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#help-17
vocal sleetBOT
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rugged hazel
if u have a table like this is it possible for x and y to be independent?
rugged hazel
like a+b+c+d = 1
and a = (a+b)(a+c)
b = (a+b)(b+d)
it doesnt look like a, b, c, d can be a value to satisfy everything
vocal sleetBOT
@rugged hazel Has your question been resolved?
weak terrace
Yenna started to deposit 2500 pesos monthly for her child education that pays 8% compounded quarterly.
How much will be her earnings after 20 years?
vocal sleetBOT
Yenna started to deposit 2500 pesos monthly for her child education that pays 8%...
weak terrace
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untold arrow
vocal sleetBOT
untold arrow
Can anyone explain this one line answer
bitter pilot
They substituted x = g(y) and then applied integration by parts.
twin meteorBOT
𝔸dωn𝓲²s
vocal sleetBOT
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marble sinew
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I need help with business math, I wanna check if my answer is correct or if I did it wrong
vocal sleetBOT
I need help with business math, I wanna check if my answer is correct or if I di...
uneven flicker
!15m
vocal sleetBOT
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.
@marble sinew Has your question been resolved?
marble sinew
Yepp, but it'll just be same, since 0 is still nothing, our teacher just wants us to add the extra zeros
somber portal
...what
you're computing your values as if your interests were 1% and 1.2% instead of 10% and 12%, you're off by way over a full order of magnitude in both cases
somber portal
the answer to first is over 5.8 million, while his is 300k
somber portal
5.8M/322k = 18?
hidden gyro
strange
vocal sleetBOT
@marble sinew Has your question been resolved?
reef bronze
Find the vector x if:
vector x is perpendicular to vector a
vector x is perpendicular to vector b
vector a = (2; 0; 1)
vector b = (1; 0; 2)
angle between x and y axis>90 degrees
and |x| = 4
still mica
What's y @reef bronze
reef bronze
Y axis
still mica
What did you try?
reef bronze
to make a picture of vectors, their (location?)
still mica
Notice that, if two vectors are perpendicular their dot product is zero
I would recommend assuming a vector (p,q,r)
reef bronze
can the cross product help me to solve that?
still mica
Not that I can think of
somber portal
Find the vector x if:
vector x is perpendicular to vector a
vector x is perpend...
are we working on R3?
reef bronze
are we working on R3?
?
somber portal
are you working in euclidean space?
reef bronze
yep
somber portal
okay, so remember that the vectorial product of two vectors gives you a third vector perpendicular to both
reef bronze
yep
somber portal
you can then scale it to have |4|, and you will obtain two possible vectors
one will have an angle between it and y axis of over 90º, and the other of less than 90º
reef bronze
i understood
i cannot load images
but from the equations of dot product i got simple equations of
2x(2)+x(3)=0
x(1) + 2x(3)=0
and of the length of the vector
16 = x(1)^2+x(2)^2+x(3)^2
that's it
thx
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limber dragon
some blender users?
vocal sleetBOT
some blender users?
limber dragon
i'm having problems to understand the function behind the socket Edge Cost of Shortest Edge Path node (in geometry node), can someone try to explain this?
i also opne a discussion on reddit if you want more detailed infos https://www.reddit.com/r/blenderhelp/comments/1gym4q7/comment/lyqh61g/
vocal sleetBOT
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main totem
vocal sleetBOT
main totem
Im not exactly sure how to reverse engineer r(u,v) parametric representations into functions of f(x,y)
so I could get z, for example
vocal sleetBOT
@main totem Has your question been resolved?
paper spoke
okay lets start off with the basics
paper spoke
Im not exactly sure how to reverse engineer r(u,v) parametric representations in...
since we are given the parametric representation of a cone, what does x y z equal to
main totem
since we are given the parametric representation of a cone, what does x y z equa...
x = ucosv, y=usinv, z = u
since we have to convert from polar to cartesian
paper spoke
where did the a and c go?
paper spoke
I think you're approaching it the wrong way
main totem
so what do I do
paper spoke
hang on
main totem
did you want:
x = ucosv/a, y=usinv/a, z = u/c
paper spoke
yea sure
now express u in terms of x and y
isolate u
this is the easiest approach, not too sure what you were doing before
main totem
this is the easiest approach, not too sure what you were doing before
no, I dont understand this approach
paper spoke
no, I dont understand this approach
okay well it's easy to understand
do you know how to isolate u?
main totem
do you mean make u the subject of the formula?
main totem
I dont know how to do that
like here: x = ucosv/a
like I dont know how to construct some sort of relationship between x & y to equate u
unless I had an idea of what axis I was converting between
main totem
express u in terms of x and y
i mean, it does say u=const, v=const
so why would I need to parameterise it in terms of variables in the first place
main totem
im sorry, I just dont understand what do
main totem
sorry was helping another jit
jit is crazy
main totem
I could take the derivative of one of them
paper spoke
no..
main totem
hmpghhhhhhh
i just dont know how you got the intuition for that though
like I would have never thought of doing that lmaoo
but anyways
paper spoke
just with practice
algebra is like sheet music, the important thing isn't can you read music, it's can you hear it
main totem
yep, I totally agree
paper spoke
so can you square both equtaions and add them?
paper spoke
what do you get
main totem
(u^2 + v^2) / a^2
main totem
well you told me to square x & y
main totem
x = ucosv/a, y=usinv/a
main totem
if x and y are this
paper spoke
thats not x and y
main totem
oh okay
main totem
yeah I see it
paper spoke
x = ucosv/a, y=usinv/a
wait why are you dividing it by a?
paper spoke
did you missread the values
main totem
wait why are you dividing it by a?
i thought it was the right thing to do? idk
main totem
okay
paper spoke
do you know where it is given to you
paper spoke
okay yes
so there shouldnt be any mistake in interpreting x y z
okay so
what does x and y equal to
main totem
x=aucos(v), y=ausin(v), z = cu
paper spoke
yessir
main totem
I just thought I would want to isolate the variables
main totem
x = ucosv/a, y=usinv/a
so I divided here
paper spoke
x=aucos(v), y=ausin(v), z = cu
focus on x and y and square both equationts real quick
and type them to me
main totem
x = a^2 * u^2 * cos^2(v), y = a^2 * u^2 * sin^2(v)
paper spoke
im having a stroke reading that i'll just show you it
$x^2+y^2=(au\cos v)^2+(au\sin v)^2$
main totem
alright
twin meteorBOT
rsizo
main totem
yep
paper spoke
when you square and add both of them it shoud look like that
main totem
thats what I wrote
main totem
(au)^2
main totem
oh shit
paper spoke
yea rookie mistake
main totem
I should expand the brackets
paper spoke
no need
what can you bring out
of the two brackets
remember, you are trying to eliminate v
paper spoke
yessir
main totem
therefore im left with a^2u^2
main totem
hence why I said (au)^2
paper spoke
ohh
main totem
arent they not the same thing?
paper spoke
sorry ididnt see that
main totem
so what do I do with the z
main totem
sqrt((x^2+y^2)/a^2)
twin meteorBOT
rsizo
paper spoke
are you on board
main totem
ive already isolated for u
main totem
sqrt((x^2+y^2)/a^2)
here
paper spoke
that's not right
main totem
x+y/a ?
paper spoke
no yo ucant just square root x^2+y^2 like that
the a^2 yo ucan cancel
square root of a^2 is a
paper spoke
so what does u equal
main totem
sqrt(x^2+y^2)/a
paper spoke
yess
good
now we have u
now just sub it into z
then you have the answer
see wasn't so hard was it?
main totem
so
paper spoke
so we know z = cu
main totem
+/- c*sqrt(x^2+y^2)/a
paper spoke
and we know u
Yes
good job
now get a blank piece of paper and put everything away
and do the problem again
with no help
main totem
thank you
paper spoke
👍
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sage lava
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sage lava
I have a test tomorrow and this is the material it’s on, I’m honestly lost
vocal sleetBOT
@sage lava Has your question been resolved?
sage lava
No
obsidian kindle
wtf even is this
vocal sleetBOT
@sage lava Has your question been resolved?
sage lava
wtf even is this
Idfk
uneven quarry
Hmm so
$$\dot{\vec a}(t) = \vec A \times \left(\vec a(t) + \vec b(t) \right)$$
and
$$\dot{\vec b}(t) = \vec B \times \left(\vec a(t) + \vec b(t) \right)$$
where $\vec A$ and $\vec B$ are constants. All are 3D vectors.
Do any of you have any intuition for the motion of $\vec a(t)$ and $\vec b(t)$, that will probably surpass mine?
vocal sleetBOT
Hmm so
$$\dot{\vec a}(t) = \vec A \times \left(\vec a(t) + \vec b(t) \right)$$
a...
twin meteorBOT
Ginger
uneven quarry
one thing we can say (like by adding the equations) is that the sum $\vec a + \vec b$ rotates steadily about the constant vector $\vec A + \vec B$
twin meteorBOT
Ginger
uneven quarry
neverminddd idk i forgot there's anoter term
it's complicated so i will close
the question
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vocal sleetBOT
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livid void
vocal sleetBOT
livid void
(-pi/16) is a constant multiple right?
dire wolf
Calculate the average value of the function $$f(x) = \frac{\pi}{16} \sin x$$ on the interval $$[0, \pi]$$
Set the function equal to its average value and solve for $$x$$ within the given interval
Calculate the Average Value of the Function
The average value $$A$$ of a function $$f(x)$$ on the interval $$[a, b]$$ is given by:
$$A = \frac{1}{b-a} \int_a^b f(x) , dx$$
Here, $$a = 0$$, $$b = \pi$$, and $$f(x) = \frac{\pi}{16} \sin x$$. Thus,
$$A = \frac{1}{\pi - 0} \int_0^\pi \frac{\pi}{16} \sin x , dx$$
The average value of the function $$f(x) = \frac{\pi}{16} \sin x$$ over the interval $$[0, \pi]$$ is $$\frac{1}{8}$$
Find Points Where $$f(x) = \text{Average Value}$$
We need to solve:$$\frac{\pi}{16} \sin x = \frac{1}{8}$$
Let's solve this equation for $$x$$ within the interval $$[0, \pi]$$.The solutions to the equation $$\frac{\pi}{16} \sin x = \frac{1}{8}$$ within the interval $$[0, \pi]$$ are $$x \approx 0.6901$$ and $$x \approx 2.4515$$ therefore Yes, (-\frac{\pi}{16}) is indeed a constant multiple.
twin meteorBOT
| ~ вєℓℓα ❄⛄
livid void
Calculate the average value of the function $$f(x) = \frac{\pi}{16} \sin x$$ on ...
b = - pi
im up to 1/8
not sure how to solves
$\frac{1}{8} = \frac{\pi}{16} \sin{x}$
twin meteorBOT
Ousel
livid void
$\frac{\pi}{2}=\sin{x}$
twin meteorBOT
Ousel
livid void
$x=\sin^{-1}{\frac{\pi}{2}}$
twin meteorBOT
Ousel
vocal sleetBOT
@livid void Has your question been resolved?
dusty cypress
Anyone know how to do c?
pale widget
Think about how the convexity lets you make an inequality in terms of the global minimizer x* and the local minimizer y*
dusty cypress
Think about how the convexity lets you make an inequality in terms of the global...
I think I solved it, F(x*) >= q(y*) ? and then I got the same inequality as (1).
but I am not sure how to explain what it means for d
do u know?
vocal sleetBOT
@dusty cypress Has your question been resolved?
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@dusty cypress Has your question been resolved?
tame river
i need help with this
vocal sleetBOT
i need help with this
sharp lynx
where is that 1! in the denominator coming from
tame river
where is that 1! in the denominator coming from
probably from the vid i was following as help
whatever im doing is probably wrong
sharp lynx
indeed
the video is making use of the fact that n! = n*(n-1)!
you need to do a little more work to get it into that form
tame river
ok.
tame river
you need to do a little more work to get it into that form
tbh, i dont have a clue on how to solve this problem
regal slate
whats 18-7?
tame river
11
regal slate
so how'd you get 1?
tame river
ohh.
tame river
so how'd you get 1?
so, 18/11 as the next step?
regal slate
whats 18!
regal slate
no, write out the terms
tame river
regal slate
can you think of a way to get rid of more terms instead? maybe something to do with the 11! in the denom?
regal slate
Almost, you wouldn't cancel out 7! if you're canceling all terms after and including 11
tame river
think about it this way
i'll come back to figuring this problem out later,
thanks thro
.close
regal slate
You can rewrite 18! in the following manner - 18*17*16*15*14*13*12 * 11!
vocal sleetBOT
regal slate
Oh, bet
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tame river
I need help with this, im not sure what to do to solve it
vocal sleetBOT
I need help with this, im not sure what to do to solve it
@tame river Has your question been resolved?
flat whale
I need help with this, im not sure what to do to solve it
Did you learn binomial theorem
tame river
Did you learn binomial theorem
yes
flat whale
Do you know summation notation
tame river
yeah
flat whale
Did you learn binomial theorem
Did you try using this
tame river
tbh, kinda struggling with it
flat whale
tbh, kinda struggling with it
Show
vocal sleetBOT
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dim wind
vocal sleetBOT
dim wind
how to do b) using the beta function?
dim wind
yes but i cant find a u sub for it
dim wind
Also show the definition of beta function you learned.
First two ig
it's [0,1] so ig we are going to use the first one
vocal sleetBOT
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dim wind
<@&286206848099549185> anyone?
compact fable
can someone explain how you know x = 2 is a local max
vocal sleetBOT
can someone explain how you know x = 2 is a local max
dim wind
And it's concave down right?
dim wind
f'(x) should be 0?
compact fable
oh gotcha yea
dim wind
then how can it be max if the function can increase or decrease
dim wind
oh gotcha yea
does that answer your question?
compact fable
well i understand the first part now
the f'(2) = 0
but im confused about the second part
f''(2) = -5
dim wind
f"(x) < 0 ?
dim wind
yes
dim wind
np local max
compact fable
.close
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vast shale
Does this hold true for every number?
(a^b)^c = a^(bc) and vice versa
tulip cedar
what do you mean and vice versa
vast shale
That a^(bc) = (a^b)^c is true, too.
Never mind
It's the same thing
Does this hold true for every number?
tulip cedar
Yea
prisma rain
assuming positive reals
vast shale
bruh
prisma rain
complex is complex
tulip cedar
😭
vast shale
I wanted to trick bean man
tulip cedar
Is this an actual question or
vast shale
it's a legit question
severe flint
im not sure if there's any good way to explain eulers equation without a decent understanding of calculus
surreal basin
have you tried https://www.youtube.com/watch?v=v0YEaeIClKY
this is what worked for me, even though it may not be immediately believable
severe flint
have you tried https://www.youtube.com/watch?v=v0YEaeIClKY
that's still technically calculus if you were more rigorous about it but yeah it's a 3b1b video, it's good
i recommend
surreal basin
have you tried https://www.youtube.com/watch?v=v0YEaeIClKY
you will see a calculus idea be used to justify doing anything like e^(i * number)
see if you understand it
severe flint
okay yeah there are derivatives in this video but it's nothing hard if you do know enough basic calculus
vast shale
so this is not true for complex numbers?
(a^b)^c = a^(bc)
surreal basin
not true
surreal basin
have you considered staying to consider when it does work
vast shale
I'll see that llater. I just wanted to know whether it's always true or not
severe flint
i mean, (e^pi)^i is still -1
surreal basin
surely theres more numbers than just e, pi, and i
see if you can find a counterexample
heavy yoke
the value you assign to (e^pi)^i is dependent on your choice of branch of the complex logarithm. so it's only -1 using the principal branch
tawny hollow
In general if you have two functions that agree with eachother for real inputs and there’s a corresponding holomorphic extension of these functions, then they must agree for complex inputs
prisma rain
$(-1)^2 = 1$ then $((-1)^2)^{1/2} = 1^{1/2}$ therefore $-1 = 1$ QED
twin meteorBOT
kaue
vocal sleetBOT
@vast shale Has your question been resolved?
vast shale
QED fr
last grail
help
viral copper
Have you learnt about the special formula for 1^infinity?
last grail
no?
twin meteorBOT
nœn
last grail
😭 can u tell me from where i could learn this?
viral copper
Organic Chemistry Tutor probably has a video on 1^infinity forms
last grail
oh
last grail
Organic Chemistry Tutor probably has a video on 1^infinity forms
can u please send me the working of this tho? i might understand
last grail
exp is basically e right?
viral copper
Paul's Online Math Notes probably
But tbh there aren't many
Other than the standard limits this is like the only big one
vocal sleetBOT
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half jetty
What am o doing wrong here exactly
ebon sand
What am o doing wrong here exactly
what is the question?the first statement?
half jetty
what is the question?the first statement?
yep
also the last term in the numerator is n
not x
ebon sand
did you try l hopital
half jetty
that's what i did
ebon sand
did you try l hopital
cause im pretty sure thats all you need to do
half jetty
without the summation
yeah im getting an arithmo-geometric progression
ebon sand
yeah im getting an arithmo-geometric progression
idk what that is but i got n is 40
half jetty
idk what that is but i got n is 40
I meant 1 + 2x + 3x^2 + ... + nx^n-1
arithmetic + geometric series
gotta figure out how to solve that noow
half jetty
oops didn't catch that
ebon sand
so n *(n+1)/2
half jetty
tysm
ebon sand
no problem
vocal sleetBOT
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golden rapids
I cant figure out how to find the point of intersection for question 16
mild flower
it's not really different than any other one
get them both into standard form first
Ax + By = C
golden rapids
Ax + By = C
So the standard form for both equations should be
2x+4y=-2
x+3y=1
Then get started using elimination menthod?
vocal sleetBOT
@golden rapids Has your question been resolved?
mild flower
yep that seems good
vocal sleetBOT
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vapid kiln
How do I find x?
vocal sleetBOT
How do I find x?
queen root
How do I find x?
can u prove that [OP) is the angle bisector of APB
vapid kiln
can u prove that [OP) is the angle bisector of APB
Yep
queen root
its simple
vapid kiln
ok do yk trigonometry?
Yeah
queen root
well then u have ur answer
OBP is a right triangle in B
and u can find angle OPB since u know [OP) is an angle bisector of APB
vapid kiln
and u can find angle OPB since u know [OP) is an angle bisector of APB
Do I use tangent 25 = 3/x
queen root
yes
vocal sleetBOT
queen root
np
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Available help channel!
last grail
guys
last grail
big doubt with limits
how is this even possible?
original q
this is my working so far
and then the next step was supposedly to make that polynomials in the fraction more simpler right?
viral copper
last grail
what I don't comprehend is that how are is it that random numbers are being subtracted from the numerator
viral copper
this is my working so far
What exactly is happening here?you just wrote it with an e^ln?
vast shale
I think they're just doing an algebra trick to simplify it to 1 - (2x + 6)/(2x^2 + 3x + 3)
last grail
What exactly is happening here?you just wrote it with an e^ln?
where did i put e^ln lol
last grail
I think they're just doing an algebra trick to simplify it to 1 - (2x + 6)/(2x^2...
i dont understand the trick
vast shale
(2x^2 + x - 3) / (2x^2 + 3x + 3) cannot be simplified as is
But if you add and subtract 2x + 6 from the numerator, it simplifies down to 1 - (2x + 6)/(2x^2 + 3x + 3)
viral copper
Oh I see what's happening
last grail
(2x^2 + x - 3) / (2x^2 + 3x + 3) cannot be simplified as is
But if you add and ...
oh, but how was i supposed to know that i needed to subtract and add the 2x-6 thingy
like what was i supposed to do, eliminate something or
viral copper
because then you can get in in terms of the standard limit that you (hopefully) know
ln(1 - x)/x as x --> 0
vast shale
You just had to match the numerator to the denominator
You could only do that by adding on 2x and then 6
It's an obscure trick but useful sometimes
last grail
okay
viral copper
(2x^2 + x - 3) / (2x^2 + 3x + 3) cannot be simplified as is
But if you add and ...
basically (2x + 6)/(2x^2 + 3x + 3) goes to 0 as x goes to infinity so same thing
last grail
but wait
what after that
tch
yeah what after this i dont really get it
like
do i add and subtract something again
somber notch
original q
first of all take x^2 common from num and den inside the bracket
last grail
first of all take x^2 common from num and den inside the bracket
okay
somber notch
you will be left with
(2+ 1/x - 3/x^2) / ( 2+ 3/x + 3/x^2) there
so 1/x and 1/x^2 terms will be zero
as x --> inf
last grail
yes
somber notch
yes
somber notch
so 1/x and 1/x^2 terms will be zero
now this
somber notch
we will deal with that now
now we have (1)^ (something)
so something is (x - 1/x)
last grail
somber notch
yes
somber notch
i dunno you solve
last grail
i learnt limits today sorry
somber notch
i will send pic
last grail
i will send pic
um?
somber notch
what I don't comprehend is that how are is it that random numbers are being subt...
they are not random
there are a few methods to solve this type of limits
what is the answer e ? @last grail
last grail
what is the answer e ? <@958724397441642506>
its 1/e
somber notch
oh yes my bad missed that - sign
last grail
uh
somber notch
so
somber notch
how is this even possible?
they did this
wait i will send pic
then you solve the power
there take x^2 common
vocal sleetBOT
@last grail Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
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silk flower
!status
vocal sleetBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
vocal sleetBOT
silk flower
gl
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neat geode
hi
neat geode
I sat a mock exam today gcse higher
well we answered some questions as a class collectively
I kind of want to go through it on call with somebody if that’s possible
if anybody’s free please let me know
vocal sleetBOT
@neat geode Has your question been resolved?
vocal sleetBOT
@neat geode Has your question been resolved?
vocal sleetBOT
neat geode
.reopen
vocal sleetBOT
✅
vocal sleetBOT
@neat geode Has your question been resolved?
hollow fern
vocal sleetBOT
hollow fern
not even AI can help me because it doesnt recognise circle theorem
ive been looking at this question for like a solid few hours 😭
pretty please
probably a really easy question to solve for some
i understand that there is a right angle
duhh
vast shale
Note that OA and OB are the same because they are both radii.
So <OBA is also 11x
vast shale
Yes
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astral rain
Please help me with this. Calc 3 stokes theorem. i have tried it 15 times lol.
tacit perch
Curl = (1, 1, 1)
astral rain
i got that and for rx cross ry i got <1,1,1>
loud walrus
What else u got?
astral rain
i did the dot product of htose to get 3 and for my bounds i did dydx with x bounds being 0 to 3 and y bounds being 0 to 2x and then i tried0 to 6-x and also 0 to 6
tacit perch
Pick the surface as
S1: y=0 {0<x<3, 0<z<-2x/3 +2}
S2: x=0 {0<y<6, 0<z<-y/3 +2}
S3: z=0 {0<x<3, 0<y<-2x+6}
astral rain
okay
tacit perch
18?
tacit perch
D:
astral rain
my friend and i both got 54 and the website says its wrong
so maybe the website is just wrong or idk this is way too hard anywyas
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glossy cypress
Can someone help me? Im not sure y only found that the base of both squares are = 8 times root of 2
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glossy cypress
Can someone help me? Im not sure y only found that the base of both squares are ...
gaunt sparrow
From the way this is asked, if you really just want to know the answer, why not assume they meet at the origin?
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pine flume
Only looking for help on a for now, honestly just completely lost and google hasnt been helping. Im confused how the Laurant series come into play.
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pine flume
Important to add, z is complex
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blazing glacier
Helpppppppppp
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Helpppppppppp
blazing glacier
Helpppppppppp
,rotate
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blazing glacier
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hidden gyro
ok
x^2-x+1
=x(x-1)+1
p(alpha) = k
p(p(p(k))) = 0
you want
(k-1)(p(k))(p(p(k))
k-1 = ((p(k))-1)/p(k)
so
(k-1)p(k)=p(k)-1
hidden gyro
(k-1)(p(k))(p(p(k))
= p(p(k))(p(p(k)-1)
=p(p(p(k)))-1
=-1
so the answer is 1
@blazing glacier
blazing glacier
Okk tbh
I didn't get anything @hidden gyro
blazing glacier
Yea
hidden gyro
so p(x)-1 = x^2-x
blazing glacier
Ohk
hidden gyro
p(x)-1 = x(x-1)
blazing glacier
Okk
hidden gyro
so (p(x)-1)/x = (x-1)
blazing glacier
Hmm seems fair
hidden gyro
so (p(p(x))-1)/p(x) = p(x)-1
blazing glacier
What ?? 🥹
hidden gyro
substudtued p(x) as x
blazing glacier
I see
blazing glacier
= ((p(p(x))^2-p(p(x))+1 -1)/p(x)
My puny brain couldn't handle this one
hidden gyro
so (p(p(x))-1)/p(x) = p(x)-1
multiply the lhs by p(p(x))
blazing glacier
Okk
blazing glacier
Wait no wth
blazing glacier
= (p(p(p(x))) - 1 )/p(x)
??
hidden gyro
p(x)=x^2-x+1 right?
blazing glacier
Yes
hidden gyro
so p(p(p(x))) = p(p(x))^2-p(p(x))+1
hidden gyro
do you get the asn from now
my prev answer was wrong, sry, it should have been |1/p(x)| r u sure the original qn did not have a p(x) term?
blazing glacier
my prev answer was wrong, sry, it should have been |1/p(x)| r u sure the origina...
No I am sure
It didn't have that
blazing glacier
How can I do it ?
blazing glacier
but that is lengthy, and will not give a nice soln
Yea exactly
hidden gyro
can you send original qn
blazing glacier
can you send original qn
The picture I sent is the question available to me
hidden gyro
oh
because i have solved a similar qn earlier, and that had a p(x)(p(x)-1)p(p(x))p(p(p(x)))
everything else was same
blazing glacier
Ohh
Then those p(x) cancel out and 1 is the answer
hidden gyro
Ohh
Then those p(x) cancel out and 1 is the answer
yeh
blazing glacier
Okk thanks for help
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golden coral
Hey, I’m currently working on a differential equations test revision and I currently have a solution for part b but am not sure it is correct: All of the information is attached below.! Im sure I got part a right i just need to rework b.
golden coral
<@&286206848099549185>
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fallow gull
now why u impersonating me
golden coral
now why u impersonating me
nah what 😭
brittle cipher
golden coral
differential equations
fallow gull
did I even get to that point in calc bc yet
fallow gull
this is supposed to be a second order diff eq
oh this is chem too..
I knew I should’ve taken ap chem this yr bro
golden coral
nah it’s not chem they’re just giving us a chem topic
fallow gull
oh okay
golden coral
which makes it 10 times harder than it needs to be 😞
sharp rain
Why are there 3 types of y 
golden coral
Why are there 3 types of y <:cat_happycry:636407813144576010>
nah it’s horrible
uppercase Y is amount lowercase with italicize is concentration and regular lowercase is chemical species y
they all are talking about the species just different measurements
sharp rain
Hey, I’m currently working on a differential equations test revision and I curr...
Why the hell is this
golden coral
basically they are both reacting with each other so they both have the same rate of change depending on their concentrations
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silver tusk
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silver tusk
i tried dearragement and didn't work
dark kiln
i think it's 14
to make a match you choose 4 couples
then there's 3 pairings, 1 with 2, 1 with 3, or 1 with 4
and then you can swap the gender of each team
so (X C 4)*8*3 should be 840
and X = 7 works
wait what
no it should be times 4 not 8
X = 8 then
visual forge
its 8 couples right? so shouldnt it be 16 ppl
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visual forge
I'm not exactly sure but this is how I did it:
- Number of ways to choose two males: nC2
- Number of ways to choose two females: nC2
- Total number of combinations: nC2 * nC2
- For each pair of males, their partners are excluded from the selection of females to avoid couples playing together. Therefore, for each selection of two males, there are (n-2)C2 ways to choose two females (excluding their partners).
- So total number of valid matches would be: nC2 * (n-2)C2 * 2 = 840
- Simplify the equation and you'll get n(n-1)(n-2)(n-3) = 1680
- I put the above into a calculator and got 4 answers: 2 complex, 1 negative and 1 positive answer.
- The positive number is the only valid one, hence the number of couples is 8.
- Which means the total number of people is 16
If someone else can verify this, that would be appreciated. Not too confident
silver tusk
I'm not exactly sure but this is how I did it:
1) Number of ways to choose two ...
wrong
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fathom bobcat
what's lim x->0+ of (lnx)^x
vocal sleetBOT
what's lim x->0+ of (lnx)^x
civic otter
I don't think that function is defined for x < 1
Because the base has to be non negative in order for that exponential function to make sense
tidal dock
if you consider imaginary numbers this limit still exists and is real
tidal dock
what's lim x->0+ of (lnx)^x
start by rewriting (ln(x))^x as exp(ln((ln(x))^x)) = exp(x*ln(ln(x)))
compute $\lim_{x\to 0^+} x\cdot ln(ln(x))$
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artemetra
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thorn inlet
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thorn inlet
i need help with this problem
im new to Taylor Expansion ngl, learned it yesterday xd
<@&286206848099549185>
vast shale
Is an online calculator allowed? That seems like a ton of work going all the way to degree 9
And not "good" work either
thorn inlet
Is an online calculator allowed? That seems like a ton of work going all the way...
nah
im an asian
we do papers around here lol
vast shale
Ok, I'd probably rewrite it using partial fractions first
thorn inlet
already do it tho
so its should look like
uhh i dont know how to use latex in discord lol
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vast shale
The Taylor series expansion would just be this summation here ... like I said earlier a lot of computation
Hopefully the derivatives are a bit easier to compute with the partial fraction version
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vast shale
I didn't really skip any steps, that's just the template for a Taylor series.
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viral igloo
hii can u please give me a function f: R -> R that is continuous only at 0 and 1. Thank you
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hii can u please give me a function f: R -> R that is continuous only at 0 and 1...
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viral igloo
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hidden gyro
hii can u please give me a function f: R -> R that is continuous only at 0 and 1...
yes
are you fine with direct answer?
if so
viral igloo
yes
hidden gyro
||if x is rational, than f(x) = x-x^2, if x is irrational, than f(x) = 0 ||
viral igloo
thank you 👍
hidden gyro
try to prove the continuity yourslef
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crude swan
need help showing that this series is a cauchy series.
crude swan
someone suggested using the fact that 1/k^2 < 1/k(k-1) and turning the latter into a telescopic series to help with the proof
i did that but i don't know where to go from here.
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plain sand
Guys I have a question, I determined that the domain of the function is the sum of all real numbers except -2,2, and I got (3,0) and (-2,0), so I should throw it out. (-2,0) so I was wondering if I get (2,0),(1,0),(0,0) and (-1,0) should I throw them out too?
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Guys I have a question, I determined that the domain of the function is the sum ...
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sly rain
i dont know if i can post physics but i somehow got 1 as the total resistance of Y and Z while i got 4 for X
the answer according to the mark scheme is option A
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i dont know if i can post physics but i somehow got 1 as the total resistance of...
boreal remnant
1/R_Y = 1/(2R) + 1/(2R) = ?
boreal remnant
try again
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strange charm
Hi
strange charm
I'm working on the second set of solutions in part b
$$a^{2n+1} \equiv -1 \pmod{p}$$
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toast
strange charm
i was wondering if this is particulary useful
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strange charm
oh i figured it out i think
ionic marlin
can i please get some help in calculating the limits for the doubel integral?
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can i please get some help in calculating the limits for the doubel integral?
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severe dagger
<:mathicoadvanced:1026533136357670922>
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blissful sentinel
Oh wow that's a cool problem, lemme take a look
What are the bullet points underneath the question for? Are those hints? Do we already know that those sets are undecidable?
Also what does <M> mean? Is that the number corresponding to the TM M?
What exactly do you mean by "reject" in your solution? Does that mean "halt and return 0" or does it mean "go into an infinite loop"
It's not clear to me what the logic of your attempt is exactly, it seems like no matter what, S yields a context-free language (either w^n or just the empty language), so R isn't really doing anything.
severe dagger
What are the bullet points underneath the question for? Are those hints? Do we a...
yes, sorry i shouldve clarified that. those problems are confirmed to be undecidable and we are allowed to use them in our proof if need be
severe dagger
Also what does <M> mean? Is that the number corresponding to the TM M?
its the input and M itself is the TM from what i gather
blissful sentinel
okay I see
severe dagger
What exactly do you mean by "reject" in your solution? Does that mean "halt and ...
i was thinking it means both? like reject is simply the non accept state
blissful sentinel
Those are two very different behaviors, so you'll prob want to clarify in any potential solution