is all i need to do is just to simplify?
#help-0
dense matrix
tacit arch
,rotate
ocean sealBOT
lofty creek
its simply simplifying
dense matrix
:D okay ill try to do and say the answer
give me a second
1,28571429 * 10^14?
the simple numbers added up to being 0,28571429 * 10^4
but to turn it to a 1,28571429 I *10 both sides
is that right?
or should i do the complete opposite with *10 the first number and then -10 the factor on the second number
lofty creek
that doesnt look quite right
dense matrix
as in 1,28571429 * 10^-6
oh nvm figured it out, was doing it wrong
sey
sry
.close
winter ivy
I know I asked this yesterday and the day before, but I am still unsure of how to contiinue from this point
winter ivy
is there only one correct solution? Because for example we can say that -1/n pi cos(npi)= (-1)^(2n+1) right?
because that would satisfy the conditions of even and unevenness
vale crag
why did your 1/n even disappear
winter ivy
oh there you mean
vale crag
what
winter ivy
I plugged in the n=0, n=1, n=2 for the top, middle, and bottom row respectively
because I have no clue what Im doing
vale crag
ok fine
winter ivy
just wanted to find an expression for b_n in terms of even and uneven values of n
little prawn
you dont need to know that tho
cos(pi(n))
is (-1)^n
so you just have (((-1)^n+1)/n
right
winter ivy
right
little prawn
that is your bn
vale crag
it also works
tacit arch
(-1)^2 = 1
vale crag
they're essentially the same though
little prawn
tehn you have to do two sums
winter ivy
thats 0
winter ivy
right? cuz cos(pi/2)=0
little prawn
np gl
winter ivy
.close
alpine sable
in pemdas what am i suppost to do with the perenthesis i thought it was to multiply
lone heartBOT
in pemdas what am i suppost to do with the perenthesis i thought it was to multi...
@alpine sable Has your question been resolved?
tacit arch
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gentle comet
can someone help me with this?
lone heartBOT
can someone help me with this?
lone heartBOT
@gentle comet Has your question been resolved?
junior vigil
can someone help me with this?
!showwork
lone heartBOT
can someone help me with this?
Show your work, and if possible, explain where you are stuck.
junior vigil
do you know what A \ B means? How to write it in terms of intersection?
gentle comet
yea i think its A - A intersection B
junior vigil
that's still not completely in terms of intersection
one way you can think about this is 'everything in A that's not in B'
how would you write this in terms of intersection?
gentle comet
how would you write this in terms of intersection?
idk what terms of intersection means
the only thing i know is P( A \ B ) = P( A ) - P( A ∩ B )
gentle comet
can someone help me with this?
so how we can calculate P(B) if P( B ) = P( B \ A) + P( A ∩ B )
and we dont know what P( A ∩ B ) equals to?
junior vigil
what is the formula for P(A U B)?
what happens if we add the formulas for P(A \ B) + P( B \ A)?
:)
gentle comet
we get P(A U B) but without the intersection?
junior vigil
what's the formula for P(A U B)
write it out like you did the others
and compare it to formula for P( A \ B) + P ( B \ A)
gentle comet
P(A U B) = P( A ) + P( B ) - P( A ∩ B )
gentle comet
idk
junior vigil
just add the formulas you got for P(A \ B) and P(B\A) together
what do you get?
@gentle comet
gentle comet
please idk what are you saying
junior vigil
P( A \ B ) = P( A ) - P( A ∩ B )
P( B \ A ) = P( B ) - P( A ∩ B )
P( A \ B ) + P( B \ A ) =
add the equations
gentle comet
P( B ) - P( A ∩ B ) + P( A ) - P( A ∩ B )?
junior vigil
yes...
and you can rearrange this...
to...
P( A )+P(B) - P( A ∩ B ) - P( A ∩ B )
do you see what you can do?
:)
gentle comet
sry but i dont
junior vigil
what was P(A U B)?
junior vigil
you know P(A U B), you know P(B/A) and P(A/B)
so you can find P(A n B)
which allows you to find P(B)
gentle comet
P( A \ B ) + P( B \ A ) = P(A U B) - P( A ∩ B ) - P( A ∩ B )
.15 + .25 = .65 - P( A ∩ B ) - P( A ∩ B )
-0.25 = - P( A ∩ B ) - P( A ∩ B )
.125 = P( A ∩ B )
right?
gentle comet
you have an extra P( A ∩ B )
i just put -2 P( A ∩ B ) instead of writing it again
junior vigil
no i mean you should just have P(AUB)-P(A ∩ B)
not P(A U B) - P( A ∩ B ) - P( A ∩ B )
P(A U B)=P( A )+P(B) - P( A ∩ B )
gentle comet
oh
junior vigil
i wrote the P(A U B) in bold
do you see?
@gentle comet
I was just writing down the equation you had for P(A \ B) + P(B\A), rearranged it
gentle comet
ok so P(A\B) + P(B\A) = P(A U B) - P( A ∩ B )?
junior vigil
yes :)
and this allows you to solve for P( A ∩ B ), exactly as you did before, without the dividing by 2
mighty cliff
The numbers 5, 6, 7, 8, 9 are all possible
five-digit numbers without repeating digits. How many
among these even numbers?
mighty cliff
need help with solution and explanation
fallen verge
!original
lone heartBOT
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.
fallen verge
The question does not make sense
mighty cliff
Why
Of the numbers 5, 6, 7, 8, 9, all five -digit numbers were compiled without repetitions
How many paired among them
mighty cliff
The numbers 5, 6, 7, 8, 9 are all possible
five-digit numbers without repeating ...
<@&286206848099549185>
lofty creek
what does it mean to be an even number
mighty cliff
If the number ends with 0, 2, 4, 6, 8, then this number is even.
mighty cliff
oh, I think I understand, if numbers can only end in 0, 2, etc. then there are only two numbers here: 6 and 8
then it turns out 6*8=48
lofty creek
then it turns out 6*8=48
not quite
how many 5 digit numbers can we make with these numbers
and how many of them end with 6 or 8
since ending wiht a 6 or 8 means its even
mighty cliff
how many 5 digit numbers can we make with these numbers
120
mighty cliff
then it turns out 6*8=48
48
lofty creek
its not 48
nevermind
it is 48
but not because its 6*8
its because its 2*4*3*2*1
mighty cliff
its because its `2*4*3*2*1`
And how it happened
lofty creek
And how it happened
hwo did you get to 120
mighty cliff
hwo did you get to 120
Well, for the first position there are 5 numbers for the second 4, etc.
lofty creek
for the first digit you have 5 possibliites, 2nd digit 4possibilities, etc right?
so now
to ge tan even number
the last digit has 2 possibilities
6 or 8
and the other digits are just the same
so the 1st digit has 4 possibilities, 2nd has 3, etc
make sense?
lone heartBOT
lone heartBOT
Available help channel!
leaden flint
hi i need help i'm lost
lone heartBOT
hi i need help i'm lost
pseudo ice
$\cos^2(\theta) - 1$ is $-\sin^2(\theta)$, not $-\sin(\theta)$, but otherwise not bad
ocean sealBOT
@pseudo ice
leaden flint
$\cos^2(\theta) - 1$ is $-\sin^2(\theta)$, not $-\sin(\theta)$, but otherwise no...
yes i forgot to add the ^2 with that but how would i find the solution though?
pseudo ice
Well almost as you did - but you also forgot some signs too
You should have then found that $-2\sin^3(\theta) + 2 = 0$, which you could then rearrange to $\sin^3(\theta) = 1$, but then you can just cube root both sides of course
ocean sealBOT
@pseudo ice
leaden flint
You should have then found that $-2\sin^3(\theta) + 2 = 0$, which you could then...
can you show the steps to get that so i can compare it to mine?
pseudo ice
can you show the steps to get that so i can compare it to mine?
add 2sin^3(t) to both sides then divide by 2
leaden flint
add 2sin^3(t) to both sides then divide by 2
i'm still kinda stuck could u try doing it from the beginning
step to step
i erased everything to try and understand from the start
last walrus
@leaden flint if you want to work on it live, feel free to swing by Twitch
pseudo ice
<@788085606483361802>
Are you at least happy that you should have had
[
2\sin(\theta)\pqty{ -\sin^2(\theta) } + 2 = 0
]
ocean sealBOT
@pseudo ice
leaden flint
Are you at least happy that you should have had
\[
2\sin(\theta)\pqty{ -\sin^2(\...
yeah i think? and i tried following your steps and here's what i got
pseudo ice
yeah i think? and i tried following your steps and here's what i got
Yep - note that all the lines are equal to zero
this is equal to zero, as is...
...both of these!
leaden flint
this is equal to zero, as is...
thank you! is this correct then?
pseudo ice
Yep that looks all good to me 
tacit arch
It's better if you ask one question at a time
lone heartBOT
topaz talon
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lone heartBOT
Available help channel!
grizzled ermine
how do i solve..?
lone heartBOT
how do i solve..?
grizzled ermine
teacher didnt explain it well so now im stuck
open urchin
factor 10^(z+3) from the left side
grizzled ermine
factor 10^(z+3) from the left side
(10^z)(10^4) ?
open urchin
no
factor 10^(z+4)+10^(z+3) into 10^(z+3)*something
figure out what that something is
grizzled ermine
i dont get how you would use factoring here
vapid shuttle
x^(a+b) = x^(a)x^(b)
Because that’s how exponents work
Each term on the left then, using that simplification, you can show contain a factor of 10^(z+3)
Write z+4=z+3+1
grizzled ermine
actually i got it figured out
valid ibex
f(x)=|-3x+1|
lone heartBOT
f(x)=|-3x+1|
valid ibex
im confused on how to select your points
elfin fiber
what are you trying to do or solve?
stark crater
im confused on how to select your points
Choose the vertex, a point to the left, and one to the right
elfin fiber
ok, so when is |-3x+1| different from -3x+1?
there's a million ways to do this but i'd start by graphing -3x + 1, then see what needs to change because of the absolute value.
valid ibex
Choose the vertex, a point to the left, and one to the right
ive tried that but i keep getting the points in a line diagonally
im not sure what im doing wrong
stark crater
ive tried that but i keep getting the points in a line diagonally
What did u get for vertex point
valid ibex
What did u get for vertex point
-1,-2
stark crater
Howd u get that
valid ibex
your supposed to go left 1 then down 2??
stark crater
You need to use ideas of transformations
stark crater
your supposed to go left 1 then down 2??
Where did u get this idea
stark crater
isnt that what transformations are?
Howd u get those numbers though
valid ibex
Howd u get those numbers though
oh i was on a different question
stark crater
I see
valid ibex
ive watched a few videos but im still a bit confused
stark crater
abs function is of form f(x)=a|b(x-c)|+d where a is vertical stretch, b horizontal stretch, c is horizontal translation and d is vertical translation
From your equation you can see a=1 and d=0 so you need to find what b and c are
alpine sable
Can we say that an asymptote is an envelope to a family of curves?
alpine sable
The definition of envelope is:
A curve L where:
- It touches a curve from the family at every point
- Different curves from the family touch L at different points
If we consider the family of curves y - Cx^{-2} = 0, then x=0 and y=0 fail to be envelopes to this family, right?
(C is some arbitrary constant that generates the family)
lone heartBOT
@alpine sable Has your question been resolved?
unborn geyser
Idk what to do now
lone heartBOT
Idk what to do now
ocean sealBOT
hypox
cinder sentinel
also move that y^-4 to the numerator
full kettle
Idk what to do now
I think you did somethingwrong here
I think you need to start by multiplying all the exponents by -1/4 before doing anything else
unborn geyser
I think you need to start by multiplying all the exponents by -1/4 before doing ...
Don’t I have to make it positive first
unborn geyser
also move that y^-4 to the numerator
I multiply it to 4/3?
ocean sealBOT
hypox
cinder sentinel
so $\left(\frac{16y^\frac{4}{3}y^4}{x^8}\right)^{\frac{1}{4}$
you can multiply them since its the same base
cinder sentinel
I multiply it to 4/3?
yes
ocean sealBOT
hypox
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
lone heartBOT
@unborn geyser Has your question been resolved?
grizzled ermine
uhhh... how???
lone heartBOT
uhhh... how???
ionic jewel
,tex .exp rules
ocean sealBOT
cinder sundial
They are the same
lone heartBOT
They are the same
cinder sundial
What’s wrong with my answer!
cinder sundial
I see
Let me make a clear one
I got the same answer as the solution given
Yet, it is still wrong
sleek girder
why did you input "y ="
astral oxide
sry if this is kinda a dumb question, but if i have something like $z=\frac{a^2b^2c}{c^2+a^2b^2}$ where theyre all measured values, how would i go about finding the uncertainty in z? or how should i find the uncertainty of a measured value when addition and multiplication are combined
ocean sealBOT
rxjn
elfin fiber
so you have the uncertainty of a, b, c
astral oxide
yes i have the uncertanities for a, b and c
elfin fiber
do you know the standard error propagation formulas?
astral oxide
like if its addition, add the uncertainties, if its multiplication add the relative uncertainties, if theres a power its the power times the relative uncertainty
i dont know how id combine it when you have addition within division/multiplication 😔
elfin fiber
that's not my understanding, even with simple addition, you'll need a square root of the sum of squares
elfin fiber
oh, this shouldn't be as difficult as I expected then
for example, can you find the uncertainty of a^2*b^2 with this information?
astral oxide
yeah 2(Δa/a)+2(Δb/b)
ohhh i see i find the uncertainties in the numerator and denominator?
elfin fiber
yes, find each component (numerator, denominator first term, denominator second term)
then, use the addition formula on the denominator first and second term
then, use the quotient formula for the numerator and denominator
elfin fiber
let me know if it goes smoothly, this is an interesting problem
astral oxide
.close
lone heartBOT
lone heartBOT
Available help channel!
shrewd panther
What's the difference between graphic and analytical in Uniform Rectilinear Motion (MRU)
lone heartBOT
shrewd panther
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lone heartBOT
Available help channel!
unborn geyser
Find terminal point on the unit circle determined by -13pi/4 radians
unborn geyser
How I do that
lone heartBOT
@unborn geyser Has your question been resolved?
cinder sundial
does the probability formula P(A)=n(A)/n(S) only works under the circumstance that all of those events have the same probability to happen.
tacit arch
does the probability formula P(A)=n(A)/n(S) only works under the circumstance th...
You need to explain your notation
cinder sundial
P(A)= the probability for events inside set A to happen
n(A) is the number of events within set A
and n(S) is the sample space
tacit arch
Yea it only holds with equal probabilities in general
You can try to come up with a simple counterexample with small sample space and different probabilities
cinder sundial
You can try to come up with a simple counterexample with small sample space and ...
I will reach a diffrent answer that is inconsistent with the one I got from events with equal probability.
Yet, it does not means that the answer is wrong
it just differs
<@&286206848099549185>
elfin fiber
Set this problem up with the lottery.
with the events Win $0, Win $100, and Win $1,000,000
tacit arch
I will reach a diffrent answer that is inconsistent with the one I got from even...
Thought you got your answer
What is your question still
cinder sundial
Yea it only holds with equal probabilities in general
why
why it only holds with equal probabilities
elfin fiber
with the events Win $0, Win $100, and Win $1,000,000
@cinder sundial what does this example imply the probability of winning the lottery is?
cinder sundial
it depends on the arrangement of the lottery
elfin fiber
but what would your formula imply the answer is?
cinder sundial
Im not familiar with the mechanism of lottery tho
and there a plenty of them with diffrent rules
elfin fiber
But your formula implies that you don't need to know anything about it, you just take 1 / 3
do you see an issue with that?
cinder sundial
But your formula implies that you don't need to know anything about it, you just...
yes, it is impossible that these probabilities are equivalent
elfin fiber
not necessarily, we could create a lottery where you have a 1/3 chance of winning, but the point is that you can't directly infer that from just the sample/event space
here's what you could do: come up with two sample spaces with the same elements, but that have different P(A)'s.
EX: A fair coin and biased coin
cinder sundial
si
lone heartBOT
@cinder sundial Has your question been resolved?
lone heartBOT
@cinder sundial Has your question been resolved?
upbeat hornet
does the probability formula P(A)=n(A)/n(S) only works under the circumstance th...
consider a biased coin: a coin that has 26% chance of landing heads and 74% chance of landing tails. There are 2 events, and 1 of them is heads. So the formula doesn’t work
vale wigeon
what's the question/problem/doubt/issue here
lone heartBOT
@cinder sundial Has your question been resolved?
cinder sundial
what's the question/problem/doubt/issue here
Why the formula “P(A)=n(A)/n(S) only works with equal probabilities
P(A)= the probability for events inside set A to happen
n(A) is the number of events within set A
and n(S) is the sample space
vale wigeon
P(A)= the probability for events inside set A to happen
there's some terminology mix-up
A is itself an event.
an event is (with some asterisks) a subset of S, the sample space.
also "sample space" refers to the set of all outcomes rather than only their count.
cinder sundial
I see
vale wigeon
anyway
if points in S don't have equal probabilities, then P(A) cannot depend only on n(A).
i can give an example if you want
cinder sundial
For sure
vale wigeon
ok
so let's say you are playing some tabletop game and at one point you are trying to hit a monster and have to roll a d20 to decide if you succeed
cinder sundial
“d20”?
vale wigeon
fair 20-sided die
tabletop game jargon
"standard" dice, as you might imagine, are known as d6
cinder sundial
I see, even I never see an die that is more than 6 sides
sleek girder
(if you want to see one, contact me)
vale wigeon
even I have never seen a die that has more than 6 sides
cinder sundial
Thank you
vale wigeon
these have the shape of an icosahedron
anyway ok
so let's say that on a roll of 1 through 8 you miss, on a roll of 9 through 19 you hit, and on 20 you get a critical hit
so there's two ways you could model this random experiment
one is you could have S = {1, 2, ..., 20} with each number assigned 5% probability, and then the events you care about would be M = {1,...,8}, H = {9,...,19} and C = {20}
and then the formula P(A)=|A|/|S| would work, bc each face is equally likely to show up
but you could also model it with a sample space of only 3 points: {miss, hit, crit}, with probabilities assigned unequally: P(miss)=40%, P(hit)=55%, P(crit)=5%
and then to claim you have a 1/3 chance of critical based on this alone would obviously be stupid
cinder sundial
I see
That’s a pretty intuitive yet life-related example
The question is solved now, thank you Ann
.close
ocean cloud
Hi, i need help with a particular problem
$(x'' - 2x' - 3x)' = -16e^{-t} + 16te^{-t}, where x(0) = 1 and for t->{inf} the equation has a horizontal asymptote$
ocean sealBOT
ZmijaZ
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
elfin fiber
!status
lone heartBOT
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
2
upbeat hornet
can you show your work?
ocean cloud
I got rid of the derivative on the left, by "integraling" both sides
got the point of
$x''-2x'-3x = -16te^-t$
ocean sealBOT
ZmijaZ
upbeat hornet
got the point of
$x''-2x'-3x = -16te^-t$
remember to +C
elfin fiber
did you solve the homogenous diffeq?
ocean cloud
did you solve the homogenous diffeq?
yes
ocean cloud
remember to +C
does it change the solution in a "meaningful" way?
upbeat hornet
does it change the solution in a "meaningful" way?
Yes, it can
ocean cloud
did you solve the homogenous diffeq?
but I'm pretty certain that the non-homogenous part is wrong
elfin fiber
Okay, what did you try?
ocean cloud
tried "guessing" it with the method of undetermined coefficients
ocean cloud
I did it
ocean sealBOT
ZmijaZ
ocean cloud
Yes, it can
hmm i'll give it a shot
elfin fiber
i get
$A = 16t/(t+2)$
i dont think that's right
one sec
ok so
you need to assume the particular solution is of the form Ate^(-t) + Bt^2e^(-t)
Let me know if that works
ocean cloud
ok, I'll give it a shot
lone heartBOT
@ocean cloud Has your question been resolved?
ocean cloud
one question
so, if i get that A is dependend on t
it's wrong?
or rather, not complete enough of an answer
upbeat hornet
it's wrong?
can you show your work?
ocean cloud
can you show your work?
ofc
well i've solved the equation
but the part with the asymptote is blocking me rn
as i'm getting that the solution has no horizontal asymptotes
lofty creek
what is x(t)?
ocean cloud
$x = c1e^{3t} + c2e^{-t} + te^{-t} + 2 t^2e^{-t}$
ocean sealBOT
ZmijaZ
ocean cloud
as the hogenous part of the equation is
$x''-2x'-3x=0$
ocean sealBOT
ZmijaZ
ocean sealBOT
ZmijaZ
lofty creek
so then you remove one c right?
because you can write c1 or c2 as the other
$c_1=1-c_2$ or $c_2=1-c_1$
ocean sealBOT
Flappie
lofty creek
so you can fill this into x(t)
lofty creek
$x(t)=c_1(e^{3t}-e^{-t})+e^{-t}(1+t)+2t^2e^{-t}$
ocean sealBOT
Flappie
lofty creek
so what happens to x(t) as t goes to infinity
ocean cloud
goes to inf?
lofty creek
im kind of confused about the question
because it does not have a horizontal asymptote at t->inf
ocean cloud
because it does not have a horizontal asymptote at t->inf
yep, it does not
lofty creek
it does have a horizontal asymptote as t->-inf
ocean cloud
ok, the question goes
Find all solutions for which $x(0) = 1$, and who have a horizontal asymptote when $t->inf$
uh, it's ugly
can i space it somehow
lofty creek
yes, you have the $'s at the start and end
only place it around the places you want it to be latexified
ocean sealBOT
ZmijaZ
ocean cloud
does that mean i can guess the cs for which horizontal asymptote exists?
lofty creek
c_1
so what c-1 do we need to plug in
such that x(t) has a horizontal asymptote at t->inf
lofty creek
**Flappie**
look at this again
ocean cloud
so c-1 = 0
lofty creek
yes
ocean cloud
c1-1, rather
ocean cloud
oh yeah, swapped c_1 and c_2
lofty creek
fair enough
ocean cloud
but yes, that
ocean cloud
$e^{-t}(1+t) + 2t^2e^{-t}$
ocean sealBOT
ZmijaZ
lofty creek
does this have a horizontal asymptote at t->inf?
ocean cloud
it's 0 right?
lofty creek
so is it a horizontal asymptote?
ocean cloud
the worst part is that i'll probably be asking a question or 2 more in the near future
after i've lost my mind with all possible ways to solve it
lofty creek
thats the cool part about this server
you can just open a new thread
whenever you need
:)
there is almost always someone online to help
ocean cloud
was kind of afraid of being to annoying tbh
lofty creek
that doesnt matter
if youre annoying then you just dont get anyone wanting to help you
but clearly i, and others, are still helping you
lone heartBOT
lone heartBOT
Available help channel!
cyan imp
Is the run of a slope always 1?
lone heartBOT
Is the run of a slope always 1?
gray isle
no, where are you getting that idea
cyan imp
A video isn't making sense
gray isle
link video and time stamp
gray isle
the slope of
y = x - 2
is 1 because x = 1x
undone ledge
He was just quoting an example , like in that equation slope was 1 , as coefficient of x in (y >x - 2 )was 1
see the next example
upbeat eagle
Hia
pliant cedar
so f(x) is supposed to be ax(3 - ax) ?
upbeat eagle
f(x) = x(3-x)
pliant cedar
what is a then
pliant cedar
yeah but
theres no a in the finite region bounded by x(3-x) and the x axis
waeit
i may not have undesttood the question
upbeat eagle
Dw me too
slow sentinel
im guessing (a) is from the parametric equation x^2 = 4ay + c
So a would be 1/4 (from my understanding)
pliant cedar
ah i get the question now
slow sentinel
Ohh
pliant cedar
lol
slow sentinel
A B C D and E are not options
pliant cedar
so (e) is asking, what is the area between the curve y=f(ax) and the x axis
where a is some constant
upbeat eagle
Yes
I understand why the limitations are 0 and 3/a
OHHHHHHHHh i understand
Yep
got it
pliant cedar
😅
slow sentinel
upbeat eagle
.close
prime dawn
im stuck on trying to solve the 2 triangles in this problem
lone heartBOT
im stuck on trying to solve the 2 triangles in this problem
prime dawn
ive found essentially everything i need if it had been 1 triangle but what next
i just realized i mistook the 8 at the start at the 5 but nonetheless how do you solve for 2 triangles
.close
celest storm
lone heartBOT
celest storm
I want to calculate Fourier's Transformation for f(x)
He asked me to show that the transformation equals this
I couldn't find it in this format
But i've found this
Is this correct but need simplification or totally wrong
<@&286206848099549185>
.close
upbeat eagle
Hello
upbeat eagle
and then you have to divide it by (x-1) again
and then use that answer to divide by (x-1)
oak chasm
Sorry, what is the problem?
upbeat eagle
Wait ill draw it
So I am dividing it by (x-1) twice
I multiply the first equation by 12, to make it easier to factories, and it gives me an answer (ANS)
Now I proceed to divide ANS by (x-1) again
And it gives me ANS2,
Would I have to divide that ANS2, by 12 to undo, me multiplying it by 12 at the beggining?
oak chasm
No, I mean what is the problem, not what are the steps.
upbeat eagle
Ok ill show u the problem
This is the equation you have to divide twice by (x-1)
My question is that since its terrible to divide
Can I multiply it by 12
oak chasm
Why are you dividing?
upbeat eagle
Because you need to prove (x-1)^2 (kajdbjadg)=0
And you know that my picture divided by (x-1)^2
gives (kajdbjadg)
and you just need to show it
oak chasm
OK, so what is the x coordinate of A?
upbeat eagle
I dont know
oak chasm
Is this for a calculus course?
upbeat eagle
x = 1
oak chasm
Right, so what's the area from O to B?
oak chasm
OK, so they have a degree 4 polynomial.
Get it equal to 0.
Then, you can multiply it by 12 if you want.
You had a quadratic before.
upbeat eagle
Yes
oak chasm
OK, so what do you have after that?
upbeat eagle
no idea
I have no clue how to find A,
Becuase it gives me imaginary numbers on the calcaultor
ocean sealBOT
Chai T. Rex
oak chasm
So, get an equation from that that's equal to zero.
upbeat eagle
Left side -5/12 = 0
oak chasm
There's no L there.
upbeat eagle
But i you factorise it? im not sure which one would be A....
oak chasm
What's A?
upbeat eagle
But it also gives you imaginary nmbers
oak chasm
Oh, the point.
upbeat eagle
Yes sry
ocean sealBOT
Chai T. Rex
oak chasm
What do you get when you multiply both sides by -12?
upbeat eagle
-3x^4 - 4x^3 +12x^2 -5
oak chasm
By -12, not 12.
oak chasm
OK, now what is (x - 1)^2(3x^2 + 10x + 5) expanded?
upbeat eagle
3x^4 + 4x^3 -12x^2 +5
here is the the whole thing again, so you dont have to scroll
oak chasm
Did you do the expansion?
upbeat eagle
Yes
oak chasm
OK, so now you know they're equal and the problem is done.
upbeat eagle
Ok
What about finding A coord?
Do you know how I would go about that
Bc I have zero clue
oak chasm
OK, so you have (x - 1)^2(3x^2 + 10x + 5), right.
Why are we going backwards?
Usually, when you want to find a root, you have the equation equal to zero so that you can use the zero product property.
upbeat eagle
Alright?
upbeat eagle
x= 1, ( -5+__/10 ) /3
oak chasm
What do you mean by __?
oak chasm
You can do sqrt(10).
upbeat eagle
bc that gives -1.8
upbeat eagle
-5 +sqrt(10) /3
oak chasm
That leaves out what they mean geometrically, particularly with (-5 - sqrt(10))/3.
Think about what happens if you go further left than (-5 + sqrt(10))/3.
upbeat eagle
Thats the full one he told me
upbeat eagle
Think about what happens if you go further left than (-5 + sqrt(10))/3.
You get closer
to -2
oak chasm
No, what happens to the area?
upbeat eagle
Bigger
oak chasm
It gets bigger until it crosses -2, then it gets smaller.
So, it needs to go far enough past -2 to cancel out what was added.
That happens where the other root is.
oak chasm
oak chasm
The + part and the - part cancel out, so the area from the other root to O is the same as the area from A to O.
oak chasm
Right.
oak chasm
You're welcome.
oak chasm
OK.
lone heartBOT
@upbeat eagle Has your question been resolved?
solemn finch
lone heartBOT
lofty creek
what is your question
undone ledge
!status
lone heartBOT
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
3
lofty creek
what is your answer
lofty creek
can you share your working out?
candid flicker
rate of change of radius is 2
solemn finch
Yes
candid flicker
that does not mean radius becomes 2+r
solemn finch
that does not mean radius becomes 2+r
What
Then how will I calculate the new value of the radius
candid flicker
what does dA/dt stand for?
solemn finch
Change of area over time change of time
candid flicker
basically, rate of change of area
so assuming the radius is r
what would d(r)/dt stand for?
solemn finch
Rate of change of radius
candid flicker
Rate of change of radius
which is given to us in the question
d(r)/dt = 2
okay tell me
what is d(4x^2)/dt
solemn finch
8x
candid flicker
8x
that's where you're going wrong.... when differentiating 4x^2 with respect to t, we also multiply with a dx/dt in the end
so therefore, d(4x^2)/dt = 8x.dx/dt
lofty creek
its the chain rule
candid flicker
d(4x^2)/dx = 8x only
but not when it's /dt
try the question again using this now
solemn finch
Ok
candid flicker
any progress? @solemn finch
solemn finch
solemn finch
any progress? <@830950291901906945>
Yesss tysmmm
candid flicker
perfect
lone heartBOT
@solemn finch Has your question been resolved?
stray burrow
Hi 👋
I need help understanding how my teacher graphed the secant function. I missed this lesson and I’m not sure what she did here. Attached is her notes.
placid zinc
secθ is just 1/cosθ
So take any important value of cosθ, take its reciprocal, and you've got a value of secθ
stray burrow
That makes sense. But uh so the graph between the two parabolas that’s cosine right? Is that also part of the secant graph?
placid zinc
There's no parabolas here
The thin graph is cosθ
The thicker graph is secθ. Note secθ is one graph, just disconnected. It also goes on forever in both directions
rain spear
I need help calculating a determinant
lone heartBOT
I need help calculating a determinant
rain spear
idk what im doing wrong I used online caculators and the last one is -512
but I get a positive number
lone heartBOT
@rain spear Has your question been resolved?
lone heartBOT
Helpers are just people volunteering their time to help you. Be polite and patient.
ocean sealBOT
aPlatypus
vale crag
@rain spear
vale crag
ok how are you computing that determinant exactly ?
it's not really apparent
like what method are you using
rain spear
like what method are you using
triangle
vale crag
?
rain spear
there is a small thing that im missing
vale crag
I'm still not sure what you're talking about
there's a few different things about determinants and triangles
vale crag
ok yea
rain spear
but I think I did that right
its just after
some calculation is fucked
and my brain is way too fried to get what im missing
I did it like 3 times already
vale crag
you only have 4 things being added on your paper
you should have 6 of them
so you missed two "triangles"
rain spear
you only have 4 things being added on your paper
I have 3 things added 3 things with minus
vale crag
I only see 4
rain spear
<@919701352739921951>
thanks a lot ❤️
now I can get to doing the hard part
damn man these multiplicactions
got me acting up
.close
slim epoch
The other day I was going over the sumatoriums and productoriums and I was wondering if there was such a thing as a "restatorium" or "divisorium"?
slim epoch
If so, it would be done just like the 2 main ones, but with a subtraction or division series?
Would it be done with another letter instead of sigma or pi?
I have a lot of questions...
lone heartBOT
@slim epoch Has your question been resolved?
slim epoch
<@&286206848099549185>
ocean sealBOT
Rize
slim epoch
No
alpine sable
but instead of this two for subtraction right?
slim epoch
Sigma is for summation.
Pi is for productorio.
"Restatorium"?
"Divisorial"?
slim epoch
but instead of this two for subtraction right?
Yes
alpine sable
what is restatorium
vale crag
so what do you mean actually, what should these new operations perform ?
the nice thing about addition and multiplication is that they're associative
the order you use to perform the additions doesn't matter, (1+2)+3 = 1+(2+3)
for substraction and division that doesn't work
slim epoch
That instead of adding or multiplying, subtract or divide
ocean sealBOT
Rize
slim epoch
for substraction and division that doesn't work
But with () yes, I think
vale crag
well you have to specify the order yes
slim epoch
$-\sum_n a_n$
No exactly
vale crag
that's exactly what I'm asking you to do
slim epoch
I mean if something like this exists: $\sum_n a_n$
but instead of the letter sigma another one that makes it subtract or divide
ocean sealBOT
H^Ψ(r)=EΨ(r)
vale crag
there's no standard thing for that
and i don't even know what that new operation of yours is supposed to do anyway
at some point, you have to explain it in detail
like give some examples or whatever
slim epoch
there's no standard thing for that
That's what I was wondering, whether it existed or not, which seems strange to me.
ocean sealBOT
H^Ψ(r)=EΨ(r)
slim epoch
Look, replace the letter sigma with any other letter that is not in use in this operation: $/sum_n a_n$.
And what that letter would do is subtract or divide the series (with it's respective rules)
ocean sealBOT
H^Ψ(r)=EΨ(r)
vale crag
and what do you mean by substract a series ?
slim epoch
The summation adds series, the "subtraction" subtracts them.
slim epoch
so what rize said ?
But with another letter
alpine sable
there is not a global letter for that I know
vale crag
(sorry for the ping rize)
alpine sable
no problem
I was curious
I’ve seen capital delta used for subtraction which can be defined in terms of capital sigma notation
last walrus
You define subtraction as addition of integers. You define division as multiplication by a rational number. Then we only require addition and multiplication 😎
alpine sable
Since a - b = a + (-b)
vale crag
let's say I give you the sequence '1 2 3 4 5 6', how would you compute the 'restatorium' of it and what would be the result ? @slim epoch
alpine sable
let's say I give you the sequence '1 2 3 4 5 6', how would you compute the 'rest...
1-2-3-4-5-6 = -19 = 1-2+3+4+5+6
vale crag
I didn't ask you
alpine sable
Thats what they mean
vale crag
who knows what they mean
alpine sable
I do
vale crag
are you them?
alpine sable
Yes
chill
logic dog wait the answer
@slim epoch put an example of divisorium also
thx
alpine sable
The summation adds series, the "subtraction" subtracts them.
Δ 1,2,3,4,5,6 = 1-Σ 2,3,4,5,6
That’s how big delta notation is defined in terms of big sigma notation
You can use an upside down pi symbol or some other symbol and do something similar for division
I don't think so by the way, the notation of - sum_n a_n is equivalent to say -(a_0 + a_1 + ... a_n) = -a_0 -... - a_n
Write it using the notation without products
but, I will wait the answer
alpine sable
Write it using the notation without products
there is not a product
You multiplied the series by negative 1
tepid hearth
there is not a product
I agree
alpine sable
Define big delta notation in terms of big sigma notation
I show a different thing
from my idea
Ok
alpine sable
**Rize**
.
What were you saying “I don’t think so” to?
About your idea, for me is better to say in this way. In fact, for be sure I wrote "but, I will wait the answer"
That’s literally how it’s defined. It’s not my idea.
alpine sable
I don't think so by the way, the notation of - sum_n a_n is equivalent to say -(...
a_0 should be positive btw
no
If you are talking about big delta notation
I'm not talking about that
lone heartBOT
@slim epoch Has your question been resolved?
alpine sable
@slim epoch
thin sedge
,rotate
ocean sealBOT
ocean sealBOT
vague coral
wrong
thin sedge
ok
vague coral
2(u+5)-5 = 2u + 10 - 5 = 2u +5
thin sedge
.close
smoky condor
smoky condor
The 45th one
haughty sun
ocean sealBOT
