mystic wraith
then all i do is put Point C into the (y-y1)=10/3(x-x1)
#help-39
pearl pondBOT
gloomy plover
sn bn u
royal root
Hi! I need help making a simple "line" animation in Geogebra. I need it to trace the perimeter of my rectangle.
pearl pondBOT
Hi! I need help making a simple "line" animation in Geogebra. I need it to trace...
@royal root Has your question been resolved?
pearl pondBOT
@royal root Has your question been resolved?
timber tartan
if you dont want to find the lines you can always find the area of triangle formed by these three points
(area of triangle formed by the three points (x_i, y_i), i = 1, 2, 3 is equal to 1/2 |determinant(x_i, y_i, 1)|)
pearl pondBOT
@royal root Has your question been resolved?
marble sigil
Hi! I need help making a simple "line" animation in Geogebra. I need it to trace...
not sure how to string them together but the parameterization would be
x=t, y=0, 0<t<12
x=12, y=t, 12<t<24
x=12-t, y=12, 24<t<36
x=0, y=12-t, 36<t<48
iron basin
Hi! I need help making a simple "line" animation in Geogebra. I need it to trace...
i guess desmos had a neat polygon option, not sure if geogebra has one though
pearl pondBOT
@royal root Has your question been resolved?
pearl pondBOT
@royal root Has your question been resolved?
lunar schooner
i'm on b
lunar schooner
i'm pretty sure that my first step should be to figure out what parent function to compare it to
in this case it's 1/(x^3/2) right
plush bramble
Do you know what $\sqrt[3]{x} = x^?$
jolly parrotBOT
riemann
lunar schooner
3/2
jolly parrotBOT
riemann
lunar schooner
oh so x^1/3
lunar schooner
Means
but is 1/x^1/3 the right base graph to compare this integral to? also if it is what do i do next
plush bramble
oh so x^1/3
Yes
plush bramble
but is 1/x^1/3 the right base graph to compare this integral to? also if it is w...
Yes
Do the integral
Maybe do u sub to make it easier
lunar schooner
Do the integral
wait but if i have the comparison graph can i not just use the p- test and see that since 1/3<1 so its divergent?
plush bramble
Sure, that's probably faster
lunar schooner
Sure, that's probably faster
okay great now i have the biggest problem with how to write my justification like i never know what to say is it just: because we compared to the graph 1/(x^1/3) which by the p-test 1/3<1 so it id divergent this integral must also converge
plush bramble
Read the comparison test and cite it
Verify all the assumptions the comparison requires
lunar schooner
Read the comparison test and cite it
okay i think that i did this right do you mind reading it?
i tried to follow a definition form Pauls online math notes
*diverges not converges i reread my answer and saw that mistake
plush bramble
okay i think that i did this right do you mind reading it?
Some parts are incorrect. Your integral limits shouldn't be the inequality, the two functions you're comparing should be
lunar schooner
.reopen
pearl pondBOT
✅
lunar schooner
okay now im on part C and i'm wondering what graph i would compare it to
lunar schooner
For large x, what does the numerator behave like
when you say large x is that x^3?
pearl pondBOT
Available help channel!
bitter steppe
solve the differential equation dP/dt =0.12(P-25000)
pearl pondBOT
solve the differential equation dP/dt =0.12(P-25000)
vagrant briar
solve the differential equation dP/dt =0.12(P-25000)
distribute 0.12 then multiply throughout by dt
then integrate both sides
pearl pondBOT
@bitter steppe Has your question been resolved?
sharp galleon
where does the v at the top go
pearl pondBOT
where does the v at the top go
rose robin
where does the v at the top go
it's consumed in the u sub
sharp galleon
it's consumed in the u sub
but why
-2 goes to the top right
and then i take it out as -1/2
rose robin
and then i take it out as -1/2
that step doesn't look right
rose robin
also is $-\frac12\ln|100-v^2|$ the answer key?
jolly parrotBOT
Sepdron
sharp galleon
yes thats the answee
rose robin
it's not right though
rose robin
,w integrate -2v/(100-v^2)
jolly parrotBOT
sharp galleon
its -1/2 ln(100-v^2)
covert whale
could someone please explain
pearl pondBOT
could someone please explain
open rivet
could someone please explain
!show
pearl pondBOT
could someone please explain
Show your work, and if possible, explain where you are stuck.
open rivet
Yup, FTC
open rivet
I think you just messed up a sign in your calculation
open rivet
Dont guess
First of all, you can just calculate the intergal
With k and -3 as your bounds
covert whale
here is what i have so far
open rivet
Nice 😄
frail ibex
Hi, I have no idea about anything with matrix form. Please would it be possible if you could help explain this to me 😭 ?
https://en.wikipedia.org/wiki/Polynomial_regression#:~:text=In statistics%2C polynomial regression is,nth degree polynomial in x.
sharp vigil
i would suggest you look up how to perform matrix-vector multiplication
the matrix notation provides a convenient form for writing a bunch of sums
frail ibex
right. Could you explain how i could calculate for that?
sharp vigil
have you used dot products before?
frail ibex
i would suggest you look up how to perform matrix-vector multiplication
yeah I had it briefly explained to me, but i probably should watch a video
frail ibex
have you used dot products before?
uhhh probably not
sharp vigil
frail ibex
https://www.youtube.com/watch?v=Awcj447pYuk
legend! Thank you very much
half sedge
pearl pondBOT
@frail ibex Has your question been resolved?
frail ibex
right. Could you explain how i could calculate for that?
okay. I get all that, but how do I work out what m is?
sharp vigil
m is just a constant, the degree of the polynomial
frail ibex
oh, ohhhhhh. Tanks!
tough nexus
Can someone please help me i think i know there Answer but AI is geeking
tough nexus
Should it be
3,3,4,4,4,5,5,5,5,5,6,6,6,6,7,7,8,9,9
So add them together
Then do 20 divide 2 + 1
?
verbal whale
Should it be
3,3,4,4,4,5,5,5,5,5,6,6,6,6,7,7,8,9,9
The median is the center value here
Center means leaving 9 points on the left and 9 points on the right
tough nexus
But isn’t the median calculation rule
If odd ( n +1 divide 2)
If even (n divide 2 + 1)
verbal whale
I've never seen this formula actually
tough nexus
It says it in my book
verbal whale
But yeah sounds correct
pearl pondBOT
toxic lichen
And Ai saying same thing
!nogpt
pearl pondBOT
And Ai saying same thing
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
tough nexus
!nogpt
yeah you’re right it gets a lot of my stuff wrong
i just used it as extra evidence
pearl pondBOT
Available help channel!
tough nexus
Hey guys for this one I sorted the numbers out and Q2 (median) was the 14TH value so being 33 so is Q1 everything before that? Thanks!
tough nexus
Hey guys for this one I sorted the numbers out and Q2 (median) was the 14TH valu...
And Is 0 accounted for in a stem plot
As in if it was 0,1
Do we say there was 1 value or 2? Thanks again
pearl pondBOT
@tough nexus Has your question been resolved?
pearl pondBOT
@tough nexus Has your question been resolved?
pearl pondBOT
@tough nexus Has your question been resolved?
magic olive
pearl pondBOT
toxic lichen
Ar + B in the first denom
magic olive
How to know that?
toxic lichen
r^2+1 is an irred quadratic
magic olive
r^2+1 is an irred quadratic
So if it’s irreducible does that mean I constantly need to put Ar + B?
toxic lichen
if it's an irreducible QUADRATIC it gets a linear numerator.
toxic lichen
(Ar+B)/(r^2+1) + (Cr+D)/(r^2+2r+2)
magic olive
Yes that’s what I meant sorry😅
Ok I get it then
Thanks 🙏
So basically I don’t have to memorize shit right?
I can just apply this rule everytime I have to do partial fractions?
Cuz everytime I gotta look up the different formats💀
toxic lichen
So basically I don’t have to memorize shit right?
well ig you have to memorize that each denominator comes with a numerator 1 degree lower
pearl pondBOT
pearl pondBOT
Available help channel!
sharp smelt
pearl pondBOT
sharp smelt
so I have $\int_{-1}^{1} (f(\alpha(t)),g(\alpha(t)),h(\alpha(t)) \cdot ( 2t,0,4t^3) dt$
jolly parrotBOT
What a wonderful world !
sharp smelt
so $\int_{-1}^{1} 2tf(\alpha(t))+ 4t^3(h(\alpha(t)) dt$
jolly parrotBOT
What a wonderful world !
sharp smelt
now I know 2t is odd as is 4t^3
but just saying the integral is zero based on that feels wrong
Is this wrong
toxic lichen
what are f, g and h again
sharp smelt
what are f, g and h again
I'm defning the vector field, $V(x,y,z) = ( f,g,h)$
jolly parrotBOT
What a wonderful world !
toxic lichen
what's capital V
sharp smelt
The vector field
toxic lichen
the problem calls it F
sharp smelt
Oops
toxic lichen
no good reason to somehow rename it
f(alpha(t)) and h(alpha(t)) are both even functions of t
sharp smelt
well, the composition of a function with an even function is even
sharp smelt
knowing that alpha itself is even
Well, I don't see how this guarentees anything unless we know something ablut f,g,h
compact ridge
yes basically $a(t) = a(-t)$ so $f(a(t)) = f(a(-t))$ i.e $f \circ a$ is also even
jolly parrotBOT
south
toxic lichen
Well, I don't see how this guarentees anything unless we know something ablut f...
you know they are functions
compact ridge
and (even function) * (odd function) = (odd function)
toxic lichen
well, the composition of a function with an even function is even
the composition of any function with an even function, in that order, is even.
sharp smelt
the composition of **any** function with an even function, *in that order*, is e...
right
thanks
so as $f(\alpha(t))$ is even the integral is 0
jolly parrotBOT
What a wonderful world !
sharp smelt
same for $h(\alpha(t))$
jolly parrotBOT
What a wonderful world !
sharp smelt
Thanks so much!
Would this be an involved proof
I think I'll skip this for nopw
*now
$\alpha(\phi) = \alpha(u^2) = (u^2,u^2) = \beta(u)$
jolly parrotBOT
What a wonderful world !
sharp smelt
$$\int_{\alpha} = \int_{0}^{1} (1,0) \cdot (1,1) dt = \int_{0}^{1} 1 dt =1$$
\
\
$$\int_{\beta} = \int_{-1}^{1} (1,0) \cdot (2u,2u)= \int_{-1}^{1} 2u du =0$$
jolly parrotBOT
What a wonderful world !
sharp smelt
**What a wonderful world !**
For this( been 15 minutes)
sharp smelt
As for this.uhh
If I can prove (a); (b) is trivially true
well, almost
$\beta = \alpha( \phi)$
jolly parrotBOT
What a wonderful world !
sharp smelt
.close
green plank
After finding the root form, what do I do after?
pearl pondBOT
After finding the root form, what do I do after?
@green plank Has your question been resolved?
pearl pondBOT
pearl pondBOT
Available help channel!
pearl pondBOT
Available help channel!
stiff mauve
how do they take the derivative
pearl pondBOT
how do they take the derivative
stiff mauve
where does -10qi come from
verbal whale
What's the derivative of 10x?
spare lark
What's the derivative of 10x?
Well the -10qi is a typo right ?
spare lark
where does -10qi come from
Nowhere its probably a typo
stiff mauve
Nowhere its probably a typo
no but it actually is the right answer it says i dont know
spare lark
This comes from an answer sheet ?
spare lark
I knew
pearl pondBOT
chatgpt
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
spare lark
no he did get it wrong
Ofc its wrong
stiff mauve
do u know micro economics
spare lark
It answers like a student that haven't learn his lesson and try to hide it
plush bramble
no he did get it wrong
don't waste helpers' time reviewing fake work
stiff mauve
don't waste helpers' time reviewing fake work
if i knew it was "fake work" i would not have been here wasting my time either
plush bramble
reviewing work that isn't yours or your teachers' is a waste of time
static bloom
Don't blindly trust AI generated stuff.
If there is something fishy it can likely be wrong.
plush bramble
no but it actually is the right answer it says i dont know
and don't pass chatgpt work off as "right"
static bloom
They human
Also true for GPTs but they are very stuboorn.
stiff mauve
well because the teacher and chatgpt both had the same answer
so i assumed the teacher was right, therefore chatgpt is also right
but the teacher didnt have his work
and so i tried to ask chatgpt how to solve the question
spare lark
Anyway there is no -10qi so ig lets move on, good day to u
static bloom
and so i tried to ask chatgpt how to solve the question
That's understandable but I think you should excercise more critical thinking, put the whole context when asking here and also diclose where it is from.
stiff mauve
i doubt they get micro economic concepts in mathematics
pearl pondBOT
pearl pondBOT
Available help channel!
hollow cliff
yo
spiral pivot
Your approach for problem 1 seems sound, though I haven't double checked any of your multiplications.
And similar for problem 2.
You caught the one thing I was checking for, which was accidentally resuing numbers.
So as long as the boring multiplication and addition stuff is correct, your answer is correct.
hollow cliff
Ok perfect
Tysm
How many cases would there be for this question?
Greater than 3
Would be case 1
Starting with 4,5,6
2nd case starting with a 3 and then 2nd digit 6?
I'm confused
<@&286206848099549185>
All ik so far is that we got 6 total digits
2: 4s
And 2: 5s
Which is 6!/2!2!
If u can help @ me
merry stirrup
@hollow cliff you need help with Question 3 or 4?
merry stirrup
Okay
Okay
So repetition is not allowed
We can approach with the fundamental principle of counting
Like how are you approaching this question can you tell me your tho@hollow cliff ught process
hollow cliff
Which is 6!/2!2!
.
merry stirrup
2nd case starting with a 3 and then 2nd digit 6?
Allow 5 too , starting with 3 2nd digit 5 and 6
hollow cliff
Ok so it'd be start with 3, 2nd digit 5 or above
merry stirrup
Okay
hollow cliff
Like this question
merry stirrup
So it'd be 1×2×4×3×2×1
And some digits are identical
So divide by 2!2!
2 digits are identical
Like 4,4 and 5,5 are identical
So divide by 2!2!
hollow cliff
I give up
merry stirrup
Whyyyy
merry stirrup
Which is 6!/2!2!
Why did divide by 2!2! Here ?
hollow cliff
I need to know how many cases there would be and how to figure out what they start with
merry stirrup
Same here there is 2 4s and 2 5s
hollow cliff
1×2×4!/2!2!
For this we already used a 4
So that means it cancels out
So there's only 1, 4 left
Doesn't make sense
Give me the cases and what they start with and I'll give u the final answer
hollow cliff
Alr
merry stirrup
Let's you know break the confusion
hollow cliff
Ok one sec
merry stirrup
Okay
hollow cliff
Why do we start with 6 for case 1?
We need numbers greater than 3
That'd be 3,4,5,6
merry stirrup
6 is great that 3
merry stirrup
6 is great that 3
Than
hollow cliff
.
Look at case 3
For the 1st question
So for this
Can't we start with a 3 or above
For the first case
merry stirrup
But can't we put it all at once
Yes you can do it
But you were getting confused
That's why I decided to break it up
hollow cliff
We got 4,3,5,4,5,6
merry stirrup
Yes
merry stirrup
Okay
merry stirrup
Yes
merry stirrup
Yes but reputation is there
hollow cliff
We got 4,3,5,4,5,6
And we already used a 5
merry stirrup
Case 1 : use 6 in first digit
hollow cliff
Why 6
merry stirrup
Since 6 has no repetition
merry stirrup
Because if you put 4 and 5 all at once it will cause problems
hollow cliff
=720
merry stirrup
4 and 5 are repeating but 6 is not
hollow cliff
Yep
merry stirrup
4 for the first box
Imagine 6 is in the first box then there would be 2 reputation
Repetition
My keyboard 🥲
merry stirrup
Imagine 6 is in the first box then there would be 2 reputation
Of 2 5s and 2 4s
But if 4 is in the first box there would be only 1 repetition
hollow cliff
hollow cliff
But if 4 is in the first box there would be only 1 repetition
That makes sense now
merry stirrup
Now start with 4 or 5
Now there is only 1 repetition
hollow cliff
Is this right?
hollow cliff
Now there is only 1 repetition
Yep
Can we start with 4 and 5
And put 2 in the box
?
merry stirrup
No issues
merry stirrup
You fixed the first
hollow cliff
You fixed the first
Wdym
merry stirrup
Or do we only count the numbers that are left
You count the numbers which are not fixed
hollow cliff
Alr
hollow cliff
I didn't even start that 😭
merry stirrup
It's the second case
hollow cliff
Wdym 4 or 5?
Can't we just do both together
And why 4 or 5?
I'm confused
3 or above
Which is 3,4,5
That's 3 digits
We put 3 in the box
Then 5!
merry stirrup
Case I : first digit is 6
Case 2: first digit is 4 or 5
Case 3: first digit is 3
hollow cliff
Alr so 4 or 5
merry stirrup
Yes
hollow cliff
Do I put 2 in the box?
merry stirrup
Yes 2 in the first box
merry stirrup
And there is 1 repetition
Is 4 is used in the first box
2 5s are left
Or if 5 is used in the first box 2 4s are left
Hence there is one repetition
Divide it by 2!
2×5!/2!
merry stirrup
You did it right , but you also need to consider the repetition
hollow cliff
What repetition
And wait
How does case 3 make any sense?
If it starts with a 3
Then the 2nd number has to be a 5 or greater
merry stirrup
merry stirrup
Then the 2nd number has to be a 5 or greater
Yeah we need to consider that
First let's sort out the easy cases
Then we would come to case 3
You have 4,3,5,4,5,6
Used 4 in the first place
You have 3,5,4,5,6 left
Notice that there are 2 5s
merry stirrup
So 5!÷2!
2×5!/2! You have considered both 5 and 4
You have 4,3,5,4,5,6
Used 5 in the first place
You have 3,4,4,5,6 left
Notice that there are 2 5s
merry stirrup
No I said case 2: use 4 or 5 in the first digit
You need to consider both of them simultaneously
Have you got it
hollow cliff
Yep
merry stirrup
Okay let's move into case 3
See we need to break case 3 in two parts
Okay
Part 1 use 2nd digit as 6
Part 2 use 2nd digit as 5
Then you would get everything that you need and sum everything up
Let me help you with diagram
merry stirrup
Yes and second digit 6 not 5 or above
hollow cliff
3×2×5×4×3×2×1
merry stirrup
No bro let me explain
hollow cliff
alr man
merry stirrup
You need to separate both of it
Because 6 isn't repeating
But 5 is repeating
If you use both of them at once
The answer would be wrong
Because 5 and 6 don't have the similar properties here , 5 is repeating and 6 is not
hollow cliff
Alr
merry stirrup
I used 4 and 5 simultaneously because 4 was repeating twice and 5 was repeating twice so they had the similar properties
But 6 or 5 don't have that
Okay?
hollow cliff
Got it
merry stirrup
Yeah let's do it
hollow cliff
Ok
So there's 4 cases then?
Start with 3, 2nd digit 5
Start with 3, 2nd digit 6
merry stirrup
Start with 3, 2nd digit 6
This is a part of 3rd case
But you can also say that they are divided into 4 cases there's nothing wrong
At last sum everything up and you would have your answer
merry stirrup
Yep
merry stirrup
Welcome
hollow cliff
.close
pearl pondBOT
pearl pondBOT
Available help channel!
ivory wasp
Total number of No. of the form abcd such that a>=b>=c>=d
pearl pondBOT
Total number of No. of the form abcd such that a>=b>=c>=d
@ivory wasp Has your question been resolved?
ivory wasp
<@&286206848099549185>
little comet
are you asking how many four digit numbers exist that satisfy that form
little comet
lol
ivory wasp
little comet
how familiar are you with combinatorics?
ivory wasp
how familiar are you with combinatorics?
not the best but decent
little comet
I think it's 715?
little comet
I think it does though I've never used it?
little comet
did u introduce dummies ?
stars and bars, which I think means the answer is yes?
little comet
lets look at a simpler problem
say we have the set {0,1,2} and want to make a 2 digit number whose digits are non-increasing.
a good way to think about this is to have some bins labeled 2, 1, 0, and two balls you can put in said bins. can you see how any possible way to put two balls into these bins results in a unique non-increasing 2 digit number?
for example,
o|o| = 21
|oo| = 11
o||o = 20
this is then equivalent to having 4 spaces and choosing 2 to serve as 'dividers'
our question involves having 10 bins and 4 balls
ivory wasp
lets look at a simpler problem
say we have the set {0,1,2} and want to make a 2...
3 ?
12 11 22 ?
little comet
thats increasing
12 is increasing, 21 is not
ivory wasp
12 is increasing, 21 is not
oh shit i thought u menat like a >b
by increasing
my bad
ivory wasp
ic
little comet
for two digit ab
ivory wasp
ye then 6
little comet
anyway, the number of "dividers" is the number of possible digits you have minus one
ivory wasp
this is then equivalent to having 4 spaces and choosing 2 to serve as 'dividers'
3 spaces right ?
little comet
anyway your problem is 4 balls, 10-1 = 9 dividers
so 13 things to move around
you can either choose where to put the balls or the dividers
13c9 = 13c4 = 715
i think this is taught as combination with reptition
yep
ivory wasp
ic
give me like 2 mins
tho
sorry
@little comet thanks a lot
i understand it now
whats ur rank in marvel rivals if u dont mine me asking
😭
little comet
i havent played since i got the emblem LOL, im probably like plat or smth idk
i mainly play fighting games i just think jeff is cute 
ivory wasp
i havent played since i got the emblem LOL, im probably like plat or smth idk
i ...
lmfao he is
but he is annoying to face against
anf thing is hes not even strong
thanks again
.close
ivory wasp
ABCD are playing foot ball and A has the ball number of ways thta A has the ball again after 7 passes is ?
limpid heath
Is this likes counting sequences
ivory wasp
i didnt get u
limpid heath
If its permutations it should have like arranging sets if its combination it should be selecting group without considering the order
limpid heath
yes it's sequences of 8 letters
Probably the formula for it is 3y(n-1) right?
ivory wasp
but we cant like tell how many times a player comes right
ivory wasp
and we ahve to make sure that After A he cant pass it to himself
it is recursive
but idk how to approach i t
limpid heath
but idk how to approach i t
List all the given first
ivory wasp
List all the given first
?
limpid heath
?
-
The four players are A, B, C, and D.
-
A starts with the ball.
-
Each player can pass the ball to any of the other three players.
vestal tapir
3 letters has 3 sequences
4 letters: 3×3 minus the three from the three
limpid heath
To create a recursive formula for this
vestal tapir
3×3×3−6 = 21
limpid heath
You need to count the number of valid ways in which, after 7 passes, A gets the ball again.
vestal tapir
81−21 = 60
limpid heath
81−21 = 60
Bro explain it to him not directly 😭🙏💀
vestal tapir
therefore (3^n + (-1)^n*3)/4 by OEIS
vestal tapir
that's right
limpid heath
therefore (3^n + (-1)^n*3)/4 by OEIS
But its kinda complicated so maybe this is short cut
vestal tapir
i went here https://oeis.org/ and searched 6 21 60
ivory wasp
I got 546
can u like tell it the exact form u got
like 3^5 or ncr
if u did do like that
limpid heath
like 3^5 or ncr
I did was like type of 2 functions i used
Its like substituting a value on a function but its a long method
limpid heath
therefore (3^n + (-1)^n*3)/4 by OEIS
I recommend you to use this is one cuz this is shortcut
ivory wasp
therefore (3^n + (-1)^n*3)/4 by OEIS
ic
vestal tapir
omg no
limpid heath
Care to explain to him frowny
vestal tapir
i didn't "get it", i googled it
vestal tapir
e.g. there are total 9 sequences that go AXX
like the first X is not A, and the second X is not the first X
vestal tapir
but then if you add A, AXXA includes AXAA
ivory wasp
theres a pronlem right
vestal tapir
so you subtract the answer for the previous length and that solves the issue
ivory wasp
so you subtract the answer for the previous length and that solves the issue
but like take ...... XXA now we know last but one is not A
so 6 ?
onyl for like last three
limpid heath
I think you make him confuse 💀🙏
vestal tapir
then AXXXA is 27 and you subtract 6
vestal tapir
yeah
ivory wasp
how do u extend for 7 then
vestal tapir
i don't know, "closed forms" for recurrences is some advanced thing,
ivory wasp
can like anyone state a relation ship between S7 = aS6+bS5 or smtg like that
like we do in normal recurrence
vestal tapir
for this problem, you're not supposed to shortcut, you;re supposed to do the long way most likely
limpid heath
for this problem, you're not supposed to shortcut, you;re supposed to do the lon...
Ye that's what i did on mine
ivory wasp
can like anyone state a relation ship between S7 = aS6+bS5 or smtg like that
my sir explained it like this
but i didnt understand
😔
but im pretty sure
he gave an eq
like this
jolly parrotBOT
frownyfrog
limpid heath
General formula for the problem?
ivory wasp
ye
ivory wasp
$A_n = 3^{n-1} - A_{n-1}$
idts
ivory wasp
can like anyone state a relation ship between S7 = aS6+bS5 or smtg like that
im pretty sure he gave like this
a and b were small integers
limpid heath
Or maybe you can use mine to make it simple for you
Like this
$f(n) = 3g(n-1) \ g(n) = 2g(n-1) + f(n-1) \ f(0) = 1, : g(0) = 0$
jolly parrotBOT
nerfLeander
limpid heath
Basically i did here was I let f(n) be the number of ways that, after "n" passes, the ball is with A. While for g(n) is vice versa
Specifically, g(n) be the number of ways that, after "n" passes, the ball is not with A.
vestal tapir
np
ivory wasp
.close
pearl pondBOT
pearl pondBOT
Available help channel!
fierce bane
I just figured out how to convert these from radians to degrees, and vise versa, dont know how to do this at all.
leaden wadi
Use its reference angle to simplify it to an angle that you know the answer to.
pearl pondBOT
@fierce bane Has your question been resolved?
fierce bane
@leaden wadi how do i find the reference angle?
leaden wadi
<@728158378622189658> how do i find the reference angle?
It will be of the form n * pi.
The nearest angle of that form.
brave sluice
pearl pondBOT
brave sluice
i'm trying to figure out what i need to do
i think i need to show three things\
$(a_i b_j) K$ is a coset of $K$ in $G$ for all $i,j$\
$(a_i b_j) K = (a_m b_n) K$ implies $i=m$ and $j=n$\
For all $g\in G$ we have $g\in (a_i b_j) K$ for some $i,j$
jolly parrotBOT
Axe
brave sluice
does that sound right?
pearl pondBOT
@brave sluice Has your question been resolved?
pearl pondBOT
@brave sluice Has your question been resolved?
brave sluice
.close
bold wigeon
Im using the lagrange multiplier and got a maximum at (2,1,4) which is correct but there is also a minimum at (0,3,0) which I cant get?
pearl pondBOT
Im using the lagrange multiplier and got a maximum at (2,1,4) which is correct b...
@bold wigeon Has your question been resolved?
leaden marsh
Im using the lagrange multiplier and got a maximum at (2,1,4) which is correct b...
Yeah see you have this equation
2xy = x^2 --- (i)
and x + y = 3 => x = 3-y
Putting this in (i)
You get 2(3-y) y = (3-y)^2
Solve this you will get two values of y
leaden marsh
Yeah see you have this equation
2xy = x^2 --- (i)
and x + y = 3 => x = 3-y
P...
Out of which one is (0, 3,0)
bold wigeon
how did u get 2xy = x^2?
wary sundial
I’m having a hard time figuring out how to solve these two questions
bitter lodge
@wary sundial can you show the description of the original safe
wary sundial
The original safe's code was 60 60 60
bitter lodge
The original safe's code was 60 60 60
So each digit can be 1-60 or 0-60
wary sundial
I think they can be any even value
except the second value which has to be between 30 to 50
pearl pondBOT
@wary sundial Has your question been resolved?
pearl pondBOT
@wary sundial Has your question been resolved?
pearl pondBOT
@wary sundial Has your question been resolved?
pearl pondBOT
pearl pondBOT
Available help channel!
barren ibex
barren ibex
ok
toxic lichen
.close
pearl pondBOT
pearl pondBOT
Available help channel!
robust ravine
help
sick sparrow
seems self explanatory to me, 1 + 1/4 = 5/4
robust ravine
seems self explanatory to me, 1 + 1/4 = 5/4
but
robust ravine
its was just 1 and 1/4 were there
robust ravine
did you miss the equal sign?
no
wet osprey
Well 1 + 1/4 is 5/4
robust ravine
Well 1 + 1/4 is 5/4
how
tardy reef
The just solved this part in step 2
wet osprey
Well 1 is 4/4
robust ravine
when i solved my answere came 8/4
robust ravine
bro in bracket there were 3^0 + 4^-1 so answer came 1 + 1/4 then when the ai added it became 5/4 how
sick sparrow
3^0 = 1
wet osprey
Ok what’s 1 + 1/4
toxic lichen
1 + 1/4 = 4/4 + 1/4 = (4+1)/4
sick sparrow
4^-1 = 1/4
robust ravine
Ok what’s 1 + 1/4
the bracet
toxic lichen
@robust ravine do you know how to add fractions?
robust ravine
<@1044962287825461260> do you know how to add fractions?
yes
wet osprey
Holy shit guys we don’t all need to be here to repeat the same thing
It’s actually not helpful to repeat the same thing others have already said
weary urchin
prove that for all strictly positive real numbers a < b < c, we have (c - a)b² ≤ (b - a)c² + (c - b)a²
chrome patio
prove that for all strictly positive real numbers a < b < c, we have (c - a)b² ≤...
!showwork
pearl pondBOT
prove that for all strictly positive real numbers a < b < c, we have (c - a)b² ≤...
Show your work, and if possible, explain where you are stuck.
weary urchin
!showwork
I didn't get it
I am trying to look for an idea but .. I didn't do anything
cinder thistle
dollowing is the answer, idk how to explain hot to get it tho, pls dont open spoiler, maybe someone else can explain how to get it
||to show
(c-a)b^2<= b(c^2-a^2) + ca^2 - ac^2
to show
(c-a)b^2 <= b(c-a)(c+a) - (c-a)(ac)
since c>a c-a is positive, so to show
b^2 <= bc+ba -ac
or to show
b^2-bc-ba+ac <= 0
or to show
(b-a)(b-c) <= 0
since b > a and b < c b-a is positive and b-c is negative, so (b-a)(b-c) is negative so this is true||
tacit saddle
to show
$(c-a)b^2<= b(c^2-a^2) + ca^2 - ac^2$
to show
$(c-a)b^2 <= b(c-a)(c+a) - (c-a)(ac)$
since c>a c-a is positive, so
to show
$b^2 <= bc+ba -ac$
or to show
$b^2-bc-ba+ac <= 0$
or to show
$(b-a)(b-c) <= 0$
since b > a and b < c b-a is positive and b-c is negative, so (b-a)(b-c) is negative so this is true
jolly parrotBOT
_xincineratex_
chrome patio
to show
$(c-a)b^2<= b(c^2-a^2) + ca^2 - ac^2$
to show
$(c-a)b^2 <= b(c-a)(c+a) ...
you can use \verb|\le| for $\le$
jolly parrotBOT
vin100
chrome patio
,align
& (c-a)b^2 &\le b(c^2-a^2) + ca^2 - ac^2 \
\iff& (c-a)b^2 &\le b(c-a)(c+a) - (c-a)(ac) \
\iff& b^2 &\le bc+ba -ac \tag{$\because c-a > 0$} \
& & \dots
weary urchin
I get it
jolly parrotBOT
vin100
weary urchin
thanks
chrome patio
sorry i can't quickly find a latex way to align the inequalities according to both the "iff" and "≤" signs
i'm sure that alignat will work
pearl pondBOT
@weary urchin Has your question been resolved?
pearl pondBOT
pearl pondBOT
Available help channel!
vernal ledge
Hi, I’m trying to evaluate this integral but I’m not very experienced with integrals.
Here’s the original expression:
f\left(t,r\right)=\int_{0}^{t}\left|\frac{d}{du}\left(\cos\left(u\right)\sqrt{\frac{2}{1+\left|\cos2u\right|}}r,\sin\left(u\right)\sqrt{\frac{2}{1+\left|\cos2u\right|}}r\right)\right|du
After simplification I arrived at this:
f\left(t,r\right)=\int_{0}^{t}\sqrt{\left(-\sin\left(u\right)\sqrt{\frac{2}{1+\left|\cos2u\right|}}+\frac{\cos\left(u\right)\frac{4\operatorname{sgn}\left(\cos\left(2u\right)\right)\sin\left(2u\right)}{\left(1+\left|\cos\left(2u\right)\right|\right)^{2}}}{2\sqrt{\frac{2}{1+\left|\cos2u\right|}}}\right)^{2}+\left(\cos\left(u\right)\sqrt{\frac{2}{1+\left|\cos2u\right|}}+\frac{\sin\left(u\right)\frac{4\operatorname{sgn}\left(\cos\left(2u\right)\right)\sin\left(2u\right)}{\left(1+\left|\cos\left(2u\right)\right|\right)^{2}}}{2\sqrt{\frac{2}{1+\left|\cos2u\right|}}}\right)^{2}}du
Then this:
f\left(t,r\right)=\int_{0}^{t}\left|\frac{d}{du}\left(\cos\left(u\right)\sqrt{\frac{2}{1+\left|\cos2u\right|}}r,\sin\left(u\right)\sqrt{\frac{2}{1+\left|\cos2u\right|}}r\right)\right|du
I don't know how to solve an integral that has the sgn or piecewise.
Thank you
vernal ledge
,tex f\left(t,r\right)=\int_{0}^{t}\left|\frac{d}{du}\left(\cos\left(u\right)\sqrt{\frac{2}{1+\left|\cos2u\right|}}r,\sin\left(u\right)\sqrt{\frac{2}{1+\left|\cos2u\right|}}r\right)\right|du
jolly parrotBOT
0880
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
coral dune
what is this monstrosity
vernal ledge
Sorry
,tex f\left(t,r\right)=\int_{0}^{t}\sqrt{\left(-\sin\left(u\right)\sqrt{\frac{2}{1+\left|\cos2u\right|}}+\frac{\cos\left(u\right)\frac{4\operatorname{sgn}\left(\cos\left(2u\right)\right)\sin\left(2u\right)}{\left(1+\left|\cos\left(2u\right)\right|\right)^{2}}}{2\sqrt{\frac{2}{1+\left|\cos2u\right|}}}\right)^{2}+\left(\cos\left(u\right)\sqrt{\frac{2}{1+\left|\cos2u\right|}}+\frac{\sin\left(u\right)\frac{4\operatorname{sgn}\left(\cos\left(2u\right)\right)\sin\left(2u\right)}{\left(1+\left|\cos\left(2u\right)\right|\right)^{2}}}{2\sqrt{\frac{2}{1+\left|\cos2u\right|}}}\right)^{2}}du
jolly parrotBOT
0880
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
open rivet
!original
pearl pondBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
vernal ledge
**0880**
Compile Error! Click the <:errors:504266556054962196> reaction for more...
this is the original problem
coral dune
just take a picture of the problem
toxic lichen
this is the original problem
what, this ugly ass integral?
coral dune
have you tried slicing the integral?
so that it removes the sgn function in the integrand
vernal ledge
This integral is a solution to another problem I had, I need an analytical solution to it
coral dune
where did this integral arised from?
im sure if this is a textbook problem, there are other clever ways that need not solving this integral
vernal ledge
It came from a graphics programming problem I have, it's not a text book problem
open rivet
This integral is a solution to another problem I had, I need an analytical solut...
!xy
pearl pondBOT
This integral is a solution to another problem I had, I need an analytical solut...
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
@vernal ledge Has your question been resolved?
copper jungle
**0880**
Compile Error! Click the <:errors:504266556054962196> reaction for more...
What am I looking at
coral dune
yeah the integral maybe ugly looking, but i believe there is some kind of symmetry to it
vernal ledge
I will try my best to explain it:
I'm trying to project a 2D point onto the surface of a square.
but I only care about the X axis
I'm trying to find points on a square that mod(p.x,2s)>s like in the picture
h\left(t,r\right)=\left(\cos\left(t\right)q\left(t\right)r,\sin\left(t\right)q\left(t\right)r\right)
is my square's function
and this is the solution I found
f\left(t,r\right)=\int_{0}^{t}\left|\frac{d}{du}h\left(u,r\right)\right|du
h\left(t,r\right)\left\{\operatorname{mod}\left(E\left(t,r\right),\frac{2s}{r}\right)>s\right\}
but I can't solve an integral in my program
jolly parrotBOT
0880
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
vernal ledge
Then I replace || with sqrt(a^2+b^2) a=h(u,r).x b=h(u,r).y
q\left(t\right)=\sqrt{\frac{2}{1+\left|\cos2t\right|}}
0880
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
coral dune
what is s
vernal ledge
s is the spacing between the dashes
pearl pondBOT
@vernal ledge Has your question been resolved?
vernal ledge
Sorry it's been 30 minutes
<@&286206848099549185>
half tendon
this is the original problem
What is this integral bro, this looks like Cleo
rain parcel
bro
coral dune
there is a simple solution to this
if you let t be a discrete intervals of Pi
$\int_0^{\frac{n\pi}{4}}\left| \frac{dh}{du}\right|du=n$
where $n=1,2,3,...$
vernal ledge
is f(u) = f(u,1)?
vernal ledge
I don't understand, isn't f(u) an integral? why put it in another integral?
vernal ledge
\frac{dh}{du}=\left(-\sin\left(u\right)q\left(u\right)r+\cos\left(u\right)q\left(u\right)r,\cos\left(u\right)q\left(u\right)r+\sin\left(u\right)q'\left(u\right)r\right)
Is this correct?
$\frac{dh}{du}=\left(-\sin\left(u\right)q\left(u\right)r+\cos\left(u\right)q\left(u\right)r,\cos\left(u\right)q\left(u\right)r+\sin\left(u\right)q'\left(u\right)r\right)$
jolly parrotBOT
0880
coral dune
yes and the norm of that is the integrand you are asking to integrate
vernal ledge
So I need to solve that
coral dune
i already answered it
vernal ledge
I will try my best to explain it:
I'm trying to project a 2D point onto the surf...
Okay but how can I use this to check whether h(u) is inside a dash?
pearl pondBOT
@vernal ledge Has your question been resolved?
pearl pondBOT
@vernal ledge Has your question been resolved?
queen cipher
I don't know what to do. I tried to take the leading terms, but then I get infinity*0. I think I have to do something different in the log, but don't know what
prisma elk
I don't know what to do. I tried to take the leading terms, but then I get infin...
what did u try
queen cipher
what did u try
this
finite onyx
What do u think intuitively the limit should be
queen cipher
yeah thats wrong
where it is wrong?
prisma elk
where it is wrong?
infty * 0
finite onyx
I don't know what to do. I tried to take the leading terms, but then I get infin...
What u gotta realise is that the log factor is gonna be very insignificant compared to the polynomial here
severe quarry
this
You can't just evaluate the limit halfway like you did in the first step on line 3
finite onyx
What u gotta realise is that the log factor is gonna be very insignificant compa...
The log factor will only contribute a sign honestly
queen cipher
What do u think intuitively the limit should be
infinity cause logn << n^2?
finite onyx
infinity cause logn << n^2?
But yea ur on the right track
Although I'm not sure this is the rigorous way to do this
prisma elk
the rigorous way, is first simplify the inner expression of the log into something like $1-d_n$ with $d_n \rightarrow 0$ as $n \rightarrow \infty$
jolly parrotBOT
Goëtia
finite onyx
I don't know what to do. I tried to take the leading terms, but then I get infin...
But this sort of stuff comes up frequently in complexity analysis
prisma elk
then using $log(1-d_n) \leq -d_n$
jolly parrotBOT
Goëtia
prisma elk
But this sort of stuff comes up frequently in complexity analysis
you mean big-O notation?
finite onyx
you mean big-O notation?
Yea
queen cipher
the rigorous way, is first simplify the inner expression of the log into somethi...
I'm lost at this. dn stands for?
prisma elk
for you to find
finite onyx
I'm lost at this. dn stands for?
the idea is log(1+x) ≈ x when x is small, so try simplifying the log term to get a similar form
queen cipher
for you to find
I mean, is dn some sort of formula or like a placeholder?
prisma elk
I mean, is dn some sort of formula or like a placeholder?
the latter
finite onyx
Tell me if this makes sense to you
It will approximate to a negative linear function
a here will be some number which idk but fairly certain it will be some small rational number
Positive rational
queen cipher
the latter
is dn = (-4n+2)/(3n^2-2n+1) ?
queen cipher
Tell me if this makes sense to you
is ln(1-a/n) = (a/n) using taylor at first order?
finite onyx
Yes
queen cipher
So is this legit? I use Px/Qx = m + Rx/Qx in the log
. Thank you
lethal trout
Hello I need help determining if an equation is a polynomial or not, Im stuck on these problems :,((
elfin cloud
What do you think a polynomial is?
lethal trout
An equation with an exponent
elfin cloud
Uhhh not reallt the definition no
west sapphire
definitely not an equation
elfin cloud
A polynomial is an ewuation which can be written as
a + b * x + c * x^2 + d * x^3 + e * ….
Where x is the variable and a,b,c,d,e,… are constants
west sapphire
can see from the context here that polynomials in more than one variable are being considered
elfin cloud
With more variables the polynomiak would look like:
a + b * x + c * y + d * x^2 + e * y^2 + ….
Where x AND y are variables
Important are that the variables themselfs are only multiplied with CONSTANTS and are raised to an integer power (whole numbers)
lethal trout
So I would put the numbers and stuff into the formula you gave? And that would tell me if it’s a polynomial?
elfin cloud
The degree of the polynomial would be the highest integer power
So in a + b * x^ 5 + c * x ^ 2
The degree would be 5
elfin cloud
So I would put the numbers and stuff into the formula you gave? And that would t...
If you can write them in the SHAPE of the formula i just gave
Lets start at a)
Can we weite x^6 + 3rd root (x) - 4 as a+ b * x + …
lethal trout
So -4 + x^6 + 3/x
elfin cloud
x^6 … yes
That would be 1 * x^6
-4 … yes
That would be still -4
3rd root of x
No, we cannot write it as an integer exponent
elfin cloud
So -4 + x^6 + 3/x
the 3rd root of x does not equal 3/x
Also, negative exponents (so division by the variable x) also disqualify the equation from beging a polynomial
elfin cloud
So this part makes it not a polynomial
Yes thats right 🙂
Can you try b) by yourself now?
lethal trout
Okay ty yes
elfin cloud
Btw I forgot a piece of information about the multivariable polynomials which youll probably need for b
Polynomials with more variables also have the multiplications with eachother
So it would be
a + b * x + c * y + d * x^ 2 + e * y ^ 2 + f * xy + g * x ^3 + h * y ^ 3 + i * x^2 * y + j * x * y^2
I HOPE this is somewhat clear but polynomials with multiple variables can become long when fully written out
and if you have a polynomial x * y ^ 4 for example
The degree would be 5, because we have x^1 AND y^4 which are multiplied wirh eachother, so in total theirs 5 times we multiply a variable
Just try it because this explanation is becoming less and less clear sry
lethal trout
B is a polynomial because there’s no negative integers or square root? And the degree would be 7
My math teacher told me the degree would be the biggest exponent
