4.80 for mangoes, 12-4.80 = 7.20
#help-0
chilly dove
i dont have the math i did before but i can just paste you some of the calculation
quaint star
Im quite sure unless it's something i dont see
so
lets start with c
we know that she has 12 euros right ?
now she buys 3 mangoes
chilly dove
yea
quaint star
no
chilly dove
thats the amount bought
quaint star
no
chilly dove
k
quaint star
if you have money and you buy something you have less money in your hands afterwords
so try it again
she has 12 euros and she spends 4.80 of it, how much money does she have left in her hands ?
chilly dove
7.10
chilly dove
7.2
quaint star
alright so she has 7.20 euros left
right ?
do you understand that far ?
now we know that each apple is 70 cents right ?
chilly dove
yea
quaint star
so how can she buy 17 apples prices at 70 cents if that amounts to 11.90 euros when we only have 7.20?
she would not have enough money
how many apples do you think she can buy with 7.20 euros ?
chilly dove
10
quaint star
good
and 10 times 70 cents is 7 euros
so if she spent 7 euros and she has 7.20 euros
how much do you think she has left ?
chilly dove
20 cents
chilly dove
well
quaint star
that's your answer
chilly dove
no
quaint star
explain
chilly dove
i think ur wrong
quaint star
explain
chilly dove
here ill just paste the math
quaint star
alright
chilly dove
i only have a part of it
and i did get (i) correct
ik its correct cuz my teacher made the question
😂
chill
ok ill just put 20 cents and after my teacher corrects it ill see if u got it correct
quaint star
1 mango = 1.60 , 3 mangoes = 4.80 . She has 12 euro , we remove 4.80 euro as she buys the mangoes, she is left with 7.20 euro, since 12-4.80. Now that we know 7.20 is her spending money, we know that apples are 0.70 a piece, which means she can buy 10. 10 * 0.70 is 7 euros, and now we can work out how much she has left. 7.20 - 7.00 = 0.20. that's the money she has left. 0.20 euros is how much she has left
which part are you not understanding
the answer you got which is 14 is because you worked it without removing the cost of the mangoes
🙂
chilly dove
why did my teacher mark it correct then
quaint star
teachers make mistakes
chilly dove
ok ill go tell my teacher that hes wrong
quaint star
if you want to workout how much change she has after buying 17 apples without the mangoes, do 17*0.7 = 11.9. 12-11.9 = 0.10 euros.
ivory pivot
why did my teacher mark it correct then
your teacher is a human
quaint star
but that's not the way to work this out
quaint star
1 mango = 1.60 , 3 mangoes = 4.80 . She has 12 euro , we remove 4.80 euro as she...
@ivory pivot you agree with this ?e
chilly dove
if you want to workout how much change she has after buying 17 apples without th...
ok ill try that
alpine sable
lone heartBOT
tacit arch
Try drawing a picture
lone heartBOT
lone heartBOT
Available help channel!
dreamy knot
find the least integer value of m for which the curve x(y+x)=2 meets the line y=mx-3
slate monolith
find the least integer value of m for which the curve x(y+x)=2 meets the line y=...
what have you tried so far
dreamy knot
b^2 - 4ac
dreamy knot
what have you tried so far
i used the discriminant thingy
dreamy knot
what do you think the word "meet" means
it intersects or touches?
dreamy knot
nope
slate monolith
so it means intersects
dreamy knot
ohh
slate monolith
how do you find the x value where two linear equations intersect
slate monolith
you use the entire formula
not quite
all you have to do is set the two equations equal to eachother
if a = 2x + 3 and b = -4x + 7
slate monolith
great!
dreamy knot
tysm omg
slate monolith
np
dreamy knot
.close
steady basin
lone heartBOT
analog widget
Im kinda confused with the question. It's asking what's gonna happen if n tends to a very large number?
steady basin
Im kinda confused with the question. It's asking what's gonna happen if n tends ...
correct
basically as n gets bigger, what does the function tend towards
analog widget
You gotta do the limit when n tends to infinity
steady basin
ok
worn fox
we dont need to
What it's asking is the same as finding the limit as n tends to inf
steady basin
What it's asking is the same as finding the limit as n tends to inf
i think my way is valid
but yh
worn fox
What is your way?
steady basin
since my lecturer taught us the method i did
worn fox
Right no matter how.you do it, you're still finding the limit
steady basin
Right no matter how.you do it, you're still finding the limit
lemme check my mark scheme acc
worn fox
we dont need to
Yes I'm just disputing the fact you said "we don't need to" in response to someone saying you have to find the limit
analog widget
Just finished let me just check if i did it right
steady basin
Yes I'm just disputing the fact you said "we don't need to" in response to someo...
yh
ruby current
also worth dividing the numerator and denominator by the highest power of n (which is n^9) to argue algebraically
pseudo ice
methinks that soon you'll become very familiar with my method of finding limits
steady basin
analog widget
The first one tends to 0
steady basin
i got this for b
whole shell
You could also use lhopital if you're lazy
steady basin
<:thinkies:827642567775748163> methinks that soon you'll become very familiar wi...
whats that method
steady basin
You could also use lhopital if you're lazy
bun that
thats too long
thats not for being lazy
analog widget
lhopital = cringe
steady basin
thats for the people who dont think
whole shell
Well Yh
pseudo ice
Putting the L in L'hopital 
steady basin
why am i wrong for this?
pale kestrel
if a limit can be solved with lh, its not hard enough 😶
whole shell
why am i wrong for this?
Can you prove that n! Dominates
ruby current
You could also use lhopital if you're lazy
l’hopital is not for you if you are lazy lol
steady basin
Can you prove that n! Dominates
pale kestrel
its an axiom ok 😶
steady basin
ur welcome
pale kestrel
but it also shouldnt be too hard to prove either
worn fox
The markscheme says its 1?
steady basin
but it also shouldnt be too hard to prove either
we r given that axiom in our exam
steady basin
The markscheme says its 1?
yes
whole shell
its an axiom ok 😶
It is?
pale kestrel
im joking about axiom, 'given fact'
pseudo ice
,w lim (2^n + 3^n)/(3^n + n!), n to inf
ocean sealBOT
steady basin
Can you prove that n! Dominates
i cba but am i not correct?
steady basin
The markscheme says its 1?
worn fox
Markscheme wrong
ruby current
???
steady basin
AGAIN
WHAT
whole shell
Your markscheme is on crack
pseudo ice
Your markscheme is on crack
You don't know the half of it 
worn fox
Get a new book bro
steady basin
n! dominates the denom?
steady basin
Get a new book bro
lecture notes
ruby current
yes
steady basin
kl
worn fox
Get a new lecturer
steady basin
Get a new lecturer
btw
ask chartbit
this is for
all my
lecturer
notes
all modules
pseudo ice
Can confirm, many of us can tbh 
worn fox
Bc your markschemes suck
steady basin
Bc your markschemes suck
but camb is best in the world
analog widget
Limit goes crazy when you start by the formal definition 💀
worn fox
Idk we don't go to the best uni in the world
pseudo ice
everyone agrees with this?
except whoever made those solutions
whole shell
everyone agrees with this?
Yh, i put 100 as n in the calculator
steady basin
Yh, i put 100 as n in the calculator
bruh
whole shell
And it gave me 10^-112
whole shell
When in doubt, try an example
analog widget
No, this rule is not always true
steady basin
No, this rule is not always true
why
analog widget
If the denominator tends to 0 and the numerator a constant, it tends to infinity
analog widget
Let me read
steady basin
ok
analog widget
my lecturer notes show it works
In this case it's because a value is tending to infinity
You can get n as big as you want
steady basin
yh
pseudo ice
algebra of limits
analog widget
The rule is Lim of h(x), where h(x) = f(x)/g(x)/ f(x) tends to a constant and g(x) = 0, if f(x)/g(x) > 0 then the limit will tend to + infinity
analog widget
If f(x)/g(x)<0 it will tend to -ininity
ruby current
struggling with c
you can note that n < 2^n
ruby current
2^n dominates what?
steady basin
2^n dominates what?
the denom
steady basin
Other way round. If n < 2^n
i said 2^n dominates the denom
ruby current
i said 2^n dominates the denom
n2^n might not be asymptotically equivalent to 2^n
whole shell
what happened to n2^n
steady basin
you can note that n < 2^n
why did u say this then
whole shell
@steady basin you were confused on whether n2^n dominates over 10^n
ruby current
because it allows you to see that n2^n < 4^n < 10^n
steady basin
n2^n is less than 4^n
where has 4^n come into this
whole shell
Because 4^n is obviously less than 10^n
steady basin
yh but
whole shell
And by showing you that n2^n is less than 4^n
whole shell
because it allows you to see that n2^n < 4^n < 10^n
^
steady basin
the ocean?
pseudo ice
where has 4^n come into this
- multiply both sides of tushar's statement by 2^n
ruby current
$n < 2^n \implies n2^n < 2^n \cdot 2^n$
ocean sealBOT
tushar
ruby current
it might be, but reasoning will always win
also good thing to note that n < x^n for all x greater than 1
steady basin
sry im still over confused of ur proof showing n2^n < 10^n
tacit arch
If n < 2^n, then you times both sides by 2^n
but where does 4^n come from
whole shell
2^n times 2^n = 4^n
ruby current
$2^n \cdot 2^n = (2 \cdot 2)^n$
ocean sealBOT
tushar
whole shell
Yh
steady basin
<:thinkies:827642567775748163> methinks that soon you'll become very familiar wi...
what did u mean by this btw?
pseudo ice
what did u mean by this btw?
Oh, basically remember how I used to say "you could do [insert a limit] with l'hopitals, but it doesn't mean you should"
steady basin
Oh, basically remember how I used to say "you *could* do [insert a limit] with l...
ye
pseudo ice
And would say e.g. divide the numerator and denominator by [something] or like that
There's a similar idea here with how you're doing these limits, you can e.g. try and manipulate these into a form where it's like limits that you can work out
steady basin
yr
steady basin
There's a similar idea here with how you're doing these limits, you can e.g. try...
ye i like this methods
its leng
whole shell
Yh that's a nice method. You can also use maclaurin series if your function doesn't contain a polynomial
steady basin
...
pseudo ice
also worth dividing the numerator and denominator by the highest power of n (whi...
See e.g. this comment here
steady basin
Yh that's a nice method. You can also use maclaurin series if your function does...
i believe i will be coming onto that soon
analog widget
10^n = 5^n.2^n
steady basin
ye
analog widget
Simplify that
whole shell
Yh I'd agree
pseudo ice
Yep that's fair
steady basin
nice
pseudo ice
or divide num and dom by n^4 and algebra of limits
steady basin
ye
analog widget
yep
pseudo ice
[if postedit didn't exist...]
steady basin
also @pseudo ice any chance u could have a look at the mock i sent u and lmk if theres any questions i can do from it as of now, reagrding the topics ive done so far, par q4 since i asked u that yesterday
my aim is to do cauchy and other convergence power series stuff tmr
whole shell
Yh you'd get (6 + 12logn/n⁴)/(3 + 1/n²). And you'd see that logn/n⁴ goes to 0 and 1/n² goes to 0 and so you're left with 6/3
steady basin
which will complete real analysis content
pseudo ice
Oh damn, well fair enough I guess, getting ahead of myself
steady basin
Oh damn, well fair enough I guess, getting ahead of myself <:catThimc:7320118024...
i think q4 and q3 r the only ones i can do as of now
pseudo ice
fair fairs
steady basin
ight thats me done for today
steady basin
fair fairs
these r the chapters i have left
gonna aim to do all of these tmr
😭
so i can do the mock sunday
ocean sealBOT
The current time for chartbit is 12:10 AM (GMT) on Sat, 21/01/2023.
steady basin
steady basin
Fair fair, yep a new day, a new grind 💪
is cauchy stuff hard
and limits of convergence
like M-n proofs
epsilon - n
whatever theyre called
pseudo ice
I mean, you kinda did some of the epsilon-n proofs today in a way
How did you find that?
steady basin
How did you find that?
not bad
semi
mid
the stuff i just did now
was the easiest
this kinda stuff
pseudo ice
Cauchy sequences, at least theoretically they're not too bad to deal with (e.g. convergence implies Cauchyness, a Cauchy sequence with a convergent subsequence converges and all)
pseudo ice
this kinda stuff
Yeah these are at least what I learned as "algebra of limits"
That stuff about finding the least N was epsilon-n convergence in disguise, in a way
steady basin
Cauchy sequences, at least theoretically they're not too bad to deal with (e.g. ...
looking at my mock tho, u think its all doable to understand most of it by tuesday
my aim is to do the mock sunday
i mean i want like a decent mark
like 60 % is a 2:1
and 70% is a first
pseudo ice
I think so if you work on it, and as always if you have questions, come here and people will be happy to help you(!)
Maybe give q3 a go too for now too? or at least think about it?
[if you haven't already]
steady basin
acc before we do that
lets finish off today with this
i had an exam in novemeber
and i got the proof wrong
lemme show u
steady basin
I think so if you work on it, and as always if you have questions, come here and...
lets do this
so far
steady basin
What have <:youTried:661788564958216223> so far <:catThimc:732011802459635713>
thinking
can i simplify Cn
at all?
hmmmm
whole shell
@steady basin what about doing it the other way round. Is there any other way you can write e^-n
I've never done these kinda stuff. So I don't know anymore than you do.
Well i do have atleast 1 idea
whole shell
@steady basin well we can start from 1 > 0
Then add e^2n on both sides
So
e^2n + 1 > e^2n
Then if we do e^n divided by those 2
We can get
e^n / (e^2n + 1) < e^n / e^2n
And e^n/e^2n = e^-n
This should be acceptable since e^n will never be negative
steady basin
<@849961886874730516> well we can start from 1 > 0
thats genius
but how did u recgonise to do that
thats what i find hard about real analysis
i never know how to start of
off
ygm
whole shell
i recognised that e^-n is the same as e^n/e^2n
Which relates to
The e^n/(e^2n + 1)
So i just formally proved that the cn denominator is always bigger . And so the number itself is smaller
whole shell
i never know how to start of
Yh it's hard to teach someone a proper algorithm for this. It's just experience and intuition i guess.
magic haven
another way to do it is to multiply the top and bottom by e^-n
so u get $c_n=\frac1{e^n+e^{-n}}<\frac1{e^n}$
ocean sealBOT
magic haven
and thats it
lone heartBOT
@steady basin Has your question been resolved?
alpine sable
If my domain is $\mathbb{Z}$ and x is an arbitrary real integer, how do I prove x is either odd or even?
ocean sealBOT
hibyehibye
alpine sable
or like what law states this?
ocean sealBOT
hibyehibye
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
slim spire
real integer?
alpine sable
well i guess i could have jsut said integer
limpid turret
Not sure, but this smells of circular logic.
It would help you to have a well-defined definition of "even" and "odd" integer
alpine sable
so say like even is 2k and odd is 2k+1?
slim spire
If my domain is $\mathbb{Z}$ and x is an arbitrary real integer, how do I prove ...
I guess proof by induction
limpid turret
so say like even is 2k and odd is 2k+1?
sure
alpine sable
Let P be a predicate that is true when an integer is even and false other-
wise.
Let Q be a predicate that is true when an integer is odd and false otherwise.
should I redefine these?
so maybe
limpid turret
Nah those definitions seem fine
limpid turret
so say like even is 2k and odd is 2k+1?
Add this as a pretext tho for definition
limpid turret
so like
- Define even and odd
- Define P and Q
- State your assertion
- Prove it
alpine sable
ah ic
limpid turret
It helps to use predicates to define even and odd as well
e.g. "n is even iff exists k such that 2k = n"
alpine sable
so like "Let an even number be a number described by 2k where k is an arbitrary integer"
oh
that sounds better
What is iff again?
limpid turret
if-and-only-if
limpid turret
yup
ocean sealBOT
hibyehibye
ocean sealBOT
hibyehibye
ocean sealBOT
hibyehibye
limpid turret
Or "Q is true when P is true" if you like being abstruse
limpid turret
your prof/TA should know what iff means
limpid turret
np
lone heartBOT
limpid turret
@alpine sable Don't forget to prove that even and odd are contrapositives
alpine sable
<@456226577798135808> Don't forget to prove that even and odd are contrapositiv...
.reopen
lone heartBOT
✅
alpine sable
urm what do you mean?
alpine sable
do u mean something like
$\forall x (P(x) \vee Q(x))$ is a true statement because any arbitrary real integer is either even or odd because [insert contrapositive proof here]$
ocean sealBOT
hibyehibye
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
limpid turret
Nah you need to prove that for all x, P(x) is true if and only if Q(x) is false
alpine sable
hm
limpid turret
You can't just say "an integer is either even or odd" because it has not been proven yet
It must be proven
alpine sable
so i have to prove by proving the contrapositive?
limpid turret
So far, you've defined that even and odd are properties an integer may posses, but have not proven that all integers must have only one
alpine sable
of $P(x) \iff Q(x)$ ?
limpid turret
so i have to prove by proving the contrapositive?
Ah I may have used that word wrong
ocean sealBOT
hibyehibye
alpine sable
Ah I may have used that word wrong
i think im just confused what u mean
limpid turret
Forget I used that word. English is not my best subject
alpine sable
o
limpid turret
Nah you need to prove that for all x, P(x) is true if and only if Q(x) is false
^ you need to prove this
alpine sable
okay lemme get back to u in like 5mins
ill try and prove it on my own
hm so
$ P(x) \iff \neg Q(x)$ is what im trying to prove
So like base case, of n=1
and then induction ?
@limpid turret is this the right lines
Or what about
base case 1 is odd bec its described by 2k+1
limpid turret
brb
alpine sable
wait
base case 0
number is even
cuz its 2 * 0
induction that if the number is even its described by 2k so the next number is 2k+1
and then if its odd 2k+1+1 = 2k+2 = 2(k+1)?
therefore every number is either odd or even
I think I got it TY
.close
lone heartBOT
limpid turret
.reopen
lone heartBOT
✅
alpine sable
ok then I had my base case as 0
oh im proving that
all positive integers are either even or odd
So 0 = 0*2 (base case)
and then induction
so
n+1 is odd or even
limpid turret
So 0 = 0*2 (base case)
Question here
alpine sable
yea
limpid turret
You've proven 0 is even, but where is your proof that it is not odd?
alpine sable
I didnt prove that bec i didnt think it was necessary
limpid turret
That's the core of what you're trying to prove though
alpine sable
$\forall x (P(x) \vee Q(x))$ is a true statement because any arbitrary positive integer has to be either even or odd.
ocean sealBOT
hibyehibye
alpine sable
thats what im trying to prove no?
limpid turret
This is where proofs are tricky. You're taking for granted what is known and what you are proving
alpine sable
alpine sable
This is where proofs are tricky. You're taking for granted what is known and wha...
wait so where did i go wrong
like im confused why it matter if n is not odd if its even
alpine sable
kk
limpid turret
If my domain is $\mathbb{Z}$ and x is an arbitrary real integer, how do I prove ...
It was your original question, wasn't it?
limpid turret
Prove that x must be either even or odd
alpine sable
even or odd
ic what u mean
ohhh
so do i just remove the either from that statement?
limpid turret
So you meant logical or, not exclusive or?
limpid turret
Ah
alpine sable
how should I rephrase that?
alpine sable
Bec the statement im trying to prove is $\forall x (P(x) \vee Q(x))$
ocean sealBOT
hibyehibye
alpine sable
and thats logical OR
limpid turret
how should I rephrase that?
you did use \vee, so it's my mistake for missing that
alpine sable
o ic
alpine sable
So 0 = 0*2 (base case)
so is this bit valid?
limpid turret
Okay I reset my brain for a second
alpine sable
lol all good
limpid turret
Clarify for me, you wanted to prove $\forall x (P(x) \vee Q(x))$ does not distribute to $\forall x P(x) \vee \forall x Q(x))$
ocean sealBOT
SWR
alpine sable
yes
limpid turret
Is that what you are doing this?
alpine sable
mhm
alpine sable
yeah!
I think the proofs honestly good now
I just changed my domain to Z+ bec it made it alot easier
limpid turret
Okay, you're going to need the XOR quality to show this tho
alpine sable
limpid turret
That's what makes the counterexample happen
limpid turret
<:sad:532803514892812288> <:sad:532803514892812288> <:sad:532803514892812288>
I understand it's hard, but it looks like you really want to understand it
alpine sable
Okay, you're going to need the XOR quality to show this tho
Where does XOR come from? 😭
alpine sable
Yeah but like how is XOR related to distributing the universal quantifier over a disjunction?
limpid turret
Logically, it's P<=>!Q
alpine sable
Like im confused why I have to have anything related to XOR tbh
limpid turret
Yeah but like how is XOR related to distributing the universal quantifier over a...
I'll start with the answer and work backwards
alpine sable
oki
limpid turret
$\forall x P(x)$ is false
ocean sealBOT
SWR
limpid turret
I'm sure you agree there, yeah?
limpid turret
Same with Q(x), yeah?
alpine sable
yeah
limpid turret
one sec, gotta write this out.
alpine sable
Preface before you read its basically my 2nd time writing proofs so its kind of bad lol
limpid turret
no worries
So this is one part of what is important:
P=even and Q=odd will definitely have this property.
alpine sable
where did the $\forall x (P(x) \iff \neg Q(X))$ come from?
ocean sealBOT
hibyehibye
limpid turret
where did the $\forall x (P(x) \iff \neg Q(X))$ come from?
We're going to prove that even and odd have this property
alpine sable
But I guess where I'm lost is why we need to prove that in the first place
limpid turret
I'm still working, so slow replies
alpine sable
like logically I dont understand the need to prove that P(x) \iff ~Q(x)
limpid turret
But I'm gonna read through your proof
alpine sable
oki
tysm for all the help btw
I know I'm kind of an idiot when it comes to discrete lol
limpid turret
like logically I dont understand the need to prove that P(x) \iff ~Q(x)
In my counterexample, I need this. But maybe you don't? I'll check now
limpid turret
I know I'm kind of an idiot when it comes to discrete lol
alpine sable
.close
wary stream
45 -45 - 90 special triangle
How did you achieve those values?
45 -45 - 90 special triangle
Do you know that concept?
Does something like this look familiar?
I mean, does it look like something you learned?
Do you know trig?
wary stream
Does something like this look familiar?
Then I am pretty sure you learned this
That had nothing to do with angles
static tree
Do you know what kind of triangle this is?
wary stream
Does something like this look familiar?
Because it's a 45 - 45 - 90 triangle, you can apply this to find the side
static tree
Apply*
What's another name for a triangle with a 90 deg angle?
Good enough
What do we know about these right triangles?
And what tools do you have that talk about the length?
wary stream
And that's what we are doing, helping you
wary stream
Does something like this look familiar?
.
static tree
Good time to investigate
If I gave you a triangle with length 3 on line segment qp and length 5 on qr, can you find length of pr?
That is, if we said the length up and down was 3 and the length left and right is 5, can you find the diagonal?
wary stream
I think they are hinting to Pythagorean theorem
static tree
Try to find the diagonal length of triangle of the example given via Pythagorean theorem.
Ah this is right
Good
Yes
So what is pythagorean theorem?
What is a and b and what is c?
Conceptually
C sqrd is 34
Why is a equal to 3 and why is 5 equal b?
But why didn't you say c =5 or c =3?
ocean sealBOT
drsleep
static tree
It def matters
Here
I got another better question
How
Does the pythagorean theorem relate to triangles?
I think that you don't know what how to use pythagorean theorem to solve this problem
We've essentially given you the tool
There is nothing incorrect about what has been given
wary stream
Two options, you can apply that image I presented, or apply pythagorean theorem, by formulating an equation using the given info from that diagram
static tree
dldh is absolutely correct
wary stream
If you choose option two, the given angles gives you a big hint on the side lengths
And you can formulate a pythagorean theorem equation based on that
static tree
We won't and no one will
wary stream
No
wary stream
Because that's not the purpose of the server
static tree
<@&268886789983436800> some deleted messages hint at what's going on here. I question if it's appropriate.
wary stream
Oof mods you banned the op
lone heartBOT
wary stream
Good work man ttyl.
Mods banned the op? They said something bad?
lone heartBOT
Available help channel!
stiff tree
lone heartBOT
wary stream
Use the help people gave you in your previous channel
stiff tree
Alright
lone heartBOT
@stiff tree Has your question been resolved?
alpine sable
how is this wrong
lone heartBOT
how is this wrong
pliant cedar
how many millilitres is one microliter
alpine sable
how many millilitres is one microliter
.001
alpine sable
ok and below
alpine sable
thats the number that must be here
.
alpine sable
.close
graceful forge
hi
alpine sable
hi
graceful forge
im new here
lone heartBOT
im new here
Please read #❓how-to-get-help
alpine sable
im new here
wary stream
<#359052581022203914>
Not really useful
alpine sable
Not really useful
they don't really have a doubt
tough jasper
🤣
graceful forge
...
wary stream
what do you need help with
You opened the channel
alpine sable
what do you need help with
...
tacit arch
Oh I see
graceful forge
could everyone just update me on everything
last ether
What
tacit arch
@graceful forge you want to help someone?
graceful forge
yea sure
tacit arch
Just read channel that starts with #help. The question is usually pinned to the channel
alpine sable
just go to the channels
graceful forge
ok
wary stream
could everyone just update me on everything
Inflation
tacit arch
Or also #1021175428326633542
last ether
Uhhh
graceful forge
srry
lone heartBOT
graceful forge
uhm
lone heartBOT
✅
graceful forge
so.........
wary stream
Denied
graceful forge
ok
wary stream
Gas is back down to $4 for me!
Lmao gas went up for me
last ether
3.50 where I'm at it's 
graceful forge
Wait so what country are yall in
wary stream
Merica
graceful forge
Im in NZ
tacit arch
Hello Kiwi
graceful forge
but for some reason i have an american accent
since im originaly from india and moved here when i was 2
wary stream
Didn't the British take over New Zealand at one point?
wary stream
Just read channel that starts with #help. The question is usually pinned to the ...
.
That's how you help people
wary stream
If you don't know how to help, just don't comment in that channel
graceful forge
ok
wary stream
what if you need help
I'm mentally unstable, if that's what you mean
graceful forge
what type of math do you all discuss of
tough jasper
🤣
wary stream
what type of math do you all discuss of
All levels
alpine sable
@graceful forge you need to look at occupied math help channels not to open a help channel
last ether
We discuss a lot of things
graceful forge
ok
last ether
Better take this to #discussion or #chill
alpine sable
graceful forge
so bye
wary stream
.close
lone heartBOT
graceful forge
ill be back in like 10-20 minutes
wary stream
Fyi this server is primarily US based meaning there is more traffic in about 12 hours
last ether
That explains why there's like 50 billion channels of linear algebra
lone heartBOT
Available help channel!
potent plank
Is there any real roots for x^3 - 15x^2 +400. When I solve this normally by taking x as common. I am getting some complex roots. When I graphed this online, It shows 3 real roots
last tendon
If it has complex roots they must come in conjugate pairs. You don't need to plot to know it has a real root.
wary stream
Is there any real roots for x^3 - 15x^2 +400. When I solve this normally by taki...
But x isn't common in all three terms
lone heartBOT
@potent plank Has your question been resolved?
rich quiver
@potent plank see if an odd power poly has real coefficients then min. One root is always real
Since, imaginary roots occur in conjugate pairs
next swan
lone heartBOT
@next swan Has your question been resolved?
hidden goblet
can someone help?
lone heartBOT
can someone help?
gray isle
what have you tried?
hidden goblet
i tried inverse properties but i think thats wrong
gray isle
inverse functions shouldn't be used here
if that's what you're referring to
or are you using "inverse" to mean reciprocal
hidden goblet
no. i was first trying to find t through the first problem (cot(t) = -sqrt35/35)
hidden goblet
then how do i find sec(t)?
vale wigeon
$\sqrt{3}5$? \catthink
ocean sealBOT
Ann
gray isle
you could consider drawing a triangle / apply pythagoras and properties of the unit circle
hidden goblet
idk if its a sqrt(35) or sqrt(3)5 btw
hidden goblet
you could consider drawing a triangle / apply pythagoras and properties of the u...
not sure how to do that sorry
gray isle
since negative lengths aren't really a thing
you could start by drawing a reference triangle with reference angle k where cot(k) = |-sqrt(35)/35)| = sqrt(35)/35
hidden goblet
oooh
hidden goblet
since negative lengths aren't really a thing
you could start by drawing a refere...
how does this find sec(t)?
hidden goblet
i drew the triangle yes
gray isle
apply pyhtagoras
hidden goblet
i dont know how to do that
gray isle
do you know what pythagoras' theorem is
hidden goblet
yes
gray isle
following my instructions
you should have a right triangle with the lengths of two sides known
and knowing pythagoras,
that can be applied to obtain the length of the third side
hidden goblet
ooh is sqrt35 the adj and is 35 the opp side?
gray isle
yeh
hidden goblet
so this is hyp?
35^2=1260 and sqrt35^2=35 so 1260+35=1260
and 1260 is the c^2 value aka hyp
ocean sealBOT
Result:
1225
35^2 is 1225 and 1225+ 35 = 1260
hidden goblet
oops
gray isle
anyway, ideally you'd use exact form and simplify the radical instead of using a decimal approximation
anyway, after determine the hyp, use the triangle to determine sec(k)
(again keeping stuff in exact form)
hidden goblet
what is exact form and simplifying radical?
gray isle
e.g. going from $\sqrt{8}$ to $2\sqrt{2}$ instead of approximating it as 2.83
ocean sealBOT
ℝamonov
gray isle
so sec(t) is sqrt(1260)/sqrt(35)?
not quite
that would be sec(k)
remember that k is the reference angle of t
consider the location/quadrant of t,
and whether sec is positive or negative in that quadrant to determine whether sec(t) is sec(k) or -sec(k)
so sec(t) is sqrt(1260)/sqrt(35)?
do i rationalize denominator too?
simplify the expression as a whole, rationalising of the denominator will be involved
and you'd also need to simplify any remaining radicals
hidden goblet
how do i know what quadrant t is?
ocean sealBOT
ℝamonov
hidden goblet
both positive so quadrant 1?
gray isle
no
do you understand that (interval) notation
t is an angle between pi/2 and pi (or between 90° and 180° if you're more comfortable working with degrees)
hidden goblet
oooooh
i see its just the radians on unit circle
so quad 2
meaning the sec(t) will be negative
so its -6?
sqrt(1260)/sqrt(35)=6 but since its quadrant 2 its negative
is this correct?
@gray isle ?
gray isle
yeh
lone heartBOT
lone heartBOT
Available help channel!
viscid moat
lone heartBOT
vale wigeon
$\varphi$ is called phi, $\psi$ is called psi, and $\Pi$ is called pi (uppercase)
ocean sealBOT
Ann
viscid moat
https://cdn.discordapp.com/attachments/490557019623915520/1066279965471031336/image.png and this one ?
vale wigeon
which one
viscid moat
on the left the q looking one
vale wigeon
?? that's phi...? didn't i just say that
vale wigeon
the one in the middle, ∈, is called "is in" or "belongs to", if that's what you intended to ask.
viscid moat
so this one and this one are the same thing ?
vale wigeon
yes they are the same Greek letter in different fonts
stone linden
There is a triangle ABC:
Find it's angles.
Can you please give me advice how to find first angle? Should I use cos theorem or dot product of vectors?
vale wigeon
wdym by "first angle"?
vale wigeon
you can use whatever you find easiest. both the law of cosines and the dot product will get you the answer
strange meadow
There is a triangle ABC:
Find it's angles.
Can you please give me advice how t...
they both work
what ann said
many ways to skin a cat
stone linden
I mean which one is simpler?
strange meadow
dot product seems simpler
stone linden
Because when I tried dot product It got confusing
vale wigeon
do you have work to show?
vale wigeon
i think you went about this in a confusing/error-prone way
strange meadow
where are the vectors
strange meadow
i think you went about this in a confusing/error-prone way
^
write the vectors out
vale wigeon
actually maybe that is wrong entirely
vale wigeon
cos(A) = AB·AC/(|AB|·|AC|)
vale wigeon
(to be clear it's an error in execution not an error in planning)
trail cairn
Amy and Ben live 17.2 km apart. They cycle to meet each other. Ben travels at
12 km/h and Amy travels at 10 km/h.
a How long (in minutes) until they meet each other?
b What distance have they both travelled?
strange meadow
why is it minus?
vale wigeon
and what does x represent?
trail cairn
yh
median oar
So 12 km/hour * x mins + 17 km/hour * x mins = 17.2km
vale wigeon
then your equation is incorrect as written
median oar
Is that what you’re saying?
vale wigeon
the speeds here are given in kilometers per hour not per minute
median oar
Notice that mins * 1/hour is not 1
trail cairn
ok lets forget that
median oar
But if you put x in hours
trail cairn
lets start fresh.
vale wigeon
you are better off declaring x as the time in hours for the two friends to meet (in which case your equation will be correct),
then afterward, converting the hours into minutes
stoic ledge
That isn't correct, they are moving towards each other so they'll meet somewhere in between and hence they won't cover the total distance of 17.2 km
I'll try solving this with taking the distance they meet at
vale wigeon
@stoic ledge i think you're talking out of your ass rn
median oar
That isn't correct, they are moving towards each other so they'll meet somewhere...
If they don’t cover a combined distance of 17.2km they won’t meet
gray isle
That isn't correct, they are moving towards each other so they'll meet somewhere...
the combined distance travelled will be 17.2km
stoic ledge
My bad
median oar
So 12 km/hour * x mins + 17 km/hour * x mins = 17.2km
So 12 km/hour * x hours + 17 km/hour * x hours = 17.2km
stoic ledge
Continue
median oar
Notice here the hours cancel out
And you get the right units on both sides
Which usually means you’re in the right direction
trail cairn
ok
Amy and Ben live 17.2 km apart. They cycle to meet each other. Ben travels at
12 km/h and Amy travels at 10 km/h.
a How long (in minutes) until they meet each other?
b What distance have they both travelled?
what should i do
median oar
Well we first know that Amy and Ben travel for the same amount of time
stoic ledge
Find the time using frosst's equation
median oar
Well we actually don’t know that they start together but it’s not solvable without that assumption
trail cairn
yh
median oar
So speed * time = length/time * time = length = distance
median oar
,calc 47/60*(12+10)
ocean sealBOT
Result:
17.233333333333
Yeah close
trail cairn
so 17.23min
stoic ledge
so 17.23min
47 minutes
trail cairn
how did you get that
stoic ledge
He did reverse calculation to check if my answer was right
Well
10x + 12x = 17.2
Solve for x
You get time in hours
Multiply by 60
vale wigeon
what a shitshow.
trail cairn
ik
stoic ledge
Now multiply the time in hours with their individual speeds and find out the distance they travelled