?
#help-41
misty igloo
faint sleet
yes
misty igloo
noice
faint sleet
but it takes more effort
misty igloo
but it takes more effort
wait,
since 11 dollars is what they gain for the club for each box
does that mean
u just do 20000 divided by 11
and thats the answer?
faint sleet
why 11 dollars per box?
faint sleet
Same logic in a purer form
misty igloo
oh
faint sleet
20000 = 20*2.50*0.12*x + 5x
faint sleet
thats the equation
misty igloo
oh
faint sleet
Your asked to find some x number of boxes which satisfies the equation
misty igloo
Your asked to find some x number of boxes which satisfies the equation
wait,
what year are u anyways?
senior? first year, third year or etc
faint sleet
not studying. i do math for fun
median parcel
<@&286206848099549185>
pallid canopy
<@&286206848099549185>
Show what you've tried
amber waspBOT
@median parcel Has your question been resolved?
median parcel
Show what you've tried
The tip says to subtract .39 from 1 to get the non fair
=.61
That’s the first step it says to do @pallid canopy
median parcel
Ok so there are 244 that are not fair
amber waspBOT
median parcel
.reopen
amber waspBOT
✅
median parcel
I’m stuck on this part @pallid canopy
craggy mango
you have to figure 244C20?
median parcel
you have to figure 244C20?
Yes
craggy mango
You have the formula right there.
median parcel
Idk how to actually solve it tho
I just know just how to plug in numbers
All I know is that the answer should be a super low decimal
craggy mango
I mean, in place of n put 244 and 20 in place of r. In the formula you have there.
craggy mango
Yes, and then divide the two.
median parcel
My calculator can’t fit it all
craggy mango
Oh don't use calculator right away.
median parcel
It’s 244 X 243 X 232… until 225 ??????
craggy mango
$\frac{244!}{(20!)(244-20)!} ÷ \frac{400}{20!)(400-20)!}$
grizzled pagodaBOT
Sakata Yaksha
craggy mango
The 20! Gets cancelled first if all.
median parcel
I thought it was 244-20 that get canceled first
craggy mango
That also gets cancelled nicely.
244×243×242...225 is the numerator for the first part.
÷ 400×399...381
median parcel
244×243×242...225 is the numerator for the first part.
Yes but when I try to do that part the number is to big for calculator
craggy mango
Now that's that, I can't really help in that case.
wind glen
PART (b)
graceful hare
(j+1)^3-j^3=3j^2+3j+1 add those equations together j from 1 to n you have (n+1)^3-1=3S+3n(n+1)/2+n. Then you can calculate S=Σj^2
There is a general way to calculate Σj^k for any positive integer k, by making a difference table ,called finite difference method or something . If you want to know this general method we can discuss it privately
graceful hare
👍
wheat canopy
Hi, for graphs such as x^(14/11), what in the world is going on at x=0? It seems like theres no stationary point there despite that the derivative seems to be 0 there, its very confusing.
graceful hare
I was thinking this kind of function are only defined for non-negative x
wheat canopy
yea in this case tho the denominator of the power is odd so it ends up looking like this
full arch
help me
graceful hare
Okay then but not v shape
The slope will approach negative/positive infinity when x approaches 0 from left/right
wheat canopy
so there still is a statoinary point here?
oh the graph i have above is for x^(14/11)
im referring to specifically this sort of shape
where it seems like theres no stationary point but at the same time should be one
graceful hare
No there won’t be
wheat canopy
oh, even though the derivative is 0 at x=0?
graceful hare
The derivative has no definition at x=0
Left of 0 approaches negative infinity , right of 0 approaches positive infinity
wheat canopy
for x^(14/11) the derivative is (14/11)x^(3/11) tho is it not
graceful hare
Yeah
versed pebble
sin^2x - sin^2xcos^2x / cos^2x = sin^2xtan^2x
amber waspBOT
sin^2x - sin^2xcos^2x / cos^2x = sin^2xtan^2x
versed pebble
Idk how to go from here
amber waspBOT
@versed pebble Has your question been resolved?
viscid breach
sin^2x - sin^2xcos^2x / cos^2x = sin^2xtan^2x
send the entire question please
fierce fox
How do you use the roots of an equation, ex) I have -3+5i as one root. I can infer the second root is -3-5i. Now that I have both roots how do I write a quadratic equation with said roots.
fluid wren
Expand (x + 3 - 5i)(x + 3 + 5i) ?
graceful hare
You wrote both -
fierce fox
Sorry but don’t u need both of the roots too write a quadratic eq?
graceful hare
He edited, it has both roots now
stray current
Yeah
vernal stone
test
vernal stone
.close
lucid tendon
how do you integrate by parts when you have limits? I'm unsure as to how I would go about this question:
$$\int_{-1}^{0}e ^x(x+2) \dd x$$
grizzled pagodaBOT
I can't believe you've done this
lucid tendon
I'm fine when doing indefinite integration by parts but I don't know how the limits affect the answer
grizzled pagodaBOT
Enoo58
finite raven
yes you could also just determine the indefinite integral
and then calculate the definite one
lucid tendon
ill try using this
finite raven
alright good luck
lucid tendon
thanks
I got 1 as my answer which I think is right so thank you for the help
.close
earnest smelt
hi
merry kiln
If you have a square with side x, what is the length of its diagonal?
earnest smelt
5.657
merry kiln
...where did you get that number from
clever saddle
As the bot said, don't open multiple channels
Even if you have any questions, you use just one channel
amber waspBOT
@earnest smelt Has your question been resolved?
kind oak
what will the equation of the curve which covers the whole x-y plane?
near oriole
-∞ < (x, y) < ∞ ?
near oriole
Don't think so
kind oak
okay, understandable
kind oak
now, in addition to the whole x-y plane, if the curve also has a non-zero "z" coordinate, then what will be the equation/inequation?
kind oak
you could say z = 0
that is true for all curves in x-y plane, but ok
tranquil dawn
can you even describe it as a curve then
kind oak
ofcourse
everything you make in the 3d space or 2d plane is a curve. doesn't necessarilly has to be a straight line. Straight line is just a special curve.
tranquil dawn
you could say z = 0
also, this is more of a condition rather than an equation
severe minnow
everything you make in the 3d space or 2d plane is a curve. doesn't necessarilly...
No lol what
vernal stone
z = 0
The set of points that satisfy this in R^3 is exactly the xy plane
Or if you want to live in R^2
0 = 0
kind oak
r^3?
severe minnow
@vernal stone nice serif lol
vernal stone
everything that satisfies this is the plane itself
grizzled pagodaBOT
𝐒𝐡𝐮𝐫𝐢𝟐𝟎𝟔𝟎
severe minnow
@kind oak why do you want an equation for the whole plane anyway? Cause 0=0 technically works but it’s not meaningful in any way
kind oak
yeah i got that, but what is r^3? Do you mean the number of dimensions we are working with?
kind oak
<@!767977911264739328> why do you want an equation for the whole plane anyway? C...
just curious
grizzled pagodaBOT
abs_0
kind oak
now, in addition to the whole x-y plane, if the curve also has a non-zero "z" co...
yo, answer this please anybody
severe minnow
now, in addition to the whole x-y plane, if the curve also has a non-zero "z" co...
You mean an equation that covers the whole plane plus some stuff in 3d space?
kind oak
The set of real numbers is written $\bR$
oh didn't know we could raise the power of R in that way
vernal stone
R^2 is the xy plane
kind oak
R^2 is the xy plane
okay
vernal stone
Look I think
it is best you look up the formal definition of what a function is
and understand it
severe minnow
oh didn't know we could raise the power of R in that way
It’s made rigorous using set theory. Specifically, $\bR^2$ is the set of all pairs $(x,y)$ such that $x$ and $y$ are in the set $\bR$.
grizzled pagodaBOT
abs_0
vernal stone
because i feel you dont
kind oak
every value of x has one and only one f(x)?
vernal stone
no
Let A and B be sets.
Then the notation f : A -> B
Means f is a function that 'maps' from A to B
What this means is that f takes in an input from A. And outputs something in B
Moreover, f needs to be defined for all possible inputs from A. And only one possible output for each input is allowed
You are probably most familiar with functions $f:\bR \to \bR$
grizzled pagodaBOT
𝐒𝐡𝐮𝐫𝐢𝟐𝟎𝟔𝟎
kind oak
that I already know. but if there is a third set? like the third coordinate
vernal stone
This is a specific class of functions.
A function always only maps between 2 sets.
$f:\bR^2\to \bR$
grizzled pagodaBOT
𝐒𝐡𝐮𝐫𝐢𝟐𝟎𝟔𝟎
vernal stone
You are probably thinking about this
kind oak
ohkay yeah
vernal stone
Now, about the graph
uhhhhhh
there are various ways to define it, but in the end it is considered to be a set of points
For a function $f:A\to B$, we can consider its graph to be the set of points $${(x, f(x)) : x\in A}$$
grizzled pagodaBOT
𝐒𝐡𝐮𝐫𝐢𝟐𝟎𝟔𝟎
vernal stone
So if A = B = R
your typical functions you are familiar with
and f(x) = x^2
Then the graph would be
$${(x, x^2) : x\in\bR}$$
grizzled pagodaBOT
𝐒𝐡𝐮𝐫𝐢𝟐𝟎𝟔𝟎
vernal stone
If you haven't seen set notation like this, I also recommend learning it
kind oak
i have
vernal stone
👌
kind oak
**𝐒𝐡𝐮𝐫𝐢𝟐𝟎𝟔𝟎**
oh, btw, how do you do these?
like i am new to discord, how do you insert maths functions?
severe minnow
Curves have a very precise definition already
severe minnow
oh, btw, how do you do these?
like i am new to discord, how do you insert maths ...
It’s called LaTeX
kind oak
how do i use it
kind oak
Curves have a very precise definition already
should i call it a combo of curves?
vernal stone
$type maths stuff here$ You can google how to type certain stuffs if needed.
grizzled pagodaBOT
𝐒𝐡𝐮𝐫𝐢𝟐𝟎𝟔𝟎
severe minnow
Surround in-line equations with single dollar signs like $x = 3$, and if you want centered equations you do two dollar signs like $$\sum = 5$$
grizzled pagodaBOT
abs_0
vernal stone
If you can't find it on google then there's #latex-help
severe minnow
should i call it a combo of curves?
You can trivially find a set of curves that cover the whole plane
kind oak
If you can't find it on google then there's <#840667252793802752>
ok will read it
severe minnow
The set of all curves of the form $$r(t) = t\hat{i} + c\hat j + 0\hat k,$$ where $c$ is a real number
grizzled pagodaBOT
abs_0
kind oak
**𝐒𝐡𝐮𝐫𝐢𝟐𝟎𝟔𝟎**
now, what if we have a relation {(x,x):x belongs to R)? This would cover the whole plane right? Now, if i look at the 3d space, it covered all z=0 coordinates ofc. What if I have a non-zero z coordinate? How would I represent it in this form and how would the equation look like?
severe minnow
No
It would contain all the points like (5,5), (6,6), (10.5, 10.5), (pi, pi), etc
So all the points along y = x
severe minnow
That isn’t the entire plane
severe minnow
now, what if we have a relation {(x,x):x belongs to R)? This would cover the who...
In 3d coordinates we’re working with ordered triples, like (a, b, c)
kind oak
yeah
severe minnow
So talking about ordered pairs cannot work in 3d space
severe minnow
(x,y):x and y belong to R
This is precisely the set R^2
kind oak
when the z is non zero, the ordered pairs become ordered triplets
severe minnow
They don’t become anything
kind oak
This is precisely the set R^2
sir, this was when z=0
severe minnow
Sets are defined by you, if you say it only contains ordered pairs, you cannot just start adding a third coordinate
kind oak
They don’t become anything
why, how
severe minnow
Look
If I have the set {(0,1), (1,0), (0,0), (1,1)}
How can you just make it contain ordered triples
You can’t
You must define a new set and use the elements of the old set to construct it
kind oak
i didn't add a coordinate.
I just took another situation with locus of point (x,y,z) where x and y belong to R and z is a constant
severe minnow
“z is a constant”
kind oak
yup
severe minnow
What does that mean exactly
We’re working with sets now, we need precise, set-theoretic statements
kind oak
it means that z is not a variable like x and y
it has some fixed value
severe minnow
Right but that is vague in the context of sets
What exactly is a variable? What is a fixed value? How are they different?
Yknwo
kind oak
how many sets are we exactly considering in 3dimension space?
kind oak
What exactly is a variable? What is a fixed value? How are they different?
okay, leave it
z=5 lets say
and x and y belong to R
amber waspBOT
@kind oak Has your question been resolved?
snow island
I learned that the order of an element a in multiplicative group Zn is the smallest t such that a^t is congruent with 1 modulo n. I wanted to write a simple routine in order to compute element orders for elements of a group automatically, but didn't find any conclusive answer on the internet that I could understand. ok, taking the naive approach of taking an element and gradually exponentiating it (for example, with a fast modular exponentiation algorithm) and then comparing to 1: how big of t's do I need to try until giving up? can t be infinite for Zn* (I know it can be for a group in general)?
plush cosmos
Note that [ 2^t \equiv 1 \mod 4 ] is not true for any $t \ne 0$
grizzled pagodaBOT
Lance
plush cosmos
in general, you want a and n to be coprime
Then, if $a$ and $n$ are coprime, Euler-Fermat tells us that \[ a^{\varphi(n)} \equiv 1 \mod n \] where $\varphi(n)$ is the Euler totient function. So the smallest $t$ is a divisor of $\varphi(n)$.
Lance
plush cosmos
and φ(n) <= n is finite :)
rapid peak
And you can further refine that by Lagrange theorem to say t divides n
plush cosmos
so answering your questions directly
how big of t's do I need to try until giving up?
if a and n are coprime, you will only need to check t <= phi(n). otherwise, you can just give up immediately
can t be infinite for Zn* (I know it can be for a group in general)?
yes, if and only if a and n are not coprime
snow island
only need to check t <= phi(n)
thanks. that was my baseless intuition
if a and n are not coprime
that cannot happen in integer groups, can it?
rapid peak
If you're talking about $\mathbb Z_n^$ then no, those groups only contain elements coprime with n. But if you're running an algorithm on the computer, you'll likely end up checking integers between elements in $\mathbb Z_n^$
grizzled pagodaBOT
Zybikron
young scroll
can someone help me with this
amber waspBOT
can someone help me with this
languid sigil
<@&286206848099549185>
Dont ping right away, #❓how-to-get-help
wait 15 mins to ping..
young scroll
ok
cinder sentinel
what's up
dense carbon
Whats the problem @young scroll
young scroll
i dont know how to do it
dense carbon
You know how to use “<“ & ”>” operators?
young scroll
no
dense carbon
You understand less than and greater than?
young scroll
yes
dense carbon
2 less than 3
young scroll
yes'
young scroll
k
dense carbon
So now you see?
young scroll
yeah sorta
grizzled pagodaBOT
Deep
young scroll
so whats the answer
dense carbon
You giving test?
languid sigil
so whats the answer
idk, figure it out based on how you've been helped
If you just want the answer, you're not gonna get much help
young scroll
.close
amber waspBOT
amber waspBOT
Available help channel!
empty garnet
amber waspBOT
empty garnet
<@&286206848099549185> I really need help and I dont have that much time
clever saddle
<@&286206848099549185> I really need help and I dont have that much time
You have to wait at least 15 minutes before pinging helpers
empty garnet
I see that but I just said i dont have that much time
empty garnet
smh if you arent going to help with the problem then why bother
clever saddle
Then why do you follow the rules of the server and wait at least 15 minutes before pinging helpers
empty garnet
Because I would rather get help when I have time then follow rules and not be able to solve the problem?
clever saddle
Either way, doesn't matter. Rules are there for a reason, follow them
clever saddle
Then next time, follow the rules and we wouldn't be in the kind of conversation
empty garnet
Or if you just mind your damn business I could have help with the problem instead of being in this conversation
Just be quiet
clever saddle
I would have minded my own business if you didn't ping helpers prematurely
empty garnet
You are not even staff or helper what does it matter
like be quiet
and mind your damn business
so i can get my problem solved
and move on with my day
you dont learn
stop talking
clever saddle
I don't have to be a helper. I can help if I wanted to
clever saddle
But your attitude kinda sucks when I told you that there are rules for a reason and you should follow them
empty garnet
Because I need help and I have to go in a little
clever saddle
And it's not really my fault that you decided to procrastinate and wait last minute to do your work where you had to prematurely ping helpers
empty garnet
Its not my fault either? I had to go somewhere this weekend you dont know everybodys stories buddy
clever saddle
Could have done the work earlier
amber waspBOT
@empty garnet Has your question been resolved?
empty garnet
<@&286206848099549185>
paper grail
@clever saddle I think this is a kid lmfao
@empty garnet Sure you're short on time, but that doesn't mean you get special perms to bypass rules lol. The world doesn't stop for you and you're not entitled to an answer either. Everything here is charity work.
empty garnet
Now I got another person on me
empty garnet
<@485903210272391178> I think this is a kid lmfao
How old are you?
paper grail
Not relevant this the topic at hand, but with the math you're doing I think I'm probably older than you. i'm not up for an argument lol.
Here this can probably help you, the class of problems you're doing involves inscribed figures, good luck.
empty garnet
You cant say your age but you are saying im a kid
paper grail
You probably are doing that type of math lol
empty garnet
and I know how to solve these problems I dont need a video that is not helpful
empty garnet
You probably are doing that type of math lol
How old are you??
paper grail
Then you don't need this channel if you know how to solve it
clever saddle
If you know how to solve it, then solve it. Should be easy as that
paper grail
Good luck
empty garnet
I wouldn’t send that specific problem if I knew how to solve it as you can see its the last problem on the page and the other ones are solved
paper grail
You cant say your age but you are saying im a kid
What age do you consider not a kid? I'm curious btw?
empty garnet
Whatever age I say you are going to say an age above it
clever saddle
I wouldn’t send that specific problem if I knew how to solve it as you can see i...
Someone sent you a resource, you declined it because you said you knew how to do it. But now you're saying you don't know how to solve it?
empty garnet
That resource just tells you how to solve the type of problems not the exact problem
.close
amber waspBOT
clever saddle
That resource just tells you how to solve the type of problems not the exact pro...
Then apply that same concept
amber waspBOT
Available help channel!
bleak flower
hlep
atomic needle
bleak flower
eh
regal glacier
Just multiply it by itself if you dont know the rules
But after that look at expenential rules
bleak flower
so what is the answer
regal glacier
Calculate it
bleak flower
e
jovial beacon
But after that look at expenential rules
amber waspBOT
@bleak flower Has your question been resolved?
clever saddle
,rotate
grizzled pagodaBOT
amber waspBOT
amber waspBOT
Available help channel!
dim jacinth
hi,
how do I write this equation in an array
(20x+17y+14z)/(x+y+z) =18
example:
this eq x+y+z = 480
is
(1,1,1,480)
dim jacinth
How do I know what the coefficients are?
mortal phoenix
multiply both sides by x+y+z
dim jacinth
multiply both sides by x+y+z
2x-y-4z =0?
and if the original was:
(20x+17y+14z)/(x+y+z) => 18
the sign change or stay?
2x-y-4z => 0
mortal phoenix
not enough info
dim jacinth
not enough info
what missing?
mortal phoenix
you dont know if x+y+z is positive or negative
dim jacinth
I know x,y,z >= 0
mortal phoenix
then the sign doesnt change
amber waspBOT
amber waspBOT
Available help channel!
safe tapir
amber waspBOT
safe tapir
Hi could someone give me some hints on how to go about this? I tried that since bb^-1 = e then ab^-1 b = a
indigo cloud
first, since $H$ is nonempty, there exists an $a\in H$. Then we have $e=aa^{-1}\in H$. Further, $b^{-1}=eb^{-1}\in H$ for all $b\in H$. Finally, $ab = a\left(b^{-1}\right)^{-1}\in H$ for all $a,b\in H$
golden stone
One direction is straight-forward.
grizzled pagodaBOT
Denascite
safe tapir
Can I say that if (ab^-1)b=a then (ab^-1)(ba^-1) = e. Since a,a^-1,b, b^-1 is in H and H must be closed under the induced binary operation * then ab^-1 must be a member of H
indigo cloud
that's the easy direction, yes
safe tapir
that's the easy direction, yes
What would the other direction be?
indigo cloud
what I wrote
amber waspBOT