okay gimme a sec
#help-0
alpine sable
$\log_2{X}+\frac{\log_2{X}}{\log_2{4}}=\frac{\log_2{\sqrt{6}}}{\log_2{0.25}}$
like that
sterile crescent
aarg im still stuck can someone solve it please
ocean sealBOT
sqrt(-1) is approx -30
lone heartBOT
lone heartBOT
Available help channel!
carmine rapids
I know you start by subtracting 1/2x but im lsot from there
lone heartBOT
I know you start by subtracting 1/2x but im lsot from there
balmy warren
I would start by adding 3x to both sides
clear stump
you move x to one side and everything else somewhere else
gray isle
i'm going to give you a few simpler examples in increasing difficulty
would you be able to solve
x - 7.3 = 13.4?
rancid trail
Why decimals tho? Just use fractions
carmine rapids
would you be able to solve
x - 7.3 = 13.4?
you add 7.3
um the fractions and decimals are two different things in my course
gray isle
its just for demonstrating basic princples
carmine rapids
what confuses me when I transfer one X to the other I now have two X's
gray isle
specifically you can add 7.3 to both sides of the equation
and what would the final result be
?
carmine rapids
ohh so I convert 3x into a fraction and add -1/2
gray isle
skipping ahead but ok...
show me your updated attempt
carmine rapids
oh sorry should of clarified I know how just the fraction variation confused me and how to isolate two X's. I don't know why we're tested on this when we never went over it
lemme upload
gray isle
well its a combination of skills
carmine rapids
gray isle
isolating/solving for a variable is the new skill in this topic
adding fractions is something you should already know how to do before this
carmine rapids
Right but usually there's a practice to clarify the nuance's
gray isle
work could be structured a bit better but final result is ok
carmine rapids
So far isolating X with only one x rather than two has been the mo.
N yeah tryna to use 4 notebooks a day
gray isle
fractions make it slightly more complicated but eg lets say you were given something like
solve
3x = 2x + 1
you shouldn't have any difficult with that
carmine rapids
yeah true
fierce prairie
lone heartBOT
vale wigeon
yes
though to prove it rigorously you may need to show that no sequence of two or less operations would do the job
probably by considering where the letter Z would go
fierce prairie
oh
i mean it's an sat practice question so i assume they don't want you to do too much
thanks
.close
harsh ocean
Knowing that when $\Omega=0$ the angle $\Phi$ reaches equilibrium and given the diff. eqs. below, how could I get its expression?
$\frac{d\Phi}{dt}$$=\Omega;$
$\frac{d\Omega}{dt}$$=\frac{g}{l} \sin\Phi -\frac{V}{l R} sgn\Phi$
ocean sealBOT
JSGF
lone heartBOT
@harsh ocean Has your question been resolved?
ocean sealBOT
Kepe
vale wigeon
,w simplify ((10a)^21 * 6^27)/(81^7 * (400a^2)^11)
ocean sealBOT
vale wigeon
you didn't tell it to simplify
vale wigeon
well if you connected every pair of nodes then each person would have 26 handshakes, not 9 as required.
@icy galleon
what do you mean?
the problem is: "Is it possible to have a graph on 27 nodes in which each node has degree EXACTLY 9?"
for every question of the form "What would prevent <deviation from problem requirement>?" the answer is the same: Doing so would prevent the problem requirement from being satisfied.
so i'm afraid i don't really understand your question here.
no
again
the problem asks you whether it is possible for a graph to exist which has 27 nodes in which EVERY node has degree EXACTLY 9
if a node in your graph has degree greater than 9 then the graph is not of the kind the problem asks you about
...no
this argument is nonsensical
"if each node has degree exactly 1 then one node will have degree greater than 1"
this is nonsense
this is not how one proves impossibility
this type of argument is akin to "it's not possible for all people in this room to make under $100k per year, because if everyone made under $100k per year then there would be someone who made over $100k per year"
ocean sealBOT
Ann
vale wigeon
the correct conclusion to draw from this picture is that this is NOT a graph in which every vertex has degree 1.
it doesn't
you have surely not exhausted all possibilities to "attempt" to make such a graph
and even if you have done so in this small case, that sort of argument doesn't scale to graphs with more nodes.
well this type of math is called graph theory
perhaps you do
your lecture slide is showing an application of the handshake lemma to prove impossibility for your particular problem.
hushed mica
lone heartBOT
worn fox
try doing it by cases, even or odd
hushed mica
guys this can be done this way too right ?
$b=4q$
$b^2 = 16q^2$
$b^2=4(4q^2)$
$b^2=4k$
ocean sealBOT
Night Wølf
hushed mica
@worn fox
worn fox
right but that only covers multiples of 4
hushed mica
can it be done this way too or do i need to use the primes to prove it?
hushed mica
right but that only covers multiples of 4
can u tell me how can i prove it the other way around?
@worn fox
alpine sable
isn't the easiest way to do it is to say that the squares mod 8 are 0,1,4?
hushed mica
isn't the easiest way to do it is to say that the squares mod 8 are 0,1,4?
by mod u mean congruent modulus?
alpine sable
yeah
hushed mica
ok i have yet to do it
alpine sable
ah ok, then you can look at even/odd numbers as suggested
even numbers look like $2n$, odd $2n+1$ for all $n\in\mathbb{Z}$
ocean sealBOT
Toby
hushed mica
even numbers look like $2n$, odd $2n+1$ for all $n\in\mathbb{Z}$
so in a way i can consider it as a basic or general equation for solving this?
alpine sable
I'm not sure what you mean by that, sorry
but basically, you square the general form of even/odd number, then check if it's of the desired form
hushed mica
but basically, you square the general form of even/odd number, then check if it'...
yes and that even or odd number can only be $2n$, odd $2n+1$?
ocean sealBOT
Night Wølf
alpine sable
yes
alpine sable
an even number is always divisible by 2, and an odd number is always one greater than an even number
ocean sealBOT
Night Wølf
alpine sable
yup exactly
hushed mica
and we assume q^2 to be equal to k in here right?
or is there any other logic behind it
alpine sable
and we assume q^2 to be equal to k in here right?
yup, that's all you need to say
hushed mica
oh thanks buddy 😄
i have just a confusion in it
that is it necessary to take
$(n+1)|(n^2-1)$
ocean sealBOT
Night Wølf
hushed mica
@alpine sable
alpine sable
the line means "divisible by", so it's rewriting the question
hushed mica
the line means "divisible by", so it's rewriting the question
i mean ik that but is it ok to introduce a new thing like $(n+1)|(n^2-1)$ and combine it with the raw equation to get the values of n?
ocean sealBOT
Night Wølf
alpine sable
yeah, if I understand you correctly, that's fine
carmine rapids
How do I graph these lines. I know how to get the point
lone heartBOT
How do I graph these lines. I know how to get the point
lone heartBOT
clear stump
smh
lone heartBOT
Available help channel!
kind loom
Is this proof of preorder being antisymmetric correct?
We know that preorder is irreflexive and transitive
Now, to check if preorder is antisymmetric we need to show that if xRy and yRx then x = y, but we know that if there were such elements that satisfy the first part of the implication then from transitivity it would imply that xRx and that's not possible because preorder is irreflexive
so the first part of the implication is always false, so the implication is always true
preorder is antisymmetric
lone heartBOT
Is this proof of preorder being antisymmetric correct?
We know that preorder is ...
@kind loom Has your question been resolved?
lone heartBOT
@kind loom Has your question been resolved?
lone heartBOT
@kind loom Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
wide hollow
hey could someone help me with that pls
lone heartBOT
hey could someone help me with that pls
hidden pier
what do you notice about the fractions
wide hollow
ig they alternate between even and uneven numbers
wait so technically since next one will be unevene its B i think
wide hollow
yeah but do u need to since the only possible answer is 91/105 since its the only uneven one
wide hollow
i mean is there a patern ?
if thats the correct asnwer i dont rlly need to make it complicated for no reason cause this is a practic for a teste and in the real test i have45 mins to naswer 30 questions
tacit arch
numerator sequence is:
https://oeis.org/A000384
denominator is:
https://oeis.org/A014105
plug in the formula separately then see which is the next fraction, might need to simplify
wide hollow
.close
valid thunder
lone heartBOT
valid thunder
can i get a rough idea if im in the right direction?
also do i just look at the derivative in part A and isolate for y?
still crest
Is that an exam?
valid thunder
nope
its homework questions
but its for marks
i already know the rules of the server
also the exams are done in person, not on computer
lone heartBOT
@valid thunder Has your question been resolved?
amber nova
Hello, I'm kinda stuck on part C of this question
lone heartBOT
Hello, I'm kinda stuck on part C of this question
lone heartBOT
@amber nova Has your question been resolved?
amber nova
<@&286206848099549185>
clear stump
no
digital shard
Oh
clear stump
@digital shard he be here
digital shard
Hey
amber nova
helloo
amber nova
frank is shooting first so thats the dependent
digital shard
Right but it’s asking whether the outcomes are dependent or not
The outcomes as in what ends up happening to each ship
Is what happens to ship A
Dependent on what happens to ship B
amber nova
Right but it’s asking whether the outcomes are dependent or not
i guess i don't understand the whole question
digital shard
Lmaoo
Sure so
Ok lets cal frankfurter ship A
And dread pirate ship B
Question a is asking
Is ship A ‘s outcome dependent on ship Bs outcome
Its a bad question tbh so vague
lone heartBOT
@amber nova Has your question been resolved?
neat sierra
Where S4 is symmetric group and A4 is alternating group
lone heartBOT
Where S4 is symmetric group and A4 is alternating group
neat sierra
Does this argument make sense?
Also for the second direction, is there a more efficient way to do it, rather than checking every element in A4.
lone heartBOT
@neat sierra Has your question been resolved?
tired drum
lone heartBOT
gray isle
how are you getting x=0
tired drum
Because they are similar triangles right
The red line is 30
Which I solve by pythag
gray isle
is that 18 on the top right
tired drum
Yep
gray isle
what did you do after
tired drum
(24k)^2 x (18k)^2 = x^2 where k is some constant since they are similar triangles, and 30k = x
Sim equations give 0
gray isle
where's
(24k)^2 x (18k)^2 = x^2
coming from
tired drum
U know there similar triangles right?
tired drum
So the smaller triangle multiplied by some value gives the bigger triangle
tired drum
what's that x on the LHS
That’s a multiplication sign
gray isle
ok. I can now see that you intend to use k for the scaling factor
tired drum
Mhm yeah that’s it
gray isle
what theorem are you applying to get that equation
tired drum
what theorem are you applying to get that equation
I’m using similar triangles and scaling factors
And pythag
gray isle
that is not a correct application of Pythagoras
tired drum
How come?
gray isle
can you state Pythag for me?
tired drum
sure, a^2+b^2 = c^2
tired drum
Oh yeah sorry that was a typo, even with a ‘+’ it gives 0
gray isle
how are you getting 0 from that
tired drum
Idk lol
gray isle
wdym you don't know
tired drum
Try putting (24k)^2 + (18k)^2 = (30k)^2 info calc
gray isle
supposedly there was some work between
(24k)^2 + (18k)^2 = x^2
and
x= 0
tired drum
Yeah
gray isle
you goal here is to find k such that the distance between those base lines is 12
tired drum
Yeah how am I supposed to use that info
gray isle
consider the area of the small triangle (in two different ways) to find it's altitude
gray isle
and then you can use altitudes to determine the scaling factor k and hence x=30k
lone heartBOT
lone heartBOT
Available help channel!
south anvil
what is 2 rounded to the nearest centimeter?
lone heartBOT
what is 2 rounded to the nearest centimeter?
lone heartBOT
alpine sable
what
south anvil
it was 3 inches
abstract fractal
This just in: 2 rounded to the nearest centimeter is 3
alpine sable
3 inches
tacit arch
2 miles
alpine sable
2 miles is now 3 centimeters
lone heartBOT
Available help channel!
alpine sable
lone heartBOT
old horizon
nah it's not that simple
and some linear equations in 4 variables
alpine sable
and some linear equations in 4 variables
ye
old horizon
lol
lone heartBOT
@alpine sable Has your question been resolved?
tulip frost
Hey everyone. This is an exercise I found in a book, and I'm trying to solve exercise 4. I'm not sure where to start and I don't know how to use the hint. I'm not even sure how to start. Could someone direct me to the solution?
lone heartBOT
Hey everyone. This is an exercise I found in a book, and I'm trying to solve exe...
@tulip frost Has your question been resolved?
tulip frost
<@&286206848099549185>
swift shore
Wow that’s tough
So basically you’re proving that (i) and (iii) are sufficient to uniquely define V_p
Jesus, I don’t even know where to start
@tulip frost do you know what they mean by the hint?
tulip frost
I think they mean "locate a prime p such that V(p) > 0"
lone heartBOT
@tulip frost Has your question been resolved?
earnest plank
Is it true?
lone heartBOT
Is it true?
earnest plank
Cuz my friend says it is.
X is of the set of measurable numbers, then can the limit of this set be nonmeasurable?
naive valley
how are you defining measurable numbers? i know about measurable sets and measurable functions, but not measurable numbers
the supremum is indeed sqrt(2) if you're in a space such as R that includes that number, otherwise the set has no supremum
earnest plank
well english is not my first language and I actually don't know how you call these numbers in english
you know, this Q
naive valley
ah, yeah in english it's rational
earnest plank
oh nice to know
naive valley
(ratio of two integers)
yes, the supremum of a set of rational numbers can be irrational
earnest plank
but since X has to be rational, how is it possible that it's sqrt(2)?
oh
nice to know
thank you very much
naive valley
think about this: any real number has a decimal expansion
and finite decimal expansions are rational approximations to that number
1.4, 1.41, 1.414, 1.4142, 1.41421, etc
is a sequence of rational numbers that converges to sqrt(2)
and this works for any real number (rational or not)
earnest plank
nice to know, thank you for your help
naive valley
pleasure
earnest plank
.close
lone heartBOT
lone heartBOT
Available help channel!
lavish pier
lone heartBOT
lavish pier
question what happens if the number on top was lower for example t4/t11 would it be -7
vale wigeon
use this symbol: ^ for exponents
frail grove
You mean t^-7?
lavish pier
yes
vale wigeon
$\frac{t^4}{t^{11}}$ could be written as $t^{-7}$ if you want, yes. it could also be written as $\frac{1}{t^7}$. those are the same thing.
ocean sealBOT
Ann
frail grove
vale wigeon
i think you're overthinking it. this is just exponent laws being applied as normal.
lone heartBOT
lavish pier
i think you're overthinking it. this is just exponent laws being applied as norm...
sorry but do u still subtract indices if the letter is different
vale wigeon
.reopen
lone heartBOT
✅
vale wigeon
(in the future, if you have some follow-ups after the channel is closed, use .reopen so as not to get locked out of it later)
i don't understand what you're talking about though.
lavish pier
vale wigeon
are you asking if the division rule for exponents still applies if the bases are different?
frail grove
I think he means if 4 is negative
lavish pier
no
vale wigeon
no, of course it doesn't. if you were to try and do this to, say
lavish pier
the base as in t
frail grove
Oh ok
vale wigeon
$\frac{a^{16}}{b^9} = ?^7$
ocean sealBOT
Ann
lavish pier
so that is the simplest form
vale wigeon
the expression i showed in particular can't be simplified further yes
frail grove
Well you can still write it like this a^16 × b^(-9)
lavish pier
.close
queen raven
lone heartBOT
queen raven
I need help with part c
when i plug it into my calculator i get that the limit is -5, but i dont know how to do it by hand
the gradient of the secant is 2h-5
vale wigeon
you calculated that in part a, yes?
vale wigeon
yes
now that you've simplified it to the point where there's no longer a division by zero, you can substitute h=0 in
which is what you did
queen raven
ohhhh
i thought i had to rearrange to figure out what h is equal to
but i see now, as it approaches 0, i can just set it to equal 0 to find the limit
correct?
vale wigeon
...yes
mighty jolt
lone heartBOT
mighty jolt
I watched some youtube videos and the homework they gave me is this
I have no clue what the hell this is, it started as parametric solution and now I have these weird stuff so I'm lost
what do I do?
lone heartBOT
@mighty jolt Has your question been resolved?
mighty jolt
<@&286206848099549185>
lone heartBOT
@mighty jolt Has your question been resolved?
lone heartBOT
@mighty jolt Has your question been resolved?
lone heartBOT
stiff surge
<@&286206848099549185>
<@&286206848099549185>
<@&286206848099549185>
Is this question that tricky???
reef wyvern
Is this some kind of puzzle?
stiff surge
Is this some kind of puzzle?
Kind of, it is Kangaroo math competition questions
It is a practise question
<@&286206848099549185>
tawdry whale
u shouldn't ping helpers more than once
stiff surge
u shouldn't ping helpers more than once
okay!
tawdry whale
also you should wait 15 minutes before pinging as well xd
stiff surge
@tawdry whale Do you know how to solve the question?
reef wyvern
No sorry I'm stupid
tawdry whale
no
stone glen
Ask a Jew, this is math server
lone heartBOT
alpine sable
186
8+22=30
30+50=80
80+106=186
Basically the second term in eq 2 but doubled and adding 6 in eq 3
This sequence starts from eq 1 by 8
(8×2+6=22, 22×2+6=50, 50×2+6=106)
Note: just a guess
106×2+6=218
186+218=404
218×2+6=442
442+404=846
stiff surge
Good!
alpine sable
Was way faster than I thought I could find the answer
stone glen
Good!
Were you here to test the people here , or you genuinely needed help with the question?
stiff surge
Was way faster than I thought I could find the answer
Wow
stiff surge
Were you here to test the people here , or you genuinely needed help with the qu...
I need help with the question!!!
I am practising for Kangaroo math
stiff surge
Were you here to test the people here , or you genuinely needed help with the qu...
Also the fact you can't answer the question 
@alpine sable
But I don't understand how you figured it out
stiff surge
Every time, there is a question like this there is a different trick
stiff surge
It is a competition
alpine sable
This is like a puzzle and puzzles usually need pattern guessing
stiff surge
This is like a puzzle and puzzles usually need pattern guessing
They won't normally ask puzzles though
alpine sable
Like a spot the hidden horse in the image bla bla bla
stiff surge
Lol
alpine sable
They won't normally ask puzzles though
Idk, but this problem really got me off guard a little
Fun one too
That's the real shi
stiff surge
Fun one too
I tried figuring out but it was hard
stone glen
Yeah these question are too hard for me 😃
stiff surge
Yeah it is mostly tricky
alpine sable
Yeah, these type of problems require creativity and not analysis
stiff surge
Yeah, these type of problems require creativity and not analysis
Yep
stiff surge
Yeah, these type of problems require creativity and not analysis
It is just guessing and luck
alpine sable
I guess Lelouch is on analysis just like most of me
stiff surge
For puzzles, you need guessing and luck
alpine sable
Yeah
alpine sable
Now I feel like a rare human being
stiff surge
Why
alpine sable
Idk, just feeling good I solved a problem with low chances
Anyway
See you in another problem
stiff surge
Yep bye!
trim axle
Hi! Am i doing this right?
lone heartBOT
Hi! Am i doing this right?
lone heartBOT
@trim axle Has your question been resolved?
trim axle
<@&286206848099549185>
tawdry whale
In how many ways can u write 5 digit numbers in a not ascending order?
mortal trellis
after you pick 5 digits you can only write them in a unique order
tawdry whale
after you pick 5 digits you can only write them in a unique order
yeah
it's 99999
then 10 combinations with 10
99988
but that would take too long
is there an easiesr way?
mortal trellis
I wouldn't call 99999 descending but ok
mortal trellis
well first count how many ways there are to write them in ascending order
then subtract that from the total
same as with descending, after you pick 5 digits there is only one way to write them in ascending order
so it's really all about how many options for picking 5 digits you have
tawdry whale
huh I don't know how to do that
If I were to count in ascending
I'd apply the same patterns
11112
11123
et etc
mortal trellis
again, I wouldn't call 11112 ascending
tawdry whale
oh
OH
OOOOOOOOOOOOOOOOOOH
ur kinda big brain
oh nvm I still don't know how to do it xd
I get 6 numbers
in an ascending order
the only ascending numbers would be
12345
23456
34567
45678
56789
that's 6
mortal trellis
we are choosing 5 different digits out of 9 available. how many ways are there to do that
well we also have 12689 or something
tawdry whale
9!/5!
mortal trellis
no
tawdry whale
there's 9 ways to pick the 1st
8 to pick the 2nd
7 to pick the 3rd
6 to pick th e 4th
and 5 to pick the th
so 9!/4!
ye
but we have 10 numbers not 9, right?
0,1,2,3,4,5,6,7,8,9
but we can dismiss the 0
in the ascending order
mortal trellis
and 5 to pick the th
by doing this argument you are counting the 12345 and 21345 as different, even tho they are the same collection of 5 digits
tawdry whale
yeah
we need to find different numbers
not different ways to combine the digits
to find all the diffrent ways to combine the digits it would be
9!/4!*5!
mortal trellis
and read as "9 choose 4" (or in our case "9 choose 5")
tawdry whale
yeah
mortal trellis
we are choosing 5 different digits out of 9 available. how many ways are there t...
this needs to pop immediately into your head if you read stuff like this
tawdry whale
oh I suppose you're correct
yeah
yep makes sense
the total number of ways is 126 then
but that's only the number of ways to choose 5 digits out of 9
mortal trellis
which as we discussed earlier is the same amount as the number of ways to write a 5 digit number in ascending order
tawdry whale
okay, I'm not sure I get that part
I get that part
nvm
okay
what's my next move?
find the total amount of ways I can write
5 digit numbers
with
0,1,2,3,4,5,6,7,8,9
mortal trellis
so all numbers between 10000 and 99999
mortal trellis
recheck your count
mortal trellis
2001 instead of ~89000 ?
tawdry whale
yes
mortal trellis
ok. are you sure we did the correct question?
tawdry whale
I'm pretty sure
I'll check again!
oh
in how many ways can u write all 5 digit numbers ABCDE if A>=B>=C>=D>=E
so it's asking us for the descending order
tawdry whale
I actually get it yeah
prime badge
there's only one order, all number sorted, this doesn't put 0 first
tawdry whale
I don't get the -1 tho
prime badge
you just subtract 1 for all zeroes
prime badge
stars and bars
tawdry whale
I get the math behind it
but I dont' know
why you chose
the stars and bars method
Ie
beggar's equation
(N+K-1)cK
could u explain why you thought to opt for that method
tawdry whale
I get the stars and bars method
but here we have 5 bins and 10 numbers
not the other way around, no?
prime badge
no we have 10 bins
tawdry whale
hm I don't get what logic u used to reverse it
prime badge
e.g. we had 2 digits number then |*|*||||||||| would mean one 1 and one 2
most bins are empty
tawdry whale
ok
tawdry whale
okok let me ask you a question then
how many ways are there to write 3 digit numbers from digits 1 2 3 4 5?
prime badge
new question?
prime badge
this is not about the amounts because you didn't add non descending or whatever
tawdry whale
fuck man xd I don't get it
like yeah, I get how I can apply the formula
But I don't understand how u thought of using it
prime badge
my thought process is like...
the order carries no information
it's just about the amounts
tawdry whale
if the order carries no information then it's just /5!
prime badge
if the order carries no information then it's just /5!
you have repeats so it won't help
prime badge
not necessarily
tawdry whale
I feel as if
I went over the basics pretty strong
I even got the stars and bars method
so I went into comb problems pretty confident
but I already found 2 I can't understand
not solve
solving isn't the issue
udnerstand
prime badge
feeling challenged is not bad, it means you're encountering new stuff, if you didn't feel stupid, it's like, what are you paying for
tawdry whale
yeah feeling challenged is not bad at all, I love it
it's jsut that I get challenged way too often
at this point
cuz my uni entrance is in 10 days
xd
prime badge
people can't handle it for long, if they could, it would just be the norm to always feel stupid
tawdry whale
Hm
so do you think I could look at it
"In how many ways can I assign 5 digits to these 10 numbers"
prime badge
yep
prime badge
that's exactly what i did
tawdry whale
dlete
all the
repetitons
and why does it exclude
all numbers
in the ascending order
prime badge
it excludes every order except one, that's what they meant
tawdry whale
included
prime badge
it's the phrasing
that's the problem
if you have 4 ones and 2 zeros, which is what you count
that only corresponds to 111100
one number per way
prime badge
yes
tawdry whale
but we didn't apply the stars and bars method here
prime badge
you want to count 111100 once, 6!/4!*2! is how many times would you count it if you counted all numbers via 10^5 aargh
tawdry whale
could u Vc by chance?
prime badge
no sorry
tawdry whale
ok npnp
prime badge
like i never talked in English in my life
prime badge
tru
prime badge
i'm pretty sure i'm one of those people who can't handle challenges, it'snot the norm to feel stupid because of guys like me
we just quit :)
tawdry whale
xd
prime badge
my process is visual
like, what are they asking us to count, what numbers would that be
there's a problem here that they didn't explain it well, based on the answer they just mean "sorted from big to small"
55321, 54444, 52211
like those
so it's the same information as if i listed: two 1, one 4, three 6
only the amounts, and i know that stars and bars does that
i can;t even call it a process, there's one step where i come up with examples, the rest is automatic
tawdry whale
I see
prime badge
i know that's no help whatsoever, sorry
tawdry whale
nono
u inspired me in a direction
I'll definitely get the method now
I'll just have to look up
a few things
prime badge
awesome
lone heartBOT
lone heartBOT
Available help channel!
grave ginkgo
Helloo! This is the current problem I’m working on and got stuck at section ב. (1) “Find coordinates of M”
My data so far is, if it’s correct
B (4,6)
BM | KB, m1= 0.50 and m2= -2
BM equation: y = –2(x-4)
I’m not so sure about how I wrote the equation.. If it’s okay to walk me through and correct the errors I made I would be so happy
high rapids
can you explain how you got BM equation?
grave ginkgo
I used the formula m1 • m2 = -1
keen pasture
Yeah, that gives the slope
grave ginkgo
Oh my I read that wrong I’m sorry
So I used the straight line formula and I plugged in what I have
I got for m2= -2
grave ginkgo
O hh
grave ginkgo
so y=-2x+b, with B (4,6), 6=-2*4+b, b=6+8 = 14
In 6=-2*4+b, you subtract/add 6 from both sides?
I’m not sure how to do that part well yet..
Sorry if I’m asking too many questions!
grave ginkgo
Oh ok ok
high rapids
now that you have the equations of OM and BM you can find the coordinates of M
M is where these two lines meet
grave ginkgo
This helped me so much!! Thank you for taking the time to explain and guide me @/ diegoro! 🤍🤍 :D
Oh no I accidentally @ someone
.close
slender sparrow
out of sheer curiosity, how come lim sin(x) as x-> inf is indeterminate but lim sin(1/x) as x-> inf is not ?
karmic rapids
out of sheer curiosity, how come lim sin(x) as x-> inf is indeterminate but lim ...
$\lim_{x\to \infty} \sin(\frac{1}{x}) = \sin(\lim_{x \to \infty} \frac{1}{x}) = \sin(0) = 0$
ocean sealBOT
illuminator3
karmic rapids
yea you can take out/in the limit when the function is continuous
slender sparrow
.close
white cosmos
Hey guys , is that intercept theorem true ?
lone heartBOT
Hey guys , is that intercept theorem true ?
@white cosmos Has your question been resolved?
vivid yoke
Hey guys , is that intercept theorem true ?
The equation is correct
white cosmos
The equation is correct
thank you!
lone heartBOT
@white cosmos Has your question been resolved?
alpine sable
summer berry
What is the inverse function of f(x) = x^2 on < - infinity, 0] how do you even begin with this problem
wide raven
well
if you look at it
it would be reflection of 0,infinity
about y axis
so just do that
wide raven
nah
summer berry
I dont understand than
summer berry
ahh yeah
summer berry
negative?
why negative?
ah negative inifinity
But I dont get it given function was f(x) = x ^2
isnt that the same as y = x^2
so for the inverse shouldnt the x be on the other side?
wide raven
no actually
alpine sable
To find the inverse of any function, swap the x and y
So f(x) = y.
y = x² becomes x = y² => y = √x.
x in [0, inf)
wide raven
the first thing that contradicts is that
the inverse is the reflection in the line x=y
summer berry
To find the inverse of any function, swap the x and y
So f(x) = y.
y = x² become...
yeah
wide raven
so ain't happening
wide raven
think this way
y=root(x)
but root will take only +ve stuff
or else it will be complex
summer berry
yes
wide raven
so we want similar to the positive range's inverse
but in the negative part
so we multiply by -1
summer berry
is that becuase -2^2 = 4 and 2^2 = 4?
wide raven
can say so
alpine sable
Basically the domain becomes range and range becomes the domain in the inverse function
summer berry
okay but y = root(x) inverse should be than x= y^2
wide raven
okay but y = root(x) inverse should be than x= y^2
not over the whole range
cuz like while in the negative range it isn't even there in the codomain
alpine sable
okay but y = root(x) inverse should be than x= y^2
Swap the x and y.
x = √y
=> y = x²
Not x = y²
summer berry
wait you only swap?
alpine sable
Yeah
summer berry
dont you need to divide or multiply or so
alpine sable
Not really. Simplification if needed to bring in terms of y = something
summer berry
but that doesnt make sense beucase
alpine sable
Because
You're swapping the domain with the range
That's what inverse mean in general
By the way
summer berry
f(x) = 6x - 2 inverse is x = 1/6y + 1/3 the inverse isnt simply y = 6y - 2
summer berry
you said to swap y and x
summer berry
no?
summer berry
yeah okay I though you mean literall
summer berry
Swap the x and y.
x = √y
=> y = x²
but here you swapped it literally?
alpine sable
Lol sorry for causing confusion
summer berry
yes
summer berry
I dont know of that term
summer berry
Given f(x) = x^2 on < - infinity, 0]
y = x^2
root(y) = root(x^2)
x = root(y) and x = - root (y)
is this correct?
and wait x = -root(y)
so two answers
alpine sable
Given f(x) = x^2 on < - infinity, 0]
y = x^2
root(y) = root(x^2)
x = root(y) ...
Just make y as x and x as y
y=x²
Make y as x
And x as y
x = y²
Express in terms of y
y = √x
There it is
summer berry
but if you want the inverse shouldnt the x in this case be on the left side
alpine sable
See you're basically framing a new function that is the inverse of your original function.
The function outputs, f(x), are always mapped on y axis
So it is crucial to represent in terms of y
The domain of y=√x
Is the Range of y=x²
But that's not the case for x=y²
alpine sable
It's a convention to use x axis for inputs
And y axis for the outputs
This is a bijection.
This function is called a bijective function.
Every element from the Domain (a Set of inputs) has a unique element in the Range (set of outputs) where every element in Domain gets mapped to one unique element only in Range as in this diagram.
Only bijective functions have inverses
Just wanted to convey this
a maps to f(a) where a is on x axis and f(a) on y axis
b maps to f(b), where b is on x axis and f(b) is on y axis
summer berry
hmm I see
alpine sable
Take your time to grasp this concept, don't rush 👍
summer berry
I will thanks for help!
alpine sable
No problem
lone heartBOT
summer berry
.reopen
lone heartBOT
✅
summer berry
Is there something else I need to know?
alpine sable
No 👍
flint heath
The question + the model answer for part (b).
Stumped at F = Nsina, how did they get they come to Nsina? I just can't figure it out.
lone heartBOT
The question + the model answer for part (b).
Stumped at F = Nsina, how did they...
@flint heath Has your question been resolved?
Available help channel!
thorn lotus
lone heartBOT
normal ingot
points B and E look like inflection points
thorn lotus
points B and E look like inflection points
wait so for sign of f' do i put dne then?
normal ingot
f''(x) is zero at inflection points
hushed mica
lone heartBOT
hushed mica
@vale crag
sry for the ping but i again got stuck 😅
can u tell me how that e|d came now?
vale crag
well the idea is that e = au + (b+ax)v = a**(u+xv)** + bv
since d|a we also have d|a(u+xv)
since d|b we get that d|bv also
hushed mica
now i got a+b=e and a+b=d
vale crag
we can deduce from those two facts that d|a(u+xv) + bv
ie d|e
here I spelled out the reasoning completely
molten pivot
Separate into two cases: a and b coprime or not
vale crag
?
molten pivot
?
hushed mica
?
vale crag
I mean why would you split cases ?
vale crag
yeah
hushed mica
ok
molten pivot
I mean why would you split cases ?
If a and b are coprime then that means that a and b+ax are also coprime because they share no factors
And then you make a similar argument for the case that they are not coprime
hushed mica
lets assume they r coprime so that it will be ez to solve right?
molten pivot
Assume a and b are coprime. Then, b mod a > 0. But ax mod a = 0.
Can you figure it out now?
hushed mica
Assume a and b are coprime. Then, b mod a > 0. But ax mod a = 0.
by mod u mean the congruence modulo?
hushed mica
Assume a and b are coprime. Then, b mod a > 0. But ax mod a = 0.
yep
but what about the x?@molten pivot
molten pivot
Doesn't matter, ax mod a = 0
hushed mica
2|12 is 0=r right?
hushed mica
Are you familiar with the words im using
ngl but i am still new to nt
hushed mica
Have you worked with modular arithmetic
nope and thats what i am doing nt for atm
vale crag
I mean your reasoning doesn't sound right
how are you using the fact that a and b are coprime ?
molten pivot
Assume a and b are coprime. Then, b mod a > 0. But ax mod a = 0.
Here
vale crag
yeah and ?
molten pivot
?