if I may
#help-26
haughty wren
$cot\theta - cot\theta \cdot cos^{2}\theta \newline cot\theta \cdot (1 - cos^{2}\theta) \newline cot\theta \cdot sin^2\theta$
thorny flameBOT
imTyp0
haughty wren
and then yeah just know cot is cos/sin
so that's sinxcosx, or if you want, sin(2x)/2
lucid junco
Ohhh
haughty wren
A good thing to do when doing these trig identities is to always take out what's in common. Then it almost always makes it easier to see what's next :)
lucid junco
So it becomes cos(theta)*sin(theta)?
haughty wren
yes
lucid junco
And we can’t simplify any further right
haughty wren
you could, but we could argue it's not really simplifying. If I was your teacher I wouldn't be mad if you left it at that
lucid junco
Ah okay cool. Thank you for the help!
lucid junco
A good thing to do when doing these trig identities is to always take out what's...
I’ll try keep that in mind
haughty wren
no worries! Also just so you know, what @quick pawn said is 100% correct. It's just that there are many, many ways to solve trigonometric identities, and that's just the one I saw first :)
lucid junco
Man I think I messed up somewhere I’m not sure what to do now
topaz sinewBOT
Man I think I messed up somewhere I’m not sure what to do now
unborn lagoon
split the beginning fraction into 2 fractions
lucid junco
split the beginning fraction into 2 fractions
Like splitting it so I can perform multiplication? Or keep it into adding
unborn lagoon
adding
lucid junco
o ok
unborn lagoon
cosx /sinx is not tanx
lucid junco
Like this?
lucid junco
cosx /sinx is not tanx
Wait wut
unborn lagoon
you got it?
lucid junco
So I just do the same thing I did but just fix up the tan
what would it look like if I had it the correct way around
unborn lagoon
look what happenes when you fix the tan
lucid junco
is it supposed to be sin(x)/cos^2(x)
unborn lagoon
yeah...
lucid junco
Well
Hey
Good exercise converting stuff in terms of sine and cosine
Lol thanks for the help
unborn lagoon
lol
lucid junco
.close
glossy imp
how would i go about solving this?
topaz sinewBOT
how would i go about solving this?
glossy imp
I have tried an alternating series test, ratio test, and divergence test with no success
oh and a limit comparison test
vernal matrix
Part b?
vernal matrix
Heeeey 
glossy imp
:D
vernal matrix
And that's the harmonic series, the absolute value of it diverges 
glossy imp
how
;-;
could i compare it to a harmonic?
so it converges conditionally?
so how would i show that on paper?
vernal matrix
Yea it converges conditionally (was gonna say that it doesn't converge absolutely, but does meet the criteria for conditional convergence)
There's a theorem somewhere for conditional convergence that if you have some decreasing positive sequence that converges to zero, then the "alternating series of that sequence" converges at least conditionally
As for not converging absolutely, you can compare the absolute value of the series to the harmonic series yea, as it would just be a scaled version of it
glossy imp
hmmm okay
im still confused on what test i would do to prove that initial one
because the alternative series was inconclusive
i think
vernal matrix
Hmm, are you happy that the series $\sum_{k=1}^{\infty} \frac{1}{k}$ diverges?
thorny flameBOT
@vernal matrix
glossy imp
yes
vernal matrix
Then for the series you have, when you take the absolute value, you have
[
\sum_{k=1}^{\infty} \abs{\frac{(-1)^{k + 1}}{2k}} = \sum_{k=1}^{\infty} \frac{1}{2k} = \frac{1}{2} \sum_{k=1}^{\infty} \frac{1}{k}
]
and so you know that you can't converge absolutely from there
thorny flameBOT
@vernal matrix
crisp loom
I have tried an alternating series test
did you?
glossy imp
sorry i had to do something
lemme do it now
yeah i got that
and now lemme compare it to a harmonic
i have that now
and how would i go from here?
would it just be a geometric?
vernal matrix
Well you've shown that it doesn't converge absolutely, and you showed that it converges conditionally by the alternating series test, so you're done, no?
glossy imp
is that automatically assumed?
im a bit confused by that
how did i show it doesn’t converge absolutely
im not as comfortable with AST as i am with other tests
vernal matrix
At this point you compared the absolute series with the harmonic series, which showed that it doesn't converge absolutely
vernal matrix
Hopefully it does 
Then, do you have the conditions for the alternating series test anywhere? 
glossy imp
i don’t believe so
vernal matrix
Finessing this one here 
vernal matrix
There's a theorem somewhere for conditional convergence that if you have some de...
That's basically the "decreasing positive sequence that converges to zero" statement that I said here
vernal matrix
lovely to help (and see!) you 
winged grove
for this question, did we have to use the numbers on the bottom of the graph? i just estimated that the limit is 4
topaz sinewBOT
for this question, did we have to use the numbers on the bottom of the graph? i ...
winged grove
i'm not sure what the numbers on the bottom even mean
neon iron
no the numbers on the buttom have no relation whatsoever
winged grove
no the numbers on the buttom have no relation whatsoever
is 4 correct anyways?
neon iron
yeah
winged grove
ok thx
neon iron
i mean as long as we dont have to prove |2x| is continous therefore u just have to calculate |-4|
topaz sinewBOT
neon iron
binomial
sturdy oracle
But if you really need to, use the binomial theorem
soft rune
Yes, as simple as that
Of course!
Coefficient, they mean only the number preceding the variable x
Variable part, they mean x^
Yess
This is an arithmetic series
f[n] = -12 + 3n
is our sequence here
As, you can see, we are summing up from (-9) to (-12+3n)
Which means we are summing up from f[1] to f[n]
Right?
zealous coyote
hello?
soft rune
Did you understand so far?
It is our sequence
Have you not studied sequences yet?!
They resemble to function f(x), except instead of x (REAL), we use n (NATURAL)
fine
😋
although try using f[n], gives you a feel as if you're dealing with functions f(x)
just instead of x which is real
we only consier the natural numbers n
Anyways
So yeahh, we have an arithmetic series here
Have you guys studied arithmetic series?
Yes
it is already given, the sequence
Look at the last
They are asking you to compute the sum of this arithmetic series
Until f[n] lol
it is obvious!!
from f[1] to f[n]
because f[1]=-9
you can just substitute
Allright
Since you have studied the arithmetic series
I assume you have been given a formula
There is a formula which you can use to find the sum of the arithmetic series
You only need to know the first and last element
first and last term of the series
exactly
you have it
it is -12+3n
-12+3n is the term
it does not have to be a number
Hahaha
You just plug the first (-9) and (-12+3n)
Since the last term is a function of the variable n
The sum also will be a function of n
One of the advantages of this is that after finding the closed form of the sum of the series
You can plug any n
And know the sum from the first term up to any nth term
Yes, it is!
soft rune
Well, first, f[0]=-2
And not f[1]
f[1]=0.8
you can see, it is the following term
and r=-0.4
And not +0.4
The sign of the terms is alternating
Our sequence is:
f[n] = (-2) . (-0.4)^n
n=0,1,2,3,...
topaz sinewBOT
@crisp scarab Has your question been resolved?
soft rune
Simply that the sequence starts from index 0
And not 1
They all start from 0 lol
The previous one did not start from 1
The sequence from the previous exercise also starts from 0
But we were interested in summing from the first term to the nth term
Look, you can either start by 0, or by 1
in case you start by 0
f[n] = f[0] . r^n
in case you start by 1
f[n] = f[1] . r^(n-1)
But which is better?
I honestly prefer 0
All the time
empty sail
I honestly prefer 0
You sound like someone who codes
soft rune
Even if you think of it logically, in math way
Sequences have a domain of definition which is the set of natural numbers
0,1,2,3,...
soft rune
You sound like someone who codes
I do actually!
0 simplifies work
r^n
not r^(n-m)
Anyways, you just use your geometric series formula
you have the first term, you have the last term
which is n
empty sail
I do actually!
Btw, if you never saw it yet, I wanted to dm you
topaz sinewBOT
topaz sinewBOT
Available help channel!
ornate magnet
topaz sinewBOT
barren lion
,rccw
thorny flameBOT
ornate magnet
I want my answer to get checked
barren lion
I want my answer to get checked
send it through
drifting swift
so there are 119 possible values of the common difference?
drifting swift
what are they?
also are we considering e.g. 59, 60, 61 and 61, 60, 59 as different progressions for this problem? the statement doesn't make that clear
barren lion
also are we considering e.g. `59, 60, 61` and `61, 60, 59` as different progress...
i'd assume the answer would be even because of this
@ornate magnet
ornate magnet
also are we considering e.g. `59, 60, 61` and `61, 60, 59` as different progress...
Yes
ornate magnet
i'd assume the answer would be even because of this
No one case will be 60,60,60
ornate magnet
the angles are in arithmetic progression?
Yes
drifting swift
arithmetic progressions with difference 0 exist
barren lion
i read Ls as in lengths
drifting swift
$\angle$s
ornate magnet
😑
thorny flameBOT
Ann
drifting swift
is what was meant
barren lion
i see
drifting swift
would have been easier not to abbreviate
this is the same kind of "takes you a moment" abbreviation as "+ve"
drifting swift
you appear to be
neon iron
$sin^2x = sin(x)^2$
topaz sinewBOT
$sin^2x = sin(x)^2$
thorny flameBOT
Ilvvus
noble laurel
Yes, although no one writes it the second way
neon iron
oh ok
thorny flameBOT
AustinU
noble laurel
is different
neon iron
alr then
thorny flameBOT
AustinU
noble laurel
but, it is much more usual/normal to write it the first way you did
thorny flameBOT
AustinU
noble laurel
like so
neon iron
alr thanks
$(\frac{sinx}{cosx} + 2) (2 \frac{sinx}{cosx} +1) = (2 \frac{sin^2x}{cos^2x} +2)$
thorny flameBOT
Ilvvus
neon iron
why is this false?
noble laurel
no worries, it happens
neon iron
its such a beginner mistake too
forgetting to multiply each member with each other member
noble laurel
I still do the box method much too often XD
neon iron
we wouldnt be able to apply an algebraic identity here right
noble laurel
What do you mean by that?
noble laurel
I'd try to avoid using that, if you can see the general pattern on your own then use it to speed up the process
but don't try to apply any formulas you can't really understand
neon iron
nah i do understand it
im just having severe brain fog rn because its very late and im tired
noble laurel
Yeah no worries
the reason it doesn't completely apply here is because the first term of the binomials isn't the same
in one you have 2sin/cos and the other you just have sin/cos
noble laurel
no problem!
neon iron
.close
karmic monolith
Fast way to do this?
topaz sinewBOT
Fast way to do this?
karmic monolith
Idk what to do
I do not want to plug in these numbers to check
how do i solve without plugging in numbers
pallid wedge
do you know how to derivative
karmic monolith
yes, i did it in image
pallid wedge
this is wrong
vernal vale
it looks fine
the derivative is wrong but its for finding critical points and they divided by 6
bad form but whatever
neon iron
topaz sinewBOT
topaz sinewBOT
Available help channel!
wicked totem
So I want to calculate a probability. I have a game, where I have m amount of meteors I need to shoot down. For that I have c amount of cannons. Each of these has a default probability of hitting one single meteors of p = 0.8. Now, I want to get the probability, that all meteors get shot down. Note that a cannon can only shoot once.
My current solution can only calculate the probability that c amount of cannons can shoot down one meteor (see png)
I don't know any advanced probability things, I just drew a tree and looked at any path that leads to the probability of shooting down a meteor. (see png 2)
Is there a way to calculate the probability, that all meteors get shot down by the cannons, instead of only for one?
topaz sinewBOT
So I want to calculate a probability. I have a game, where I have `m` amount of ...
@wicked totem Has your question been resolved?
topaz sinewBOT
@wicked totem Has your question been resolved?
topaz sinewBOT
@wicked totem Has your question been resolved?
wicked totem
<@&286206848099549185>
topaz sinewBOT
@wicked totem Has your question been resolved?
wicked totem
.close
summer badger
Need help with angles ;
How do I convert:
(30.0/0) facing south towards positive Z
To
(??/??) facing east towards positive X
hollow bay
topaz sinewBOT
hollow bay
Can someone explain graphically why it's continous at 0
prisma mesa
this is the graph
basically when it's slightly greater than 0, it's just 0. When it's slightly smaller, it's x*-1
and x*(-1) at 0 is 0
topaz sinewBOT
@hollow bay Has your question been resolved?
minor plume
im trying to find the range of this function however I cant quite get the final step the question is: Given the function f(x) = 1/(x^2 - 1), find the domain and range of the function.
topaz sinewBOT
im trying to find the range of this function however I cant quite get the final ...
minor plume
struggling with how to convert x=sqrt(1+1/y) into an answer
<@&286206848099549185>
stable mulch
x=√(1+1/y)
y cannot be zero
and 1+1/y cannot be less than 0
(it is in square root)
say 1+1/y<0
1/y<-1
y>-1
so y cannot be between 0 and -1
can be -1, cant be zero
{R/(-1,0]}
minor plume
so does that mean y is anything greater than 0
or should i write it as y cannot equal specifically -1 and 0
minor plume
ok thanks
but how can that be written in set builder notation
bcs thats what my school requires
stable mulch
y>0 and y<=-1
minor plume
great thanks
stable mulch
or (0,inf)U(-inf,-1]
cinder oxide
https://www.youtube.com/watch?v=iSaRqVkImfw is Mathematical Induction more or less about finding patterns?
topaz sinewBOT
https://www.youtube.com/watch?v=iSaRqVkImfw is Mathematical Induction more or le...
cinder oxide
sometimes induction holds up, sometimes it doesn't
I've also heard Induction described with TAPE:
Test
Assume
Prove
Explain
pastel oracle
yes, I'd say finding patterns is important
hollow fractal
Progrssion
hollow fractal
I've also heard Induction described with TAPE:
Test
Assume
Prove
Explain
I usually do Base Case, Assumption, Induction, Conclusion
pastel oracle
@cinder oxide this might be too detailed for you, but see if it helps: https://math.stackexchange.com/a/1255268/993372
cinder oxide
I usually do Base Case, Assumption, Induction, Conclusion
BCAIC?
knotty ledge
IYDEQYWNASA
cinder oxide
Bruh you don't need to make acronyms out of everything
BYDNTMAOOE
hollow fractal
<@313298495417221121> this might be too detailed for you, but see if it helps: h...
You assuming he isn't intelligent enough?
"This might be too detailed"
L
knotty ledge
avid has been around for a while, we know the level he's at right now
ashen sparrow
hes made Progrssion he is ready
pastel oracle
"detailed" != "difficult"
knotty ledge
whats your problem?
pastel oracle
<@&268886789983436800> likely troll
cinder oxide
knotty ledge
you do attract them avid
cinder oxide
.close
desert pulsar
How do I prove that every term in the sequence n^2-8n+21 is positive?
drifting swift
you could prove that n^2 - 8n + 21 is positive for all real n
desert pulsar
How do I do that
shut obsidian
you could prove that n^2 - 8n + 21 is positive for all **real** n
For natural n, complete induction would probably work
frail reef
Why not just use the discriminant
restive inlet
completing the square would be useful
drifting swift
Why not just use the discriminant
you meant discriminant for sure
drifting swift
For natural n, complete induction would probably work
overkill
desert pulsar
How do I use discriminate / completing the square
desert pulsar
For natural n, complete induction would probably work
What’s this
lean dove
b²-4ac < 0
lean dove
because a > 0, so it opens upwards. Therefore it must not intersect the x axis for it to be positive. So it shouldn't have any roots, so b²-4ac < 0
desert pulsar
Isn’t it for quadratic equations?
desert pulsar
because a > 0, so it opens upwards. Therefore it must not intersect the x axis f...
So I should just prove it is negative and I’m good to go
desert pulsar
why not complete the square on it
That’s all?
I guess I need to learn how to do that again
But how do I know it’s positive?
drifting swift
yes
frail reef
you meant discriminant for sure
Yeah sorry it autocorrected I think
drifting swift
complete the square and it will become obvious to you. or not. if it doesn't you can post the completed-square form here and we can give you pointers.
drifting swift
dunno but you don't need induction of any kind here
frail reef
That’s for more complex proofs
frail reef
What about that complete induction thing? What’s that
Can be used for proving things like summations but you only need to complete the square for this
frail reef
Since (n-4)^2 has to be greater than it equal to 0
That expression must be greater than or equal to 5
And hence always positive
drifting swift
^
your thing is 5 + something nonnegative
it is not only positive, it is bounded below by 5
drifting swift
@desert pulsar is it like
"i don't understand what some or all of the words mean in what you said"
or
"i understand what you're saying but not why it's true"
desert pulsar
The words you used
frail reef
The words you used
Ok so do you know that a number multiplied by the same number can never be negative?
desert pulsar
Yes
frail reef
So treat the expression (n-4) the same way
You have written down (n-4)^2 + 5
You can rewrite that as (n-4)(n-4) + 5
From what I said before a number multiplied by itself must always be positive
desert pulsar
Oh
frail reef
So what you have there if you think about it is some positive number + 5
A positive number + a positive number can never be negative
frail reef
Yes
desert pulsar
What about the discriminant method?
frail reef
All you need to do to finish it is say that since the brackets can’t be negative then when you plus it to 5 it must always be positive
Basically the same thing
desert pulsar
I got a negative number
desert pulsar
All you need to do to finish it is say that since the brackets can’t be negative...
Alright
frail reef
?
desert pulsar
Using b^2-4ac
desert pulsar
Yes
frail reef
Then you know that x = (-b +/- the square root of the discriminant)/2a
desert pulsar
Yes
frail reef
If you want to show that the expression is always greater than 0, a way to do that is to show there are no solutions for x
Since whatever x equals is where the expression crosses the x axis
desert pulsar
Mhm
frail reef
If you were to say for example that y = (x-4)^2 + 5
If the equation never crosses the x axis ( in other words it never goes negative) then there would be no solutions for x
When you figure out the determinant, if it is ever less than 0, you have proved that it never crosses the x axis
Since then x equals some number +/- a root of a negative number
Since you can’t do the root of a negative number, the equation has no solutions
Understand?
topaz sinewBOT
@desert pulsar Has your question been resolved?
frail reef
np
frail reef
Well yes but we are dealing with real numbers in this case
So I didn’t bother mentioning them
cyan pasture
can someone give me the points for this graph
topaz sinewBOT
can someone give me the points for this graph
topaz sinewBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
molten vine
can someone give me the points for this graph
you mean the equation?
civic briar
(1, -2) (-5,5)
cyan pasture
than did i solve it right
cuz i plug them in the distance calculator
and got 9.21
@civic briar
pastel oracle
should be -2 - 5, not -2 + 5
cyan pasture
ohhhhh
im so stupid
tysm
wait one more
is the point (5,1) and (5,-5)
@pastel oracle
pastel oracle
(5, 1) is right, yes
pastel oracle
no
cyan pasture
is it 1,-5
pastel oracle
no
cyan pasture
-1,-5?
pastel oracle
no
pastel oracle
how did you get (5, 1) for the one point?
pastel oracle
yes
pastel oracle
same thing for the other point
pastel oracle
you shouldn't need to confirm, just count the number of lines to over and up/down
civic briar
You are right. its (0, -5)
cyan pasture
thankks
topaz sinewBOT
@cyan pasture Has your question been resolved?
topaz sinewBOT
unborn lagoon
,rotate
thorny flameBOT
topaz sinewBOT
@sour robin Has your question been resolved?
spare smelt
Every day the value of my $1 portfolio either doubles with probability p, or halves with probability 1-p. What is the expected long run value?
topaz sinewBOT
Every day the value of my $1 portfolio either doubles with probability p, or hal...
@spare smelt Has your question been resolved?
topaz sinewBOT
@arctic surge Has your question been resolved?
sweet shard
!show
topaz sinewBOT
Show your work, and if possible, explain where you are stuck.
@arctic surge Has your question been resolved?
topaz sinewBOT
lucid isle
21
lucid isle
What is it then 😂
knotty ledge
<@182179228840755200> Grow up brother
what?
lucid isle
<@182179228840755200> Grow up brother
Tell ‘em 😂
karmic monolith
@knotty ledge You're acting childish. You should grow up and stop feeling the need to mess with people who are just bored.
Them taking up a single help channel isn't gonna change your life
@neon iron It's already closed you just have to wait for it to go away
knotty ledge
hahahaha what is your problem
knotty ledge
i think you're being naive
knotty ledge
i literally just told them to go and mess around literally anywhere other than a help channel
why are you so pressed
karmic monolith
Why? tho
They did nothing to you, but you felt the need to say that to them and close their channel before they got an answer to their question
Like seriously grow up and learn what empathy is
knotty ledge
okay you carry on living in your little naive and oblivious bubble
karmic monolith
If what they're doing has zero impact on your life or the life of others why do you feel the need to go out of your way to attack them
vivid flame
This isn't even the proper channel to joke around like that. This is the math help channel. Not the #chill channel.
rigid ivy
If what they're doing has zero impact on your life or the life of others why do ...
We're volunteer helpers and appreciate not having our time or resources wasted. Simple as that
karmic monolith
We're volunteer helpers and appreciate not having our time or resources wasted. ...
Exactly
tender mantle
karmic monolith
so why waste your time attacking someone for asking what 9+10 is
just go to another channel
tender mantle
This is what the question was referring to
topaz sinewBOT
Available help channel!
sturdy oracle
so why waste your time attacking someone for asking what 9+10 is
.are you not familiar with the 9+10 meme? It's a common Shitpost in here
.also that's something literally google can solve
.there's nothing wrong with a closing a channel that's obviously a Shitpost
topaz sinewBOT
sweet shard
<@&268886789983436800>
topaz sinewBOT
sweet shard
Ty wocket
knotty ledge
wocket... wacoon
topaz sinewBOT
Available help channel!
grizzled sigil
topaz sinewBOT
grizzled sigil
How do I find x?
frail dove
can you find an equation for x?
sweet shard
,rotate
thorny flameBOT
dreamy drum
the total angle is 255, can you make an equation relating x to this amount?
oops
sorry I didn't notice y'all were helping
mb
frail dove
hint: what is 2x+90°+3x equal to?
grizzled sigil
5x + 90°?
sturdy oracle
.close
topaz sinewBOT
topaz sinewBOT
✅
topaz sinewBOT
topaz sinewBOT
Available help channel!
neon iron
hey
neon iron
topaz sinewBOT
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
keen matrix
sum of interior angles of a quadrilateral is 360deg
use the givens and that info the compute x
neon iron
sum of interior angles of a quadrilateral is 360deg
OK but how do i know its 360
deft arch
In general the sum of interior angles for any polygon is 180(n-2) where n is the number of sides
keen matrix
OK but how do i know its 360
$S=180(n-2)$
thorny flameBOT
XxMrFancyu2xX
neon iron
And triangles are 180
keen matrix
plug in n=4 to the formula to achieve the desired result
neon iron
Is it because they have 3 edges
keen matrix
👍
keen matrix
Is it because they have 3 edges
ayo your about me 💀
neon iron
$S=180(n-2)$
So do i add 92 and 44 and then take away from 360 and then divide the answer by 2
neon iron
ayo your about me 💀
It was a dare sorry if it offends you
sturdy oracle
It was a dare sorry if it offends you
It could get you banned from this server (for some reason) so I'd change it
keen matrix
nah idc but just came as a shock when I clicked it lmao
sturdy oracle
Personally if it's in your bio, idrc
It's not like a nickname but
This server just doesn't like it so I'd change it
empty sail
It could get you banned from this server (for some reason) so I'd change it
It's more because it has a racial slur
sturdy oracle
I get that but it's in a bio, not a nickname
neon iron
It's more because it has a racial slur
its normal nowadays a lot of discord servers r starting to allow it
sturdy oracle
Not even in status, but I'm fine with it in status also
neon iron
not the hard r tho
sturdy oracle
But just note that can get you yeeted from here
keen matrix
aight again we don't care but you prob won't be on the server for long after this
anyways
we or just I digress
neon iron
Can you give me the andwer
keen matrix
So do i add 92 and 44 and then take away from 360 and then divide the answer by ...
this is slightly wrong
you have the equation $360=92+44+2x$
thorny flameBOT
XxMrFancyu2xX
keen matrix
but you did you're solving incorrectly
neon iron
so its the same thing but i worded the equation wrong ?
keen matrix
you said add 92 and 44 which is correct
but then take away 360 is not correct
this means $0=136-360+2x$ which is counterproductive
thorny flameBOT
XxMrFancyu2xX
keen matrix
yw! have a good day ma'am also don't forget to close your channel 
topaz sinewBOT
hi!! how do i find the x-intercepts for this graph?
sweet shard
hi!! how do i find the x-intercepts for this graph?
Do you know what x intercepts are on the graph
And how that relates to f(x)
cursive jackal
hi!! how do i find the x-intercepts for this graph?
check where y becomes zero - here y means function itself
x intercepts is where y becomes zero , and vice versa
topaz sinewBOT
@loud violet Has your question been resolved?
tight ridge
In a rational graph, can i x value that is a hole also be a virtical asymptote
clever citrus
How would I write in two intervals?
topaz sinewBOT
How would I write in two intervals?
winged grove
How do you solve both 2 and 3?
topaz sinewBOT
How do you solve both 2 and 3?
winged grove
youre on the wrong channel
topaz sinewBOT
@winged grove Has your question been resolved?
sweet shard
How do you solve both 2 and 3?
Find sine and cosine of u first
Then use half angle identity
topaz sinewBOT
topaz sinewBOT
Available help channel!
coarse urchin
I’m struggling to understand how a sequence of continuous functions can converge pointwise in [a,b] with a single continuous limit function without uniformly converging. I just don’t understand how that’s possible by definition if I can find a boundary for the superimum of every function
topaz sinewBOT
I’m struggling to understand how a sequence of continuous functions can converge...
sweet shard
same reason as before
sequence grows unbounded to infinity, but its support goes to 0
topaz sinewBOT
@coarse urchin Has your question been resolved?
coarse urchin
sequence grows unbounded to infinity, but its support goes to 0
I just don’t understand how that’s possible by definition
sweet shard
because the sequence converges pointwise to 0
so |f_n(x)| converges to 0 as n goes to inf
sweet shard
the max of the function of grows unbounded yes
sweet shard
same reason as before
i should have said sup norm grows unbounded
have you seen this before
thorny flameBOT
riemann
coarse urchin
No I have no idea what this means
coarse urchin
the max of the function of grows unbounded yes
But can't I take that max (assuming it's always in the same position) and make it so |f_n(max) - 0| < epsilon?
sweet shard
But can't I take that max (assuming it's always in the same position) and make i...
no
x is fixed, then n is taken to infinity
coarse urchin
But for every x and epsilon I can do that, no?
sweet shard
$||f_n||\y = \textrm{max}{x \in [0,1]} f_n(x)$
thorny flameBOT
riemann
sweet shard
But for **every** x and epsilon I can do that, no?
you're not really reading the definition of pointwise convergence correctly
coarse urchin
Evidently, can you please enlighten me then?
sweet shard
But for **every** x and epsilon I can do that, no?
"every"
sweet shard
x is fixed, then n is taken to infinity
.
coarse urchin
thats cryptic
sweet shard
you're trying to claim something for all x at the same time
when the definition of pointwise specifically fixes x before taking the limit
coarse urchin
you're trying to claim something for all x at the same time
"For any x, and any epsilon, you can find an n large enough so that |f_n(x) - f(x)| < epsilon
That's how I'm reading it
sweet shard
But can't I take that max (assuming it's always in the same position) and make i...
go back here and compare
you're claiming you can change x to be x_max
but x is fixed
coarse urchin
you're claiming you can change x to be x_max
Just take x_max and make sure its smaller than epsilon
I didn't claim to change anything
Well, not the x at least
sweet shard
x_max can depend on n
it's a sequence of functions
x_max doesn't need to be the same for all f_n
coarse urchin
So the trick is to make x_max shift?
sweet shard
that's at least one way yes, there might be more that i'm not thinking of
coarse urchin
that's at least one way yes, there might be more that i'm not thinking of
So I need a sequence, that converges pointwise to 0, in [a,b], where the maximum of the function is unbound, and ever shifting?
sweet shard
converges pointwise to 0, in [a,b], where the maximum of the function is unbound
finding that is probably enough
coarse urchin
> converges pointwise to 0, in [a,b], where the maximum of the function is unbou...
But if it doesn't shift, can't I just take that x and bind it with a large enough n?
"any x"
Or do I still not understand the definition of pointwise convergence
sweet shard
"that x" need not be unique
sweet shard
the x is x_max
a function can attain its max on multiple values on a domain
e.g. f(x) = 1 on [0, 1]
coarse urchin
a function can attain its max on multiple values on a domain
Oh like, the maximum just has multiple maximums?
Or did you mean "multiple n's"
sweet shard
multiple x values
sweet shard
e.g. f(x) = 1 on [0, 1]
the max of this function is 1. it attains that max on all of [0, 1]
coarse urchin
the max of this function is 1. it attains that max on all of [0, 1]
But if that's true, I'll find an n where the max is at most epsilon, and then shrink that epsilon to naught, until the value itself is close to 0?
Like
|f_n(1)| < epsilon
Again, assuming it doesn't move at all
sweet shard
right that's why you need to change the support as well
rain radish
topaz sinewBOT
rain radish
Numerical single digit: i.e. Answer is a single digit whole number
nevermind got the answer. it is 6.
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
analog sierra
This is kinda chemistry and math together if anyone knows this could you tell me if it’s right or wrong and what the right thing is
topaz sinewBOT
This is kinda chemistry and math together if anyone knows this could you tell me...
empty sail
This is kinda chemistry and math together if anyone knows this could you tell me...
The model questions, all you do is count how many of each element is on the left and compare it with the right. If it's not the same, then doesn't follow law of conservation
For the other two, do you know what that blank, unit means?
analog sierra
The model questions, all you do is count how many of each element is on the left...
Im reading
Sorry
Ok so
analog sierra
The model questions, all you do is count how many of each element is on the left...
You see
What I’m asking
Is
Are they right
For the
Ones you just labeled off
empty sail
all you do is count how many of each element is on the left and compare it with the right. If it's not the same, then doesn't follow law of conservation
Can you count?
Can you compare?
empty sail
You don't need to get confirmation if it's right or not. Say you have 2 Si on the left side and 4 on the right, that doesn't follow conservation because you magically gained 2 Si
If it was 2 Si on the left AND 2 on the right then it obeys because it's the same on both sides
analog sierra
Ok so using that
empty sail
Model a is correct b incorrect ?
Model A, how many Fe's are on the left?
analog sierra
What you just said
Model a would be wrong
Bc
Fe on the left
And O and fe
4
And 4 on the right
empty sail
Does the amount of O's and Fe's on the left equal on the right side?
empty sail
As I mentioned, it's not a hard task, you literally count and compare both sides
empty sail
If it's 6 on the left and 6 on the right that means nothing was lost/gained, aka it follows
empty sail
So then does it follow?
analog sierra
No it doesn’t
empty sail
There you go, you can do the rest on your own and you don't need to get confirmation
empty sail
Because as mentioned you just need to compare
empty sail
Do you know what formula mass means?
empty sail
Do you know how to find formula mass of molecules?
empty sail
Formula mass is the total mass of the molecule which is found by summing up the mass of all the elements in that molecule
analog sierra
Im listening just noting it down
empty sail
For example H20, the formula mass is 18 g/mol because you have 2 H and 1 O, where the mass of H is 1 and O is 16. So 2 x 1 + 16 = 18 g/mol
Can you do that for Pb(SO4)?
empty sail
As stated, you sum up the masses of all the elements in that molecule
Pb(SO4)
How many Pb's are there?
empty sail
What's the weight of Pb?
analog sierra
207.2
empty sail
Next S, how many S's are there?
analog sierra
1
empty sail
What's the weight of S
empty sail
How O's are there?
analog sierra
4
empty sail
What's the mass of O?
analog sierra
15.999
empty sail
What's the total mass of Pb in that molecule?
analog sierra
255.264
empty sail
?
empty sail
Units as in g, m, km, secs, etc
Those are units
What units is formula mass represented in?
empty sail
What units represents time?
.
empty sail
What about speed?
analog sierra
And@merters
topaz sinewBOT
@analog sierra Has your question been resolved?
neon sage
anyone know a quick method for solving polynomials
topaz sinewBOT
anyone know a quick method for solving polynomials
pliant briar
hi
so i have a very easy question to ask u
for me it might be hard
but plzzz help
what is wait le me check
topaz sinewBOT
@neon sage Has your question been resolved?
sweet shard
anyone know a quick method for solving polynomials
just ask your question
finite moth
anyone know a quick method for solving polynomials
for all polynomials, it's not very easy
topaz sinewBOT
topaz sinewBOT
Available help channel!
snow token
Is there a difference between $x^{-\frac{\alpha+3}{2}}$ and $x^{\frac{-\alpha-3}{2}}$?
topaz sinewBOT
Is there a difference between $x^{-\frac{\alpha+3}{2}}$ and $x^{\frac{-\alpha-3}...
thorny flameBOT
Bennxy
snow token
Does the minus sign matter if it is placed outside or inside the fraction?
mellow arrow
Does the minus sign matter if it is placed outside or inside the fraction?
no
both are same
drifting swift
are you asking this because you saw this in a written solution and the two were apparently not treated as the same thing
snow token
No I was asking this because I saw that $x^{-0.5}* x^{- 1}* (x^\alpha)^{-0.5}$ was written as $x^{-\frac{\alpha+3}{2}}$
thorny flameBOT
Bennxy
snow token
And I thought it was $x^{\frac{-\alpha-3}{2}}$
thorny flameBOT
Bennxy
drifting swift
... and as has been explained to you, those two are one and the same.
snow token
But what if I had written it as $x^{-\frac{\alpha-3}{2}}$
thorny flameBOT
Bennxy
snow token
Will this still be the same?
thorny flameBOT
snow token
Huh wait
I feel stupid right now
But how are $x^{-\frac{\alpha+3}{2}}$ and $x^{\frac{-\alpha-3}{2}}$ the same?
thorny flameBOT
Bennxy
bold nebula
you can put the minus sign wherever you want
here it's about the top
-(alfa + 3) = - alfa - 3
snow token
So writing $x^{-\frac{\alpha-3}{2}}$ is the same as $x^{\frac{-\alpha-3}{2}}$?
thorny flameBOT
Bennxy
bold nebula
But how are $x^{-\frac{\alpha+3}{2}}$ and $x^{\frac{-\alpha-3}{2}}$ the same?
this one ^
bold nebula
**Bennxy**
for this one it would be -alfa + 3
snow token
But won't this become $-(\alpha-3) = -\alpha+3$
thorny flameBOT
Bennxy
snow token
for this one it would be -alfa + 3
Ohh yeah right
So the minus sign outside the numerator does effect the fraction
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
half pike
can someone check if I did these right
topaz sinewBOT
can someone check if I did these right
safe burrow
thorny flameBOT
OutOfNosh
neon iron
And another one on 8c