plug it in
#help-17
modest coral
replace n with n+1
shell laurel
cant even answer your ouwn goddamn question
modest coral
I can but not doing it for u
shell laurel
.close
misty lotus
Hey someone can help me with this exercice , i dont understand and I can't do anything , i need find value S :
Shamir's sharing
Can you find the secret number?
Challenge taken from the book "25 fun puzzles to get started with cryptography" by Pascal Lafourcade, modification of the challenge from the original statement to adapt it to the Root-Me Pro platform.
In 1979, Israeli cryptographer Adi Shamir invented an elegant technique so that a secret number would only be accessible if at least k people collaborated. This technique is called secret sharing.
To illustrate how this method works with k = 3, it is enough for each of the people involved to receive the coordinates (x, y) of a point on the plan, different for each. These points are not chosen at random: they all belong to a certain curve whose equation is of the form
y = ax^2 + bx + s
The parameters a, b and s are not given, and the secret number is s, the constant term of the equation of this curve.
Alice, Bob and Carol respectively received the points:
A = (-10;23510983338944)
B = (15;82564483227494)
C = (20;140951404822754)
Can you discover the secret number s?
vocal sleetBOT
Hey someone can help me with this exercice , i dont understand and I can't do an...
wet dune
very long story for just plugging into quadratic equation
plug in those points
you'll get 3 equations
find them
misty lotus
this is 3 equations but in text he talk about k=3 , how i k=3
23510983338944=(100a)+(-10b)+s
82564483227494=(225a)+(15b)+s
140951404822754=(400a)+(20b)+s
and now how i can solve S
wet dune
this is 3 equations but in text he talk about k=3 , how i k=3
23510983338944=(1...
k is just the amount of people
misty lotus
ok
coarse ridge
How do I show that $\sum_{k=1}^{n} k \binom{n}{k} = n2^{(n-1)}$?
twin meteorBOT
Normed
coarse ridge
Like this
LHS counts the number of ways to select k elements out of a n element set then replace one of the element of the k element set with some element (not from the n element set)
vocal sleetBOT
@coarse ridge Has your question been resolved?
vocal sleetBOT
@coarse ridge Has your question been resolved?
hard atlas
well ok thats an interpretation. what do you want from us?
coarse ridge
well ok thats an interpretation. what do you want from us?
How do I prove this? my interpretations aren't working
coarse ridge
**Normed**
I need to show LHS and RHS are answers to the same counting problem
hard atlas
imagine you want to pick a group of people and one of them should be the leader
coarse ridge
hmm okay LHS counts the total number of ways to do this
n choose k counts the total number of such k member groups and there are k ways to select a leader given a particular group
but how does this helps?
haughty narwhal
use this
coarse ridge
!occupied
vocal sleetBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
hard atlas
n choose k counts the total number of such k member groups and there are k ways ...
so this picks the group first and then the leader
coarse ridge
Yes
coarse ridge
@hard atlas
hard atlas
well what happens if you pick the leader first and then the group
hard atlas
thats with a fixed size k
coarse ridge
But in this way the selected leader may not be in the selected group?
hard atlas
what if I just want to choose some group
coarse ridge
thats with a fixed size k
Yeah so k ranges from 1 to n
hard atlas
the leader is in the group by default. you are picking from the remaining n-1 people whether they are in the group
coarse ridge
Ohh yeah
hard atlas
for the right side you should not have anything involving k
cause there is no sum on the right side
coarse ridge
Yeah so the number of groups is all the subsets of the remaining n-1 members (once the leader is chosen) and there are n times 2^(n-1) ways to do this
And this is equal to first choosing the group and then the leader
Thanks a lot
hard atlas
yes
unborn crater
Find the asymptotes of $$y= \frac{x^2(x-1)}{x^2-4}$$
vocal sleetBOT
Find the asymptotes of $$y= \frac{x^2(x-1)}{x^2-4}$$
twin meteorBOT
Feevo
unborn crater
tried long division on this one, got an answer that didn't really make sense
like x^2-9x
I know that the vertical asymptotes are x=2, x=-2
and no horizontal ones
but the slant one, can't seem to get the equation for it
safe wyvern
in your long division you used x-4 rather than x^2-4
unborn crater
OH FFS
safe wyvern
there's also a trick here that I don't see people use very much
you can write x^2 as (x^2-4+4) which will get you quite far towards simplifying the problem
unborn crater
so this is where I'm at now, can't say I'm less confused tbh
doing the next step, I get to 4x-4 at the bottom
can't really go further tho without getting negative indices
or is x-1 just the answer?
safe wyvern
yes, so once you get a polynimial of degree <2 that's the remainder (since x^2-4 has degree 2)
so what you've found is that
x^3-x^2=(x^2-4)(x-1)+4x-4
leaden crane
Uhhmm... what?
vocal sleetBOT
Uhhmm... what?
leaden crane
There's so many things wrong with this lol
flat whale
There's so many things wrong with this lol
Such as?
twin meteorBOT
leaden crane
Taut is a word, yes, but a guy wire? xd
flat whale
Taut is a word, yes, but a guy wire? xd
Google it
leaden crane
does that mean it's the hypotenuse side?
ah
Okay, so hypotenuse side is 1216
the adjacent side is 644
and we're looking for the angle connecting the hypotenuse and adjacent?
nope
oops, meant to use cos
.close
north ruin
no
north ruin
eg 4 doesnt divide 2, but it does divide 16
green crystal
eg 4 doesnt divide 2, but it does divide 16
what would be the variables for those numbers?
north ruin
p = 4, d = 4, n = 2
green crystal
p = 4, d = 4, n = 2
bcuz when i plug those numbers in, it doesnt satisfy this
north ruin
the fact those numbers dont satisfy this statement is a disproof of the statement
green crystal
the fact those numbers dont satisfy this statement is a disproof of the statemen...
wait sorry i mean it does satisfy
if you flip the last 2 cols they would be F and T
when plugged in your variables
north ruin
wdym F and T
green crystal
false and true
north ruin
forgetting the table for the moment, the fact that d=4, doesnt divide n=2, but d=4 does divide n^p = 16 shows that the claim is false
since the claim claims that if d doesnt divide n then d doesnt divide n^p
for d=4, p=4, n=2, this new claim is true yes
lemme think for a sec if its true always
green crystal
you can use the table i provided
north ruin
the new claim is true i think
green crystal
the new claim is true i think
so for the original claim i provided, is there a way to prove it through counterexample that uses the table?
north ruin
there is no way to prove it, since it is not true
north ruin
green crystal
oh wait i was thinking the opposite way
fierce rain
vocal sleetBOT
https://www.chegg.com/homework-help/determine-force-member-truss-shown-method-jo...
vast shale
https://www.chegg.com/homework-help/determine-force-member-truss-shown-method-jo...
Do you have a question?
also you already have a pre existing channel occupied
don't just send random links
vocal sleetBOT
@fierce rain Has your question been resolved?
flat whale
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
woeful oasis
Let U be the set of triangles in the plane RxR and let S be the defined relation in U by: (x, y ) E S only if x is similar to y.
Proof that S is a equivalent relation.
regal bane
.
woeful oasis
Oh my bad
regal bane
You're good, I learned something today
Two triangles are said to be "equivalent" by your equivalence relation if they are similar triangles
But we need to prove it's actually an equivalence relation. Know the axioms for an equivalence relation?
regal bane
An equivalence relation over U is a relation U×U, such that the relation is:
- Reflexive
- Symmetric
- Transitive
woeful oasis
xd that is
regal bane
I'm sorry I don't know the terms in Spanish
regal bane
Do you want more help with it? Or did you want to attempt it?
woeful oasis
I don't understand the part of the triangle in R x R
In a cartesian plane the triangle has 3 vertex
so It has 3 ordened pairs
regal bane
Fair! I think they're just saying that these triangles exist in the plane. But if you wanted to properly define a "triangle" you'd need more than that
Points would be something like (R²)³, and they couldn't be colinear
woeful oasis
In other words, does It say U contains every point in the cartesian plane?
regal bane
U contains triangles, which they're not choosing to fully define here
U×U contains relations over triangles. In this case, a pair of triangles is a member of U×U, if those triangles are similar
regal bane
There's probably infinitely many ways, but they're all the same in the end
bleak oak
and you know what similar triangles are
you just need to show:
every triangle is similar to itself
if one triangle is similar to another, then the second is similar to the first
if triangle A is similar to B and B is similar to C then A is similar to C
woeful oasis
🤯
woeful oasis
In other words, does It say **U** contains every point in the cartesian plane?
Ok therefore this could be right?
vocal sleetBOT
@woeful oasis Has your question been resolved?
wary spear
how do I make a compounding formula like this
vocal sleetBOT
how do I make a compounding formula like this
woeful oasis
how do I make a compounding formula like this
I don't know what do you refer with "compounding formular" but that is a square root function
woeful oasis
Try y = a(x - h) " 2 + k. Where h is the vertex's first component and k is the vertex's second component
vocal sleetBOT
@wary spear Has your question been resolved?
wary spear
I don't know what do you refer with "compounding formular" but that is a square ...
i meant that but yeah
basically when x = 16 then y = 1
then it compouds at a rate and decreases the higher it gets
basically square rooting
polar nest
To write a quadratic function that would shift the graph to the right we need to modify the standard form of a quadratic function which is f(x) = ax^2 + bx + c
To shift the graph to the right we need to add a value h to the x-coordinate which represents the horizontal shift. If we add h to x the new function becomes f(x - h) = a(x - h)^2 + b(x - h) + c
In this case, since we want to shift the graph to the right, we need to increase the x-coordinate value. So, the value of h will be positive. Lets say we want to shift the graph to the right by 2 units. The new function would be f(x - 2) = a(x - 2)^2 + b(x - 2) + c*
polar nest
basically square rooting
U got the answer alrdy?
vocal sleetBOT
@wary spear Has your question been resolved?
turbid turret
There is a swing. When the swing is at a vertical position, the seat is 0.6m off the ground. When the swing is at an angle of 30 degrees, the seat is 1.5m off the ground. Find the swing chain length.
vocal sleetBOT
There is a swing. When the swing is at a vertical position, the seat is 0.6m off...
@turbid turret Has your question been resolved?
turbid turret
<@620023183290007616> Has your question been resolved?
no
polar nest
There is a swing. When the swing is at a vertical position, the seat is 0.6m off...
3 meters
vocal sleetBOT
@turbid turret Has your question been resolved?
warped heart
How did they get from LHS to RHS?
drowsy gulch
just to make sure, this is
[
\frac{n^2(n+1)^2}4 + (n+1)^3 = \cdots = \frac{(n+1)^2(n+2)^2}4
]
twin meteorBOT
@drowsy gulch
drowsy gulch
right? @warped heart
warped heart
yes
drowsy gulch
let's start by moving the $(n+1)^3$ into the fraction, like so:
\begin{align}
\frac{n^2(n+1)^2}4 + (n+1)^3 &=
\frac{n^2(n+1)^2 + 4(n+1)^3}4
\end{align}
twin meteorBOT
@drowsy gulch
drowsy gulch
that clear how that works?
warped heart
yes
drowsy gulch
from there, notice that both parts of our sum share a factor of (n+1)^2
so we can factor that out, using the reverse of the distributive property
\begin{align}
\frac{n^2(n+1)^2}4 + (n+1)^3
&=
\frac{n^2(n+1)^2 + 4(n+1)^3}4
\&= \frac{(n+1)^2(n^2 + 4n + 4)}4
\end{align}
twin meteorBOT
@drowsy gulch
warped heart
I don't follow this step
drowsy gulch
ah, okay, we can break it down a little bit
let's focus on the numerator and ignore the denominator for now
So we have
[
n^2(n+1)^2 + 4(n+1)^3
]
warped heart
did you mean to do 4(n+1)^3?
drowsy gulch
ah good catch
twin meteorBOT
@drowsy gulch
drowsy gulch
\def\a{{\color{red} a}}
for readability, let's define $\a = n+1$, so we have
[ n^2\a^2 + 4\a^3 ]
We can factor out an $\a^2$ like so:
[
n^2\a^2 + 4\a^3 = \a^2(n^2 + 4\a)
]
twin meteorBOT
@drowsy gulch
drowsy gulch
Does that follow?
warped heart
yes
drowsy gulch
\def\a{{\color{red} a}}
\def\it{{\color{red} n+1}}
Then let's substitute back in our original definition
[
\a^2(n^2 + 4\a) = (\it)^2\bigl(n^2 + 4(\it)\bigr)
]
twin meteorBOT
@drowsy gulch
drowsy gulch
That's great!
warped heart
You were amazing
drowsy gulch
Thank you so much for your help
Of course!
vocal sleetBOT
vocal sleetBOT
Available help channel!
timber fable
Im not sure how to do this problem. i think I'm supposed to plug something from the graph into the equations to solve them but I'm not sure.
vocal sleetBOT
Im not sure how to do this problem. i think I'm supposed to plug something from ...
@timber fable Has your question been resolved?
timber fable
<@&286206848099549185>
lapis maple
For solving the inequality you do you same as If it had the = sign instead of the inequality sign exept you change > to < (and < to >) when multipleing by -1
lapis maple
Its hard to explain more but i can give you an example with step by step
So an example with question
3x+12<-(1/3)x+5
Minus 12 to both sides
3x<-(1/3)x-7
Add (1/3)x to both sides
(3+(1/3))x<-7
Change the fraction on the left
(10/3)x<-5
Multiple both sides by 3
10x<-15
divide both sides by 10
x<-3/2
timber fable
ok so for a
it would go like
2+8=-1/2x+3
subtract 8 from both sides
2=-1/2x-5
then add -1/2x to both sides (add to itself and 2)
so then it would be 2 and 1/2x=-5?
lapis maple
Yea then if 2+(1/2)x=-5 then you can subtract 2 from both sides
timber fable
so 1/2x=-7?
lapis maple
Yes then you multiple both by 2
timber fable
so x=14
lapis maple
Yes
then it allso wants integral notation
In Integral notation you put the minimum x allowed and the maximum x allowed
Ex. (-infinity,5) is the same as x<5
timber fable
well a doesnt have a < or > sign its just an equals sign
so how would that work out
lapis maple
Well it isn't a normal question to be asked for intigral notation for equality its more common in inequality but it should be [14]
Allso in intigral notation [ mean it includes the smallest number ( means it dose not and vice versa for ] and )
timber fable
answer for a says that it is {-2}
lapis maple
Then I think there is an error then I'm guessing the problem a supposed to be 2x+8=-(1/2)x+3 not 2+8=-(1/2)x+3
Judging by problem b and c being the same problem just with a difrint sign
timber fable
hm
ill try it as 2x+8=-(1/2)x+3 then
yeah the teacher wrote it wrong
its 2x+8=-(1/2)x+3
not what we were working on
lapis maple
You can do nearly the same thing to solve 2x+8=-(1/2)x+3 as you did with the other equation
covert salmon
Any ideas on this...?
covert salmon
so the tangent plane should be flat
Do u know how to tell which one is the flattest?
@proven garden u know?
proven garden
maybe use normal vector to determine flatness
vocal sleetBOT
@covert salmon Has your question been resolved?
covert salmon
Any other <@&286206848099549185> got an idea?
tropic anchor
Need help no.1
vocal sleetBOT
Need help no.1
twin meteorBOT
proven garden
plug in p and q then compare terms
tropic anchor
3ax-bx+2ay-3by=a+9b
sweet grotto
someone help me :D
tropic anchor
what do i do agter that
sweet grotto
tropic anchor
3ax-bx+2ay-3by=a+9b
@proven garden
tropic anchor
x(3a-b)+y(2a-3b)=a+9b
tropic anchor
group them in a and b
wdym?
sweet grotto
how to create a channel
tropic anchor
the equality must hold for all a and b
Wdym?
proven garden
a and b are free variables
they can be any value
and we want x and y such that no matter what a and b are, the equality still holds
the only way is for two sides to be 0
tropic anchor
and we want x and y such that no matter what a and b are, the equality still hol...
ok thankss i think i understand now I asked my friend
vocal sleetBOT
@tropic anchor Has your question been resolved?
fluid ivy
I understand
x + y = 80
but what would the second equation in this system of equations look like? I'm guessing
260x - x^2 + 220y - y^2
?
fluid ivy
ok that is the 2nd equation
so system of equations would be
x + y = 80
260x - x^2 + 220y - y^2
but how do you find the maximum value? I only know how to find the minimum
spiral inlet
maximums and minimums will both occur where the derivative is 0
(or where the derivative doesn't exist)
fluid ivy
oh so same process for finding minimum?
Got a negative number for X so I think I distributed the negatives wrong somewhere
spiral inlet
yeah
fluid ivy
okie dokie
spiral inlet
and make sure to keep it in parentheses afterwards
because you'll also have to distribute the - sign in front of it
fluid ivy
si si
spiral inlet
ya ya
fluid ivy
50, 30 wwwww
finally 1 last question on this study guide then i gotta wake up in 5 hours at 9:30am for the quiz
fluid ivy
Am I allowed to factor like that?
(-x + 8) (x + 8) just feels illegal
Oh well if I go normal and take derivative I still get 0 = -2x + 16 which is x = 8 same result
WAIT BRUH I J REALIZED IVE BEEN STUDYING THE WRONG STUDY SHEET
NOOOOOOO
I JUST WASTED THE PAST 2 HOURRRSSS
.close
split wind
what have you tried?
subtle glen
Please someone help me
vocal sleetBOT
Please someone help me
subtle glen
i dont know how to solve this
proven garden
what do you get after writing tan into sin and cos
vast shale
Please someone help me
when we talk abt this sinx/x and tanx/x is a special limit that always equals to even
vocal sleetBOT
when we talk abt this sinx/x and tanx/x is a special limit that always equals to...
vast shale
same for sin inverse and tan inverse
vocal sleetBOT
@vast shale Has your question been resolved?
crimson pumice
I'm watching through a teacher explaination of a question but I am not exactly sure why the part I pointed with the arrow, he said "what value of x for that chunk would give you zero" could someone elaborate on what the implications of this is and why you would want to do this?
vocal sleetBOT
I'm watching through a teacher explaination of a question but I am not exactly s...
paper depot
crosses the x-axis
y = 0
paper depot
when y=0 only
crimson pumice
when y=0 only?
oh are you saying we only want to do this when it is clearly stated y=0
crimson pumice
I am kind of confused what is trying to be explain here, sorry
😅
what I'm understanding from you and them is that, the highlighted chunk, you want to get that to 0 so you want to find a value for x that would give you that
but this reasoning is only allowed within the realm when you are given y=0, therefore that chunk has to equal to 0 only when they say y=0
did I understand it correctly?
<@&286206848099549185>
man..
outer warren
no, you want the highlighed chunk to be 1
as the log of 1 is 0
essentially you want the value of x where y=0,
the x-intecerpt
supposedly dx/dt is in terms of x and/or y
you'd want those value(s) at the location of interest
crimson pumice
ahhhh
man I'd never think of that
so you don't want to find x=0 you want to find a value of x that would give you y=0
@outer warren sorry for ping
outer warren
yes
crimson pumice
that makes sens then
outer warren
recall coodinate geometry concepts
vocal sleetBOT
vocal sleetBOT
Available help channel!
hard kraken
vocal sleetBOT
hard kraken
which one is the right picture?
vast shale
vocal sleetBOT
vast shale
im supposed to find Vzero
my teacher got a different result tho so i cant figure out where i went wrong
karmic imp
my teacher got a different result tho so i cant figure out where i went wrong
What did your teacher get? And can you show the original question?
karmic imp
Can you provide the original problem that was given to you?
vast shale
Can you provide the original problem that was given to you?
the first line was the problem he provided to me where i had to find V zero. Its not written down somewhere cuz he wrote it in a blackboard
languid venture
vocal sleetBOT
languid venture
Why
wicked sonnet
Do you know what the argument of a complex number is?
languid venture
The real part?
wicked sonnet
No?
languid venture
Whats then
languid venture
Yes
wicked sonnet
Do you know what "polar representation of a complex number" means
languid venture
R and arg?
languid venture
The angle and radius of the complex?
wicked sonnet
Kinda like that...
hybrid flicker
but whats polar representation
The name of how we write a complex number, given R and arg
languid venture
The complex number on the complex plane
vast shale
The name of how we write a complex number, given R and arg
is that the definition, shit mb
wicked sonnet
is that the definition, shit mb
I thought you were asking him.
vast shale
i thought plotting complex numbers on a complex plane is the polar representation
languid venture
But idk how to find arg value
wicked sonnet
But idk how to find arg value
Well, let's say you have an arbitrary complex number
z=x+iy
languid venture
Ok
wicked sonnet
languid venture
Ok?
languid venture
How
wicked sonnet
Yeah I'm asking you
languid venture
Idk
hybrid flicker
Find a nice triangle...
languid venture
Now I understand this but i have 1 wonder
wicked sonnet
mhm?
wicked sonnet
Well, De Moivre's Theorem
hybrid flicker
$Arg(x^n) \equiv nArg(x)$ mod $2\pi$
twin meteorBOT
rafilou2003
languid venture
Mod?
hybrid flicker
$Arg(x^n)$ is the same as $nArg(x)$ up to a multiple of $2\pi$
twin meteorBOT
rafilou2003
hybrid flicker
How did they get to 1/ sqrt2
$z = R(\cos(Arg(z))+i\sin(Arg(z)))$
twin meteorBOT
rafilou2003
hybrid flicker
This is polar form
languid venture
The arg was 7/4pi
knotty kestrel
why is this true? Isnt x^2/3 less than x?
vocal sleetBOT
why is this true? Isnt x^2/3 less than x?
somber portal
Just because it goes to infinity slower than x doesnt mean it does not go to infinity
soft walrus
think about what happens as we plug in bigger numbers
somber portal
x/2 is also less than x.
And it also goes to infinity.
soft walrus
as does sqrt(x)=x^(1/2)
somber portal
the x gets as big as you arbitrarily want
knotty kestrel
as long as its more than 0
somber portal
so the sqrt of x also gets as big as you arbitrarily want
or in this case, the cubic root of x squared
frank iris
Need help asap please
vocal sleetBOT
Need help asap please
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
@frank iris Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
vast shale
Can anybody solve the second one? !help
vocal sleetBOT
Can anybody solve the second one? !help
vast shale
<@&286206848099549185>
flat whale
Can anybody solve the second one? !help
what are you stuck on
vast shale
what are you stuck on
on the que 2. the B part
vast shale
what are you stuck on
can i dm u?
vast shale
what about it are you stuck on?
i am stuck on how to solve that. I tried applying newton lebitiniz but the greatest integer function is pain in the ass that i am not able to solve
flat whale
i am stuck on how to solve that. I tried applying newton lebitiniz but the great...
floor functions return integers. turn your integral into a sum. split the domain into different sums where each part has the same value and count them. do it for small integers to find a pattern
like n=2,3,4
vast shale
floor functions return integers. turn your integral into a sum. split the domain...
don't you think newton-lebitiniz would work here? since splitting would be too tedious
vast shale
you said you tried it
i tried it but i don't know whether it's right
flat whale
show it
vast shale
wait
vast shale
floor functions return integers. turn your integral into a sum. split the domain...
Also splitting wouldn't work here since it has variable limit
flat whale
yea that's not right
flat whale
Also splitting wouldn't work here since it has variable limit
so?
the sum can (and probably does) converge
vast shale
yea that's not right
yeah that's why i am not able to figure it out
flat whale
floor functions return integers. turn your integral into a sum. split the domain...
do this
flat whale
that's convenient yes
flat whale
like n=2,3,4
.
vast shale
the variable limit putting me off
flat whale
could you do this for me? i am not able to grasp that
there is no limit
just plug in n=2, 3, 4 and evaluate that
vast shale
there is no limit
alright i get that part. I do find pattern but how do i integrate the function when the root x is inside greatest integer function
flat whale
just plug in n=2, 3, 4 and evaluate that
.
vast shale
.
i mean i can't able to evaluate when i plug 1 it becomes 0, when i plug 2 it becomes 1 to 4 with that function
vast shale
also could you that problem for me? it would be much appreciated
vast shale
use the definition of floor
floor has nothing to do with it since it's not dependent on x
flat whale
floor has nothing to do with it since it's not dependent on x
that's floor(sqrt(x))
vast shale
why can't you do your own work?
i tried but i can't figure it out so i asked here
vast shale
that's floor(sqrt(x))
i know that
flat whale
floor has nothing to do with it since it's not dependent on x
then why do you think this
maybe you should plot the function first
vast shale
maybe you should plot the function first
Brother, I need an standard or proper approach to this question so I can get the clarity how to turn it around the greatest integer. Plotting the floor function here is not necessary I believe since it has more easy approaches around there. I was looking for a solution to the problem so I can analyse how it's done. Not just to get my work done, that was rude way to describe it cause I am not able to get it correctly. Anyway thanks for the efforts, . I'll look elsewhere.
.close
vocal sleetBOT
flat whale
Brother, I need an standard or proper approach to this question so I can get the...
no one here's to do your work for you
vast shale
no one here's to do your work for you
Then leave the discussion. Not here to do my work.
vocal sleetBOT
Available help channel!
cerulean ermine
any idea or hint on how i can approach this?
vocal sleetBOT
any idea or hint on how i can approach this?
hard atlas
try some examples
cerulean ermine
the wording confuses me a bit
my logic is that g is injective but not necessarily surjective, since if we took A:{1, 2, 3} and B: {i, j, k}, and C:{1, 2}, with f(1) = i, f(2) = j, and f(3) = k, then any subset of A is injective because since f(x) = g(x), then any subset of elements will have to be injective. but this is not necessarily surjective, since not all elements in B have a proper mapping from C
vocal sleetBOT
@cerulean ermine Has your question been resolved?
vocal sleetBOT
@cerulean ermine Has your question been resolved?
patent onyx
surely C injective and not necessarily surjective (when C not equal A)
i mean g*
since f bijective, f injective and every element of A goes to different elements of B thus every element of C (also in A) goes to different elements in B
g not necessarily surjective, a counter example is to consider B=A, C proper subset (which is a subset of A but not A) and f is identity, all C go into C != A
astral needle
COnsider the function $f(x,y) = \begin{cases*} \dfrac{xy^4}{x^2+y^8}, &(x,y) \neq (0,0) \~\ 0, &(x,y) = (0,0) \end{cases*}$
vocal sleetBOT
COnsider the function $f(x,y) = \begin{cases*} \dfrac{xy^4}{x^2+y^8}, &(x,y) \ne...
twin meteorBOT
tales
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
astral needle
The question asks if the function is continuous at (0,0)
Then I took $\displaystyle \lim_{(x,y)\to (0,0)} \dfrac{xy^4}{x^2+y^8}$
twin meteorBOT
tales
astral needle
The path (x,x) leads to
$\displaystyle \lim_{x \to 0 } \dfrac{x\cdot x^4}{x^2+x^8} = \displaystyle \lim_{x \to 0 } \dfrac{x^3}{1+x^6} = \dfrac{0}{1+0} = 0$
twin meteorBOT
tales
astral needle
The path (x^4,x) leads to
$\displaystyle \lim_{x \to 0 } \dfrac{x^4\cdot x^4}{x^8+x^8} = \displaystyle \lim_{x \to 0 } \dfrac{x^8}{2x^8} = \dfrac{1}{2}$
twin meteorBOT
tales
astral needle
Different paths lead to different limits, so the limit doesn't exist and the function is discontinuous
Right until now?
obsidian stream
That's fine
twin meteorBOT
tales
astral needle
My friend says it doesn't exist, because f is discontinuous at (0,0)
But if you use the definition
$\dfrac{\partial f}{\partial x}(0,0) = \displaystyle \lim_{h \to 0} \dfrac{f(0+h,0) - f(0,0)}{h} = \displaystyle \lim_{h \to 0} \dfrac{\dfrac{h\cdot 0^4}{h^2+0^8}- 0}{h} = 0$
twin meteorBOT
tales
astral needle
You can calculate the partial derivative
What is the correct answer? Undefined or 0
obsidian stream
Why do you think it is undefined if you do a calculation and got 0
astral needle
Because if you differentiate using quotient rule, you will get a indeterminate form when plugging (0,0)
obsidian stream
Okay but that only tells you there is more work to be done, not that it's a dead end.
Anyway its been a while and I don't really like multivariable calculus but that answer looks okay to me. If I remember right, continuity of f depends on the differentiability of all partials, so I would expect that if you do the derivative with respect to y, the limit won't exist there, or it would contradict your discontinuity you found earlier.
I expect that's the next part of the question to illustrate this fact
astral needle
But f is differentiable with respect to x and y
obsidian stream
Sorry I meant that they exist and are continuous on the same set, the plane in this case
obsidian stream
The point is that in single variable calculus, differentiability at a point implies continuity at that point, but here you can see an example of a function that is discontinous at a point but admits a partial derivative
vocal sleetBOT
vocal sleetBOT
Available help channel!
rich abyss
vocal sleetBOT
rich abyss
I need to know why it gives 9.91m/s because when I plug it in into calculator it gives me 9.89
<@&286206848099549185>
.close
vocal sleetBOT
twin meteorBOT
rip_sky
vocal sleetBOT
vocal sleetBOT
Available help channel!
cinder oyster
if i wanted to find gog(x)
I just put |x+2| into x
But is confusing because the absolute value 😭
livid narwhal
What is confusing about it
livid narwhal
Yes.
livid narwhal
Yes.
livid narwhal
$$ | |x+2| + 2| $$
twin meteorBOT
Riven Minx
vocal sleetBOT
@cinder oyster Has your question been resolved?
silent orchid
vocal sleetBOT
silent orchid
is this correct?
in order to find p prime, i had seen the difference from x and y and it was -1 and +2
vocal sleetBOT
@silent orchid Has your question been resolved?
robust parcel
need help solving this
for the numerator I got: 1+1
for the denominator is got: 1-i
vocal sleetBOT
need help solving this
for the numerator I got: 1+1
for the denominator is got: ...
robust parcel
is this right so far?
2 over 1-i
and then I need to multiply both sides by 1+i right?
misty kelp
top and bottom
robust parcel
yeah top and bottom
misty kelp
yup thats all just multiply by the complex conjugate
misty kelp
yeah
misty kelp
yes
vast shale
hello,
I'm trying to solve this problem rn
Find the volume of the solid bounded by the planes x = 0, y = 0, z = 0, and x + y + z = 4.
I tried setting up a double integrals in the order dxdy with bounds 0 to 4-y and then 0 to 4-x (integrand was 4-x-y), but this was not successful, how should I set up the integral?
vast shale
sorry just realized I'm supposed to send here
rugged vortex
Volume of it right
And you went from a triple integral straight to double so
I do this thing called crushing dimensions
Since you took care of the z stuff, crush the solid down to the xy plane
Determine either x or y bounds from there
Like literally imagine if you just put your hands on top and below the solid and just crushed it like a soda can
vast shale
triple integral mag be correct but we just learned Abt that stuff in the last lesson and this set was for double integrals so I was assuming you dong use a triple one (would that make it easier?)
rugged vortex
It should be some kind of right triangle
rugged vortex
triple integral mag be correct but we just learned Abt that stuff in the last le...
Well yeah I'd triple integral this but the integrand would just be 1, and then the next step would literally be the integral that you have. So it doesn't matter if you do a triple integral or not
vast shale
I mean wouldn't it just be a triangle at (0,0) (4,0) (0,4)
rugged vortex
Yeah
vast shale
Well yeah I'd triple integral this but the integrand would just be 1, and then t...
if you did a triple integral would bounds just be 0 to 4-x,y,z respectively
rugged vortex
Uh. No. Literally the bounds of the double integral, the third integral's bounds are 0 and 4 - x - y, and the integrand is 1
vast shale
ohhh okay
let me try and evaluate that just bc it feels easier to conceptualize visually
rugged vortex
That's just to find the y and x bounds
Supposed you went with the y bounds
Then what equations (y = ...) make up that triangle
Or like
vast shale
ohhh okay
vast shale
that makes sense
rugged vortex
And then crush dimensions again down to the x axis
Find x bounds (they should be integers)
vast shale
okay that makes sense I think I screwed up in actually solving the integral bc I remember having one approach from 0 to 4-x then 0 to 4
which seems to be the correct bounds so probably arithmetic error
I solved it and the answer was correct though thank you for help!
.close
rough depot
vocal sleetBOT
rough depot
the big portion is the proof of isomorphic that phi(x*y) = phi(x) # phi(y)
I thought about setting a boundary of for m belongs to Z, 0<=m<=n
fleet ember
take two cyclic group G and F of order n
by def, there is a generator g of G, and f of F
take a function that sends g to f
can you make it so that it's a morphism ?
fleet ember
hint G = {e, g, g², ..., g^(n-1)}
F = {e, f, ..., f^(n-1)}
fleet ember
take the function that sends g^k to f^k for every k
can you see how it's both a morphism and a bijection ?
dense moon
is it f^n, or f^n-1
n-1
fleet ember
yeah my bad
rough depot
npnp
fleet ember
I took groups of order n+1
rough depot
lol
fleet ember
corrected lol
rough depot
well, for k belongs to Z, 0<=k<n, we could say a function maps g^k to f^k
that would make sense, yeah?
fleet ember
yes
rough depot
so for every term in f, there is a term in g. each term in g would go to f only once. bijection
fleet ember
yes, the inverse bijection is simply f^k -> g^k
rough depot
because of how order works, there is a same number of terms in both groups as well
fleet ember
since there are n distinct elements exactly in both and we send g^k to f^k, by uniqueness we can send back f^k to g^k without confusion
fleet ember
take any two elements g^k, g^l
phi(g^k g^l) = phi(g^(k+l)) = f^(k+l)
what can you say about phi(g^k) * phi(g^l) ?
rough depot
I see. The opperation is unnoted, so can I work with mult rules on exponents, or must I still conjsider (star) and [star]?
fleet ember
(note that we took phi such that phi(e) = e, obv)
rough depot
or does nature of cyclic mean mult?
fleet ember
I see. The opperation is unnoted, so can I work with mult rules on exponents, or...
usually, you use * when you use multiplicative notation (ie g, g², g^3...)
or + when you use additive notation (g, 2g, 3g)
it doesn't mean it's the usual addition/multiplication, it's just a notation
rough depot
yeah
fleet ember
out of habit I use mult notation but like you also intuitively use additive notation when you work in (Z, +)
doesn't matter
rough depot
yup. but since the notation isnt listen, do I have to be picky in that regard? I feel that i would have to
fleet ember
if you feel there might be confusion, just say what notation you use, there's no reason to be picky
rough depot
Okay, my professor always says to be picky, so thats why I stress on that regard
well phi(g^k)[]phi(g^l) ---> f^k[]f^l ---> f^(k+l)
fleet ember
it's even more logical to prove that the function I gave to you is a morphism before even showing it's one to one, since one to one is easier to justify after
rough depot
yeah that is fair, but the bijection aspect feels easy still
I think I have the idea now, and the big part was the star. just go with an opperation and call it good. TYTY again. might be back later
fleet ember
like, if you get the function phi(e) = e, phi(g) = f etc is a morphism
then phi(g^k) = phi(g)^k = f^k is forced, once you proved phi is a morphism
so if phi(g^k) = phi(g^l)
phi(g)^k = phi(g)^l
f^k = f^l
so k = l (since we wrote F as {e, ..., g^(n-1)}
and g^k = g^l
so phi is injective in two sets of same cardinality
and is one to one
wispy bloom
vocal sleetBOT
wispy bloom
can someone explain to me how part b works
pallid zenith
do you just use your answer in part a
they tell you the qty of the first group
that should be enough to get the total, right?
wispy bloom
what does it mean by sheets per n mm
pallid zenith
oh man thats a good question
wispy bloom
im looking at the answer, i dont understand why its like this
pallid zenith
i take it back i have no idea what this means
wispy bloom
you know frequency density?
pallid zenith
so each bin is some sheets per thickness range
pallid zenith
you know frequency density?
mb not hahah
wispy bloom
in this one its unusual cus the frequency density is simplified
i can calculate the actual value of frequency density, but idk what they mean by sheets per n mm
vocal sleetBOT
@wispy bloom Has your question been resolved?
hollow karma
vocal sleetBOT
hollow karma
I dont understand the question
I find the inverse of the given system of equations then what do I do for X
karmic imp
Multiply both sides by that inverse
hollow karma
Multiply both sides by that inverse
so multiply the original matrix by its inverse?
karmic imp
Multiply both sides
Because the system is in the form of Ax = B
If you multiply by the inverse you will find x
hollow karma
If you multiply by the inverse you will find x
so multiply [ 0 -11 3 ] by the inverse?
karmic imp
Yes
vocal sleetBOT
@hollow karma Has your question been resolved?
hollow karma
.close
unborn quail
vocal sleetBOT
unborn quail
how do i do qusetion C (i)
vocal sleetBOT
@unborn quail Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
oblique hinge
.open
undone aurora
vocal sleetBOT
oblique hinge
alr got it its ok
undone aurora
ai
so basically for this question wont P(C) = summation_(i = 1)^inf 1/2^i ?
idk how u would get 1 from that
paper depot
.open
for future reference: this is not a command, it does nothing.
in fact, starting your message with a . will PREVENT a channel from opening over it.
oblique hinge
okay thank you!
paper depot
idk how u would get 1 from that
do you know about geometric series
undone aurora
ngl I dont remember that
did it like 2 semester ago
so for
|r| < 1, S = a_1/(1 - r)
undone aurora
alr so common ratio of 1/2^x would be
1/2 right
and our first term is 1/2 so
(1/2)/(1 - 1/2) = 1?
vocal sleetBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
paper depot
of course it would...
btw i kinda wonder
whose idea was it to write
C_1 = {c : c is H, TH, TTH, TTTH, or TTTTH}
instead of just
C_1 = {H, TH, TTH, TTTH, TTTTH}
undone aurora
idk the dude who wrote the book
So P(C1 n C2) = 1/32 and P(C1 U C2) = P(C1) + P(C2) - P(C1 n C2) right
slow atlas
hey
slow atlas
i need help
this image is bette
why is r+s=6
and r-s=-2
i can kind of understand where they are coming from but not really
twin citrus
if we have two vectors a(a1;a2) and b(b1;b2) how can we finde their sum a+b=?
you need to know two definitions:
- sum of vectors 2) scalar multiplied by vector
slow atlas
ok
what is sum of vectors
and scalar multiplied by vectors
like what are those rules
<@&286206848099549185>
loud pivot
what is sum of vectors
You add two vectors by adding their corresponding components.
neat wave
sum of vectors is basically matrix addition. add the x's, y's, z's, etc. scalar multiplication is the same as multiplying a 1D matrix by a constant. (every value in the vector gets multiplied.)
for example. you have vector[4 1], you do 5 * [4 1] you get [20 5]
loud pivot
sum of vectors is basically matrix addition. add the x's, y's, z's, etc. scalar ...
Best not to include matrices here and keep it simple because I doubt they've learned that yet
"matrix addition" probably just confuses them more
neat wave
i feel that it gets confusing using vectors down the line as they get introduced to the dot product equation and it seems like students commonly mix up scalar multiplication and dot product, but ofc im just a student myself haha
loud pivot
I get that. It's just from my experience people aren't usually introduced to matrices when they start out with vectors
neat wave
I get that. It's just from my experience people aren't usually introduced to mat...
oh yeah that is a good point, I should have read what textbook the problem was from! I thought this was a linear algebra question 😉
loud pivot
oh yeah that is a good point, I should have read what textbook the problem was f...
Nope, calculus 😄
vocal sleetBOT
@slow atlas Has your question been resolved?
cinder oyster
vocal sleetBOT
cinder oyster
wat im doing wrong 😭
like should i do something before doing inverse instead?
i think i get it now
I find inverse but it need to be working with the domain
so have to be -
nvmmm im dumb i got it now ignore that dumb statement imade
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
chilly temple
i need help with this problem
vocal sleetBOT
i need help with this problem
chilly temple
part b only
paper depot
!status
vocal sleetBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
also since you have the "ask pronouns" role: what are your pronouns?
chilly temple
im a genderfluid
chilly temple
4?
paper depot
show your work and answer
chilly temple
ok
I substitued w with (3u+4v) and multiplied that term by v
and got 3 u^2 + 4uv
and since u and v are unit vectors
i made u and v equal to 1?
paper depot
- w is not equal to 3u+4v
- you need to be careful with notating dot product and esp. u^2 is icky
no, u and v are vectors, not numbers. they are not each themselves equal to the number 1.
chilly temple
oh
then im completely lost
could you perhaps please guide me through this problem ?
srry for the inconvience
nvm a friend showed me his solution
ty you anyways
.close
vast shale
What does the formula on the right include?
vocal sleetBOT
What does the formula on the right include?
@vast shale Has your question been resolved?
vocal sleetBOT
@vast shale Has your question been resolved?
grizzled halo
try a venn diagram to visualise
vocal sleetBOT
@vast shale Has your question been resolved?
pliant hinge
Hi there
grizzled halo
good question
signal flicker
,rotate
twin meteorBOT
pliant hinge
Umm can anyone confirm the answer of a part is True b is false c is false d is also false and j is false
merry cosmos
why is b false?
B is false because the limit does exist. Limits do not care weather the point is defined or undefined since it dosent really reach that point it’s approaching
pliant hinge
B is false because the limit does exist. Limits do not care weather the point is...
Agreed
merry cosmos
C is true btw
signal flicker
B is false because the limit does exist. Limits do not care weather the point is...
oh i got confused read "does exist"
merry cosmos
D is true too
d is true because it’s one sided limit indicated by the “-“. This means the limit as x approaches 1 from the left side. So it would be 2. But if it was a two sided limit, then it wouldn’t exist since as x approaches 1 from left and right do not equal
signal flicker
in c shouldnt it be 1 on the rhs for it to be true?
merry cosmos
Yes