write out the full expression for both derivatives and set them equal to 0 and it should become clear
#help-23
median vigil
it would look like an inflection point, something like this
an inflection point is the transition between a function being concave up (∪) and concave down (∩)
safe radishBOT
safe radishBOT
Available help channel!
weak dagger
how can I solve a function with x to a power if i plug in something like (x + bx)?
safe radishBOT
how can I solve a function with x to a power if i plug in something like (x + bx...
weak dagger
i'm just expanding (x+bx)^2 into x^2+2bx^2+b^2x^2 but i'm not sure that's correct
lean otter
thats correct
lean otter
how can I solve a function with x to a power if i plug in something like (x + bx...
what do u mean
weak dagger
like i'm trying to evaluate f(x) = x^2 + 25 with f(x + bx)
weak dagger
yeah but i tried without doing it and it was wrong
because wouldn't that make it x+bx+5
lean otter
can you show me the question?
weak dagger
lean otter
oh god
weak dagger
yeah i'm pretty sure im doing something totally unnecessary
lean otter
sqrt(a² + b²) =/ sqrt(a²) + sqrt(b²)
weak dagger
oh wait nvm
languid wing
think of it like a quadratic
lean otter
yea try sqrt((x+bx)² +25)
languid wing
right
weak dagger
you can't simplify it?
lean otter
not really
lean otter
yea idk if thats easier
languid wing
oh wait
weak dagger
i did that
languid wing
nevermind
lean otter
yea try sqrt((x+bx)² +25)
but if that doesnt work try foiling
lean otter
i did that
show me
weak dagger
and how are you guys writing the squares btw
lean otter
i'm just expanding (x+bx)^2 into x^2+2bx^2+b^2x^2 but i'm not sure that's correc...
yes but thats not the answer yet
almost
weak dagger
you have to square root it right?
lean otter
yea try sqrt((x+bx)² +25)
did u try this one already?
weak dagger
yes it was wrong
lean otter
you have to square root it right?
yes with the 25
weak dagger
has to be simplified probably
lean otter
has to be simplified probably
hm mayb
weak dagger
so then if you can't simplify the bx portion then it's just like sqrt(x+bx)² + 5
i suppose
languid wing
i don't think you can simplify it anymore
lean otter
so then if you can't simplify the bx portion then it's just like sqrt(x+bx)² + 5
noo
thats very wrong
u cant do that
languid wing
sqrt(x^2+25) can't be split into a foiled format
weak dagger
oh i thought you wrote equal lol
lean otter
it works with multiplication not with addition
lean otter
oh i thought you wrote equal lol
my bad
weak dagger
im so confused
lean otter
so then if you can't simplify the bx portion then it's just like sqrt(x+bx)² + 5
one step before
the step u did was wrong
weak dagger
so i go back to sqrt((x+bx)² + 25)?
im not sure what to do from there though besides multiplying it out if you can't do anything else
lean otter
so i go back to sqrt((x+bx)² + 25)?
YES
nono
its the answer already
u cant do more
lean otter
then expand it
weak dagger
idk why
lean otter
in it
weak dagger
sqrt((x²+2bx²+b²x²)+25)?
lean otter
yep
lean otter
awesome!
weak dagger
.close
kind kindle
help
kind kindle
how can i do this?
light shoal
what do the three angles of a triangle add up to?
safe radishBOT
@kind kindle Has your question been resolved?
kind kindle
all angles together are 180
how
safe radishBOT
@kind kindle Has your question been resolved?
safe radishBOT
dapper venture
do you know how to calculate with fractions?
obtuse furnace
Ok
obtuse furnace
<#488120190538743810>
I'm a helper ?
dapper venture
oh sry
obtuse furnace
Yea no problem
Hey @lean otter to solve this
Hey um im so sorry something came up @dapper venture would you mind taking over ?
dapper venture
ok
obtuse furnace
ty 🙂
dapper venture
so first make the denominators the same
do you know how to find lcm?
least common multiple
umm don't show your face
It's not good to give away personal information
the Internet can be dangerous
delete that
also your method is wrong
btw how old are you
I don't think this server allows children less than 13 years old
clever pier
how
clever pier
stucked
agile phoenix
whats the problem
clever pier
so is the negative angle one of the answer?
clever pier
so sin x = -1 has to be rejected?
tall crow
There are many solutions for sin(x) = 1/2 @clever pier
tall crow
Do you mean using
agile phoenix
tall crow
sun x periodicity table with 2n cycle
clever pier
270
agile phoenix
ye
clever pier
so 270 is another solution
clever pier
how about the 150?
tall crow
$$
x=\frac{3 \pi}{2}+2 \pi n, x=\frac{\pi}{6}+2 \pi n, x=\frac{5 \pi}{6}+2 \pi n
$$
flat frigateBOT
𝕏
agile phoenix
thats radians
tall crow
Convert it
clever pier
so sin x cuts y = 0.5, the solutions could be 30 and 150
agile phoenix
yes
agile phoenix
between 0 and 360 of course
clever pier
if more than 360 then there more solution?
agile phoenix
np
regal flax
18 please guide me, what do i need to find?
safe radishBOT
18 please guide me, what do i need to find?
violet viper
18 please guide me, what do i need to find?
find the value of x
regal flax
should i change cos into sin?
violet viper
its already a quadratic in sin
not rlly
you still have to rerwite 1 using trig
and let the right hand side =0
harsh parcel
cant u appl
location of roots
on the discriminant
well thats easier
rewrite 1 youll get a whole square
regal flax
sin x = 1/4
violet viper
show your work?
regal flax
lemme get my phone
harsh parcel
sin x = 1/4
that doesnt work
violet viper
you don't have to
regal flax
then
violet viper
you can just move it to the left side
violet viper
how do i expand it from that
so what did you got
regal flax
more?
harsh parcel
yes
regal flax
but this is the general answer is it?
regal flax
oh similar to number 17?
regal flax
+-
harsh parcel
so youll get 2 more solutions
regal flax
so youll get 2 more solutions
Alright
ok gonna finish 19-24 ill ask again later thx @harsh parcel
.close
safe radishBOT
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Available help channel!
frank valley
Define $\phi: \mathbb{R} \rightarrow \mathbb{R}$ by $$\phi(x)= \begin{cases}\exp (-1 / x) & \text { if } x>0 \ 0 & \text { if } x \leq 0\end{cases}$$ Then $\phi$ has derivatives of all orders on $\mathbb R$. The infinite differentiability of $\phi(x)$ at $x \neq 0$ follows from the chain rule. Moreover, its $n$th derivative has the form $$\phi^{(n)}(x)= \begin{cases}p_{n}(1 / x) \exp (-1 / x) & \text { if } x>0 \ 0 & \text { if } x<0\end{cases}$$ where $p_{n}(1 / x)$ is a polynomial of degree $2 n$ in $1 / x$. This follows, for example, by induction, since differentiation of $\phi^{(n)}$ shows that $p_{n}$ satisfies the recursion relation $$ p_{n+1}(z)=z^{2}\left[p_{n}(z)-p_{n}^{\prime}(z)\right], \quad p_{0}(z)=1 . $$
safe radishBOT
Define $\phi: \mathbb{R} \rightarrow \mathbb{R}$ by $$\phi(x)= \begin{cases}\exp...
frank valley
I do not see how this follows by induction. I can verify the recurrence relation, but how would you go about proving this by induction? I would need some help starting from the base case.
flat frigateBOT
sunside
frank valley
We have by the chain rule that for $x>0$, $\phi'(x)=\exp(-1/x)\frac1{x^2}$, which is of the form $p_n(1/x)\exp(-1/x)$, where $p_n(1/x)$ is a polynomial of degree $2$ in $1/x$. I guess that proves the base case.
flat frigateBOT
sunside
frank valley
Assume the formula holds for n. Now show it holds for n+1.
This is where I'm stuck.
I guess we are interested in computing the derivative of $\phi^{(n)}=p_n(1/x)\exp(-1/x)$ and use the recursion relation somehow, but I just don't know how.
flat frigateBOT
sunside
safe radishBOT
@frank valley Has your question been resolved?
safe radishBOT
@frank valley Has your question been resolved?
wraith prism
if two line equations are given. Is there any method we can assume their intersecting point will be in which quadrants Directly without finding points by substitution method
safe radishBOT
if two line equations are given. Is there any method we can assume their interse...
final halo
yeah sketch them
safe radishBOT
@wraith prism Has your question been resolved?
vital dirge
if two line equations are given. Is there any method we can assume their interse...
you can't just set them equal to each other?
balmy bluff
yeah sketch them
^
lean otter
if two line equations are given. Is there any method we can assume their interse...
Could you restate??
wraith prism
Will you sketch it@final halo
lean otter
Like two linear equations and how to find the intersecting point?
Alr
Lemme see this.
wraith prism
I can tell you about the sign of roots of it directly
final halo
You said two LINES
lean otter
Yeah.
final halo
That's a totally different question
wraith prism
This is another question
wraith prism
Tell me what you will do?
@final halo
If you are going to sketch or find roots by the formula
final halo
No, stop pinging me
lean otter
I could help?
vital dirge
If you are going to sketch or find roots by the formula
you asked a completely different question
there are different ways to approach different questions
wraith prism
We don't need to find actual roots we can just assume by the equation and find roots of quadrant
wraith prism
No, stop pinging me
No one is interested. The thing is just for unusual answer
I am asking do you know a 3 second method to find roots of quadratic equation roots
Time is precious for me in the exam. I can find the actual roots of various paths by taking 5-10 minutes
So here there is a chart for it for quadratic
That's why i asked about the line equation I hope u understand
@final halo
📌
final halo
<@182179228840755200>
<@&268886789983436800> I have asked not to be pinged
Arjuun i will no longer be helping you in the future i wish you luck
wraith prism
No problem
I don't want sketch type suggestions
I took back the friend request
.close
safe radishBOT
white umbra
<@182179228840755200>
Stop pinging people who don't want to be pinged
wraith prism
I'll never talk to this guy again in my life
white umbra
Okay I guess
wraith prism
Thanks
safe radishBOT
Available help channel!
fluid zealot
safe radishBOT
fluid zealot
This is right, right?
I mean at the start if you can do a grouping like this one
I got x and 2 instead of -x and -2, is it still ok
Can you do this, i got the same result as photomath with different method
lean otter
The internal dimension of a lidless wooden box is 48 cm x 38 cm x 31 cm.If the thickness of the box is 1 cm,find the volume of the wood
primal granite
The internal dimension of a lidless wooden box is 48 cm x 38 cm x 31 cm.If the t...
this channel is taken, please read #❓how-to-get-help
lean otter
this channel is taken, please read <#488120190538743810>
sry
primal granite
This is right, right?
yes i believe its right
these are the steps you took correct?
fluid zealot
So basically
Even If at the start it's -x and -2 when i group them i can let them be +x and +2?
Isnt it wrong?
Now im confused
primal granite
are you talking about this?
primal granite
ah i see and you grouped like this?
fluid zealot
I grouped the x with x^3
And the 2 with 2x^2
But i changed them from - to + so it could work lol and i got the right result
But im not sure If you can do this
primal granite
oh i think i see what you mean now, so after you got to this step
$$\left(x^{3}-x\right)+\left(2x^{2}-2\right)$$
you factored out a +x from the first group and a +2 from the second right?
flat frigateBOT
Judgemental Snail
primal granite
if so, yes you can do this
safe radishBOT
@fluid zealot Has your question been resolved?
fluid zealot
Hmmm
Is this right too
I get the same result but with opposite signs
My result is now (-x-2)(1-x)(1+x)
primal granite
yes you would still get the same result 👍
fluid zealot
yes you would still get the same result 👍
So even though the + and - are the opposite both are ok yeah they just told me
Thanks you too
primal granite
np
fluid zealot
Thats interesting
primal granite
as long as your math is correct you should be good
fluid zealot
different method i used and i get the same result
But with opposite + and - lol
And both are correct thats Interesting
primal granite
if you also want to see why they are the same, factor out a negative from both factors $\left(-x-2\right)\left(-x^{2}+1\right)=0$
fluid zealot
Yeah
flat frigateBOT
Judgemental Snail
fluid zealot
Thanks!
primal granite
np!
safe radishBOT
safe radishBOT
Available help channel!
marble willow
How do I solve this problem?
safe radishBOT
How do I solve this problem?
upbeat ridge
!status
safe radishBOT
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
!show
safe radishBOT
Show your work, and if possible, explain where you are stuck.
marble willow
The start, how do I start it
marble willow
what do you mean by that
upbeat ridge
What does f(x) -> 250 mean in the first case
marble willow
What does f(x) -> 250 mean in the first case
f(x) is equal to 250 as x approaches five
safe radishBOT
safe radishBOT
Available help channel!
vivid stone
shouldn't we do
safe radishBOT
shouldn't we do
vivid stone
1!,2!,3!.................9!
?
at the end of 10c1,10c2,10c3..................10c9 respectively
whole acorn
in any order
whole acorn
wdym by 1! 2! 3! etc at the end of 10c1, 10c2 ....
vivid stone
i mean by that
is
assume
the lock is goin to open by
4 number
{5,3,6,1}
so since we can choose any number first
i can even open the lock by {1,3,5,6}
vivid stone
so considering that
whole acorn
you can just write 10P1, 10P2, etc
vivid stone
its the same thing
vivid stone
but the thing is that
whole acorn
and then subtract 10P5
whole acorn
ok...
vivid stone
wait let me try to figure out
he is saying that
if there was any specific combination
at that time we have to take factorial
@whole acorn man you there?
whole acorn
if there was any specific combination
this is the 10Ck part
and then multiply each of them by k!
like..
10C6 * 6!
etc
et
vivid stone
yes i did this
whole acorn
c
vivid stone
but i can't understand the meaning of specific combinations?
whole acorn
okay so
whole acorn
aops yes
vivid stone
the ans is
in
like
if you do
any 10c1 and etc
then only you get ans
they haven't multiply the fac
whole acorn
that was what threw me off too
for example we have a combination of 1, 2, and 3
do we count it as 1
or do we count it as
{1, 2, 3}
{1, 3, 2}
{2, 1, 3}
{2, 3, 1}
{3, 1, 2}
{3, 2, 1}
6
whole acorn
it's more of an understanding the question type of problem tbh
vivid stone
yeah man
idk at first i can't even get the langauge of the ques
maybe i am new to this type of stuff
thats why
whole acorn
hmmm
maybe i can explain the specific combinations part first
have you ever learned sets?
so basicalyl
vivid stone
vivid stone
have you ever learned sets?
yes
whole acorn
A = {1, 2, 3, 4, 5} and B = {1, 2, 3, 4, 5}
then A = B right?
vivid stone
yep
whole acorn
A = {1, 2, 3, 5, 4} and B = {1, 2, 3, 4, 5}
A is still = B right?
whole acorn
so basically specific combination is when the elements inside is not the same
like...
vivid stone
oh so by that they mean that
whole acorn
A = {1, 2, 3, 4} and B = {1, 2, 3}
A ≠ B
vivid stone
{1,2,4,5} will be equal to {5,4,1,2}
whole acorn
yes, that is one specific combination
vivid stone
like these are same premutations
vivid stone
A = {1, 2, 3, 4} and B = {1, 2, 3}
A ≠ B
ohk
whole acorn
{1,2,4,5} will be equal to {5,4,1,2}
your prof counts that as 2 meanwhile the aops counts that as 1
basically your prof thinks that the order matters when counting the number of combinations
whereas aops don't
vivid stone
no he did like how aosp did
but i am one who have doubt on that
ki how did is it even possible even with arranging
whole acorn
oh.
vivid stone
yes
whole acorn
ok.
vivid stone
i got it man
what you explain
that we can treat the
numbers as set
oh wait
i got even better explaination ig
whole acorn
ok
vivid stone
so
the thing is
that
even thought the arrganmetns are diff
(plz ignore my spells)
but at the end it is doin the same thing
like opening the lock
like if {1,2}
{2,1}
either we press {1,2} or {2,1}
we are goin to get same result
the opening of lock
what you think is that right or pure BS
whole acorn
if it works for you, it works ig
vivid stone
yeah ig
this explaination making sence for me
atleast
can't belive i just spend 23 min in single ques
😂
but never mind it atleast improve my thought process
thanks @whole acorn for da help
.close
safe radishBOT
whole acorn
youre welcome
whole acorn
can't belive i just spend 23 min in single ques
pfft... rookie number
i've spent 2 days on one question 
i gave up tho
safe radishBOT
Available help channel!
trim perch
how can ifind the Quadratic equation here?
safe radishBOT
how can ifind the Quadratic equation here?
tall crow
x^2- ( Sum of roots )x + ( Products of Roots ) = 0
stray socket
Well and then you need to consider the vertex too
upbeat ridge
Have you heard of vertex form
tall crow
Well and then you need to consider the vertex too
?
stray socket
It's better if you do this: if you have two roots, $a$ and $b$, you can do:
$$y = k(x-a)(x-b)$$
Since you have the vertex you can solve for k
flat frigateBOT
Umbraleviathan
upbeat ridge
Why is it red ☠️
stray socket
Because I'm special
upbeat ridge
That's scary
tall crow
Blud got the limited edition LaTeX 😭🙏
trim perch
uhhhhh
stray socket
I got the free latex version no virus Punjabi edition 🙂
trim perch
im pretty sure i know the vertex thing
stray socket
**Umbraleviathan**
But use this
You don't need vertex form
The diagram gives you the values of a and b
trim perch
whats the K
stray socket
And you know the vertex
That's the leading coefficient
You need to solve for that
Substitute the vertex in for x and y
And then you can solve for k
As a linear system
desert pasture
The equation of a general parabola is $ax^2+bx+c,$ substitute the 3 point syou have have into that ans solve
flat frigateBOT
physicsrocks
stray socket
Close the channel if you're done
trim perch
how
desert pasture
type " . close "without the space
trim perch
.close
safe radishBOT
safe radishBOT
Available help channel!
cold aurora
Hello
tall crow
cold aurora
I'm writing. Lol
cold aurora
I need to prove this and i would like a hint.
My progress is, thus far, well, none. I haven't seem to gotten anywhere.
To prove: GCD(m, n) = GCD(m+n, m-n)
Btw, i do have this. GCD(m, n) = GCD(m, n+am) where ${a \in \mathbb{Z}}$.
flat frigateBOT
Enemagneto
quasi bison
I need to prove this and i would like a hint.
My progress is, thus far, well, n...
hold up is that even true tho
do you mean prove or do you mean determine truth then prove or disprove as appropriate
cold aurora
My professor gave it in his tutorial so i think so.
cold aurora
do you mean prove or do you mean *determine truth then prove or disprove as appr...
Prove
cold aurora
It is?
quasi bison
just gave you a counterexample
hard crest
not to mention what happens when n = m
quasi bison
cold aurora
Sorry for a million times. 🤦♂️
quasi bison
least you owned up to it.
that already elevates you above the commoners who don't. just post the full thing this time.
cold aurora
Thank you. I would have wasted so many people's time. 🤦♂️
Let me write the full question now.
Show that if m and n are integers such that $(m,n) =1$, then (m+n, m-n) = 1 or 2.
flat frigateBOT
Enemagneto
quasi bison
ah.
cold aurora
Showing 2 is easy, i think. Case where m and n are both odd.
I'm mainly stuck at GCD being 1 part.
peak estuary
what other factors should it get. if sum or difference isnt even, then 2 cannot be a common factor
wraith prism
The legend Enemagneto
How long do you know him?
I guess he is an old user with a new account
cold aurora
what other factors should it get. if sum or difference isnt even, then 2 cannot ...
Umm... I don't really see how to move ahead with that. If they are not even then, well, how can i conclude that they aren't both divisible by any number bigger than 2?
peak estuary
let d be a common factor of m+n and m-n
peak estuary
happens
cold aurora
So, let me just write once and you can confirm that.
Let (m+n, m-n) be d.
So, d| (m+n) and d(m-n), therefore d| (m+n) + (m-n), i.e. d|2m.
Upon subtraction, d|2n.
So, d divides both 2m and 2n.
Case 1: if d doesn't divide 2, then d divides m and n, but no number other than 1 divides both m and n, and 1 divides 2. Therefore, no such d exist which doesn't divide 2.
Basically, this case is not possible.
Case 2: if d divides 2, then d is either 2 or 1.
Is that it?
It seems a little weird. Lol
@peak estuary Can you have a look? I'm sorry if i shouldn't have tagged.
cold aurora
Hmm. Do you have something in mind to improve upon this? Or, do you mean to refer to another approach entirely which is cleaner?
peak estuary
not right now
the approach is correct
just the argument with d not being able to not divide 2 is a bit weird. there might be a cleaner way to say it but I am not sure right now what would be better
cold aurora
Maybe i can do it this way.
Start with the claim that if (m, n) = 1, then GCD(m+n, m-n) = d is such that d divides 2.
Then i can prove in the contradiction setting that it is not possible that d doesn't divide 2.
Okay, but it's almost the same thing.
Well, this will have to do.
Thank you, everyone.
.close
novel magnet
safe radishBOT
worthy hemlock
Because $9.5 \mu g = 9.5 \times 10^{-6}$
flat frigateBOT
dldh06
novel magnet
Not nanogram
so like this?
novel magnet
also you are asked for an answer in **nano**coulombs
hmm
worthy hemlock
so like this?
Yes
novel magnet
also you are asked for an answer in **nano**coulombs
that answer is in coulombs right now right?
worthy hemlock
No that answer is 9.31 x 10^-12 picocoulombs
worthy hemlock
No
novel magnet
:/
worthy hemlock
How did you even get that
worthy hemlock
so like this?
When you typed this in
novel magnet
When you typed this in
that answer is in picocolumbs?
worthy hemlock
I had it mixed up, this is in coulombs
worthy hemlock
so would the final answer be 0.31*10^-3
But not sure how you are getting this
worthy hemlock
so like this?
From this
novel magnet
That needs to be in nanocoulombs
so 9.31 nc?
worthy hemlock
Yes
safe radishBOT
@novel magnet Has your question been resolved?
jolly bridge
unable to find the pattern here
safe radishBOT
placid oak
just ask your question in the old channel
or close the old channel and open a new one like this
jolly bridge
.reopen
safe radishBOT
✅
jolly bridge
unable to find the pattern here
i was unable to simplify this
these are the options
what should be the aproach
plucky elk
Did you try trig identities
plucky elk
,tex .double angle
flat frigateBOT
riemann
plucky elk
but there are a lot more here you could try as well
https://en.m.wikipedia.org/wiki/List_of_trigonometric_identities
safe radishBOT
@jolly bridge Has your question been resolved?
odd nest
In dimensions like below, is the first number width or length? I’ve also seen 100x120x50 numbers.Can someone tell me what’s the format?
safe radishBOT
In dimensions like below, is the first number width or length? I’ve also seen 10...
brave wolf
I think it's length x width, but I'm not sure
karmic hedge
Usually it’s length width height
lean otter
depends by the context , i think
safe radishBOT
@odd nest Has your question been resolved?
ember mural
I'm looking to develop a function to handle numerical values within specific conditions. The function should adhere to the following guidelines:
- The function should be defined over the domain [0, +infinity].
- The function should have a range within [0, 10].
- There are three known points on the function:
- Point A: Coordinates (low_threshold, 2.5)
- Point B: Coordinates (average_threshold, 5)
- Point C: Coordinates (high_threshold, 7.5)
- The function should be monotonically increasing, meaning it should only rise as the input value increases.
In the picture, you can see what I've tried doing but it doesn't quite meet all of the requirements, but I hope you get the idea.
What approach can I use to create such a function that meets these requirements?
safe radishBOT
I'm looking to develop a function to handle numerical values within specific con...
vast obsidian
I'm looking to develop a function to handle numerical values within specific con...
You want a strictly increasing function with the limit 10 that goes through three points (a,2.5),(b,5),(c,7.5)?
quasi bison
how exactly do you want the function to behave between the anchor points, besides monotony?
perhaps putting the function in some context might enlighten us.
ember mural
so you want f(0) = 0 and f(+infty) = 10?
Exactly
ember mural
perhaps putting the function in some context might enlighten us.
I am using the function for a scenario probability model
ember mural
how exactly do you want the function to behave *between* the anchor points, besi...
A straight line would work
ember mural
Sure
Just a second
The function I'm working on is a critical component of my scenario probability program. This program is designed to predict the likelihood of different scenarios occurring based on various parameters. These parameters can be of different types, such as boolean, scale, or numerical values, and they all contribute to the overall probability calculation.
The numerical values in the context of the program represent factors that can influence the likelihood of a scenario. However, not all numerical values have the same impact on the outcome. That's where the function comes in.
The function I'm developing acts as a way to adjust the influence of these numerical values on the calculated probability. It's designed to ensure that the impact of these values is consistent, meaningful, and aligned with the context of the scenario. This is achieved through the use of contextual scaling, where the function takes into account the relationship between the value and the provided thresholds: low_threshold, average_threshold, and high_threshold.
By using this function, I'm able to dynamically adjust the impact of each numerical value on the final probability calculation. This approach allows me to differentiate between scenarios where a certain value might have a larger or smaller impact on the outcome, depending on the provided thresholds and the specific context of the scenario.
In essence, this function adds a layer of sophistication to the program, making it more accurate and reflective of real-world situations. It ensures that numerical values are not treated in a one-size-fits-all manner but are rather considered in a way that aligns with their significance in the given scenario.
ember mural
yes
ember mural
but i read it and it explains what i need the function for
quasi bison
this is supremely unhelpful
ember mural
did you read it?
quasi bison
yes, and it all reads like water sloshing in a bucket
or maybe it is business executive speak that i, a mere mortal, cannot understand
but also like
i asked YOU to explain in YOUR words what YOU are using the function for in YOUR program... how could gpt possibly know of that?
it's a little insulting to be hit with gpt's form-sans-content output.
ember mural
sorry if you consider that insulting
but i just tried to make you understand what my program is about the best possible way
quasi bison
you've summarily failed to do so thus far.
white umbra
The function I'm working on is a critical component of my scenario probability p...
Please don't use GPT to post in this chat
This is a warning
ember mural
I'm sorry I didn't know
white umbra
It's okay, just please don't do it going forward
quasi bison
well i am still confused as to its purpose
like i could conjure something up, sure.
but i can't know if it's actually gonna work well
bc you are abstracting a lot of info away so there's isn't much to go on
ember mural
The function I'm working on is a critical component of my scenario probability p...
Are you sure you read this, i think it explains really well
yeah i represent the info in a kind of messed up way indeed
quasi bison
it's all wishy washy abstract bullshit clarifies exactly zero things for me
are you willing to answer some concrete questions for me, WITHOUT gpt
ember mural
yes i am
quasi bison
ok
your function has domain [0,+infty] and range [0,10].
is the following statement true or false?
Your function gets its input value from somewhere else in the program.
ember mural
the statement is true
quasi bison
ok
where exactly does the function get its inputs from, and what do said inputs represent?
ember mural
where exactly does the function get its inputs from, and what do said inputs rep...
the inputs are x, low_threshold, average_threshold and high_threshold.
x is the numerical value given by the user to describe a parameter that affects the scenario probability.
the thresholds help on the Contextual Scaling of the numerical values; they define the range within which the numerical value's impact on the prediction will be scaled. I can give you an example ive already written if you want.
quasi bison
...
yes an example would be nice
cause im still utterly confused
it feels like you left my question unanswered and i still kind of suspect you're gpting this
so hngh
ember mural
yes an example would be nice
How much the numerical value will change the prediction really depends on the parameter. for example, in a scenario about how much I disturb my neighbor, a value of 10 for the numerical parameter "decibel of the music" will make the probability of me disturbing him low. however in a scenario about how possible is it for my wife to break up with me, a value of 10 for the numerical parameter "times she cheated on me" would be too much and should affect the probability a lot more than the value 10 would do in the other scenario about me disturbing my neighbor.
what I thought I could do is a Contextual Scaling for numerical values.
ember mural
you still didn't understand?
quasi bison
indeed i still do not.
and my desire to go to sleep is now stronger than my desire to extract any understanding from the watery pap you've been passing off as explanations.
ember mural
It's okay
Have a good night!
Hopefully somebody else will be willing to help me
@white umbra Sorry for the ping but in this case, do I have to re-create the help channel and ask the question again or not?
white umbra
<@531535537362829315> Sorry for the ping but in this case, do I have to re-creat...
No you can keep this open; you may want to provide a brief summary of your original question though
Hope you find an answer :)
ember mural
Yeah that would be a good idea, thank you
I'm looking to develop a function to handle numerical values within specific conditions. The function should adhere to the following guidelines:
- The function should be defined over the domain [0, +infinity].
- The function should have a range within [0, 10].
- There are three known points on the function:
- Point A: Coordinates (low_threshold, 2.5)
- Point B: Coordinates (average_threshold, 5)
- Point C: Coordinates (high_threshold, 7.5)
- The function should be monotonically increasing, meaning it should only rise as the input value increases.
In the picture below, you can see what I've tried doing but it doesn't quite meet all of the requirements, but I hope you get the idea.
What approach can I use to create such a function that meets these requirements?https://media.discordapp.net/attachments/903481106819612714/1144727820694736988/image.png?width=1368&height=655
More information if interested:
The function I'm working on is a critical component of my scenario probability program.
The inputs of the function are x, low_threshold, average_threshold and high_threshold.
x is the numerical value given by the user to describe a parameter that affects the scenario probability.
The thresholds help in the contextual scaling of the numerical values; they define the range within which the numerical value's impact on the prediction will be scaled.
How much the numerical value changes the prediction depends on the parameter. For example, in a scenario about how much I disturb my neighbor, a value of 10 for the numerical parameter "decibels of the music" will make the probability of me disturbing him low. However in a scenario about how possible is it for my wife to break up with me, a value of 10 for the numerical parameter "times I cheated on her" would be too much and should affect the probability a lot more than the value 10 would do in the other scenario about me disturbing my neighbor.
So I thoughtof adding contextual scaling for numerical values.
safe radishBOT
@ember mural Has your question been resolved?
safe radishBOT
@ember mural Has your question been resolved?
safe radishBOT
@ember mural Has your question been resolved?
placid oak
if you're just looking for a monotonic function that passes through those three points, you can just linearly interpolate between each of the pairs, then slap on whatever monotonic function with a horizontal asymptote you want on the end
here's a really crap demo
https://www.desmos.com/calculator/cfptgmbarq
safe radishBOT
safe radishBOT
Available help channel!
reef quartz
can someone help me with this?
safe radishBOT
can someone help me with this?
reef quartz
both questions if possible
wait i got the first question
can i have help with question B
nvm i got it
.close
pulsar pecan
Hi
hasty wagon
what have you tried?
pulsar pecan
nothing yet, but i can see that there is 2^1, 2^2, 2^4, 2^5
hasty wagon
nothing yet, but i can see that there is 2^1, 2^2, 2^4, 2^5
yea
on first thought i have 2 methods to do it
- factorize
- differentiate
which one would you like?
pulsar pecan
factorization is probably the easiest
pulsar pecan
i guess starting with 2 is the easiest?
hasty wagon
so, first, you can see all the coeff are of powers of 2
yea
wait...
you wanna do long division?
pulsar pecan
i think it can be achieved with just factorization
hasty wagon
so we can first do
2(z⁴-2z³-8z+16)
now we can group into 2 terms by 2terms
2( (z⁴-2z³) - (8z-16) )
all good till here?
pulsar pecan
sec lemme write it down
hasty wagon
next step would be your turn.
pulsar pecan
hmm not sure how exactly
feral linden
You can show that by showing f(2)=0=f’(2) and f”(2) doesn’t equal 0
‘ means derivative
So you don’t have to factor anything
hasty wagon
that is
try factorizing
z⁴-2z³
and
8z-16
hasty wagon
You can show that by showing f(2)=0=f’(2) and f”(2) doesn’t equal 0
please read above convo
pulsar pecan
that is
try factorizing
z⁴-2z³
and
8z-16
z^3(z-2)
8(z-2)
oh nice, now we got the root
hasty wagon
2( (z⁴-2z³) - (8z-16) )
good, now plug back into this
pulsar pecan
right so we got:
2(z^3(z-2)-8(z-2))
hasty wagon
yes
feral linden
You can show that by showing f(2)=0=f’(2) and f”(2) doesn’t equal 0
a is multiplicity r-root of a polynomial f is equivalent to f(a),f’(a),…,f^(r-1)(a)=0 and f^(r)(a) doesn’t equal 0
hasty wagon
right so we got:
2(z^3(z-2)-8(z-2))
next, we can factor out (z-2)
then we have
2 (z-2) (?????????)
hasty wagon
yes
hasty wagon
how do we factor out z-2
I'll have to explain
let's treat a=z-2
then it will become
2( az³-8a )
then we can factor out
2a(z³-8)
pulsar pecan
right okay
hasty wagon
how do we factor out z-2
all good till here?
pulsar pecan
ye
pulsar pecan
yeah
pulsar pecan
2(z-2)(z-2)^3
pulsar pecan
oh
hasty wagon
if you don't know the identity for
z³-2³, you can try search online
pulsar pecan
not completely sure what you mean with identity
pulsar pecan
so z^3-2^3 = (z-3)(z+3)(z+3)
hasty wagon
correct!
hasty wagon
nah
hasty wagon
so we have 2(z-2)(z-2)(z^2+2z+2^2)
this is nearly the answer
we can stop factorizing here
and we group them neatly and get
2(z-2)²(z²+2z+4)
do you see the answer?
pulsar pecan
well, it shows why 2 is a double root
and from what i can see, we can get more answers
if we put it = 0
hasty wagon
well, it shows why 2 is a double root
but that's enough isn't it
hasty wagon
yes
pulsar pecan
-1+-i*sqrt(12)/2
nnice
next one is to explain a bunch of terms. not exactly math, so i dont know if i should close it here?
hasty wagon
-1+-i*sqrt(12)/2
remember to simplify it
hasty wagon
Wait you want me to close it or not? xD
yes, you can close it
pulsar pecan
.close
sterile juniper
Help please
safe radishBOT
Help please
sterile juniper
split fulcrum
(How do you write so neat)
jaunty owl
he must not be a doctor
split fulcrum
defo
lean otter
What’s the answer slmeone help
Handwriting font too small
worthy hemlock
What’s the answer slmeone help
First we're not here to give out answers
safe radishBOT
@sterile juniper Has your question been resolved?
obtuse folio
I need help, I have a slider in Geogebra a from -5 to 5,
I know how I can make a second variable that goes from 0 to 1 and is dependent on the slider a
But I would like to add a phase, so that when I turn the slider a on my variable starts from let's say 0.2 goes up to 1 and then 0 and back to 0.2
safe radishBOT
I need help, I have a slider in Geogebra *a* from *-5* to *5*,
I know how I can ...
upbeat ridge
Do you have any visuals?
obtuse folio
well here is the way I made the slider a go from 0 to 1
hard crest
this will involve some sin wave i think
obtuse folio
But I would like to avoid using sine, plus isn't it possible to just adjust the starting point some way?
hard crest
you want it to go back and forth though don't you?
obtuse folio
Yes
hard crest
can you draw a sketch of what this new variable should be, for points of a from -5 to 5?
like it should go up and then back down... linearly? like absolute value kind of? when should it hit 1? when should it hit 0?
obtuse folio
Simply put I want a variable like the variable b in my image, but instead of starting the cycle that goes between 0 and 1 from 0 I would like it to start from 0.2
hard crest
that's actually a lot easier to see if you keep your b variable around and use that instead
$c = (1-0.2)b + 0.2$
flat frigateBOT
hayley!
obtuse folio
Can you please explain what you actually did
hard crest
this is called a linear interpolation
i wanted c = 0.2 when b = 0, and i wanted c = 1 when b = 1
obtuse folio
Hmmm doesn't this value go from .2 -> 1 and then back?
hard crest
it will only go from .2 -> 1 as a goes from -5 to 5
obtuse folio
would it be possible to make that this c variable starts at .2 goes to up 1 and then down to 0 and back to .2?
I would want it move between 0 and 1 just that it starts at a different value like .1, .2, .3 .......
hard crest
obtuse folio
yes up and down between 0 and 1 but with a different starting point
hard crest
again if you can draw some kind of sketch of what you're looking for that would be helpful
obtuse folio
ok I'll try
It's hard to explain, I would like the c variable to move along the same values like b but instead starting from a different value (the red dot represents starting value), I would like it to work the same way like a "phase" does in a sine curve, but alas it seems I can only achieve this by using a sine function.
hard crest
sine is pretty fundamental if you want any kind of rotational motion
you could probably do something with absolute value if you were okay with it being linear
but then it'll have a sharp point and sine just feels much more natural
obtuse folio
So this effects can't be achieved otherwise and will the movement be linear if I use sine?
hard crest
if you use sine it will be nice and smooth
obtuse folio
but I don't wanna use sine >:(, jokes aside is it even possible without sine because if it isn't I'll happily use sine
hard crest
you could use cosine instead 
safe radishBOT
@obtuse folio Has your question been resolved?
obtuse folio
you could use cosine instead <:s_troll:893955844054581299>
thank you so much
.close
obtuse folio
Ok I have a new question
safe radishBOT
Ok I have a new question
obtuse folio
I have a function that represents the movement of a caroussel. The function goes as such: $67.5\sin (\frac{\pi}{15}x+\frac{3\pi}{2}) + 69.5$
hard crest
i feel like there are some parentheses missing near sin 
hard crest
of course
obtuse folio
The question is how long the caroussel will be above 100 meters at a time
hard crest
100 meter high carousel 
hard crest
yes... but i have more suspicions about your equation
obtuse folio
x represents time in minutes by the way
obtuse folio
yes... but i have more suspicions about your equation
what
hard crest
why would you not just add 67.5 and 69.5 right away
obtuse folio
öhhhhh
flat frigateBOT
N1x1T4
obtuse folio
typo error, it should have been a multiplication between 67.5 and the sine
hard crest
ah yes i misread that 
obtuse folio
anyways can you help me solve the problem
hard crest
yes solving where the expression = 100m is a good idea
obtuse folio
ok so the equation should look like this $67.5\sin\frac{\pi}{15}+\frac{3\pi}{2}+69.5=100$
flat frigateBOT
N1x1T4
obtuse folio
Ok heres one try to calculate it
Is this wrong, plus I should also take into consideration the supplement of sine?
hard crest
you do need to consider the supplementary solution yes
as well as the 2pi period
,calc asin(30.5/67.5)
flat frigateBOT
Result:
0.46884010106234
This is kind of off topic but can I put the 2pi inside the sine function
hard crest
oh you did handle the period mb i didn't notice that
but yes you need the supplement as well
obtuse folio
like this $67.5 \sin (\frac{\pi}{15}x+\frac{3\pi}{2}+2\pi n)$
flat frigateBOT
N1x1T4
hard crest
the 2 pi n stuff
obtuse folio
yes yes
obtuse folio
**N1x1T4**
but is this mathematically legal to do?
hard crest
**N1x1T4**
yes i think that makes sense