sinewBOT
open kindle
I need to isolate those two Āµ
Need to make a excel sheet to solve Āµ with those other variables
Really forgot how to make this, brah šæ
acoustic pecan
solving that isnt so difficult
you have T=F[A+Bu+Cu]
open kindle
Yeah but I need all the right side variables to be in the left side
topaz sinewBOT
@open kindle Has your question been resolved?
quartz shoal
Yeah but I need all the right side variables to be in the left side
Yep, so you can distribute F to everything, then get all the u terms on one side and everything else on the other
topaz sinewBOT
@open kindle Has your question been resolved?
deft spade
Does anyone have any idea how I could start this question?
As far as I am aware I know, I just need to find the derivative of this function, but I'm stuck on what to do next
topaz sinewBOT
Does anyone have any idea how I could start this question?
As far as I am aware...
@deft spade Has your question been resolved?
deft spade
<@&286206848099549185>
deft spade
To add to what I got, this is the equation of the tangent line
I'm still kind of stuck on what to do next from here, I'm not sure how to make this fit into the formula to find the area of the triangle
<@&286206848099549185>
deft spade
.close
topaz sinewBOT
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half breach
Bro what the hell I have to solve this with u sub
topaz sinewBOT
Bro what the hell I have to solve this with u sub
half breach
So far I have u = sin(1.5x) and du = 1.5cos(1.5x)dx and i guess the identity where cos^2(1.5x) = 1-u^2
Which is what the hint gave me but I am so lost
unique quarry
i think u is supposed to be 1.5x
lapis sorrel
nah u can do it with u = sin(1.5x)
then cos(1.5x)dx = du/1.5
so we know that u = sin(1.5x)
lapis sorrel
So far I have u = sin(1.5x) and du = 1.5cos(1.5x)dx and i guess the identity whe...
so then what does u^2 =?
half breach
lowkey had an epiphany
someone told me to separate cos into cos(1.5x)cos^2(1.5x) and so u^2 = sin^2(1.5x)
and it worked so far
This problem is still aids though
lapis sorrel
exactly thats what i was gonna tell u to do next lol
topaz sinewBOT
@half breach Has your question been resolved?
half breach
Wait can someone explain this garbage
My professor did it yesterday in class and this was some sorcery
I don't understand making u = something not even in the integral
topaz sinewBOT
I'm pretty sure something went wrong, but not sure what
tame frost
Hello, I can help you. Give me a moment to review it
glass harbor
it's right ??
tame frost
yeah
thats why it took me a sec
i couldnt see it do i did full working
are u doing the limit as h goes to 0?
glass harbor
š oh-
not yet, at least. He wanted us to just simplify the difference quotient for this question
tame frost
yes
glass harbor
:D
tame frost
but that result is very important (its next in your course)
its the exact instantaneous rate of change
instantaneous velocity in this instance
glass harbor
we're doing a very weird mix of derivatives and then not derivatives
tame frost
have you done limit h goes to zero
glass harbor
I'm not good at them, but I know them sorta
tame frost
for derivatives?
glass harbor
I believe so š¤
tame frost
do you know what the derivative of 40+40t-16t^2 is
glass harbor
it's kinda all blurring together at this point, but I think he's had us do it once or twice
-32t+40?
tame frost
wouldn't it just be 40-32t
coincidence?
glass harbor
... OH
tame frost
xD
the whole purpose of these difference quotients
is to do an instantaneous change
you are doing "gradient" or change in y over change in x
but doing it after a small gap of "h"
glass harbor
that explains so much š
tame frost
or change in variables, whatever they are. gradient is an easy go to because you can see it, but it works for any function
haha
its always hard to get students to "see" this stuff
glass harbor
that's fair haha
glass harbor
š«”
tame frost
do the velocity between t = 2 and t = 2.01
on a calculator
similar to what is in 7.
glass harbor
oh no
tame frost
but with my numbers: f(2.01) and f(2)
glass harbor
I've been scared of 7
tame frost
instead of t+h and t
so f(2.01) = 40 + 40(2.01) - 16(2.01)^2
and f(2) is the same with 2 in that place
then divide by (2.01-2)
tame frost
what was your answer
glass harbor
my friend called so I had to tell him to call back later xD
lemme type this in super fast
tame frost
haha all good
glass harbor
speedrun time
tame frost
i have to go in a sec, i have a student
glass harbor
ooooh go ahead then!
I'll work this out B)
plot twist, anyone know what I should do with 5? Not sure what to do with just one set of points D:
OH WAIT is it point-slope-
mmm ok maybe not, this is going weirdly
also that wouldn't involve the DQ x-x
topaz sinewBOT
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glass harbor
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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
novel echo
!show
topaz sinewBOT
Show your work, and if possible, explain where you are stuck.
novel echo
what was your answer
burnt swift
25,15 and 5 have something in common
burnt swift
is 5 + a product of -2 and a fraction
novel echo
are you familiar with PEMDAS?
can you think of a way to apply that here?
do it on a piece of paper, step by step
why 1?
That is incorrect, you donāt know the value of x and y. youāre assuming that x and y are 1 in this expression
letās work on it step by step
first, (25x - 15y)/5
can you simplify that
No
you can rewrite that expression in the following manner: (25x/5) - (15y/5)
can you simplify this?
correct
now
what are these terms being multiplied by?
No
look at the expression again
it can be rewritten as 5 - 2(5x-3y)
think about PEMDAS
almost
itās -2
what do you get after multiplying the terms by -2?
correct
yes
topaz sinewBOT
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plucky crypt
Is the working for this question right?
topaz sinewBOT
Is the working for this question right?
plucky crypt
Integration question
fallow heart
cos(2x) = cosĀ²x - sinĀ²x
plucky crypt
Of course...
Oh damn
That was a stupid mistake
Thanks .-.
What would be the right answer then...
topaz sinewBOT
@plucky crypt Has your question been resolved?
versed cairn
What would be the right answer then...
What u have except the negative sign
willow kraken
Where did i go wrong? The answer im supposed to get is q=-3 but i got q=-4 instead.
topaz sinewBOT
Where did i go wrong? The answer im supposed to get is q=-3 but i got q=-4 inste...
flint stump
second pic, can you explain how you got to the 3rd step from 2nd step?
willow kraken
Because positive 4q will be negative 4q cuz it crosses the equal sign
willow kraken
Oh
flint stump
that should just give you 15+4q instead of the quadratic
willow kraken
Ohh so should i move q to -1
So itāll be 15+4q=-q
flint stump
15+4q = -q OR 5q = -15 OR q = -3
willow kraken
15+4q = -q OR 5q = -15 OR q = -3
Ahh alright thanks
flint stump
npnp
delicate cobalt
chilly walrus
if i have two non-negative functions, $f$ and $g$, continuous on $I_1$ and $I_2$ respectively, can we say that $f(x)+g(x)$ is continuous on $I_1 \cap I_2$?
topaz sinewBOT
if i have two non-negative functions, $f$ and $g$, continuous on $I_1$ and $I_2$...
thorny flameBOT
artemetra
chilly walrus
i assume it is continuous there but it can be continous on a "bigger" set too right?
chilly walrus
if i have two non-negative functions, $f$ and $g$, continuous on $I_1$ and $I_2$...
also $I_1 \neq I_2$
thorny flameBOT
artemetra
chilly walrus
i first thought of $f(x)=\mathrm{mod}(x,1)$ and $g(x) = 1-\mathrm{mod}(x,1)$ but they are continuous on the same sets
thorny flameBOT
artemetra
odd pagoda
it is at least continuous on the intersection and can clearly also be continuous on a bigger set
depends on how well g and f behave on the other interval
sturdy lion
help
odd urchin
it's asking u to factorize it
torpid sparrow
That is the opposite of factorizing
torpid sparrow
Factor this
sturdy lion
how do i factor it
torpid sparrow
$a+ab$
thorny flameBOT
Samuel
torpid sparrow
How do you factor this?
sturdy lion
aa + ab?
odd urchin
a (1+b)
sturdy lion
idk how
sturdy lion
a(1+b)?
torpid sparrow
Yes
torpid sparrow
You take out the common factor
In this case a
Open parenthesis and inside
You put the non factored part
For a to become a you multiply by 1
For ab you multiply by b
a(1+b)
Now in your exercise
sturdy lion
but we didnt even learn this
torpid sparrow
15+3x
sturdy lion
we only learnt k*(a+b) = ka+kb
torpid sparrow
Not 5x
sturdy lion
3(5+x)
sturdy lion
ok than ks
torpid sparrow
we only learnt k*(a+b) = ka+kb
You learnt expanding
This is the opposite
It is like you learn to add and now you have to learn to subtract
sturdy lion
okok now the question is 4x5 - 4x
torpid sparrow
What do you think
torpid sparrow
What is the common factor
sturdy lion
4
sturdy lion
4(5-4x)
torpid sparrow
You forgot to take out the 4 from 4x
torpid sparrow
Perfect
sturdy lion
a(b-c)
torpid sparrow
As you can see is very easy
sturdy lion
yes
i did it
my homework
that was hard
im more use to other types of maths
how do i close this
.close
topaz sinewBOT
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jolly agate
topaz sinewBOT
jolly agate
For a case like this, can i just start from 2 and decide the determinant ?
So I do 2 * ((c1)-(2**6)) - 0(
and just keep going ike that
until the 1 one come and then im done
ionic oar
yes
ionic oar
what's your answer
ionic oar
Do the whole calculation of that just become 0 ?
yes
jolly agate
-2c^2 +2c + 18
jolly agate
ye
ahh fuck sake
i ment -c^2
and then + 2c + 18
how did u calculate it so fast?
lusty marsh
ionic oar
how did u calculate it so fast?
because one of the entries was 0
jolly agate
Oh ye i know this
ionic oar
topaz sinewBOT
@jolly agate Has your question been resolved?
topaz sinewBOT
@jolly agate Has your question been resolved?
elder steppe
i need help
topaz sinewBOT
i need help
keen plinth
do you know how to do differentiation?
elder steppe
yes
keen plinth
then you should understand the meaning of derivative, which is the slope of the function
what does it mean when the slope is 0
elder steppe
the y intercept are at points (0,0)
elder steppe
what does it mean when the slope is 0
stationary
keen plinth
yes, then what is the derivative of this equation
elder steppe
y = 6x^1 - 3x^2
keen plinth
so you can then factorize it to get 3x(2-x) right, it should be obvious till this point
topaz sinewBOT
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supple bay
How do I know when to solve for y or x in a system of differential equations?
steady escarp
can u give an example of what u mean?
steady escarp
i dont think it matters what u eliminate first
but here the obvious choice seems to be to eliminate x'
topaz sinewBOT
@supple bay Has your question been resolved?
flat tapir
topaz sinewBOT
neon iron
I am not so sure about the worked solution
But I can instruct you on how you can solve these kinds of questions
flat tapir
i understand the concept
i just want to check if im missing something
cause rn the solution is wrong to me
500/sin30=750/sinx
x does not equal 131 in this equation
thorny flameBOT
neon iron
,w 3/4 radians to degrees
flat tapir
you wont get 131
thorny flameBOT
neon iron
,w 180-42.97
thorny flameBOT
flat tapir
why would i subtrac it from 180
neon iron
Cause
flat tapir
this is just wrong
thorny flameBOT
Edmund Cloudsley
neon iron
this is just wrong
Yeah does look wrong to me too
flat tapir
then im correct
neon iron
,w solve 0.848 radians to degrees
thorny flameBOT
neon iron
,w solve 180-48.59
thorny flameBOT
neon iron
Sorry I think I made an error in the wolfram alpha statement
neon iron
why would we subtract
Ambiguous case of the sine rule
flat tapir
what do you mean
flat tapir
how would i spot that though
neon iron
Also remember this shorthand
$$\sin \theta = \sin (180-\theta)$$
thorny flameBOT
Edmund Cloudsley
neon iron
how would i spot that though
If it looks obtuse, remember that itās 180 minus the angle calculated
It is obtuse in this case
And not an acute angle
flat tapir
so i just go off looks
neon iron
Yup I think so
One more thing
And this is just a suggestion
I personally feel that the triangle rule is not really a good way to do vector addition
Itās really hard to visualise (atleast for me) and thereās a better way to do it
This video may help
Breaking the vector into vector components makes the job a lot easier
next rain
How did bro do this this diagram? Usually I'd finda number between the certain specified values and plug them into the original question to see if the inequality holds, but this expression is long asl n I'm wondering if there's a shortcut
keen plinth
How did bro do this this diagram? Usually I'd finda number between the certain ...
if u mean the red equation, it is the multiple of all equations above, so if there are even number of negative signs on the above, it is positive, else negative
topaz sinewBOT
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jolly elbow
i am trying to prove that there exists a multiplicative inverse for (1 + x) if there is some n in N for which x ^ n = 0. i've been give the hint that i should think about the geometric summation formula, which makes sense, given that 1 + x is exactly that for n = 1. i don't think i need much, but i really don't see it
topaz sinewBOT
i am trying to prove that there exists a multiplicative inverse for (1 + x) if t...
jolly elbow
ah, forgot to mention, these are all elements of some Ring R
jaunty leaf
i am trying to prove that there exists a multiplicative inverse for (1 + x) if t...
Perhaps they want you to use the formula for 1 - x + x^2 - x^3 + ... + (-x)^{n-1}
jolly elbow
(1-q^n+1)/(1-q)?
jaunty leaf
Perhaps they want you to use the formula for 1 - x + x^2 - x^3 + ... + (-x)^{n-1...
Multiply this by 1+x
jaunty leaf
yes, so (1 - x + x^2 + ... + (-x)^{n-1})(1 + x) = 1
Which implies that (1 + x) has an inverse
jolly elbow
yeah
thank you, i am not sure why they specifically hinted for the positive only variant then
well i guess itād make it trivial
.close
topaz sinewBOT
jaunty leaf
thank you, i am not sure why they specifically hinted for the positive only vari...
It's not positive only, it works for negative values as well
topaz sinewBOT
Available help channel!
olive lichen
Does anyone know why exactly we sometimes need to pool data when doing a chi squared test?
Is pooling important if we're doing the work on a computer?
topaz sinewBOT
Does anyone know why exactly we sometimes need to pool data when doing a chi squ...
@olive lichen Has your question been resolved?
topaz sinewBOT
@olive lichen Has your question been resolved?
bold kernel
Is this correct
topaz sinewBOT
Is this correct
sweet shard
how did you get the domain
smoky sparrow
how did you get the domain
that's correct though
smoky sparrow
Is this correct
yes this is all correct
bold kernel
I got the domain by setting the inside of the ln as greater than zero
And for range I think all logarithmic equations ever are always R
Is this true?
smoky sparrow
I got the domain by setting the inside of the ln as greater than zero
yes and yes
smoky sparrow
exactly, cause logarithmic and exponential functions are inverse functions
smoky sparrow
oh you could have just noticed that domain of inverse is range of f(x)
and range of inverse is domain of f(x)
bold kernel
Thatās what I did haha
smoky sparrow
yeah cool
bold kernel
.close
topaz sinewBOT
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patent lynx
Help please
topaz sinewBOT
Help please
patent lynx
this is my work
half edge
What is the problem asking u, in basic terms @patent lynx
patent lynx
What is the problem asking u, in basic terms <@593935571961774081>
area under the curve
patent lynx
-3 to 4
half edge
is that what you did