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#help-13
crimson sedge
cedar kilnBOT
cedar kilnBOT
Available help channel!
regal cobalt
Why is this false? Can I not do a partial integral necessarily? Is it not being partially differentiated with respect to X? 
short blade
there is no such thing
consider as a counterexample f(x,y) = x^2y/2 + y
what is the partial of this wrt x?
regal cobalt
The partial would be 2x*y + y
regal cobalt
I'm confused, do I not treat y as a constant in ssense?
Would it then be x^2/2 + 1
Am I confusing which one should be a constant?
regal cobalt
would be zero
oh so it would be x^2/2 + 0
gotcha, so in other words I could have lost a term of y
I think I understand what you mean now... it could have been y there or some constant times y
Am I missing anything else? Thank you for your help btw, brain is sputtering apparently
short blade
<:sotrue:826971355542192148> I think I understand what you mean now... it could...
not just a constant times y
any function of y
short blade
if (g) is a function of (y) only, then (\pdv{g}{x} = 0)
wraith daggerBOT
maximo
short blade
meaning that the constant of integrating wrt x is now an arbitrary function of y
rather than a constant number
the idea is that the integral should be the antiderivative + (anything that would derive to 0)
if you integrate wrt x, in this context (anything that would derive to 0) is an arbitrary function of y
so (f(x,y) = \frac{1}{2}x^2y + g(y))
wraith daggerBOT
maximo
regal cobalt
Ahh yeah, I think I was losing track what was a constant
I appreciate your help... so it really means I can't integrate the output of a partial derivative and expect a simple answer because I could be missing an entire function of y (the thing I treated as a constant) π
Thank you @short blade I think you've put me on the right track
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crimson sedge
crimson sedge
how do I find fn inverse
unique valley
why are you asking the same question on two channels?
drifting marlin
You have someone helping you in your first channel, ask there
unique valley
x = (e^y +e^-y)/2 and find y
celest seal
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hardy fossil
Hello, could someone help me solve this problem please. Iβm unsure how to do it
hardy fossil
royal loom
hardy fossil
royal loom
Iβd rewrite at the first line
Instead of using double angle
You have
cos(2x)=cos(x)
And then you can solve that immediately
flint plinth
antipodal rodent spotted
short blade
based lisa moment
hardy fossil
But what about the sin? Do we just ignore it
hardy fossil
Ohhh thank you
royal loom
We just rewrote it
royal loom
that still takes in count for the interval right?
What do you mean?
royal loom
What can n be?
hardy fossil
Any number?
royal loom
No definetly not
cedar kilnBOT
@hardy fossil Has your question been resolved?
desert zinc
hey
desert zinc
How do I do this
short blade
desert zinc
solid juniper
maximo these pics are awful
desert zinc
I didnt try cos that would lead me to spend all night experimenting and I just wanna know how to do this
desert zinc
i would suggest you try *something*
subtract 2 from every Y value
and do the equation
dire geode
maximo these pics are awful
blame austin
short blade
maximo these pics are awful
pardon you
desert zinc
I meant +2
solid juniper
helpers lounge must have really fallen apart without me damn
short blade
helpers lounge must have really fallen apart without me damn
we are stronger than ever
solid juniper
this is what you guys are up to nowadays
desert zinc
Bruh what is going on
short blade
layla you better start using these
short blade
Bruh what is going on
consider how f(x-2) transforms f(x)
think geometrically of what the integral looks like
short blade
you should see a correlation between the integral you sent and the one in this picture
desert zinc
you should see a correlation between the integral you sent and the one in this p...
is it the same thing
the same result
short blade
why do you say that
desert zinc
the function is translated to the right by 2
and the boundaries are now 1 to 3 rather than -1 to 1
10.52 is the integral btw (with no translation)
short blade
yes they are equal
desert zinc
what do I do about this
I know I can rewrite the equation
because all the Y values are greater than 2
But the mark scheme doesnt care about that
Ohh I see (I think
Subtract the square of 2
cos the area when the height is 2 is 2^2
so you basically remove a square chunk from underneath
yeah this is way quicker and more sensible
But all of these are easy just because the y values are greater than 2
so I dont have to worry about when the translation allows for points where y is below 0
How do I do this <@&286206848099549185>
IF ANYONE SEES THIS, PLEASE CAN YOU TYPE THE WHOLE EXPLANATION AND WALKTHROUGH IN MY DMS
I GOTTA SLEEP, ITS 1:38
GN
cedar kilnBOT
@desert zinc Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
@indigo cedar Has your question been resolved?
indigo cedar
cedar kilnBOT
indigo cedar
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cedar kilnBOT
Available help channel!
gray verge
I'm still stuck on my problem from earlier about finding point C on a triangle. I have the positions of point A and B, know the distance from point A to C, and the vector direction of point B to C. I also know distance from point A to C is always greater than the distance from A to B. I don't know how to find point C using this. I know it's the intersection of that direction from B to C and a circle made around A with it's distance from C as the radius, but no idea how I can actually do that. My maths is appalling and forgotten all about trigonometry like this.
violet flume
I'm still stuck on my problem from earlier about finding point C on a triangle. ...
just reading the info im picturing like
you know the distance from A to C
so im imagining a circle of that radius around A
somewhere on that circle will be C
then you know the direction from B to C, so thats like a ... a line in that direction
does that make sense?
violet flume
well you could do it very very explicitly
find the equation for the circle
and the equation for the line coming out of B
i think itd be easy to do like
do you know to parameterize?
well we dont have to use that word
lets call the line coming out of B and going towards C
so what you would like to do is find the distance from some point on that line (or ray, i guess, whatever) to A
gray verge
I think that makes sense as a way to interperate it?
gray verge
Right
violet flume
at most 2 points on this line will be right
i mean equal to the distance from A to C
because each point on this black line is candidate for the placement of C, we want the length of the red line to be equal to that given distance
so, if that makes sense, heres where you could parameterize
i think thats gonna be the easiest way
gray verge
Makes sense so far.
violet flume
although im sure theres some higher-level geometric interpretation im missing
or lagrange
anyways
should we do this generically?
are you given actual numbers at all here?
it doesnt really matter either way
gray verge
I need to write a script for this, so I can't know the numbers ahead of time.
violet flume
it might be easier generically but it will be more symbols
okay
so the only topics are parameterization of a vector and distance formula
say you have some starting point, $B= (b_1, b_2)$ given
wraith daggerBOT
jan Niku
visual jewel
can i do business and economics here
violet flume
and you know the vector $\vec{BC} = (m_1, m_2)$
wraith daggerBOT
jan Niku
violet flume
im gonna use round brackets, i hope you understand these are vectors
visual jewel
im gonna use round brackets, i hope you understand these are vectors
hey
violet flume
can i do business and economics here
#βhow-to-get-help , but yes
just not in this specific channel
violet flume
im not sure, sorry.
@gray verge the parameterization of this line is $P(t) = (b_1 + m_1 t , b_2 + m_2 t)$
wraith daggerBOT
jan Niku
violet flume
parameterization because we introduced a parameter, t, that picks a point out of the line
all you have left is the easy part, which maybe you feel comfortable with
say youre given $A = (a_1, a_2)$ and $D$ which is the distance from $A$ to some $P(t)$ desired
wraith daggerBOT
jan Niku
violet flume
what should t be?
violet flume
@gray verge is that enough of a hint
i dont wanna resolve the whole thing for you because theres probably value in thinking through it 
but all you should need now is the distance formula
gray verge
<@1008380451464945837> the parameterization of this line is $P(t) = (b_1 + m_1 t...
I am a little confused why the t introduced here isn't (b_1 + m_1 t**_1** , b_2 + m_2 t**_2**)
violet flume
I am a little confused why the t introduced here isn't (b_1 + m_1 t**_1** , b_2 ...
it has to be the same for both
one way to think of this is as $B + t M$ where $B$ and $M$ are vectors, and $t$ is just some number
wraith daggerBOT
jan Niku
violet flume
it has to be the same, because it makes sure we stay on the vector that will connect B and C
this is where a little vector intuition helps
gray verge
Not entirely sure how P(t) can equal (x * t, y * t) but I can role with that enough to think through the rest of what you just posted, which I'll take a second to try understand.
gray verge
what should t be?
t here would be the length between B and C, I think.
violet flume
Not entirely sure how P(t) can equal (x * t, y * t) but I can role with that eno...
i gotta sleep but i asked if other people can come help
if youre still on this tomorrow and no one helps will you ping me?
gray verge
Oh. Well in that case thank you for getting it this far and have a good night.
violet flume
but see if other ppl come
gray verge
if youre still on this tomorrow and no one helps will you ping me?
Will do π I'm GMT + 9 so you might be pinged at a strange time, mind you.
cedar kilnBOT
@gray verge Has your question been resolved?
cedar kilnBOT
@gray verge Has your question been resolved?
wicked mantle
Will do π I'm GMT + 9 so you might be pinged at a strange time, mind you.
Japanese?
gray verge
Japanese?
Yup.
Not japanese myself, but I live here now. Learning the language slowely.
cedar kilnBOT
@gray verge Has your question been resolved?
cedar kilnBOT
@gray verge Has your question been resolved?
cedar kilnBOT
@gray verge Has your question been resolved?
crimson sedge
guys
muted oyster
dont really know what to do after obtaining distance as it comes in sin and idk how to sum all those sin terms
muted oyster
!status
cedar kilnBOT
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
ans is 12 btw
in case it helps
bcs u write the eqns of lines
and then u find the distance of the point from those lines
but after that
what can u do
dire geode
dont really know what to do after obtaining distance as it comes in sin and idk ...
draw a picture
dire geode
and then u find the distance of the point from those lines
if you have the distances as a function of n, sum them?
muted oyster
if you have the distances as a function of n, sum them?
i get the general distance d(n) as sum function of sin 1/n
some*
and then
dire geode
show your work
muted oyster
its very rough
but i got the three equations
of the line
which comes as y = β3 x, y= - β3x + 4β3
and y = 0
and then u just take the point as
(1/n,sin1/n)
and then when u calculate the sum of the distances u get something like sin 1/x + 2β3
sin 1/n*
idk i know that the sum is incorrect
but idk where im going wrong
dire geode
where do you calculate the perpendicular distance?
muted oyster
where do you calculate the perpendicular distance?
unless im making some silly mistake
the sum of perpendicular distances
will come
in terms of sin 1/n
which cannot be summed over
dire geode
,rotate
wraith daggerBOT
dire geode
you're not explaining how you're using perpendicular distances still. can you just find d(2) using your three lines
muted oyster
okay
cedar kilnBOT
@muted oyster Has your question been resolved?
muted oyster
its
crimson sedge
i can help you out if you still need
crimson sedge
advanced or mains?
crimson sedge
ok here
first lets start with finding d(n)
suppose theres a point (x,y) then what is the sum of absolute values of the distances to all sides?
crimson sedge
you should be able to show it is $$|y|+\left|\frac{y-\sqrt3x}2\right|+\left|\frac{y+\sqrt3x-4sqrt3}{2}\right|$$
muted oyster
and ive written it here
wraith daggerBOT
Barycentre
muted oyster
sorry
crimson sedge
yhat should be it right?
muted oyster
yeah
crimson sedge
then put in y=sin(1/n) and. x=1/n
note that we are evaluating n from 1 onwards
and $sin(1/x) $is positive for $x\geq 1$
wraith daggerBOT
Barycentre
crimson sedge
So you can remove the absolute value from the sin term
muted oyster
but wait
for the second erm
assume d = 2
so we have 1/2 and sin 1/2
sin 1/2 comes to around 0.4 and β3/2 comes to around 0.8
u cant really remove the absolute for that then can u
ull have to add a negative
crimson sedge
for the next two terms notice that $\sin(1/n)<\frac{\sqrt{3}}{n}$ for $n>1$
wraith daggerBOT
Barycentre
muted oyster
i got the idea
if its possible
could u write down ur solution somwhere
on paper
and i could then go through it and get it clarified w u
muted oyster
yes okay
dire geode
Ill write it down on latex
!nosols
cedar kilnBOT
Ill write it down on latex
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
dire geode
could u write down ur solution somwhere
!noans
cedar kilnBOT
could u write down ur solution somwhere
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
muted oyster
?
can learning not be done by seeing how someone else approached the problem
wtv
@crimson sedge thanks for tryna help
if u have some solution ready just send it in dms π
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cedar kilnBOT
crimson sedge
As a helper, please do not give out answers that could be copied as a homework s...
iβm not even a helper
dire geode
iβm not even a helper
good point. the rest still applies
crimson sedge
Understood. Thanks, uh, ββ-. Youre not really riemann, so I wont call you that.
cedar kilnBOT
Available help channel!
unique grail
I am stuck with this question .
let x , y ,z be integers . suppose gcd(y,z)=1 , further suppose that xy is divisible by z , then x is divisible by z
cedar kilnBOT
I am stuck with this question .
let x , y ,z be integers . suppose gcd(y,z)=1 ,...
crimson sedge
I am stuck with this question .
let x , y ,z be integers . suppose gcd(y,z)=1 ,...
gcd(y,z)=1 implies theres no prime that divides y,z simulataneously. Hence if a prime $p | z$ and at the same time $p | xy$ but since $p\nmid y$ then we can say that $p\mid x$
wraith daggerBOT
Barycentre
crimson sedge
can you conclude your result then?
crimson sedge
I wouldnt skip immediately to the conclusion because $z$ can have powers of some primes too. More generally, if $\gcd(y,z)=1$ and $p^n|z$ then $p^n \nmid y$. Thus follows youe result.
wraith daggerBOT
Barycentre
unique grail
Oh thank you
slim pond
Is this a good enough proof that x MONUS 1 is a primitive recursive function?
dire geode
try 
pearl palm
recursive in math? i didnt know that was a thing
dire geode
also #get-advanced-access if you need it
slim pond
Thank you ill switch over
cedar kilnBOT
@slim pond Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
sick ledge
is this correct?
cedar kilnBOT
is this correct?
cedar kilnBOT
@sick ledge Has your question been resolved?
mental mulch
i'm lost as to when i need truncate/round when solving lineal systems with the Gaussian elimination method because i don't understand the finite precision system well. I understand how to solve the exercise with out the rounding, but i'm otherwise stuck. any help would be appreciated.
Example:
Consider the finite precision system F (10, 4, ββ, β).
Solve the linear system by the Gaussian elimination method using rounding as the method
approximation in the finite precision system.
cedar kilnBOT
i'm lost as to when i need truncate/round when solving lineal systems with the G...
@mental mulch Has your question been resolved?
unborn night
For these derivatives, I understand Ux and Ut as they just use the chain rule but need some help comprehending Uxx, Uxt and Utt (or not in this case).
unborn night
This is kinda stupid but where is the term I'm missing
Hm. I guess If i use schwarz theorem I can see that Ut has Ua and Ub and do it that way around. But how do I know it will be Uba + Ubb instead of Uab +Uaa
cedar kilnBOT
@unborn night Has your question been resolved?
cedar kilnBOT
odd sierra
this seems so basic
but i cant do it for no reason
and i dont wannt to use the graphs i wanna do it with like tables and sketch it out
Like i cant get a u shape from my points that i made
wraith daggerBOT
cedar kilnBOT
@odd sierra Has your question been resolved?
cedar kilnBOT
odd sierra
for (fg)(x)
is like
f(g(x))?
Like i do it
and got like 36-(x+3)^2
in the sq root
solved it out and got that
and it has red x so wrong π
short blade
can you elaborate
short blade
what is your question
odd sierra
Like
if i want f/g of x for this one
will just be the f on the top
and the g on the bottom?
short blade
f divided by g, yes
cedar kilnBOT
cedar kilnBOT
Available help channel!
pliant orbit
-9/4 / 10
pliant orbit
how is this -9/40?
digital cliff
-9/4 * 1/10
pliant orbit
whats the name of this rule?
digital cliff
just what division is, if i divide by a im multiplying by 1/a
cedar kilnBOT
quiet sinew
HELP
How do I begin to answer 12.
I completely forgot
And am panicking
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digital cliff
cedar kilnBOT
Available help channel!
shy kayak
(4a + 1) (2a + 6) = ? w/ solution pls
cedar kilnBOT
(4a + 1) (2a + 6) = ? w/ solution pls
short blade
!noans
cedar kilnBOT
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
short blade
what have you tried @shy kayak
mental herald
are you just trying to find out what a is
sharp lotus
do you understand distribution?
shy kayak
are you just trying to find out what a is
im trying to solve it
shy kayak
do you understand distribution?
i dont, can you explain it?
sharp lotus
x(2a+6) = 2ax + 6x
does that seem familiar?
just distributing multiplication across addition
shy kayak
yeah actually, our math teacher used that same exact example
but what do we do if were supposed to multiply the 2 terms?
sharp lotus
wdym multiply the two terms
shy kayak
(4a + 1) (2a + 6) = ? w/ solution pls
the first term multiplied by the second term
sharp lotus
they're called factors, not terms, when they're being combined by multiplication
a + b + c - d
a, b, c, d are terms
(a)(b)(c)
a, b, c are factors
just to clarify those erm...terms
sharp lotus
x(2a+6) = 2ax + 6x
so are you CRYSTAL CLEAR on distribution?
shy kayak
yes yes
sharp lotus
is that something you feel like you've mastered?
ok well it's basically the same concept
shy kayak
is that something you feel like you've mastered?
not mastered but i can do it
sharp lotus
we did:
x(2a+6) = 2ax + 6x
but now just replace x with (4a+1) on the left and you'd get your original problem:
(4a+1)(2a+6)
right?
shy kayak
yea
sharp lotus
x(2a+6) = 2ax + 6x
ok now replace x with (4a+1) on the right side:
2a(4a+1) + 6(4a+1)
and it basically simplifies to two distributions
(2a)(4a)+2a + 24a + 6
sharp lotus
solve for what, this is just changing to a different version...
sharp lotus
first factor?
shy kayak
the (4a + 1)
shy kayak
explain on how i solve it, and i can use that for the other factor and for other questions aswell
because i really dont get it man
sharp lotus
you've completely lost me
mental herald
(4a + 1) (2a + 6) = ? w/ solution pls
are you just trying to distribute this whole thing
to get a polynomial
sharp lotus
that's all thats happening, yes
i recommend you just watch a video on foil-ing https://www.youtube.com/watch?v=Dn6f_fL79Ws&ab_channel=TabletClassMath
mental herald
explain on how i solve it, and i can use that for the other factor and for other...
so basically when you do this
you are trying to multiply each term by each term
i'll just use this as an example
sharp lotus
yes, that's essentially what ends up happening
each term in the first parenthesis by each term in the second one
sharp lotus
just watch the video
sharp lotus
yep
mental herald
@shy kayak do you understand this so far
shy kayak
shit
mental herald
kk
shy kayak
im watching the video
math class is done already but im still gonna try stuff for next time
mental herald
okay
shy kayak
thanks for helping but im just gonna review when i get home from school
love you guys
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
rapid juniper
please someone help me on this
cedar kilnBOT
please someone help me on this
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
1
fallen moat
please someone help me on this
you can start by naming them and finding them one by one
where A,B,C can be seen and D is at the back
cedar kilnBOT
@rapid juniper Has your question been resolved?
cedar kilnBOT
@rapid juniper Has your question been resolved?
crimson sedge
can elements be agebraic expressions or equations in a set?
cedar kilnBOT
can elements be agebraic expressions or equations in a set?
short blade
yes
solid juniper
short blade
cedar kilnBOT
@crimson sedge Has your question been resolved?
short blade
within reason, yes
crimson sedge
and EVERYTHING
short blade
not everything
crimson sedge
?
short blade
for example, a set can't contain itself
crimson sedge
for example, a set can't contain itself
ye
wait
but
it can doe
like
Real numbers
set
got
Z
short blade
(\mathbb{R}\not\in\mathbb{R})
wraith daggerBOT
maximo
short blade
you cannot have X in X
crimson sedge
OH ITSELF
short blade
it is paradoxical
short blade
well sure, but probably nothing worth mentioning
crimson sedge
okay
crimson sedge
understandable stuff?
short blade
most of the time elements will be numbers, sets, functions, letters, etc.
regular stuff yeah
shell gust
hi
shell gust
Can someone help me rq with this online math quiz
Iβm lost
I canβt find much timely help online and the answer is out there but itβs locked behind a paywall
hot crag
is this a test, or just practice?
frigid sinew
cedar kilnBOT
rocky harness
it is sqrt(x) here right?
Yes
frigid sinew
Yes
What do i do after finding that
just anti derivative?
okay wait so just to be certain rn this
rocky harness
Yes
frigid sinew
Im trying to find a way to turn this into integral
wraith daggerBOT
smidgin
rocky harness
Yes
frigid sinew
and anti derivative of sqrt is 2/3 x^3/2
so answer is 16/3
okay idk why it took me so long
tysm
!
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cedar kilnBOT
cedar kilnBOT
Available help channel!
opaque crypt
Hi, suppose I have the matrix $T=\mqty(1 & 1-i\1+i & 0)$. I can diagonalise it to give $T_{diag} = \mqty(2 & 0\0 & -1)$. I can easily work out eigenvectors using $\mqty(2 & 0\0 & -1)\mqty(a\b)=-1,2\mqty(a\b)$. But is it possible to work out the eigenvectors using $T$ instead of $T_{diag}$? I can't seem to get anywhere with $\mqty(1 & 1-i\1+i & 0)\mqty(a\b)=-1,2\mqty(a\b)$.
wraith daggerBOT
EvilScientist
flint plinth
sure, you can work them out using T
what went wrong when you tried to solve
$$\begin{pmatrix}1 & 1-i \ 1+i & 0 \end{pmatrix} \begin{pmatrix}a \ b\end{pmatrix} = -\begin{pmatrix}a \ b\end{pmatrix}$$
wraith daggerBOT
Bungo
cedar kilnBOT
@opaque crypt Has your question been resolved?
opaque crypt
I got $a=b(1-i)$ and $b=\frac{a}{2}(1+i)$, so if I set $a=1$, I get $b=\frac{1}{1-i}$. But this contradicts the answer I'm getting when I solve $\mqty(2 & 0\0 & -1)\mqty(a\b)=2\mqty(a\b)$.
wraith daggerBOT
EvilScientist
opaque crypt
In that case I get a=1, b=0
I suspect it's something to do with the meaning of diagonalisation. It's been a while since I've used this.
opaque crypt
I got $a=b(1-i)$ and $b=\frac{a}{2}(1+i)$, so if I set $a=1$, I get $b=\frac{1}{...
Oh sorry, this is for me solving for the eigenvalue of 2. Not -1
flint plinth
well remember that the two matrices are expressing the same transformation with respect to different bases
so when you compute the eigenvectors using the two matrices, they are also expressed with respect to different bases
you can't compare them directly
opaque crypt
Oh that's what I missed. Thank you. So the diagonalised case is in the basis of its eigenvectors which is why the elements of the matrix are so simple. Is this correct?
opaque crypt
cool, so what basis would the undiagonalised matrix be in?
flint plinth
i guess you could say it's in the "original" basis (the one corresponding to the original matrix before you diagonalized it)
flint plinth
if you find the matrix V such that A = VDV^-1 (where A is your original matrix and D is the diagonal version), then the columns of V are the eigenvectors in the original basis
flint plinth
Would that be like (0,1) and (1,0)?
that's what they look like in the diagonalized version
opaque crypt
I understand! Thank you so much!!! Also, how are there so many helpers? Are you guys paid?
flint plinth
nope, all volunteers
opaque crypt
wow thank you! I appreciate it a lot
flint plinth
sure, gl
strong jacinth
hi @rich idol
cedar kilnBOT
hi <@254396796976103424>
strong jacinth
sorry to bother u but
strong jacinth
howed u get this #help-23 message
rich idol
b = -a/2?
strong jacinth
ya
pearl palm
SHOW THE INTEGRAL!!!!
strong jacinth
wot
rich idol
SHOW THE INTEGRAL!!!!
WRONG CHAT
rich idol
howed u get this https://discord.com/channels/268882317391429632/903481106819612...
yeah so
a + 2b =0
rewrite it
pearl palm
WRONG CHAT
i know but its your integral
rich idol
b = -a/2
pearl palm
I ALREADY SAID SHOW THE INTEGRAL THERE!!!!!
rich idol
I am not varia π
pearl palm
oh
strong jacinth
wait wait but wasnt it 2ab +a^2=0?
strong jacinth
ohh
strong jacinth
you can factor out an a
y cannot it be 0
rich idol
y cannot it be 0
try plugging in 0 it doesnt work 
so you get a= 0, and a^2+2b = 0
but if you plug in a=0 it doesnt work
so you just go with a^2+2b = 0
strong jacinth
o
rich idol
its like facttoring quadratic equations
except you see here that one of the answers doesnt work
so u go with the other one
strong jacinth
a(a+2b) = 0
isnt is a(a+2b)?
strong jacinth
all good lol
rich idol
yeah u just factor it out and then set it equal to 0
a=0 doesnt work so the other one does
and just rewrite it
a+2b = 0 is the same as b=-a/2
strong jacinth
could i js write a=-2b?
rich idol
the reason why u write it as -a/2 is so that you can easily convert it to -3a/2 = -3
but i mean maybe you can do it another way
strong jacinth
the reason why u write it as -a/2 is so that you can easily convert it to -3a/2 ...
uhh whered u get the 3 from
rich idol
uhh whered u get the 3 from
cedar kilnBOT
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shy geyser
i need help, i dont understand physics, like i cant seem to apply the concepts when solving, where do i go to learn it beginner friendly and hopefully master it? im afraid i will fail my physics class because of vector problems
undone epoch
Realities examples helps understanding of concepts. Use your knowledge in practice. https://www.youtube.com/watch?v=ApUFtLCrU90&pp=ygUTY2xhc3NpY2FsIG1lY2hhbmljcw%3D%3D Here is a video that I haven't seen it myself, but it seems to introduce vectors.
shy geyser
thank youu, im behind in class now since were now in momentum and collisions topic
undone epoch
i need help, i dont understand physics, like i cant seem to apply the concepts w...
Vectors are present change that is expected. You have three force acting on a object, those vectors are the expected present change.
shy geyser
Realities examples helps understanding of concepts. Use your knowledge in practi...
i will watch this video and solve, hopefully i get goodπ₯Ή
oh btw do you have an idea how to derive these 3 formulas? where do i start? our physics is calculus based
undone epoch
There's been a time when I did momentum. A elastic collision, for example two colliding balls, is when the balls collide, they go with the same velocity on its way back. Expecting the energy is being kept, the momentum will be the same as $$m_Av_{0A}+m_Bv_{0B}=m_Av_A+m_Bv_B$$
wraith daggerBOT
Good
undone epoch
https://youtu.be/aIhScO3_I50?feature=shared https://youtu.be/-q-WiX-KVXo?feature=shared These two would explain better than mine.
shy geyser
thank you so much 
undone epoch
I hope those will help, I already forgot momentum...
cedar kilnBOT
@shy geyser Has your question been resolved?
hearty basin
how do u answer the question in red please ππΎππΎ
cedar kilnBOT
how do u answer the question in red please ππΎππΎ
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coral jewel
$\int_0^{\frac{\pi}2}\frac{-4\sin x+7\cos x}{2\sin x+3\cos x}dx$
wraith daggerBOT
FungusDesu MSC2020 34A05
coral jewel
2
i solve this by multiplying both numerator and denominator by sec^3x and subbing u=tanx
but the problem ensues when i realized tanpi/2 is undefined
so is this an improper integral?
hollow minnow
It is an improper integral.
coral jewel
so after subbing u=tanx in i get
$\int_0^{\infty} \frac{-4u+7}{2u(u^2+1)+3(u^2+1)}du$
do i just...continue as usual?
wraith daggerBOT
FungusDesu MSC2020 34A05
hollow minnow
do i just...continue as usual?
Indeed, you do.
candid mason
i solve this by multiplying both numerator and denominator by sec^3x and subbing...
Have you considered letting x = tan(u/2)?
All good I think your approach will work as well
hollow minnow
Have you considered letting x = tan(u/2)?
Weierstrass sub will be more complicated than this method.
silk hound
$\frac{7cosx-4sinx}{2sinx+3cosx} = -2\frac{2cosx -3sinx}{2sinx+3cosx} -1$
wraith daggerBOT
Solomaniac
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coral jewel
**Solomaniac**
wuh
how didnt i see that
but anyway yeah i think i know now
.close
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hallow bear
could anyone help me with it?
In the isosceles trapezoid ABCD with acute angle A equal to 60Β°, a median EF is drawn, intersecting diagonal AC at point O. It is known that FO is 10 less than OE. Find EF if the perimeter of the trapezoid is equal to 120.
golden grotto
could anyone help me with it?
In the isosceles trapezoid ABCD with acute angle ...
Draw it down
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pseudo merlin
hi
subtle harbor
subtle harbor
well you are given formulas for activity and amounts of strontium
pseudo merlin
what they both look the smae
same
arent they both half life
i thought the formula for activity was A=N/T
subtle harbor
A=A_0 (1/2)^n where A_0 is initial activity, n is number of (months presumably) and A is current Activity
N=N_0 (1/2)^n where N_0 is initial number of strontium atoms, n is number of months, and N is the current number of strontium atoms
subtle harbor
i thought the formula for activity was A=N/T
well I'm unsure what the A formula in the slides means then lmao
pseudo merlin
how come N is the number of months when activity is measured in BQ/s
pseudo merlin
i thought all the units had to match
so then N had to be the number of seconds in a month
wait
pseudo merlin
i said n is the number of months
does n just mean number of half lives
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chrome turtle
I am tryin to find a vector
cedar kilnBOT
I am tryin to find a vector
chrome turtle
Inclined at 60Β° to all the theee axis
Assumin it to be xi yj zk
i am doing i β’ (xi+yj+zk)/|i||vector| = cos 60
and getting
x/β(xΒ²+yΒ²+zΒ²) = 1/2
chrome turtle
Oh ye
slow jewel
There can be infinitely many vectors, so you can multiply with a constant later on
strange berry
cuz there are infinitely many magnitudes possible
slow jewel
Lol
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junior flame
okay hello people, i was playing with numbers in my mind and i was stuck on a problem, the previous part is quite irrelevant but my problem or more like question is, Is there a direct way to calculate the fourth root of a given number by the long division method, with as much as i could think, i could do it by taking the square root of the number two times by the long division method, the prime factorization rather works for smaller numbers but gets very inefficient as the number becomes larger in magnitude bcoz then the divisibility identification and constant factorization can make it a bit messy and that is why i would wanna know if there exists a direct long division method to do it, i tried grouping the numbers in a pack of 4 starting from left(edit: i meant right*), the standard method you use in long division method to find square roots and cube roots but i couldn't go further than the first step of taking a number who's fourth power would be smaller than the first group that of the dividend
cedar kilnBOT
okay hello people, i was playing with numbers in my mind and i was stuck on a pr...
@junior flame Has your question been resolved?
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@junior flame Has your question been resolved?
violet vortex
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@junior flame Has your question been resolved?
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blazing sleet
I want a function looking like the red line. It passes through x of 4 and y of 1, the other coordinate needs to be about x of 0,05 and y of 0.
digital cliff
looks loggy
blazing sleet
True.
wraith daggerBOT
Aβ€Γ
wraith daggerBOT
Aβ€Γ
blazing sleet
unless you need the asymptote at x=0
I do not mind, if I can, I will get it, not necessity.
blazing sleet
**Aβ€Γ**
That is the one I am trying myself, yet, a bit different. Let me check what you provide.
digital cliff
**Aβ€Γ**
this one is if you want the asymptote
blazing sleet
Yes, I did read that, thank you.
Quite good, thank you! May I close this?
For if you read mine response that is.
digital cliff
sure
blazing sleet
.close
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barren spade
cedar kilnBOT
barren spade
I've been trying this for a bit but can't seem to find a solution
dire geode
compare $e^{\sqrt{\sin(x)}}$ with $e^u$
wraith daggerBOT
riemann
dire geode
what should u equal in the substition
dire geode
show
barren spade
cos = root (1-sinx)?
barren spade
cos^2 + sin^2 = 1
that's the one I was thinking of
ah minus
but how do you write that in terms of u
root 1-u^2
dire geode
u = sqrt(sin(x)). sin^2(x) = ?
barren spade
u^4?
dire geode
yes
barren spade
ah
dire geode
you also need du in terms of dx or vice versa
dire geode
dont' know how you got that
barren spade
I see
that's probably where I am getting it wrong
didn't realise there was chain rule
it's 2u/cos(x)
π
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topaz yew
cedar kilnBOT
spiral fog
Whats the Q
topaz yew
this is my work. I dont know what to do for the complex numbers with modulus less than one
i need to prove it
for any complex number z
mortal grove
for any complex number z
the easiest way to do this is to show that even the smallest possible value for each makes that equation hold true
then obviously, everything bigger will also hold true
so it boils down to minimizing |z+1| and |z^2+z+1|
or let z = a+bi and do a ton of Algebra lol
topaz yew
so it boils down to minimizing |z+1| and |z^2+z+1|
so i need to find a z such that both expressions have the smallest values possible?
mortal grove
so i need to find a z such that both expressions have the smallest values possib...
not necessarily a z, but find the minimum value of each of those expressions
then if it holds at the minimum value, it holds for anything bigger
topaz yew
and how exactly can i find those minimum values
spiral fog
$|(z + 1)^2 + 1| \geq 1$
wraith daggerBOT
casework
spiral fog
If $|z| < 1$ then the real part of that thing has to be bigger than 1
wraith daggerBOT
casework
topaz yew
:)
maybe some notations would be useful
i tried t = z+1
but it didnt go anywhere
i think this is correct
thanks for help anyways
.close
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steel coyote
Hi, I need help with this question.
cedar kilnBOT
Hi, I need help with this question.
@steel coyote Has your question been resolved?
steel coyote
<@&286206848099549185>
royal loom
steel coyote
step 2
cedar kilnBOT
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steel coyote
.close
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barren dove
cedar kilnBOT
barren dove
Can anyone help with this?
tepid sail
Like a drawing of the diamond
can you share it
tepid sail
Thats all i got lmao
no thats perfect
can you give me a variable for distance between player and home
barren dove
Y is fine
tepid sail
Y is fine
then we have x^2 + a^2 = y^2
I'm keeping a = 90
to make things easier
@barren dove do we know dx/dt?
barren dove
Yes somewhat lmao im just not the best at calc
tepid sail
Yes somewhat lmao im just not the best at calc
okay let's first implicilty differentiate
you want me to guide you through this process
?
barren dove
So like 2x/2y?
barren dove
okay so its just 2x=2y and we carry the y over?
tepid sail
okay so its just 2x=2y and we carry the y over?
not exactly
ur not impliclty differentiating properly
barren dove
Am i forgetting the 90/a^2?
tepid sail
Am i forgetting the 90/a^2?
2x * x' + 2a * a' = 2y * y'
barren dove
Oh lmao π i dont get it much why do we derive the x twice?
tepid sail
Oh lmao π i dont get it much why do we derive the x twice?
I'm so sorry; I shouldn't have you given the answer first
but basically
barren dove
No ur fine dw iβm just kinda slow within these topics
tepid sail
we apply chain rule and we are doing $\frac{d}{dt}(x^2)$
wraith daggerBOT
nosqldb
tepid sail
so we get $2x \cdot \frac{d}{dt}(x)$
wraith daggerBOT
nosqldb
tepid sail
we do that for every term
barren dove
after that do i substitute the numbers then?
Yeah i get the chain rule portion i j need to learn how to do it more fluently on my ownπ
tepid sail
Yeah i get the chain rule portion i j need to learn how to do it more fluently o...
2x * x' + 2a * a' = 2y * y'
so what's da/dt
I'm keeping a to be the 90