Forgot the formal notation
#help-4
frank path
steady charm
small notation issues like that would cost a very small amount of points
frank path
And it’s for AP Physics C and I’m p sure that on the scoring guidelines it says that u wouldn’t lose any pts rlly unless it makes the statement ambiguous
Which I don’t think it did in my case since I’d already defined velocity
@steady charm so what do u think
frank path
or an in-class exam
Like, both
I just took an in-class test, but I’m curious abt what u think w regard to both
steady charm
for the in-class test i'd say it would probably cost you a small amount but it's very dependent on your teacher
for the ap exam it may also cost a little but you don't really see the effect of that unless it pushes you across a points boundary (unlikely)
frank path
time is often implied (see overdot notation)
Yeah that’s what I was thinking
Especially since I clearly defined velocity as dx/dt
And then put =d(function)
frank path
for the in-class test i'd say it would probably cost you a small amount but it's...
Is there a chance he wouldn’t deduct anything at all
And I feel like if it’s repeated they’d only really deduct once
steady charm
i mean it's possible, i don't know your teacher
frank path
At least I think that’s what they do on the actual exam
tidal swift
is there a reason why you do not want to write it though
frank path
is there a reason why you do not want to write it though
No lol
I’m saying I forgot to
tidal swift
oh
tidal swift
depends on your examiner then, i suppose
frank path
We were recently introduced to the topic of derivatives and all
frank path
depends on your examiner then, i suppose
Yeah ig
Wtvr ig
I’ll just try to keep it in mind for next time
frank path
.close
lean temple
guys just wanted to ask a general question
does horizontal reflection have no affect on the function when X is inside the modulus?
like 2 - | 3 - x/2|
we simplify it like 2 - | -((x+6)/2)| now it doesn't really matter in desmos wheather I add the - or not in the modulus
why is that
hazy pivot
|x| = |-x|
lean temple
ok so when applying transformation in modulus functions we can basically common the negative and remove it then right?
tacit mantle
think it better as this |x|= √(x²)
small vine
When you say "horizontal reflection", do you mean in the x-axis or y-axis?
tacit mantle
so as to always obtain positive result on non complex numbers
lean temple
When you say "horizontal reflection", do you mean in the x-axis or y-axis?
y axis f(-x)
y mb
small vine
Well then you're replacing x with -x
lean temple
so as to always obtain positive result on non complex numbers
oh so we can common the negative out then right?
small vine
If x is the only thing inside the modulus, it will have no impact
But it might otherwise
,w plot y = abs(x)
rocky lotusBOT
small vine
,w plot y = abs(-x)
rocky lotusBOT
rocky lotusBOT
small vine
,w plot y = abs(-x-3)
rocky lotusBOT
hazy pivot
If you negate the entire argument inside the mod, it stays the same
lean temple
|(6-x)/2|
here we can common the negative out and ignore it then it stays same though right?
hazy pivot
Yes
lean temple
but like f(-x) here would change the function
hazy pivot
Yes
hazy pivot
Close
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Available help channel!
edgy wolf
hi i need help on calculating exponents easily
vale dockBOT
hi i need help on calculating exponents easily
edgy wolf
please
merry crystal
do u have a specific problem?
edgy wolf
https://en.wikipedia.org/wiki/Exponentiation_by_squaring
thank
merry crystal
yes recursive method is quite efficient
brittle bolt
thank
I only know of it from CS, but I'm sure that there's plenty of people who use it in everyday math.
edgy wolf
I only know of it from CS, but I'm sure that there's plenty of people who use it...
ok thank
im 2 year
old
can x be any number
brittle bolt
yeah
brittle bolt
Alright. If that's all, I'll close the thread so someone else can use it if they need. Anything else before I close it?
vale dockBOT
@edgy wolf Has your question been resolved?
swift wasp
hello
tame nebula
I need help
vale dockBOT
I need help
steel valley
please help me solve this question
pliant nova
send your question
clever sentinel
repat?
pliant nova
repeat?
pliant nova
what do you mean by that
tame nebula
Like:
i = 1100
i go less by one untill it hits zero
lyric sundial
!xyproblem
vale dockBOT
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.
pliant nova
huh
brittle bolt
Recursive functions?
pliant nova
are you just asking how to make a circuit with logic gates that can do that
tame nebula
Recursive functions?
Exactly
brittle bolt
I think you're looking at a very broad field of study, called discrete mathematics.
lyric sundial
Yeah give the exact context
Otherwise it's just random and probably useless suggestions
tame nebula
Like
for (int i = 10; i--; i == 0) {
n=f(n);
}
but 4 math
brittle bolt
I'm assuming you mean n =f(i) here?
tame nebula
n is 2n or something like that
brittle bolt
this is just something like a_n+1 = f(a_n) for some function, I think
tame nebula
n is f(n)
f(x) can be 2n n+7...
brittle bolt
where _ denotes subscript
tame nebula
I think it is not possible right now.
lyric sundial
Not that it's not possible, it simply isn't clear what you have/wantbto do
brittle bolt
.close
tame nebula
.close
swift wasp
hello
swift wasp
need help
tacit mantle
?
swift wasp
what is standard form in rational numbers
???
tacit mantle
what grade are you in
swift wasp
umm ... 8
tacit mantle
standard form is before 8th.
swift wasp
idk diffrent in countries
tacit mantle
besides its just simplification
swift wasp
man just explain
merry crystal
standard form is when the integers in the numerator and denominator are coprime
swift wasp
oh thnx
merry crystal
6/8 can be converted to 3/4
swift wasp
oh thnx
merry crystal
u want it such that the numerator and denominator share NO common factors other than 1
lyric sundial
Give a look at Khanacademy or at orgchemtutor
ebon glade
do you know how to multiply (x+5)*y?
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swift wasp
.close
lethal vessel
vale dockBOT
safe fulcrum
,rccw
rocky lotusBOT
drifting hornet
how do I pick between A and B
Can you estimate the slope? At least very approximately
safe fulcrum
well, if the point has y-coordinate y
then a line with gradient y would be one through the origin and that point
lethal vessel
maybe 1
lethal vessel
yea
drifting hornet
and what about the y-coordinate of the point (i.e. f(1))
safe fulcrum
well, if the point has y-coordinate y
then a line with gradient y would be one ...
so you just need to compare the slopes of that line and the tangent line
lethal vessel
and what about the y-coordinate of the point (i.e. f(1))
no clue
i mean with no scale how can I tell
drifting hornet
the scale is usually taken to be the same on x and y axes
unless drawn otherwise
lethal vessel
ah
so f(1) is maybe around 2
oh I see now
f(1) is bigger than 1
f'(1) is smaller than 1
safe fulcrum
you got it!
vale dockBOT
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Available help channel!
pseudo holly
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stark wedge
is that $\sin(\sqrt{2}) \cdot \theta$ or $\sin(\sqrt{2}\theta)$?
rocky lotusBOT
Ann
pseudo holly
thats whati was wondering
the book has it written like this
for some reason
ok lets do both cases anyway
stark wedge
can you show the book
as in, can you show the problem as it is written in the book
and relatedly: do you know what the value of $\lim_{x \to 0} \frac{\sin(x)}{x}$ is?
rocky lotusBOT
Ann
stark wedge
yeah its 1
cool, you're going to need that.
or maybe not depending on whether the theta is supposed to be inside the sine or not
charred nacelle
wouldn't the numerator be sqrt(2) sin(theta)
pseudo holly
charred nacelle
Never seen a book write as sinsqrt(2) theta
pseudo holly
this question is weird...
charred nacelle
I would assume sqrt(2)theta is the angle
stark wedge
if it wasnt then the thing would simplify to sin(sqrt(2))/sqrt(2)
stark wedge
wrong
stark wedge
θ/θ literally simplifies to 1
pseudo holly
OH WAIT
NO
YES
IM SO DUMB
i get confused when its not variables like x y
thanks for ur help
stark wedge
theta is just another variable tbh
it's good to familiarize yourself with the entire greek alphabet to cover all your bases on that front imo
pseudo holly
yeah it is but im more used to seeing x and y we rarely use theta 💔
pseudo holly
it's good to familiarize yourself with the entire greek alphabet to cover all yo...
will do
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Available help channel!
vagrant glen
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vagrant glen
So
I dont how how to find the change 
I tried (76/8)/4
then replaced the 8 with the 4
neither worked
flint phoenix
I tried (76/8)/4
From here it begins to be incorrect
flint phoenix
yeah
vagrant glen
flint phoenix
You're looking for the slope
vagrant glen
Do you know linear function?
Ya
I needa know how much its changing per n (week)
to do my explicit and recursive formulas
flint phoenix
I needa know how much its changing per n (week)
It's not that difficult of a task if you find the line
Consider those information to be 2 given points on the plane
and with those two point, you find the line
flint phoenix
Fr 🤟
vale dockBOT
vagrant glen
:
flint phoenix
Thank yu fren
I didn't help much lol
You figured that out yourself
have a good one!!
vale dockBOT
Available help channel!
fluid blade
Is this wrong my friend solved it using weirstraus or sum which idk and idk if mines an alternate answer or just wrong
rocky lotusBOT
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@fluid blade Has your question been resolved?
fluid blade
<@&286206848099549185>
sullen summit
Jus put x = 1/t
fluid blade
Bru that’s not what I asked I asked if my answer was right
Ik there’s other ways to solve it
sullen summit
Ian looking at allat imma go
fluid blade
K
fluid blade
I have to write bit for it to be
😭✌️
That’s the drawback
And it’s still not like good looking it’s like decent
faint ferry
Also what’s the question
fluid blade
I mean I’ve seen some bad hand writing because of when I see math teachers answering tests
fluid blade
Also what’s the question
Js if my solution is right
faint ferry
not compared to like others it’s probably like average
I swear everyone has like doctor writing
fluid blade
My friend got a dif solution but he solved it a dif way
fluid blade
Js if my solution is right
I mean if I did nothing wrong it should be right but I have no idea if it is 😭
vale dockBOT
@fluid blade Has your question been resolved?
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@fluid blade Has your question been resolved?
fluid blade
Thank you
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@fluid blade Has your question been resolved?
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Available help channel!
tiny torrent
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tiny torrent
I'm having trouble understand what a^m could be
m is the least positive integer such that a^m belongs to H
hazy pivot
a multiplied by itself m times
tiny torrent
or I mean im having trouble understanding what m could be
m isnt necessarily always 1
right?
hazy pivot
Lemme read the proof one moment
Yeah no it need not be 1
Let's consider ℤ as a group under addition
tiny torrent
if m is not always 1 then im having trouble understanding how we can show any element in H with k could be a multiple of m
hazy pivot
If it isn't
You can use division
Let's say k = qm + r
Then $a^{qm+r}$ is in the subgroup
rocky lotusBOT
Xavier 🌺
hazy pivot
Then since $a^{qm}$ is in the subgroup...
rocky lotusBOT
Xavier 🌺
hazy pivot
So is $a^{-qm}$
rocky lotusBOT
Xavier 🌺
zealous pendant
Remember a^m is in the subgroup so a^qm is
hazy pivot
Now you multiply to show $a^r$ is in the subgroup
rocky lotusBOT
Xavier 🌺
hazy pivot
And then r is smaller than m cuz it's the remainder of division by m
This contradicts minimality of m
Hence anything in H must be of the form a^km
@tiny torrent do you follow
zealous pendant
This sort of qm+r minimality proof happens a few times in groups and related fields like number theory I think
tiny torrent
<@472906604572966924> do you follow
yeah I follow the steps but im having trouble conceptualizing why k will always be a multiple m, i guess like an example. because if m = 7, then a^7 is in H and anything below 7 is not in H. But a^8 can be in H still. So let b = a^8 so m = 7 but k = 8 and k isnt a multiple of m so where am I going wrong with my understanding
the proof makes perfect sense and all the steps are clear
but I think im misunderstanding something fundamental
tiny torrent
mmm ok I see
hazy pivot
Essentially whenever you find a minimal element
tiny torrent
wait so if a^8 and a^7 are in H
hazy pivot
It generates the rest of the subgroup
zealous pendant
H=G
hazy pivot
Yes
tiny torrent
Contradicting that
where in the proof represents this contradiction
is it just when we say least positive integer
zealous pendant
We defined m to be smallest one
hazy pivot
The proof takes a slightly different approach
Instead of going for a contradiction
zealous pendant
I’m going to sleep anyway just wanted to help one last one
hazy pivot
They go for the fact that m is the least non-zero power
And 0 ≤ r < m
So r must be zero
hazy pivot
I’m going to sleep anyway just wanted to help one last one
Fair enough, but sometimes two people using two different approaches only confuses the helpee lol
zealous pendant
I thought they were same but 2 different ways of saying it
hazy pivot
They go for the fact that m is the least non-zero power
@tiny torrent do you understand what I said here
The proof you've shown doesn't use contradiction at all
It uses the assumption to show r = 0
tiny torrent
im struggling to see how they relate the same information, might have to look at it for a bit longer
zealous pendant
Isn’t that possible to do with any contradiction?
Maybe I’m going into a different question for another day
hazy pivot
It's possible, but they sent a specific proof that they're trying to understand
hazy pivot
im struggling to see how they relate the same information, might have to look at...
You're given that a^m is the lowest non-zero power in the set
Then you have another a^n
Then you express it as a^(qm+r)
And you show that a^r is in the set
But m is the lowest non-zero power
And 0 ≤ r < m due to how division works
So r must be zero
So if you have any a^n in the set, it's of the form a^qm
tiny torrent
ok let me stare at that for a bit I can feel it clicking
hazy pivot
Feel free to tag me for any questions
vale dockBOT
hazy pivot
Yayyyyy
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Available help channel!
half cargo
@zealous pendant my question has not been resolved
vale dockBOT
<@992807158406189066> my question has not been resolved
half cargo
sorry i went afk
rough talon
whsts the question?
vale dockBOT
@half cargo Has your question been resolved?
half cargo
I will say the question tommorow because I am going to sleep
vale dockBOT
@half cargo Has your question been resolved?
vale dockBOT
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Available help channel!
knotty garden
Hello. Time to address that practice exam again.
I am doing part 3 and my teacher recommended I go down a list of techniques when trying to solve ODEs
knotty garden
For 3a they recommended I go with separible variables.
How do I isolate dy and dx in this situation?
zealous pendant
I haven’t seen dx and dy separated like that a lot
knotty garden
I haven’t seen dx and dy separated like that a lot
in part 3?
zealous pendant
Usually I’ve seen dy and dx together in a fraction but it’s totally fine
zealous pendant
How do I isolate dy and dx in this situation?
Haven’t you already isolated it?
knotty garden
Isn't the equilibrium solution f(x) = c?
For that we need to isolate dy and dx in the last part
zealous pendant
Yes, don’t forget c
zealous pendant
That one is trickier
First step is to make the y’ be on its own by dividing by x
Then you’ll have to multiply by the integrating factor
vale dockBOT
@knotty garden Has your question been resolved?
knotty garden
SLR got a snack
Do I move a part to the other side first?
Or just straight up divide by x?
zealous pendant
Divide by x I think
Try simplify the x terms in y term but keep inside brackets don’t expand
knotty garden
Okay I am lost there.
Also its almost 1 am. I should probably not do all these late at night.
Thanks for the help on 3a. I'll try the rest later.
.close
cobalt raptor
Hi
cobalt raptor
I’ve just finished gcse math and entered a level maths
I love maths and I’m alright at it, but right now it’s just memorising math
I don’t understand why things work
I’m logical and can input things in place
but I love maths for what it is
and memorising just feels wrong
I want to understand procedures
frozen ledge
whats your question
zealous pendant
#discussion might be a better place (or some other place)
cobalt raptor
whats your question
sin cos tan?
frozen ledge
cobalt raptor
Trigonometry and circle theory
zealous pendant
<#268882317391429632> might be a better place (or some other place)
But if you have an example of something you want to talk about go ahead
cobalt raptor
<:what:561568026210730004>
Like I understand sine plugs a value and
outputs a result
but I don’t understand how
And I don’t understand how using sine helps find out missing lengths or angles
or of course tan or cos
frozen ledge
sal khan is your friend
fleet burrow
And I don’t understand how using sine helps find out missing lengths or angles
do you remember your SOH CAH TOA?
cobalt raptor
do you remember your SOH CAH TOA?
Yes of course I know how to use it too
I’m good at trignamoatru I do well in it
Ijust don’t get why it works
cobalt raptor
ah so you want an intuition behind it
yes!
fleet burrow
go to #geometry-and-trigonometry or smth
zealous pendant
!done
vale dockBOT
If you are done with this channel, please mark your problem as solved by typing .close
zealous pendant
We have a lot of people needing help at the moment so I recommend casual discussion in there
flint umbra
flint phoenix
fr
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@cobalt raptor Has your question been resolved?
river shale
.solved
eager flume
vale dockBOT
tidal terrace
I have this feeling that it’s factoring by grouping
zealous pendant
Should we expand the sin 2x?
tidal terrace
Should we expand the sin 2x?
Yes
zealous pendant
Just thinking about the stray sin left afterwards
tidal terrace
Just thinking about the stray sin left afterwards
Move it and factor by grouping
Oh wait this is ugly
zealous pendant
You can solve by squaring here but keep in mind you might gain false solutions
normal hollow
You can solve by squaring here but keep in mind you might gain false solutions
U can always verify even if u do get false
zealous pendant
After squaring, try to get everything in terms of $\cos(x)$ by using:
$$\sin^{2}(x)+\cos^{2}(x)=1$$
rocky lotusBOT
BBMaths
zealous pendant
**BBMaths**
Now this ^
Wait this feels wrong, we aren’t dealing with quartics here are we?
shy ravine
I haven’t tried it but you could try substituting sin^2 = 1-cos^2 and see what it gives you
zealous pendant
I see there is at least one rational value of cos x which is a solution, might be 2, then we can reduce to quadratic
shy ravine
Hmmm, well you can factor out a -4 to get 16cos^4(x)-4cos^3(x)-15cos^2(x)+cos(x)+3=0
After that I’m not sure tbh, I suppose you could use something like the quartic formula if you want to but I would hope there’s an easier way
eager flume
I found u=||1/2||
-1/4≠ 0, I substituted the value
shy ravine
I could be wrong on this but cos is an even function and a product of even functions is even so I think real solutions should be symmetric about 0
zealous pendant
No since that would be for x not u
zealous pendant
All roots are irrational
Oops
Phone issues
Okay so it would solve the question but you need to know the quartic formula
And we are not using that
rocky kettle
eager flume
.close
vale dockBOT
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Available help channel!
spare salmon
I have to find A B and C.
vale dockBOT
I have to find A B and C.
spare salmon
I started by simplifying the left side to log(9x^5/y^3).
How would I go about the other side?
How do you add logs?
zealous pendant
Keep going on the left side
cinder creek
Do you remember how aritmetic operators work with logarithms?
spare salmon
Do you remember how aritmetic operators work with logarithms?
Nope. I forgot the properties.
zealous pendant
Since we have a division, we want the quotient rule
spare salmon
So log 9x^5 - log y^3?
lyric sundial
Yup
cinder creek
3logy, yes. 5log9x, no.
flint phoenix
We're not monetizing....
spare salmon
3logy, yes. 5log9x, no.
Why not? Not saying you are wrong, just looking for a reason.
fleet burrow
Why not? Not saying you are wrong, just looking for a reason.
power of 5 is applied to the x
not to (9x)
fleet burrow
So just leave that one then?
you can apply another rule to split up log(9x^5)
spare salmon
Or would it be log9 and 5logx?
spare salmon
you can apply another rule to split up log(9x^5)
Or yeah. That.
Would they be added to each other?
zealous pendant
Or would it be log9 and 5logx?
If and is + yes
fleet burrow
Would they be added to each other?
mhm
cinder creek
Or would it be log9 and 5logx?
You can go further down with log9.
spare salmon
If and is + yes
😛😛Aright. Getting somewhere.
fleet burrow
tha'ts right
cinder creek
You're right with 2log3. 9=3^2
spare salmon
Oh.
Ok.
A is 2 B is 5 C is -3??
Wait what?
I am confused a little bit. Can I just do that?
cinder creek
Yeah. The problem is asking you to break the left expression down to smaller units, wanted as the right hand side.
cinder creek
It's straightforward.
spare salmon
Very. Thank you!
zealous pendant
!bnuuy
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zealous pendant
!done
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spare salmon
.close
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fair imp
@spare warren
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<@620914784434651147>
vale dockBOT
Please do not ping individual helpers unprompted.
honest stone
@fair imp please close the channel using .done.
@river shale sorry to ping. You’re one of the only helpful I know, and this person won’t close. Can you do it pwease? 👀
inner abyss
.close
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inner abyss
you can reopen (or use a new channel) if you have a question
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Available help channel!
hot escarp
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fleet burrow
!status
vale dockBOT
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
show your working
spring jackal
did you mean $\sqrt{22} - 6$ or $\sqrt{22 - 6}$?
rocky lotusBOT
χασιβ ♥
spring jackal
forest cedar
For questions like these, it’s best to convert the roots into exponents and work from there
hot escarp
**χασιβ ♥**
First one
woeful trench
(and were you told that it was "wrong", or that you could e.g. simplify further?)
hot escarp
That it was wrong
rocky lotusBOT
@woeful trench
hot escarp
I found that was a difference of squares then
fleet burrow
Try combining these into one $\sqrt[4]{}$
hot escarp
Just continued from there
woeful trench
I found that was a difference of squares then
Sure, how did you get the difference of squares?
woeful trench
(if you wrote anything down in your working out, it would be useful to show, please 
)
hot escarp
I just tried to do it in my head
rocky lotusBOT
woeful trench
That's fair enough, for me I always find it's better to write things down, whenever I try doing them out, it's easier to make mistakes 
hot escarp
Right
woeful trench
Assuming you're taking a as sqrt{22} and b as sqrt{6}, you mean?
woeful trench
<@788085606483361802>
So you're saying that if you applied the difference of squares formula and simplified, you got this here?
hot escarp
Yeah
woeful trench
Hmmm, you might want to be a bit careful then 
did you combine the "insides" of the fourth roots first before you did the difference of two squares, as suggested here?
hot escarp
Hmm doing that would get a different answer
woeful trench
Hmm doing that would get a different answer
It would? (bear in mind that we need to be able to have something that "looks like" (a - b)(a + b) first before we can apply difference of two squares, we can't do that before 
)
hot escarp
So I would have to combine them together first before starting the d of s formula
woeful trench
Yea, so that you have [the factored version] of the difference of two squares, then from that point, everything should be easier 
hot escarp
I looked at an online tool and found that doing that could get the answer 4square root of 478
Could that possibly be correct if not I have to do lots of review lol
woeful trench
Hmmmm, it should be much simpler than that 
What online tool did you use, and how did you put it in?
vale dockBOT
@hot escarp Has your question been resolved?
hot escarp
What online tool did you use, and how did you put it in?
I just sent in the screen shot on math ai
Idk if its even creditable
rip
woeful trench
Possibly not, and I find that sometimes these things misread questions to begin with
It could be more reliable if you type things in tbf (but then there are also other tools you can use that are better!)
woeful trench
Well, I don't have any suggestions that I can give off the top of my head
woeful trench
There is, it's "very simple" (and may surprise you!)
woeful trench
Hmm doing that would get a different answer
Well, if you did it the other way here, did you notice anything different? 
vale dockBOT
hot escarp
.reopen
vale dockBOT
✅
hot escarp
Well, if you did it the other way here, did you notice anything different? <:cat...
Idk how to do it that way sadly
woeful trench
Oh yea, forgot to mention to make sure you react to the bot in time
Anyways, one thing that we do have is true, is that
[
\qty( \sqrt[4]{ \sqrt{22} - \sqrt{6} } ) \qty( \sqrt[4]{ \sqrt{22} + \sqrt{6} } )= \sqrt[4]{ ( \sqrt{22} - \sqrt{6} )( \sqrt{22} + \sqrt{6} ) }
]
and as before, it's the insides of the fourth root that we can apply dots on, what happens when you work out $ ( \sqrt{22} - \sqrt{6} )( \sqrt{22} + \sqrt{6} )$?
rocky lotusBOT
@woeful trench
hot escarp
From working that out u get
a^2 - b^2
square root 22 is a
And square root 6 is b
= (squareroot 22)^2 - (squareroot 6)^2
(sq22)^2 = 22
(sq6)^2 = 6
So then I find that
(sq22)^2 - (sq6)^2 = 22 - 6
= 16
zealous pendant
Now 4th root it
hot escarp
Hb that @woeful trench 😳
hot escarp
Now 4th root it
wdym
zealous pendant
<@788085606483361802>
It’s in a root
woeful trench
But that's easy to work out 
hot escarp
Ok
vale dockBOT
If you are done with this channel, please mark your problem as solved by typing .close
hot escarp
Yes thanks for all the help
zealous pendant
What answer did you get?
zealous pendant
Just doing this to check you’re 4th rooting correctly at this point
hot escarp
Ok
zealous pendant
Idk maybe you’ll square root
zealous pendant
Can you simplify that to a whole number
zealous pendant
$\sqrt[4]{16}$=?
rocky lotusBOT
BBMaths
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hot escarp
Thanks for all the help
zealous pendant
Make sure to type .close
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@hot escarp Has your question been resolved?
hot escarp
.close
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Available help channel!
subtle crown
Claimed while I write my question up
vale dockBOT
Claimed while I write my question up
subtle crown
G'day, Im doing a time series internal for NCEA Statistics. There's several things I don't understand how to do. Firstly, I don't understand where the data comes from to get that table within the recomposition model and the forecast. I also don't understand how to talk about the mutli-colored seasonal effect graph. The pages shown in the images are off the exemplar.
I did do it earlier in the year, but my memory fails me
I'm a bit pressured for time as well, the assessment is due in 4 hours.
If I understand how to do this I'd be whizzing away
The information provided by teachers tells what the graphs are, but not how to construct them
I'll keep trying to understand it, pls ping me if someone can be of help otherwise I won't notice that you've answered.
I realise now, there's an option on the graphing website that spews out data
Thanks to anyone that gave it a glance
.close
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Available help channel!
devout galleon
I think I just expand (hx+k)(x+j) but i dont know what to do from there.
flint phoenix
I think I just expand (hx+k)(x+j) but i dont know what to do from there.
what's the result after you expand it?
devout galleon
hx^2+hxj+kx+kj
flint phoenix
Alright, you already know one variable so far
devout galleon
h=4?
storm harbor
hx^2+hxj+kx+kj
just compare each coefficient...
flint phoenix
Can you write the relation between b and j?
devout galleon
4*j=b
flint phoenix
Fantastic, now you can look for the possible answer
flint phoenix
what do i do with kx+kj
toss that into the garbage can
devout galleon
lmao
flint phoenix
Fantastic, now you can look for the possible answer
flint phoenix
why?
flint phoenix
LOL
alright
4*j=b
Look, we have this cute equation right here
A. $\frac{b}{h} = \frac{4 \times j}{4} = j$
rocky lotusBOT
This is sad 😢
devout galleon
wait so you got A as the answer?
flint phoenix
flint phoenix
wait so you got A as the answer?
uhhh why not?
rocky lotusBOT
This is sad 😢
flint phoenix
So this is everything we have so far, so you agree?
devout galleon
yes
flint phoenix
We know $kj = -45$\
How on earth are we going to determine whether D is correct without knowing the value of j or b lol
rocky lotusBOT
This is sad 😢
flint phoenix
Let's dig further to verify
devout galleon
how did u find kj=-45
flint phoenix
b = k + 4j
kj = -45
storm harbor
how did u find kj=-45
when you compare the two quadratic equations u get
k*j=-45
flint phoenix
how did u find kj=-45
the constant
flint phoenix
oh and we can find j which is j=-45/k
mhm
night ginkgo
We know $kj = -45$\\
How on earth are we going to determine whether D is correct...
Are you actually asking this or are you trying to guide the user?
raw tinsel
Hi , i speak spanish perfectly and i'm to help in trigonometry
devout galleon
ok thanks @flint phoenix @storm harbor
flint phoenix
Are you actually asking this or are you trying to guide the user?
What do you think? 200% the latter 💀
storm harbor
ok thanks <@875020730910273597> <@1417977279148982362>
you'r welcome bro
devout galleon
.close
coarse walrus
.open
A square of side 2a has its centers on the origin and its sides are parallel to the x and y axis. Find the coordinates of the 4 vertices
coarse walrus
I know the answer is (a,a), (-a,a), (-a,-a) and (a,-a) but I don't know how to write it rigorously
tawny moon
if your syllabus accepts sketching, you can sketch out the square
tawny moon
weird. no sketches on a geometry question
well then you can say that since the square has its center on the origin, then its left/right and top/bottom halves are symmetrical about the origin
might be able to use this to work your way
coarse walrus
like I've been trying to argument is define the points in the respective square, and then try to prove that there's some sort of simmetry, but I think It's implied since it's a property of the square right?
tawny moon
there is a symmetry about the origin
coarse walrus
yeah so like what I've written is like define the points, then say the facts about the square, then using that it means that O is the middle point of the directed segmented formed by the intersection of the X axis with the square, do that as well for the Y axis, then since every perpendicular foot of each point falls on for example A falls on a on the X axis and then falls on a on the Y axis, then the coordinates for A are (a,a), and repeat the argument for each point
tawny moon
maybe show your work thus far?
coarse walrus
It's written in spanish, it may take me a while
tawny moon
ah then hm
ah i got an idea
the sides of the square are parallel to the axes and the square itself is symmetric wrt both axes
you can then make a conclusion regarding the possible coordinates of the vertices
coarse walrus
Let O the center at the origin, let A, B, C and D the vertices at quadrants 1, 2, 3 and 4 respectively. It's already know that the diagonals of a square bisect at the center, then AO=OD, since triengle AOD is isosceles, then the perpendicular that goes through O is the perperndicular bisectos, and then cuts through the middle point, the same happens in triangles BOC, COD and BOA.
Then Triangles COD and AOB are congruent, which implies that their perpendicular bisectors are of the same lenght, and then the perpendicualr bisector that goes through O cuts the segment in two equal segments.
If P is the intersection of the X axis with the directed segment AD and Q is the intersection of the X axis with the directed segment BC, then since QP and CD are parallel and QO+OP=QP and |CD|=2a, this means that |QP|=|CP|=2a, and since O is the middlepoint of QP, then QO=OP which means that 2QO=QP, and then |QP|=2a=2|QO|=|CD| and then |QO|=a=|OP|. If the coordinate of Q is (-a1,0) and the coordinate at P is (a2,0) then by definition of distance |QO|=|0-(-a1)|=|a1|=a1, and |OP|=|a2-0|=|a2|=a2 and since |QO|=|OP|=a then a1=a2=a, then the Q coordinates are (-a,0) and P coordinates are (a,0)
then do the same for the Y axis and finish with the foot of the perpendicular through the points fall on Q, P and the Y points however you want to name them
tawny moon
very thorough
tawny moon
promising (if a little overkill)
coarse walrus
It's like 1 and a little bit of a page long
tawny moon
the sides of the square are parallel to the axes and the square itself is **symm...
consider trying this approach
use your quadrant-based approach to identify that there must be one vertex per quadrant
coarse walrus
wdym by symmetric with respect to both axes?
tawny moon
wdym by symmetric with respect to both axes?
the top half is symmetric with the bottom half about the x-axis
same with left and right about the y-axis
so that means that the coordinates must be +/- some value
call it x_0 and y_0, then find them both from there
coarse walrus
Was my other solution right tho?
coarse walrus
Why is it incomplete?
tawny moon
Let O the center at the origin, let A, B, C and D the vertices at quadrants 1, 2...
where's the conclusion about the coordinates of the vertices?
you found the coordinates of P and Q
but not any of the vertices
coarse walrus
call it x_0 and y_0, then find them both from there
I'll try this one
coarse walrus
Okay
Do I need to prove that the vertices are on the quadrants?
Or is it obvious
Like wlog suppose that the point A is not on the first quadrant, then that would mean that A is in either 2nd, 3rd o 4th quadrant and then the diagonals should intersect at 0,0, but they do not, which means that O is not located on the origin and then it's a contradiction
tawny moon
i think that is given
coarse walrus
Okay okay
tawny moon
if two points are in the same quadrant, the center of that square cannot possibly be on the origin
coarse walrus
Oh yeah, that's right
tawny moon
because then the average of the coordinates between those two points will not fall on the origin
coarse walrus
Oh true
Oops, sent it early
let A, B, C and D the vertices at quadrants 1, 2, 3 and 4 respectively, since the X axis cuts the square through the center, then the X axis cuts the square through the midpoints of directed segments CB and DA, Let's call these midpoints P and Q respectively, then PO=OQ, if P(a,0) then Q(-a,0) because they're at the same distance from the origin but at different coordinates, this means that their coordinates are P(a,0) and Q(-a,0).
Also the Y axis cuts the square through the midpoints of directed segments BA and CD, let's call these midpoints R and S respectively, then SO=OR, if S(0,-a) then Q(0,a), because they're at the same distance from the origin but at different coordinates, this means that their coordinates are S(0,-a) and Q(0,a).
Since the foot of the perpendicular that goes through A and cuts the X axis at coordinates (a,0) and the foot of perpendicular that goes through A and cuts the Y axis at coordinates (0,a) then the coordinates of A are (a,a).
Since the foot of the perpendicular that goes through B and cuts the X axis at coordinates (-a,0) and the foot of perpendicular that goes through B and cuts the Y axis at coordinates (0,a) then the coordinates of B are (-a,0).
Since the foot of the perpendicular that goes through C and cuts the X axis at coordinates (-a,0) and the foot of perpendicular that goes through C and cuts the Y axis at coordinates (0,-a) then the coordinates of C are (-a,-a).
Since the foot of the perpendicular that goes through D and cuts the X axis at coordinates (a,0) and the foot of perpendicular that goes through D and cuts the Y axis at coordinates (0,-a) then the coordinates of D are (a,-a).
Therefore the coordinates of the square are (a,a), (-a,a), (-a,-a) and (a,-a)
What do you think?
coarse walrus
Oh, yeah, ty lol
tawny moon
quite a little overkill, but i think it works
coarse walrus
smts I forget I'm in math
how would you make it not be overkill?
I've heard that since i'm in olympiad
that I overkill and shouldn't do it, but Idk how to fix that lol
It's either 2 sentence proofs or 2 pages proofs
tawny moon
we know that the square:
- has sides 2a, and parallel to the axes
- is centered at (0, 0).
because the square is centered at the origin, it is symmetrical wrt both axes.
also, because its sides are parallel to the axes, they must be horizontal or vertical.
this implies that every point share one of its two coordinates with a neighbour.
assume that the coordinates of any given point are (+/- x_0, +/- y_0).
the square has sides 2a, so the horizontal distance between two horizontally-adjacent points must be |x_0 - (-x_0)| = 2|x_0| = 2a => |x_0| = a.
a similar argument establishes |y_0| = a.
therefore, x_0 = y_0 = +/-a, and the coordinates of the four vertices are (a, a), (a, -a), (-a, a) and (-a, -a).
crystal gulch
Let a,b,c > 0 and a+b+c = 1
Prove: $(a+b)^2(1+2c)(2a+3c)(2b+3c) \geq 54abc$
rocky lotusBOT
shio6695
crystal gulch
i found the equality happens at a=b=3/8 and c = 1/4
i found this problem on stack exchange but i wanted to prove it directly instead of having to stablize the a+b value
also i'm not really convince by the commenter proof since there's ab on both sides so you can't just assume equality happens on ab max
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@crystal gulch Has your question been resolved?
crystal gulch
@scenic kettle
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@crystal gulch Has your question been resolved?
crystal gulch
hmmm can i ping again
<@&286206848099549185>
oh yeah the last ping was a random guy
vale dockBOT
@crystal gulch Has your question been resolved?
crystal gulch
<@&286206848099549185>
crystal gulch
welp ig nobody wanted to solve this, im having class later so i'll just ask my teacher
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wet sundial
need help checking my h/w
vale dockBOT
need help checking my h/w
woeful trench
Be careful of the negation one, remember that the only time "if A then B" is false is when you have A true but B not 
For the same reason, check the (dis)proof you've given
Personally happy with the rational one
wet sundial
thx
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astral marten
which solution is correct?
vale dockBOT
which solution is correct?
stark wedge
looks like neither.
and in part b, the calculation is correct but the f(x)= has no business being there.
astral marten
OH yeah that shouldve been 57-
stark wedge
the way to do this would be to write down the function representing the cost to produce x shirts & then divide that by x
astral marten
divide by x?
stark wedge
divide by x?
individual cost of a T-shirt is what you get when you take the total cost to make x shirts and divide them equally among the shirts
astral marten
individual cost of a T-shirt is what you get when you take the total cost to mak...
OHH
astral marten
you're missing an equals sign here btw
so this all divided by x?
astral marten
so ((250*20) + (200*10) + 150(20) + 10(x-50))/x
stark wedge
don't use the letter x as a multiplication symbol.
that's almost guaranteed to make you confuse yourself.
astral marten
it turns into that-
astral marten
okayy
astral marten
so ((250\*20) + (200\*10) + 150(20) + 10(x-50))/x
yes?
and then i use that
for the 57 shirts?
stark wedge
no
part b you put x=57 but just the numerator
cause b asks for total cost not cost per shirt
astral marten
so i will make 2 of those, 1 with denominator and 1 w/o?
astral marten
so ((250\*20) + (200\*10) + 150(20) + 10(x-50))/x
and is it just this alone?
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@astral marten Has your question been resolved?
astral marten
<@&286206848099549185> sorry to ping but need asapp, its due in a few
keen tundra
what is the situation?
astral marten
which solution is correct?
!!
keen tundra
this is what you want to use
but as Ann said the answer for part a will be the this divided by x
and for part b it will be this when you plug x=57
astral marten
but as Ann said the answer for part a will be the this divided by x
so thats the only function?
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west rapids
Can someone help me out on linear functions? i have abit of background knowledge on them
runic scroll
please share your question.
west rapids
there isnt a question i want to learn to solve linear functions in general
runic scroll
then do you have an example question to show the kind of things you want to solve?
west rapids
yes one second sorry
runic scroll
we can work through one, if you'd like.
west rapids
yes if possible
runic scroll
sure thing.
west rapids
i feel like i know linear functions perfectly fine but at the same time i dont think i can do them (the complex ones atleast
runic scroll
sure... but what kind of questions?
west rapids
like for example if you give me a function in the form of f(x)=3x−2 id be able to do it easily
night ginkgo
Can someone help me out on linear functions? i have abit of background knowledge...
Are you talking about functions like the polynomials of degree 1 or more in the linear maps direction?
west rapids
like for example if you give me a function in the form of f(x)=3x−2 id be able ...
but i feel like theres harder than this
runic scroll
no, see, my question is... what kind of questions are you asked to do with linear functions?
do you have a picture of those questions?
vocal tusk
@west rapids if 2x = 6 what is x?
west rapids
<@795952472870354954> if 2x = 6 what is x?
3
vocal tusk
can u draw y = 2x
tidal swift
so OP, are you gonna show an example of questions that is/are stumping you...?
i've been waiting 7-8 minutes to pin your actual question
west rapids
im really sorry about this i cant find a single one for some reason
merry crystal
can u answer convergence' question
merry crystal
Are you talking about functions like the polynomials of degree 1 or more in the ...
this one
merry crystal
like are u talking about y=ax+b
OR
a map u: V->W that satisfies u(ax+by) = au(x)+bu(y)
west rapids
probably i dont know english math naming
runic scroll
I assume you mean linear functions as in f(x) = ax + b, so...
novel canyon
Are you talking about functions like the polynomials of degree 1 or more in the ...
holy convy in help channel
west rapids
turns out i dont need harder functions sorry to waste everyones time
im really sorry
vocal tusk
can u draw y = 2x
^
west rapids
can u draw y = 2x
on a graph?
vocal tusk
turns out i dont need harder functions sorry to waste everyones time
harder than what
west rapids
harder than what
basic linear functions
vocal tusk
on a graph?
on paper
vocal tusk
on a graph?
yes
west rapids
yeah one sec
vocal tusk
u don't have to, just wanna know if yk
runic scroll
basic linear functions
I mean, I am still waiting to hear what kind of things you want to know or solve about linear functions, because that word can mean many things depending on the question.
west rapids
I mean, I am still waiting to hear what kind of things you want to know or solve...
oh what im supposed to know is just the basic f(x) = ax + b
runic scroll
noted, and it seems like you do know them.
so what exactly did you mean by "solve" linear functions? are you asked to find a point that lies on it, its slope, its y-intercept, something else...?
west rapids
so what exactly did you mean by "solve" linear functions? are you asked to find ...
write the points on a graph is pretty much what were asked to do
runic scroll
so you are asked to graph a linear function.
west rapids
yes
runic scroll
in that case, since you are dealing with a linear function, pick any two x-values, find the corresponding y-values, then plot them and join them as accurately as possible.
you need only two points to draw a straight line.
of course, make sure to try to follow best practice, like:
- having equal spacing on axis scales (don't have half a box = 1 unit on the x-axis and 1 box = 1 unit on the y-axis)
- using a ruler to draw the straight line
- proper plotting, etc.
vocal tusk
@west rapids can u graph (7, 15) on the cartesian plane
west rapids
<@795952472870354954> can u graph (7, 15) on the cartesian plane
fuh i forgot to send the graph you asked me about one second
west rapids
u don't have to, just wanna know if yk
vocal tusk
ermm
vocal tusk
ok looks fine
west rapids
oh thank god
vocal tusk
nothing
runic scroll
I'd say, if the line is meant to go through the origin, make sure it does.
vocal tusk
oh yeah
runic scroll
this one is quite noticably off the origin.
west rapids
I'd say, if the line is meant to go through the origin, make sure it does.
pretty sure its not
runic scroll
y = 2x has a y-intercept of 0.