What is "the problem"?
#help-0
analog basalt
rough orbit
Is the scanned doc
analog basalt
Yes, but what are you asked to do?
analog basalt
Oh
rough orbit
I wasnt paying attention in class so if you could do the porblem while explaining that would be help ful 😅
analog basalt
I'm rusty on geometry, I don't think I can solve this right away
rough orbit
Its all good just please @ me when somebody solves this
tacit arch
Its all good just please @ me when somebody solves this
No one's gonna solve your whole problem
Ask a more specific question
lone heartBOT
@rough orbit Has your question been resolved?
terse oak
n(n+1)/k^n
lone heartBOT
n(n+1)/k^n
wary stream
<@&286206848099549185>
!15m
lone heartBOT
<@&286206848099549185>
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.
@terse oak Has your question been resolved?
lone heartBOT
@terse oak Has your question been resolved?
real gazelle
n(n+1)/k^n
are you trying to find the value or prove whether it converges/diverges
indigo heart
What's the formula for summation of even numbers
lone heartBOT
What's the formula for summation of even numbers
indigo heart
I couldn't find anything on Google
worn fox
double whatever the summation is if you halved everything
indigo heart
1+2+3+4+5+6
6*(6+1)/2
but how do i get 2+4+6
worn fox
2(1+2+3)
indigo heart
so i take the result of 6*(6+1)/2 and double it?
or should i like half N at the start
i am confused
keen pasture
1+2+3+...+n = n(n+1)/2
indigo heart
that's true, but i want it to be the even numbers only
keen pasture
2+4+6+..+2n = 2(1+2+3+...n) = 2n(n+1)/2 = n(n+1)
indigo heart
for 6, it'd be 2+4+6 = 12
n(n+1)
6(6+1)=42
sorry if i am misunderstanding
keen pasture
2+4+6 = 2(1+2+3)
indigo heart
i am coding, so
if a user inputs 6,
i'd half it, then take the summation of that
then multiply it by two?
example:
6
6/2=3
summation of 3 = 1+2+3
*2
= 12
keen pasture
Take the half of the end number 2n in your case 6
indigo heart
Yes
real gazelle
you can also find an explicit formula for it (it is an arithmetic series)
but tobias's way is also nice and simple :)
keen pasture
2+4+6+..+2n = 2(1+2+3+...n) = 2n(n+1)/2 = n(n+1)
You mean this?
indigo heart
yeah i basically just did that
and if a user entered an odd number, i'd remove 1 from it
keen pasture
Sorry, I've no idea about coding
indigo heart
well it's basically the same but i don't know exactly what n will be
how do i close the help channel?
keen pasture
and if a user entered an odd number, i'd remove 1 from it
With .close
indigo heart
.close
narrow cape
Probability;
Roll a 20 sided die, if it's not a 20 reroll it once.
How do I get the Probability for the final being 20 or not-20?
prime badge
you add up 2 cases you want to add up
narrow cape
Follow up would be scaling;
Roll a 20 sided die, if it's not 18 or higher, reroll it up to 3 total times.
prime badge
you have two ways to get that 20, immediately, or after a fail
you're really just looking for the chance to fail three times in that case
scaling complete
ocean sealBOT
Result:
2.0354162426216e-4
So for first, is it
5% 20
95% reroll, then 5% 20
So total 20 is 5%+(5%×95%)?
ocean sealBOT
Result:
0.0975
,calc 1 - 0.95^2
ocean sealBOT
Result:
0.0975
,calc 1-(17/20)(17/20)(17/20)
ocean sealBOT
Result:
0.385875
fail three times is the only way to not roll 18+
narrow cape
Ok so for 2nd
15% 18+
85%reroll, then 15% 18+
85%of 85% to reroll again
So 15% for 18+ after 1 roll (3/20)
27.75% for 18+ after reroll (15%+(85×15)
38.58% for 18+ after 2 rerolls(27.75+(85%×85%×15%)
prime badge
right
narrow cape
Is there a better way than just doing each equation one by one?
narrow cape
I mean I could make a spreadsheet and turn that into a graph for each variable
prime badge
yeah
narrow cape
No I mean the 38.58 is one equation
narrow cape
What about
Roll d20, if not 20 reroll, then if not 19 or more (20-1) reroll, then if not 18 or more reroll.... then if not 2 or more reroll
prime badge
that's bad yeah
narrow cape
That's just 1/20×2/20×3/20....x19/20
prime badge
yeah that makes sense
prime badge
one minus
lone heartBOT
narrow cape
:)
lone heartBOT
Available help channel!
honest cliff
I have a really simple question that I'm too dumb to figure out, if I have a 0.06% of getting something everyday, How likely is it I get it after for example 30 days or 365 days?
prime badge
,calc 1 - (1 - 0.06)^365
ocean sealBOT
Result:
0.99999999984452
,calc 1 - (1 - 0.0006)^365
ocean sealBOT
Result:
0.19673107946895
20%
lone heartBOT
@honest cliff Has your question been resolved?
craggy summit
I'm trying to understand how the second-order formula
[
\forall P Py \land (\forall a \forall b Pb \land Parent(a, b) \rightarrow Pa) \rightarrow Px
]
expresses that $x$ is an ancestor of $y$. It's not very clear to me.
What is the scope of the first $\forall$? Is it
[
\begin{array}{l}
\forall P (Py) \land \boldsymbol(\forall a \forall b Pb \land Parent(a, b) \rightarrow Pa\boldsymbol) \rightarrow Px, \
\forall P \boldsymbol(Py \land (\forall a \forall b Pb \land Parent(a, b) \rightarrow Pa)\boldsymbol) \rightarrow Px, \text{or} \
\forall P \boldsymbol(Py \land (\forall a \forall b Pb \land Parent(a, b) \rightarrow Pa) \rightarrow Px\boldsymbol)
\end{array}
]
What about the scopes of the $\forall$'s in $\forall a \forall b Pb \land Parent(a, b) \rightarrow Pa$?
Also, can we switch $b$ and $a$ and say $\forall a \forall b Pa \land Parent(a, b) \rightarrow Pb$ to say that the set is closed under the parent relation?
ocean sealBOT
q5
lone heartBOT
@craggy summit Has your question been resolved?
lone heartBOT
@craggy summit Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
uneven cosmos
lone heartBOT
vernal thunder
First of all, you need to draw triangles with respective side lengths
Make sure it’s in the appropriate quadrants
uneven cosmos
First of all, you need to draw triangles with respective side lengths
first is -rt(51)
real gazelle
do you know the sum formulas
uneven cosmos
yeah
vernal thunder
first is -rt(51)
I don’t have my math equipment rn, so you might need to check it
uneven cosmos
or do you know how
I just wanted a walkthrough on this problem
havent done one like it before
uneven cosmos
so do you know how to figure out what cos x is
find the missing side yeah
real gazelle
cool
vernal thunder
so do you know how to figure out what cos x is
There are 2 ways, I gave one of them
real gazelle
so what is cos x?
real gazelle
how did you get -rt(51)?
real gazelle
what did you calculate in order to get the 51
uneven cosmos
what did you calculate in order to get the 51
26^2=24^2+x^2
real gazelle
like what did you plug into the calculator to give you 51?
oh okay
26^2 - 24^2 is 100
so I'm not sure where the 51 came from
real gazelle
maybe a typo yea
but yeah take the square root and then you get -10/26 as the cosine of x
that's right 👍
what about cos y?
uneven cosmos
58^2=-42^2+x^2
real gazelle
cos(x+y) = cos(x)cos(y) - sin(x)sin(y) right
just plug the values you have into this equation and you are good
real gazelle
40/58 is cos
yup that's right except for a thing, should it be positive or negative?
if it's QIII
uneven cosmos
neg
real gazelle
yup
uneven cosmos
yup
doesnt seem right
let me check my work
all im getting is cos(2920/29
and i cant use trig equations for my answer
uneven cosmos
> cos(100+ 20/29)
you shouldn't be doing anything resembling that
right I use the addition formula
thats what you said right
cos(x)cos(y) - sin(x)sin(y)
gray isle
what eric said
real gazelle
where did you get the 100
should be -10/26 like we said earlier, no?
otherwise it looks good
remember that cosine and sine are always between -1 and 1
lone heartBOT
Available help channel!
sharp moth
What is the highlighted portion referring to
lone heartBOT
What is the highlighted portion referring to
sharp moth
Is that like a coordinate plane
fluid basin
not really, no, it's a subregion of the domain over which the function is defined
for a function defined over the real numbers, it'll be some interval of the real number line
like 0 < x < 2, often written as (0,2)
that's what is meant by an "interval"
sharp moth
Ah okay that kind of bridges the gap between what I'm writing and what it means
fluid basin
any further questions i can help with?
lone heartBOT
@sharp moth Has your question been resolved?
last ether
Well it's for any function
Usually continuous, preferably continuous within the interval I
They're basically saying that if f(a) is the lowest output within a certain set of inputs, then f(a) is the absolute minimum.
On the other hand, if f(a) is the largest output within a certain set of inputs, then f(a) is the absolute maximum.
sharp moth
This says that a is any value within the interval, right?
last ether
Yup
Well
a is an element of set "I"
Which means that a could be any number within the set "I"
sharp moth
Which means that a could be any number within the set "I"
Thank you very much for your help, I really appreciate it.
lone heartBOT
Available help channel!
sharp moth
What does f(c) refer to?
lone heartBOT
What does f(c) refer to?
gilded citrus
the value of the function at x = c
karmic rapids
where I presume c is any value in the domain
remote heron
helo caarson
sharp moth
Hello!
sharp moth
the value of the function at x = c
This is going to seem like a very basic question, but wouldn't that just be x = x
If x = c then wouldn't it be c = c
How could x = c when x has to be x
gilded citrus
if f(x) is x^2 + 2x + 1, the expression "the value of the function at x = c" is f(c) = c^2 + 2c + 1
sharp moth
Thank you
lone heartBOT
Available help channel!
lapis night
lone heartBOT
lapis night
would really appreciate some help
strange hound
Do you have the triangle DEF plotted?
strange hound
Do you have graph paper?
lapis night
no
strange hound
Ok. Draw an xy coordinate plane on paper.
strange hound
Like this, right?
lapis night
yes
strange hound
Draw the point D
lapis night
ok
strange hound
Just curious? What is the x value of your point D?
lapis night
6
strange hound
Groovy. Do points E then F and draw the triangle.
lapis night
done
strange hound
That was question A. B says reflect over x = 2. Do you know reflections?
lapis night
a little not so sure
strange hound
Imagine a mirror at x=2. This is for every y. Draw a light line from x=2 all the way up and all the way down.
lapis night
this is where i am at. does that look right for now?
strange hound
Yep. Label your points though.
Just think about D. If x=2 was a mirror, where would the reflection look to be?
lapis night
(-6,2)?
strange hound
Close. The distance of D from the "mirror" is 4. (6-2)
The distance of the reflection will be the same. 2-4
lapis night
hm so would it be (-2,-2)
lapis night
wait
yes
thank you!!!!!
just one question
does that look right
cause the shapes look a little different
strange hound
The points aren't labeled. So I can't tell you which one is incorrect.
strange hound
I'll tell you the problem, you can tell me the answer, and good job on noticing the shapes weren't the same.
E is 6 away from x=2. E' is -6 away from x=0.
strange hound
(-)4
lapis night
like this?
strange hound
Bingo
lapis night
ah thank you very much
strange hound
I'll double check your last triangle, if you like.
strange hound
Oops. You reflected (correctly) DEF. Question C asked to reflect D'E'F.
lapis night
im confused
strange hound
Point E' has x=-4. If you reflect E' over x=-4, E' doesn't move and becomes E''.
lapis night
still confused
strange hound
First triangle: DEF, pronounced Dee Eee Eff was reflected to become a new triangle, a second triangle: D'E'F', Dee prime, Eee prime, Eff prime.
Question C want the reflection of D'E'F', the second triangle, to become D''E''F''.
lapis night
so they want me to reflect D"E"F" from D'E'F'?
strange hound
yup.
lapis night
So i just need to change question c>
strange hound
That's right. Erase the apostrophes from question c and your answer is correct.
strange hound
I'll do the x part of D.
b) Reflect D over x=2.
D = 6
Distance = 4
D' = 2 - 4
D' = -2
c) Reflect D' over x=-4
D' = -2
Distance = 2
D'' = -4 -2
D'' = -6
lapis night
so do i need to change both answers?
strange hound
B is correct. In C you reflected the wrong triangle.
Triangle 1, DEF. Triangle 2, D'E'F'. Triangle 3, D''E''F''.
In question C they want the reflection of D'E'F'.
strange hound
That's it. Well done.
strange hound
No worries. Use the names of the points, make an effort out loud and in your head to call it Dee... then Dee prime... then Dee double prime.
From Dee we reflected over x equals 2 to find Dee prime. Then we reflected Dee prime over x = -4 to find Dee double prime. The ex coordinate of Dee double prime is negative six.
I use this math all the time when I design video games.
lone heartBOT
@lapis night Has your question been resolved?
jolly notch
What ratio do i divide the line into? 1:2 for A right?
lone heartBOT
What ratio do i divide the line into? 1:2 for A right?
jolly notch
I know the formula is (mx2 + nx1)/m+n and vice versa for y
But im unclear about the ratio to use here
alpine sable
for the x cord divide it by three and multiply it by 2
for the y cord same things
use similar triangles
easier to visualize
jolly notch
for the x cord divide it by three and multiply it by 2
So youre saying that i should ((x1+x2)/3)*2?
jolly notch
no need to add x2
Cos its 0 right?
alpine sable
yes
jolly notch
.close
indigo cedar
how do you do 3 + 3 (1+1)?
lone heartBOT
how do you do 3 + 3 (1+1)?
karmic rapids
,, 3 + 3 \cdot (1 + 1)
ocean sealBOT
illuminator3
indigo cedar
woah, ok, but after i do parenthesis and get the answer, what do i do with the answer??
karmic rapids
what's 1+1
indigo cedar
2
ocean sealBOT
illuminator3
karmic rapids
what's $3 \cdot 2$
ocean sealBOT
illuminator3
indigo cedar
6
karmic rapids
,, 3 + 6
ocean sealBOT
illuminator3
indigo cedar
9
karmic rapids
,, = 9
ocean sealBOT
illuminator3
karmic rapids
so all in all $$ 3 + 3 \cdot (1 + 1) = 9 $$
ocean sealBOT
illuminator3
vale wigeon
no
karmic rapids
no
indigo cedar
bruh
vale wigeon
your bad spacing is what is making you confused
karmic rapids
parenthesis, then products, then additions
vale wigeon
it would have been better if you had written it as 10 + 11(2+5)
indigo cedar
idk what products are
vale wigeon
that way it would be clearer that the multiplication is to be done first
karmic rapids
,, 10 + 11 \cdot (2 + 5)
indigo cedar
legit same thing
ocean sealBOT
illuminator3
ocean sealBOT
illuminator3
vale wigeon
yes there is
indigo cedar
WHERE
karmic rapids
there is
vale wigeon
the 11 is being multiplied by the parenthetical
10 + 11*(2+5)
to write it out more explicitly
indigo cedar
im soooo confuseddd
karmic rapids
$$a(b) = ab = a \cdot b$$
ocean sealBOT
illuminator3
vale wigeon
when we put two things next to each other in algebra, it means multiplication
indigo cedar
thats stupid
karmic rapids
no?
vale wigeon
how old are you
vale wigeon
,w (((((14!)!)!)!)!)!
ocean sealBOT
Requested by Ann#0413
vale wigeon
LMFAO
indigo cedar
bruh
indigo cedar
lmaoo
karmic rapids
didn't you run out of puns for today already
vale wigeon
you are fourteen years old. that is plenty old enough to know what multiplication is and how it is written
vale wigeon
do you have paper
indigo cedar
no
vale wigeon
then go get some
indigo cedar
no
vale wigeon
and work it out step by step
indigo cedar
i got a pc
i can write it
type*
look ok
this is what i know
u do the () first
ok
u solve it
get the answer
but MY question is
WHERE do u put the answer of the ()
karmic rapids
in place of the ()
vale wigeon
wherever the () were in the expression...
indigo cedar
oh damnn
vale wigeon
just like with any other operation
indigo cedar
and then
karmic rapids
lol nice about me
karmic rapids
weird, horny, smart
vale wigeon
no
vale wigeon
calm down
vale wigeon
ok so you are trying to calculate 1 + 1*(1+1), yes?
indigo cedar
1 +1 (1+1)
vale wigeon
yes, that's what i wrote.
vale wigeon
- stands for multiplication.
vale wigeon
1(1+1) also means 1 multiplied by (1+1)
ember lava
💀 💀
indigo cedar
why
vale wigeon
that is how mathematical notation works
indigo cedar
1(1+1) isin't even valid]
vale wigeon
sure is.
indigo cedar
NO
languid bolt
it is
vale wigeon
and the grammar of mathematical notation does permit such a thing...
indigo cedar
wow
vale wigeon
no matter how much you want to deny it
vale wigeon
so your expression becomes 1 + 1*2
once you replace the stuff in the parentheses with the value you worked it out to be
indigo cedar
4
vale wigeon
no
indigo cedar
bro what
indigo cedar
waaat
karmic rapids
ong
indigo cedar
so 3
vale wigeon
you are fourteen, you are plenty old enough to know the order of operations from school
indigo cedar
i dont listen to school
vale wigeon
ah.
gilded citrus
troll detector is off the charts
indigo cedar
IS IT 3?
vale wigeon
WHY ARE YOU YELLING
indigo cedar
UR NOT ANSWERING ME
vale wigeon
SURE, IT IS 3, BUT THERE'S NO NEED TO ALLCAPS
karmic rapids
i dont listen to school
YOU DON'T NEED TO LISTEN TO SCHOOL TO KNOW THAT
languid bolt
ITS NOT 4
karmic rapids
how in the world did you get 4
languid bolt
YES ITS 10
indigo cedar
not 4 as in the answer
indigo cedar
YES ITS 10
ok cool
vale wigeon
how in the world did you get 4
i think what they meant is "2+2=4" but they never listened to school so they didn't know how to properly format intermediate steps in their work
indigo cedar
im smart again
vale wigeon
shit happens
indigo cedar
i think what they meant is "2+2=4" but they never listened to school so they did...
yes
vale wigeon
sometimes you get teenage contrarians
indigo cedar
xd
karmic rapids
what is a contrarian
vale wigeon
who don't like clear communication and think it is cringe
indigo cedar
im just tryna be fast ok
karmic rapids
slay girly
indigo cedar
anyway
vale wigeon
vale wigeon
im just tryna be fast ok
math is not a race.
indigo cedar
math is not a race.
whatever bro
vale wigeon
please don't call me bro.
indigo cedar
ok dude
karmic rapids
LMAO
vale wigeon
please don't call me that either.
vale wigeon
i'm not a boy you dipshit
indigo cedar
Ok girly
vale wigeon
...
karmic pond
I need someone to check my work for a calculus worksheet, Im unsure whether it is correct or not. I tried sending a image but it wont let me
karmic rapids
that's not an image
karmic pond
fianlly it worked
karmic rapids
send it as png or jpg
karmic pond
oh no wonder sorry ill screenshot it
This is all i have gotten so far, do you see any mistakes?
i believe its wrong
@karmic rapids are you still there lol
karmic rapids
yes but you asked a bad question
karmic pond
oh my apologizes
karmic pond
oh my apologizes im new to this
karmic pond
How may I find F(0) for question 1?
karmic rapids
you're being given the function equation for each line part
use the linearity of the integral operator and do piecewise integration
ohh
you mean f(0) or F(0)
@karmic pond ?
karmic pond
f(0)
ocean sealBOT
illuminator3
karmic rapids
**illuminator3**
without all the info from the exercise you're solving, what is this equal to
like without even knowing what f(x) is
karmic pond
0?
ocean sealBOT
illuminator3
karmic rapids
and you have the integral you're trying to solve
so what's $$\int \limits_0^0 g(t)dt$$
ocean sealBOT
illuminator3
karmic pond
0
karmic rapids
yes
karmic pond
ohhh
tyty @karmic rapids
I underestimated this question and assumed there was no answer for it. ty for clearing that up
Did i find all the critical points or am I missing any for question 2?
karmic rapids
yes but idk what critical points are lol
karmic pond
lmao its fine
karmic rapids
you gotta wait for someone else
karmic pond
.close
lone heartBOT
lone heartBOT
Available help channel!
covert cairn
lone heartBOT
analog basalt
What do you know of $[\sqrt{x}]$ if (a) $1 \leq x < 4$ or (b) $25 \leq x < 36$?
covert cairn
Can u pls elaborate??
analog basalt
Woops I forgot a thing, let me rewrite it
ocean sealBOT
Yuese
analog basalt
Just to give an example: what is $[\sqrt{3}]$?
ocean sealBOT
Yuese
analog basalt
Exactly
You actually don't even need to calculate the value for this, just because we know that $[\sqrt{1}] = [1] = 1$ and $[\sqrt{4}] = [2] = 2$, we know that $[\sqrt{x}] = 1$ if $1 \leq x < 4$ because in that case $1 \leq \sqrt{x} < 2$
ocean sealBOT
Yuese
covert cairn
Smth like this??
analog basalt
Yes great!
Now we only need to find out exactly how many we have of each term, and then we can calculate the sum
covert cairn
Now we only need to find out exactly how many we have of each term, and then we ...
Yeah yeah
analog basalt
So we now know that every for $x$ with $n^2 \leq x < (n+1)^2$ it holds that $[\sqrt{x}] = n$
ocean sealBOT
Yuese
covert cairn
Yeah
analog basalt
And because $x$ is an integer, we know that there for every $n$ there are exactly $(n+1)^2 - n^2$ of those
ocean sealBOT
Yuese
analog basalt
For example there will be $3$ numbers giving $1$, $5$ numbers giving $2$, etc.
ocean sealBOT
Yuese
analog basalt
You are actually computing the sum $$\sum_{n=1}^{44} \left( (n+1)^2 - n^2 \right) n$$
ocean sealBOT
Yuese
analog basalt
This is true but how did u get that?
We just "count" how many numbers are greater or equal to $n^2$ but smaller then $(n+1)^2$, and this is just the same as subtracting the lower bound from the upper bound, and thus $(n+1)^2 - n^2$ (this can actually be simplified to $(2n+1)$)
ocean sealBOT
Yuese
analog basalt
This means that our answer will be $$\sum_{n=1}^{44} n(2n+1) = \sum_{n=1}^{44} 2n^2 + n$$, there exist formulae to calculate such sums or you can use a calculator
ocean sealBOT
Yuese
covert cairn
Sir I am getting confused
lone heartBOT
@covert cairn Has your question been resolved?
covert cairn
<@&286206848099549185>
alpine sable
firstly there are 2n+1 numbers x such that $n^2 <= x < (n+1)^2$ ([x] = n)
ocean sealBOT
Jester
alpine sable
since 2025 = 45^2
we count how many numbers between the squares and multiply them by their floors
1->2 would be 1 * (2 * 1 + 1)
alpine sable
I have proceeded
covert cairn
How?
alpine sable
covert cairn
How did u get n^2+n
sonic prism
lone heartBOT
sonic prism
uh i got one of the solutions which is -1 <= x <= 5
how do i obtain the other solution
nvm
.close
zealous wraith
Really easy question but i cant remember how to do this
lone heartBOT
Really easy question but i cant remember how to do this
zealous wraith
raven dagger
Write √x as x^1/2
Then see what rules of indices you can apply
zealous wraith
ive got x^1/2(1/3x^2)
raven dagger
What happens to input of exponents when the outputs are dividing?
lone heartBOT
@zealous wraith Has your question been resolved?
sonic egret
What is the definition of a group $G$ generated by a set $S$ \ $G = \langle S \rangle$ \ ?
ocean sealBOT
Mr.Brawler
pliant dune
there are equivalent definitions but one way to think of it is that it's the smallest group containing S
pliant dune
if you want to calculate the subgroup a set generates then it's the set of all finite products of that set S
in this case all finite additions might be better wording
pliant dune
like ideals in rings?
sonic egret
yes
pliant dune
it's similar in that it's the smallest ideal that contains S, but now for S a subset of a ring R, then <S> is the set of all finite sums of products between elements of S and R
that last bit is kind of a soup of words
sonic egret
ok cool
got it
basically
$(a,b) = {a,a^2,...,b,b^2,...ab,ab^2,ababa^2..., ab+b^2+a^{192}+ab^4a}$
pliant dune
it's similar in that it's the smallest ideal that contains S, but now for S a su...
$ \langle S \rangle = \{r_1s_1 + r_2s_2 + ... + r_ns_n | n \in \mathbb{N}, r_i \in R, s_i \in S\}$
ocean sealBOT
Mr.Brawler
pliant dune
might be missing some elements and depending on the ring there might be repeats but all of those should be in the ideal
lone heartBOT
sonic egret
$ \langle S \rangle = {r_1s_1 + r_2s_2 + ... + r_ns_n | n \in \mathbb{N}, r_i \in R, s_i \in S}$
just checking
pliant dune
$ \langle S \rangle = \\{r_1s_1 + r_2s_2 + ... + r_ns_n | n \in \mathbb{N}, r_i ...
idk why the bot doesn't like it
sonic egret
ok nice
lone heartBOT
Available help channel!
sonic egret
r_i can be repeated right?
lone heartBOT
r_i can be repeated right?
pliant dune
Yes
pliant dune
like is s_i * s_j in <S> ?
sonic egret
yes
pliant dune
yes, you can get it from this definition since S is a subset of R
so r_i can be from S
quiet sinew
how do i find the arithmetic sequence of 2-6+10-14+18....
i tried using the basic formula a+(n-1)b, which obviously didn't work. i also tried using the an²+bn+c formula but it also didnt work.
languid bolt
isnt this a geometric sequence?
quiet sinew
i dont even know
languid bolt
do you know what a geometric sequence is?
languid bolt
wait...
quiet sinew
i dont think it will work
languid bolt
hmm
quiet sinew
hmm i just realized somethint
languid bolt
difference is 4 if it's all positive
wanton turtle
Two different APs?
quiet sinew
yes but the question is different
wanton turtle
Separate the positive and negative terms and you get two separate APs ye?
quiet sinew
ohhh lemme try
quiet sinew
tbh i dont need the direct answer, i need the step
sooooo
2 + 10 + 18.....
-6 - 14 -22
what should i do with this?
whats ap
sorry
languid bolt
arithemetic progression
quiet sinew
english is my 2nd lang
ocean sealBOT
quiet sinew
the first one is
2+(n-1)8
the second is
-6 +(n-1)-8
is that correct
oh sn
i thought ap formula is a+(n-1)b
oh
ocean sealBOT
quiet sinew
the first one is
2+(n-1)8
the second is
-6 +(n-1)-8
so this one then
ahhh i see
n/2(2a+(n-1)b)
i need the ap formula
or as i call it un
but i need for it to be 2-6+10-14...
yes
yep
uhmmm no
but
uhhh i have no idea
OH I GET IT
(-1)^n
i see
-sin(n-1/2)π
thanks for the help
.close
plucky geyser
the derivative of sx and this comes from triangle similarity rule
plucky geyser
@tawny merlin
I think it's correct
derivative of sx with respect to t
I found sx from triangle similarty
I found the relationship between s and x to find the rate of s
isn't clear
the entire problem
yeah
am I correct
thank you Keb 🫂
.close
eager jackal
how do i find the phase shift of the function y=sin6(x-30)+1
lone heartBOT
how do i find the phase shift of the function y=sin6(x-30)+1
@eager jackal Has your question been resolved?
Available help channel!
lone heartBOT
How would you prove (a * b)^n =a^n * b^n if a * b=b * a
alpine sable
a^n is defined as a * a * a ..... a n times
pliant dune
(a*b)^n = (ab)(ab)...(ab) [n times]
= abababab...ab [with n a's and n b's]
then since ab=ba we can move all the a's to the left and all the b's to the right to get
= aaa....a * bbb...b
= a^n * b^n
alpine sable
(a\*b)^n = (ab)(ab)...(ab) [n times]
= abababab...ab [with n a's and n b's]
the...
hmmm all the a's to the left
it may be true that u can do that
pliant dune
basically whenever you see an 'a' to the right of a 'b' replace the 'ba' you see with 'ab' and repeat until you don't see an 'a' to the right of a 'b'
wheat zenith
maybe nicer to do it with induction
alpine sable
ohhh
alpine sable
basically whenever you see an 'a' to the right of a 'b' replace the 'ba' you see...
this is actually clever
wheat zenith
bc the base case is trivial and each step u just gotta switch the last two
alpine sable
then the number of a's and b's stay consistent after each operation
pliant dune
maybe nicer to do it with induction
I'm not sure what the specifics of induction would be but if you want to show it formally it's probably a good idea
alpine sable
basically whenever you see an 'a' to the right of a 'b' replace the 'ba' you see...
but how do we know that this operation ends?
wheat zenith
what tom said is good intuition tho at least; ab=ba just means a and b commute so you can rearrange them and (ab)^n just gives you a string of n as and n bs
wheat zenith
but how do we know that this operation ends?
bc its finite string
alpine sable
yeah but that doesnt mean it ends
wheat zenith
well if u want to do it rigorously you need induction
lone heartBOT
empty plover
is it possible tho we don't know n
empty plover
do you know how to find an equivalent to S(n) ?
no no i dont
marsh rapids
TCSI
empty plover
seems like something magical tbh
marsh rapids
then you sum over all p
empty plover
youre talking about integral series comparaison?
marsh rapids
Théorème de comparaison entre séries et intégrales oui
marsh rapids
nature of the series
la nature de la somme des S(n) / n^alpha ?
vaut mieux trouver un équivalent alors oui
marsh rapids
ça à l'air bien
empty plover
mais je comprends rien
marsh rapids
"what I did" mais c'est pas toi ?
empty plover
meme ca n a pas meme l air juste. pour alpha =-100 la serie converge aussi :l
empty plover
"what I did" mais c'est pas toi ?
wdym?
marsh rapids
meme ca n a pas meme l air juste. pour alpha =-100 la serie converge aussi :l
ignore les termes n < 102 et c'est clair
empty plover
c'est juste que t'a pas confiance en ta démo ?
C'est pas ma demo c'est la correction :p
C'est maths france
marsh rapids
je sais pas lire, je lu I au lieu de they
empty plover
hahaha
marsh rapids
C'est maths france
t'a un lien ?
empty plover
le web est devenu payee mais j ai toujours tous les pdf gratuits sur mon ordi
marsh rapids
pas grave. Les profs donnent déjà bien assez d'exos comme ça
empty plover
marsh rapids
type transition entre sup et spé ?
empty plover
Oui je commence spe en quelques semaines
marsh rapids
où ça ?
empty plover
En Liban, il y a un parcourt de concours international a polytechnique
t'es en uni?
marsh rapids
prépa. J'entre en MP* l'année prochaine
empty plover
Ah pareil
marsh rapids
En Liban, il y a un parcourt de concours international a polytechnique
prépas libanaises ?
empty plover
prépas libanaises ?
oui
marsh rapids
ok
empty plover
quelle grande ecole tu aimeras integrer?
marsh rapids
...
lol
faudra que je regarde un de ces 4
les formations les plus intéressantes
empty plover
quelle 4?
marsh rapids
un de ces quatres <=> un moment ou un autre. Expression française
empty plover
meme ca n a pas meme l air juste. pour alpha =-100 la serie converge aussi :l
bah je comprends toujours pas comment ca marche
marsh rapids
is it possible tho we don't know n
Regarde le sujet Centrale MP 2007 d'ailleurs. Tout un sujet sur le DL du reste de Cauchy des S(n)
tant que j'y pense
empty plover
Waaw je le trouve ou?
marsh rapids
Regarde le sujet Centrale MP 2007 d'ailleurs. Tout un sujet sur le DL du reste d...
apparemment c'est pas ça
empty plover
un de ces quatres <=> un moment ou un autre. Expression française
Et est ce que tu pense passer l ENS?
empty plover
Hahha oui c'est logique
marsh rapids
mais peut-être que j'obtient Ulm, qui sait
marsh rapids
pour un salaire non, pour les maths et la physique oui
empty plover
quelle est ton banque d 'exercices si c'est pas maths france, et est ce qu il ya des youtube channels sur les maths que tu aimes?
marsh rapids
https://cahier-de-prepa.fr/mpsi2-llg/docs?rep=18 regarde le DS 8 qu'on a fait. Vu que je retrouve pas le sujet dont il s'inspire
du coup voilà le site de mon prof de maths de l'année dernière
empty plover
Ok genial
marsh rapids
https://cahier-de-prepa.fr/mpsi2-llg/docs?rep=18 regarde le DS 8 qu'on a fait. V...
la question 7 fait plus que trouver un équivalent
empty plover
Les cours et les exercices de maths france sont complets si tu veus un chapitre dit le moi
marsh rapids
pas grave. Les profs donnent déjà bien assez d'exos comme ça
j'ai pas besoin de plus que ce que les profs donnent tkt
empty plover
c'est bizarre que t'as jamais entendu de maths france j ai cru que c'etait une source universelle
empty plover
j'ai pas besoin de plus que ce que les profs donnent tkt
juste sur ce site?
marsh rapids
maintenant il y aussi le site de la prof de maths de spé, mais celui là jsp si je peux publier le lien comme ça
empty plover
et est ce que tu regardes des chaines youtubes ou pas necessairement?
marsh rapids
maintenant il y aussi le site de la prof de maths de spé, mais celui là jsp si j...
rien dessus sans le mot de passe non
empty plover
mes profs sont nuls alors les chaines youtube m'aide a comprendre les notions beacoup plus profondement
marsh rapids
maintenant plus trop vu que les cours sont bien. Avant j'étais au lycée donc rien de bien utile pour la spé
empty plover
maintenant il y aussi le site de la prof de maths de spé, mais celui là jsp si j...
ok ca va je comprends
marsh rapids
c'est bizarre que t'as jamais entendu de maths france j ai cru que c'etait une s...
entre les trucs anglais au lycée et les cours en prépa, j'ai jamais eu à chercher quelque chose qui m'aurait amené là
empty plover
est ce que je peus te parler d un temps a un autre si j ai besoin de mieux comprendre une notion?
marsh rapids
vu que je suis pas vraiment en avance sur toi je pense que ç'est mieux pour toi de demander sur le serveur quant t'a besoin. Je dis pas non mais je garantis rien
empty plover
soit honnete mdr est ce que ca va si je te demande des quest ou non, si l idee te derange c'est pas grave
le serveur marche mais c est pas efficace j aimerai avoir des personnes que je peus analyser avec les notions
marsh rapids
pourquoi pas, si tu veux
marsh rapids
bah je comprends toujours pas comment ca marche
et maintenant ?
empty plover
et maintenant ?
non je comprends toujours pas
j etais entrain de voir le site que tu m as envoye
supposons n=2
ok non en fait c'est clair oui
lone heartBOT
@empty plover Has your question been resolved?
alpine sable
anywhere to get help with the mathematics associated with algorithms? like reading pseudocode and converting into mathematical notation?
marsh rapids
and also probably ask in some CS / python / more programming oriented discord server as well if you want to
marsh rapids
anywhere to get help with the mathematics associated with algorithms? like readi...
but feel free to ask here
alpine sable
alpine sable
and also probably ask in some CS / python / more programming oriented discord se...
oh, i have lol
marsh rapids
so what's your question ?
alpine sable
how one would read the pseudocode and convert it to the mathematical notation. i think i could do it if someone walks me through it
marsh rapids
wdym convert it to math notation ? It's not like an algorithm is a sort of mathematical sentence or a logical statement (think theorems, properties etc)
If you could give an example of what you're looking for it'd be helpful
half epoch
I’m guessing he is wondering how to go from the algorithm to the time complexity
gilded citrus
do you mean going from the code to the expression for the runtime
marsh rapids
just count the number of iterations of loops
marsh rapids
you got 2 for loops and each iteration ends up with an theta(1) operation
and for chained loops the number of iterations is the sum over all the outer loop iterations, of what's done inside 1 iteration, which here is the length of the inner loop
half epoch
Focus on the outer loop. We go from i = 1 to i = n - 1 and for each iteration we do n - i times the inner loop
Another way to put it is that the inside has a time complexity of n-i, for iteration i. Thus we need to sum up n-i for the amount of times we run the outer loop to get the total time
alpine sable
yeah i'm not seeing it. the algorithm makes sense but i don't understand which part gives rise to which expression or why in the second expression it becomes equal to n(n-1) - summation(i)from i=1 through n-1
i see where the n^2 - n comes from, they expanded the n(n-1) in the previous expression
half epoch
That’s just a math trick, summation can be split in two
alpine sable
so that must mean that the second summation we see gave rise to the n^2 - n / 2 expression?
half epoch
$\sum_{i = 1}^{n -1} (n - i) = \sum_{i = 1}^{n - 1} n - \sum_{i = 1}^{n - 1} i$
ocean sealBOT
Learath2
alpine sable
is the entire running time given by:
half epoch
is the entire running time given by:
Yes
alpine sable
thanks im going to write that down. but how would you interpret it? why is there only a single summation when we have multiple loops
half epoch
thanks im going to write that down. but how would you interpret it? why is there...
Because the inside of the inner loop has constant runtime. There is actually indeed two summations here, but they drop the constant runtime stuff at the very start
alpine sable
why does it get converted into n(n-1) in the first step
half epoch
They split the summation as I pointed out, then you use the sum rule for sum of consecutive numbers
$\sum_{i=1}^{n} i = \frac{n(n-1)}{2}$
ocean sealBOT
Learath2
alpine sable
i don't understand why multiplication comes in at all i thought summations were simply adding up a bunch of expressions
alpine sable
why does it become n*(n-1)
half epoch
i don't understand why multiplication comes in at all i thought summations were ...
It’s a rule. I think there is a video on it I watched a while back that gives good intuition
alpine sable
i get you said its breaking apart the expression but i don't understand the multiplicative aspect
half epoch
half epoch
i get you said its breaking apart the expression but i don't understand the mult...
The thing on the left is nothing but the sum of consecutive numbers. Which can be shown to be equal to that expression 0.5*n*(n+1)
alpine sable
this summation is in a different format its going to confuse me. i'll watch
the variables being in different spots is difficult for me
its a brilliant proof
ok so how do i use that info in the context of the algorithm
half epoch
Oh, I misread that, sorry. You don’t even need the summation thing there 😦
It’s just the summation of a constant, my bad
$\sum_{i=1}^{n - 1} n$ notice there is no $i$ in the sum, thus it’s just $(n-1)*n$
ocean sealBOT
Learath2
alpine sable
lets just analyze this piece:
half epoch
The second part is where you use the theorem, the sum with the i in it
Okay, that’s just the sum rule, you split the sum in 2 because it’s linear
half epoch
Look at the inside of the outer loop. For each iteration, we do “something constant” n - i times
alpine sable
i can see why it's n-1..
half epoch
In other words inner loop happens n - i times
I guess the fact that they discard constant times from the very start is what is confusing you
Doing it without that “optimization” will give you the 2 summations you expect, would you like to try it like that?
alpine sable
sure whatever will help me understand
half epoch
Okay, so let’s give each operation a time of 1. Just 1, we aren’t concerned about units
Now let’s calculate the runtime of the inside portion of the outer loop, from line 2 to 9
It’s $1 + \text{ inner loop } + 1$
ocean sealBOT
Learath2
half epoch
Do we agree on that?
alpine sable
ok
half epoch
This is how much time each iteration of the outer loop will take
Now we need to add together the time taken by each iteration. So we use a summation
$\sum_{i=1}^{n - 1} (1 + \text{inner loop} + 1)$
ocean sealBOT
Learath2
half epoch
Do we agree with this one?
alpine sable
! = statements seem to be at odds
half epoch
We are just calculating the inner portion now
Inner portion of the outer loop* from line 2-9
min = i, is 1. The swap is 1
alpine sable
ok i see whats going on
half epoch
It’s the assignment + the inner loop + the swap
alpine sable
ok ok