V = 1200b - b^3 /4
#help-17
still mica
What did you get from solving it?
rare solar
im so confused, what
rare solar
oh it's 40
still mica
Yea
still mica
Wdym
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rare solar
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vast shale
sorry for the yappuccino
vocal sleetBOT
sorry for the yappuccino
trim trout
prob not the best channel for this
vast shale
what's the best channel for this question?
trim trout
higher level math channels
silk comet
vast shale
i'm not sure because even if it is about foundations it still lacks depth
okay i will ask on that channel just in case
.close
vocal sleetBOT
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rotund hinge
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gentle sleet
product rule on xy'
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karmic forge
It something to do with Riemann integration I know the formula but not know how to apply in this question
vocal sleetBOT
It something to do with Riemann integration I know the formula but not know how ...
cerulean drift
Uhh
vast shale
like sum of k/n become an integral ?
karmic forge
like sum of k/n become an integral ?
But I need 1/n outside
vast shale
yes
karmic forge
But I getting 1/k outside
karmic forge
Ok by log
We get 1/k log(1+k/n)
I can't apply Riemann integration
I/n not outside
vast shale
but u can divide by n outside and multiply inside
mental meadow
i want a very quick help
vast shale
u will get 1(k/n)
vast shale
i want a very quick help
open a new channel
mental meadow
open a new channel
how
vast shale
np
vocal sleetBOT
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jagged cargo
i want to check my work for part c
vocal sleetBOT
i want to check my work for part c
jagged cargo
this is 1.40
hard atlas
there is no "the" basis of a subspace
jagged cargo
on second equality, i compare two sides pairwise
so z1 = 0
thus 6z1 = z2 = 0
z3 = 0
z4 = 0
thus z5 = (z3 - 2z4)/3 = 0
desert hornet
i want to check my work for part c
why did you want to show U\cap W = {0}?
jagged cargo
so that U + W is a direct sum
desert hornet
ah okay
hard atlas
this sequential logic with slowly showing that some entries are zero and then more have to be zero doesnt work that nicely written like this
desert hornet
i thought oplus was just the symbol for addition lmao
hard atlas
would be better to write something like "because (z1,...,z5) is in W it follows that z1=..=0. then ... "
I assume axler hasnt done some equivalent condition for direct sums in terms of bases yet?
jagged cargo
i think so? the only theorem which involves direct sum is this
hard atlas
how does he show that?
jagged cargo
hard atlas
ok
so you can basically just write "by the proof of 2.33 U+W is a direct sum"
the proof really just shows that if you obtain W by extending the basis then it will automatically work
no need to show it again for your particular case
jagged cargo
oh what
so if i just prove U + W = C^5, then im allowed to immediately conclude its a direct sum?
hard atlas
you dont even have to show U+W=C^5
it really just follows from the proof of 2.33 that you only needed to extend the basis
jagged cargo
damn
hard atlas
"by the proof of 2.33 we just need to set W=span(v4,v5) where v4,v5 are the vectors from above"
important thing to take away from this: sometimes the proofs of statements show even more than just the statement itself
thats often the case for existence results
instead of just showing the existence of W, the proof actually shows how to get it
we would also say the proof is constructive
(thats not always the case for existence proofs)
jagged cargo
so this suffices?
i think its better for me here to explicitly provide such an example of W
hard atlas
yes the question asks you to find a subspace W
thats more explicit than showing one exists
really the point of the question is to make you realize that questions (b) and (c) are essentially the same question
vocal sleetBOT
left portal
really the point of the question is to make you realize that questions (b) and (...
denascite can u help me aswell . . .? (sorry for asking it here)
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summer brook
hey, I don't understand what's the least Herbrand Model here. It seems for me like it does not exist, but my teacher's solution says it's
ML={q(b),q(f(b)),..., p(a),p(f(a)),...}.
vocal sleetBOT
hey, I don't understand what's the least Herbrand Model here. It seems for me li...
summer brook
write down in help-22
vast shale
@outer warren
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slim igloo
hi
slim igloo
need some help man
tiny fable
what do you need help with?
slim igloo
well its a physics question
by no means is it complicated
may I ask it here, even though this is 'math'
its just about a force diagram
it's a super simple thing that I'm failing to accept
tiny fable
well, i'm no long time member of this server, but i'd be happy to answer ur question 😄
slim igloo
it seems obvious by the way my friend and teacher are talking about it
slim igloo
well, i'm no long time member of this server, but i'd be happy to answer ur ques...
so like
there are two cylinders. On top, between them there's another cylinder kept. All surfaces are with friction and all cylinders are of equal mass.
like so
tiny fable
*try and answer ur question
slim igloo
and
apparently the lower two cylinders apply reactive forces like these
towards each other
my argument is that such forces aren't generated in a system that's stable under the given conditions
because I don't see any reason why such forces would be induced
tiny fable
you must have a different understanding of simple compared to me lol 😅
sorry
i can't really help you
slim igloo
oh its alright man
you think someone else could help?
or is the server just for pure math
tiny fable
probrably, there's a lot of smart people on this server
slim igloo
including you
vocal sleetBOT
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silver tusk
How to do this
vocal sleetBOT
How to do this
brittle wasp
Find the complement
silver tusk
Find the complement
of?
brittle wasp
of the set of integers less than 2310 which are relatively prime with 2310
silver tusk
of the set of integers less than 2310 which are relatively prime with 2310
relatively prime is just 2,3,5,7,11 right
brittle wasp
no
that's prime
you need to look up the definition of relatively prime
and I need to take the dog out. Good luck!
solemn frigate
Hey
So for this question try taking the combinations of all multiples of 2310
@silver tusk
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@silver tusk Has your question been resolved?
vast shale
excuse me where is mathematical analysis room?
vocal sleetBOT
excuse me where is mathematical analysis room?
velvet zephyr
Which type of analysis?
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@vast shale Has your question been resolved?
tired sable
What can I do if my calculator doesn't give me the actual fractions n gives me decimals?
vocal sleetBOT
What can I do if my calculator doesn't give me the actual fractions n gives me d...
vast shale
u cant
potent beacon
What can I do if my calculator doesn't give me the actual fractions n gives me d...
There is nothing we can do
Unless there is an option to turn that setting
I meean sin pi/3 isnt good for a calculator
cosmic cloud
remember the fractional values
tired sable
.solved
vocal sleetBOT
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obsidian tiger
Hello I need a tiny bit of help
vocal sleetBOT
Hello I need a tiny bit of help
obsidian tiger
It asks to determine the range of this function
Since it has infinitiy amounts of extreme points, it makes it hard to simply determine it that way
desert hornet
what's the derivative?
flat whale
Looks like it goes off to infinity
desert hornet
it doesn't
obsidian tiger
Since it has infinitiy amounts of extreme points, it makes it hard to simply det...
Yup
desert hornet
you can at least show that this doesn't have any more roots past some value
but it doesn't look like the lower bound has a nice value
obsidian tiger
It doesn't
desert hornet
yep
obsidian tiger
Should I use the first derivative and use an approximation method?
desert hornet
well sure
but I don't see a point
the minimum value is equal to cos(1/x) where x is the largest root of x=cot(1/x)
which turns out to be roughly x=0.222548..
obsidian tiger
Yeah it's not 100% perfect
limber falcon
you can probably just say that's where the minimum value is attained, and then argue that the range is of the form [y, +\infty) for that value y
desert hornet
you can probably just say that's where the minimum value is attained, and then a...
no, the upper limit is 1
limber falcon
er true, I misread
obsidian tiger
Yeah it's nearing 1, but never reaches it
desert hornet
the minimum value is equal to cos(1/x) where x is the largest root of x=cot(1/x)
I don't think you can get better than this
I suppose you could say cos(1/x)=x/sqrt(1+x^2) for that value of x
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ivory salmon
im stuck on this one
i just reach an irrational number when i try to do (-1)^(4/3)
terse cipher
your cooked
ivory salmon
i know lmao
terse cipher
metoo 
ivory salmon
do u know how to do
terse cipher
i will try
ivory salmon
ty
heady vine
im stuck on this one
i just reach an irrational number when i try to do (-1)^(4...
It’s just power rule
heady vine
and like the other nerd guy said
Bro
ivory salmon
It’s just power rule
i did power rule
then when i try to evaluate it i get i
lets say i do t^(1/3)
that becomes (3t^(4/3))/4
and then i do 0 - ((3(-1)^(4/3))/4)
heady vine
that becomes (3t^(4/3))/4
Yep
heady vine
and then i do 0 - ((3(-1)^(4/3))/4)
I should be a real value tho ?
ivory salmon
i assume
heady vine
and then i do 0 - ((3(-1)^(4/3))/4)
Something wrong with the calc I guess or you input it wrong
ivory salmon
heady vine
Give it another try
vocal sleetBOT
@ivory salmon Has your question been resolved?
modern steppe
Hi i wanted to know if I could do this for having a equivalance
vocal sleetBOT
Hi i wanted to know if I could do this for having a equivalance
modern steppe
Like my demonstration is good or can u find any conter example ?
ousp it's 1 at the end
There's the corrected version
gaunt sparrow
If you want it to signify that this approximation is true when $x$ is close to 0 or 1, then I think you should just make that explicit unless you are the only one reading it and understand it as so
twin meteorBOT
Azyrashacorki
modern steppe
Pour -> For
On a -> We have
Alors -> Then
modern steppe
If you want it to signify that this approximation is true when $x$ is close to 0...
how I could make this more explicite ?
I'm very bad at writing math
gaunt sparrow
By just writing it after. sin(x-1) ~ x-1 pour x suffisamment près de 1
vocal sleetBOT
@modern steppe Has your question been resolved?
modern steppe
By just writing it after. sin(x-1) ~ x-1 pour x suffisamment près de 1
I see
Thanks u
charred cairn
I need to find the circumference and area.
vocal sleetBOT
I need to find the circumference and area.
vocal sleetBOT
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Please do not ping individual helpers unprompted.
silk osprey
charred cairn
no
silk osprey
this is wild
charred cairn
NO.
silk osprey
🍉
charred cairn
Is this 19 cm to the whole side or just to the height? @silk osprey
vocal sleetBOT
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silk osprey
!noping
vocal sleetBOT
Please do not ping individual helpers unprompted.
charred cairn
They came to this channel, so I have full rights to do that.
flat whale
.close
celest holly
Had a differential equation question : $xy''-2(x+1)y'+(x+2)y=2e^{x}$ I asked on here yesterday and was able to solve it after, unfortunately when I substitute the answer back in the result I get $2xe^{x}$, which is off by a factor of $x$. Subsituting in a wronskian with a higher power of $x$ by 1 gives me the right answer, but obviously I can't just do that with no reason. The answer I came to was $y=e^{x}+\frac{x^{3}e^{x}}{3}-x^{2}e^{x}$ this should obviously be $y=e^{x}+\frac{x^{3}e^{x}}{3}-xe^{x}$. Would appreciate any help I can get on how to arrive at that answer.
vocal sleetBOT
Had a differential equation question : $xy''-2(x+1)y'+(x+2)y=2e^{x}$ I asked on ...
twin meteorBOT
JuiceeGreen
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@celest holly Has your question been resolved?
shadow spindle
it might help to show how you got to that answer
celest holly
Essentially I separated the homogeneous version of the equation into $x(y''-2y'+y)=0$ and $2(y'-y)=0$ and the common solution I got was $y_1=e^x$. Then I used reduction of order to get the other homogeneous solution $y_2=\frac{x^{3}e^{x}}{3}$. Then I used variation of parameters to find the inhomogeneous solution using the wronskian.
twin meteorBOT
JuiceeGreen
celest holly
I've checked and re-checked my mathematical working so many times I'm almost certain there were no silly errors there. So I'm guessing it's my understanding of using the method wrong that might be the issue.
celest holly
<@&286206848099549185>
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olive stirrup
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brazen totem
abstract palm
Let $A=\begin{pmatrix}
2&2\3&3
\end{pmatrix}$ and $B=\begin{pmatrix}
4&3\6&1
\end{pmatrix}$ be matrices over $\mathbb{Z}_7$. how to solve $AX^T=B$. i know that $A,B$ are not regular matrices so i cant just use inverse. how should i do it then?
vocal sleetBOT
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Slowaq
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abstract palm
sorry
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gaunt pelican
Hey! Can someone help me understand this group theory question?
Prove that if G/Z(G) is cyclic then G is abelian.
I don't understand it. I understand Z(G) is the centre of G, which is defined as Z(G) = {gx=xg | for all g \in G} and I can see that gx=xg is in the centre definition, which is also the definition for a group to be abelian. but apart from that i have no idea
dim pumice
first of all, if G/Z(G) is cyclic, what does that even mean?
vocal sleetBOT
@gaunt pelican Has your question been resolved?
gaunt pelican
first of all, if G/Z(G) is cyclic, what does that even mean?
means it can be generated by one element
dim pumice
so there is some $\bar{g}$, so that $G\setminus Z(G) = {\bar{g}^0, \bar{g}^1, ...}$
twin meteorBOT
rbit
gaunt pelican
yeah, i agree with that
dim pumice
in other words, $G\setminus Z(G) = {g^0\cdot Z(G), g^1\cdot Z(G), ...}$
twin meteorBOT
rbit
gaunt pelican
wait, how?
dim pumice
remember how factor groups are defined?
gaunt pelican
i get the first part, and i assume the second part follows from the fact that its a coset
yeah, cosets right?
dim pumice
yeah, we just take g^k and multiply it with every element in Z(G)
like, $\bar{h} = h\cdot Z(G)$
twin meteorBOT
rbit
dim pumice
left multiply every element in Z(G) with h
gaunt pelican
i see. but why is it h*Z(G) and not Z(G)*h?
is that where being abelian follows from?
dim pumice
$h\cdot Z(G) = Z(G) \cdot h$ is not true in general, but it's true for normal subgroups
twin meteorBOT
rbit
dim pumice
and Z(G) is a normal subgroup
gaunt pelican
ah i see
gaunt pelican
yeah, i agree with that
dim pumice
so now let's take any $a, b \in G$
twin meteorBOT
rbit
dim pumice
and show they commute
gaunt pelican
do you mean in G \ Z(G)? we dont know that much about G do we?
dim pumice
no, but we want to show G is abelian right?
gaunt pelican
yeah, i just dont know what we'd use to show it
dim pumice
so the first step is to always take two random elements
gaunt pelican
okay
dim pumice
we at least know a partition of G
gaunt pelican
yeah, okay
dim pumice
so the element a will fall into some set of the form $g^k\cdot Z(G)$
twin meteorBOT
rbit
gaunt pelican
okay, and because Z(G) = {xy=yx for all x, y in G}, we can then show that multiplying g^k by it must also be commutative because Z(G) is commutative?
or is that the wrong thinking
dim pumice
we will make use of that property at least yes
$a = g^n \cdot x$ and $b = g^m \cdot y$
twin meteorBOT
rbit
gaunt pelican
yeah, i agree with that
gaunt pelican
would i need to show that g^n*x commutes with g^m*y?
dim pumice
yeah, it's a matter of rearranging the terms so that (g^n x)(g^m y) = (g^m y)(g^n x)
gaunt pelican
okay
is it enough to just say that multiplying an element by a commutative element must also commute?
dim pumice
it will commute with the element that is commutative
gaunt pelican
so therefore a commutes with b?
dim pumice
but a itself is not commutative, we haven't shown that yet
dim pumice
right
gaunt pelican
therefore, x*g^n = g^m*y?
dim pumice
that would be like saying a = b
gaunt pelican
oh, right yeah
gaunt pelican
so `g^n*x = x*g^n`
where would I go from here? how do we bring in g^m*y?
dim pumice
so far, you got $ab = g^n x g^m y = x g^n g^m y$
twin meteorBOT
rbit
dim pumice
while yes, that doesn't do much for us now
gaunt pelican
**rbit**
do we just need to change the elements on the right hand side to be (g^m y)(g^n x)?
gaunt pelican
so the first step is to get xg^mg^ny
twin meteorBOT
rbit
gaunt pelican
would we use the fact that xy=yx from the Z(G) property?
im not really sure how else we'd get there
twin meteorBOT
rbit
gaunt pelican
oh, you're right
i completely missed that
so therefore g^nx g^m y = xg^n g^my = x g^{n+m} y = x g^m g^n y as addition is associative
dim pumice
yeah, and now g^n and g^m have switches sides
gaunt pelican
and as x and y are commutative, g^m y g^n x
dim pumice
right
gaunt pelican
which completes the proof?
dim pumice
yeah
gaunt pelican
ah i see, thank you so much. that question was really annoying me haha
vocal sleetBOT
@gaunt pelican Has your question been resolved?
mint badge
don't know where to start
vocal sleetBOT
don't know where to start
quick vigil
just use vector addition and then solve the inequality for the range of theta
i think youll get something like -1/2 <cos theta < 1/2
then use the graph of cos theta
to find the range of theta
vocal sleetBOT
@mint badge Has your question been resolved?
mint badge
just use vector addition and then solve the inequality for the range of theta
explain
wdym just use vector addition??
there's nothing to add
quick vigil
wdym just use vector addition??
The unit vectors 😭
We are literally given the range of their resultant
What else can we do but add them 😭
mint badge
What else can we do but add them 😭
bro i don't understand
quick vigil
bro i don't understand
Do you know what unit vectors are
quick vigil
No
That's wrong
Well if you haven't even learned proper vector addition then why are you even trying this question 😭
mint badge
Well if you haven't even learned proper vector addition then why are you even tr...
bro
tell me what it is then
tell me..
what is vector addition
mint badge
aight bro sure
I KNOW WHAT VECTOR ADDITION IS
YOU LITERALLY JUST ADD IT UP
WDYM THAT'S WRONG
mint badge
ragebait used to be believable
mint badge
u = 2i + 3j
v = 3i + 2j
u + v = 5i + 5j
quick vigil
quick vigil
u = 2i + 3j
v = 3i + 2j
u + v = 5i + 5j
YOU DO THAT WHEN THEY ARE IN THE RESPLVED FORM
WHATTHEHELL
quick vigil
THIS
mint badge
aight calm down lil bro
quick vigil
😭
I ain't helping no more cuz you probably don't know how to solve inequalities too 😭
quick vigil
I'm too tired to teach everything from scratch 😭
mint badge
bro ik what inequalities are
quick vigil
like genuinely what's your problem
You 😭
quick vigil
bro ik what inequalities are
Well then you should be able to do it without my help anymore
Good luck
Ima go
mint badge
is belittling others your pastime or something?
quick vigil
wow thanks for nothing ig?
Welcome
quick vigil
I ain't even do nun
mint badge
someone's doing math at a lower level than you and you expect them to be a god? i come here for help so ofc u should expect that i can't do it
quick vigil
And I ain't got anymore time for you
mint badge
like what 😭
mint badge
And I ain't got anymore time for you
aight sure lil bro
gg bro
i ask questions in a server designed for you to ask questions and i get berated
vocal sleetBOT
@mint badge Has your question been resolved?
vocal sleetBOT
@mint badge Has your question been resolved?
willow pike
don't know where to start
do you know what the magnitude of the resultant of two vectors is?
$R = \sqrt{A^2 + B^2 + 2 \cdot AB \cdot \cos \theta}$
twin meteorBOT
willow pike
where A and B are the magnitudes of the vectors
and the angle between them is θ
we are using this formula since the angle is the main thing asked for in the question
hollow scroll
i need help with grade 10 quadratic expression
vocal sleetBOT
i need help with grade 10 quadratic expression
hollow scroll
how do i determine the x int and the vertex of the quadratic formula
2nd how do i write a quadratic equation in the form of ax^2 + bx+c=0
3rd how do i find the equation of the parabola using this equation form y=ax^2 +bx+ c
dapper sequoia
how do i determine the x int and the vertex of the quadratic formula
by making perfect sq
hollow scroll
wait whats a perfect square again i kinda forgot
hollow scroll
ok
graph the quadratic function y=-(x-2)(x+8)
by determining the x int and the veryex
vertex
dapper sequoia
it will be x^2 + 6x -16
hollow scroll
wait so i just combine it all together?
dapper sequoia
you can convert it to (x+3)^2 -25
now (x+3)^2 is a perfect square so it will be always positive value
hence least value = -25
hollow scroll
it will be x^2 + 6x -16
wait so i just unfactore it?
dapper sequoia
at x=-3
dapper sequoia
unfactor then make perfect sq
hollow scroll
okok
dapper sequoia
like i did
hollow scroll
what about for my second question
dapper sequoia
you know how to make perfect sq or not?
hollow scroll
no
hollow scroll
so x?
dapper sequoia
so it will be x^2 +bx/a + c/a = 0
now you can add or subtract the constants so ignore that for a bit
how can you make x^2 + bx/a in perfect sq
by making (x+b/2a)^2
now as you have added b^2/4a^2
you also have to subtract it
hollow scroll
wait i think i get it now. To find the perfect square i square root the number that has to be the same so like the sqrt of 49 is 7 because 7x7=49
then 49 would be a perfect square?
dapper sequoia
yeah
hollow scroll
ohh okayy
can you give me an example so i can find the perfect square
because i have a math test tmrw
dapper sequoia
x^2 + 6x + 8=0
first give me the values of x using middle term splitting (by making factors)
hollow scroll
cross method?
dapper sequoia
no
by making factors
dapper sequoia
graph the quadratic function y=-(x-2)(x+8)
like this
hollow scroll
dapper sequoia
so x = -2 and -4 right?
hollow scroll
yea
dapper sequoia
now try making perfect sq like i told you
hollow scroll
okok
dapper sequoia
yes
i am bacxk
dapper sequoia
so is it y=(x+3)^2-1
now try to equate it with zero here
hollow scroll
huh
dapper sequoia
now try to equate it with zero here
put y =0 here
x+3 = +1 or -1
x = -2 or -4
@hollow scroll
hollow scroll
ya
dapper sequoia
that is the proof of your quadratic formula
hollow scroll
okok
vocal sleetBOT
@hollow scroll Has your question been resolved?
pale light
Is there an efficient way to tell if a binary matrix can be made symmetric by permuting its rows?
vocal sleetBOT
Is there an efficient way to tell if a binary matrix can be made symmetric by pe...
@pale light Has your question been resolved?
vast shale
vocal sleetBOT
vast shale
the answer scheme assumes $20 to be E(x)
since the expected gain must equal to the money paid for the game to be fair
however, what is wrong in the reasoning in which we consider $20 as negative?
so essentially E(x) = 0
and then
-20 * 0.7 + k * 0.3 = 0
,w -20 * 0.7 + k * 0.3 = 0
twin meteorBOT
vast shale
THis gives us the value for k as 46.67
This doesn't match the answer of 66.7 given in the text book
which calculates the value of k as follows:
,w evaluate 0.7 * 0 + k * 0.3 = 20
twin meteorBOT
heavy yoke
but the textbook assumes that k is the amount he's paid back, whereas you are assuming that k is the net profit he makes
vast shale
right
silk osprey
,calc 66.67-46.67
twin meteorBOT
Result:
20
I am still a bit confused
heavy yoke
so you are modeling a random variable, x, which is "how much money does he make from the transaction (net)" and the textbook is modeling a random variable, y, which is "how much is he getting paid (gross)". since he pays $20 upfront, he must make $20 less than he's paid, i.e. x = y - 20
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torpid sequoia
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torpid sequoia
given the region W, I need to calculate the triple integral
After calculating bounds, I got this, but I'm not sure it's right
is that right?
$\int _0^{\frac{1}{4}\pi }\int _0^{2\pi }\int _{\frac{\sqrt{2}}{cos\left(\phi :\right)}}^{\sqrt{2}}::::\frac{1}{\rho ^2}\cdot \rho ^2\cdot :sin\left(\phi \right):d\theta :d\rho :d\phi$
twin meteorBOT
Chuti | Argentina
torpid sequoia
there
lilac bronze
I think it should be $\frac{1}{\rho^4}$ because $\rho^2$ is squared again
twin meteorBOT
fish
torpid sequoia
you are right
$\int _0^{\frac{1}{4}\pi }\int _0^{2\pi }\int _{\frac{\sqrt{2}}{cos\left(\phi :\right)}}^{\sqrt{2}}::::\frac{1}{\rho 4}\cdot \rho ^2\cdot :sin\left(\phi \right):d\theta :d\rho :d\phi$
twin meteorBOT
Chuti | Argentina
lilac bronze
also, i think you have the order of variables wrong, you should have $d\theta$ after $d\rho$ because of the bounds you set
twin meteorBOT
fish
torpid sequoia
indeed
$\int _0^{\frac{1}{4}\pi }\int _0^{2\pi }\int _{\frac{\sqrt{2}}{cos\left(\phi :\right)}}^{\sqrt{2}}::::\frac{1}{\rho 4}\cdot \rho ^2\cdot :sin\left(\phi \right):d\rho :d\theta :d\phi$
twin meteorBOT
Chuti | Argentina
lilac bronze
that should be good
torpid sequoia
so limits are good?
lilac bronze
yeah
torpid sequoia
cool
tysm
it would be incorrect to say that radius goes from 0 to 2, correct?
my friends are telling me that
but its clear to me that the radius is at max sqrt(2)
mild trench
vocal sleetBOT
oak magnet
Yes
mild trench
it is pi r ^2
oak magnet
It is
oak magnet
Yes
oak magnet
what happen there
Distribute the r
mild trench
oh nvm
oak magnet
You just cancel pi*r
mild trench
i get it ty
oak magnet
So it last r
oak magnet
Yw
vocal sleetBOT
@mild trench Has your question been resolved?
oak magnet
yea i see i thought all of pi r^2 was cancelled
You can type .close if you done
dusty night
Can anyone explain
sly summit
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sly summit
to measure the whole area between f(x) and g(x) my teacher did the intergral of g(x)-f(x) but i don't understand, wouldn't that leave you with nothing?
ignore the area that's not orange for this question
drifting jackal
to measure the whole area between f(x) and g(x) my teacher did the intergral of ...
What do you get when you do g(x)-f(x)?
drifting jackal
I mean what do you get if you subtract the two functions?
drifting jackal
(-x^2 + 9) - (x^2 - 9)
sly summit
you get -2x²+18
drifting jackal
And as you can see, that's not nothing
sly summit
but what can i do with that function
drifting jackal
Take the integral
sly summit
does it then give me the area between the two functions?
drifting jackal
You need to use the bounds as well
sly summit
what are bounds? do you mean the places where they intersect?
drifting jackal
Yes
drifting jackal
Do the math and see if you get the same result
sly summit
but f(x)+g(x) would be wrong right?
fading merlin
Hey
fading merlin
Bye
vast shale
Bye bye
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@fading merlin Has your question been resolved?
drifting jackal
You didn't even ask a question
Do you have a math question?
Then why did you open a channel and ping helpers if you don't need help with math?
lime viper
?
lime viper
Then why did you open a channel and ping helpers if you don't need help with mat...
isnthis somthing I can ping mods for?
limber falcon
.close
vocal sleetBOT
limber falcon
isnthis somthing I can ping mods for?
yes, but this user has been muted already for other reasons
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crisp axle
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crisp axle
-4 is right, how would I get it without graphing?
3,-4
are you supposed to just plug numbers in
twin meteorBOT
sentinel
severe flint
and then factor that
crisp axle
and then factor that
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lime viper
yes, but this user has been muted already for other reasons
ok thx
lime viper
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unborn trellis
idk what the answer is can someone pls explain
vocal sleetBOT
idk what the answer is can someone pls explain
flat whale
idk what the answer is can someone pls explain
Did you plot both of them
unborn trellis
Did you plot both of them
i mean as far as i can tell theyre the same
the lecture notes were pretty much useless so idk what to do
wait is it that the parametric has direction
and the regular equation is just left to right
oh i forgot to close
.close
vocal sleetBOT
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pseudo herald
Bruh, how do I do the top one?
vocal sleetBOT
Bruh, how do I do the top one?
pseudo herald
Here’s the image
vocal sleetBOT
@pseudo herald Has your question been resolved?
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
@pseudo herald Has your question been resolved?
celest parrot
$\int_{0}^{2}\int_{2y}^{6-y}\left(1\right)dxdy$
vocal sleetBOT
$\int_{0}^{2}\int_{2y}^{6-y}\left(1\right)dxdy$
twin meteorBOT
Kavaige
celest parrot
how can i switch the order from dx dy to dy dx
basically, the question asked to create two double itnegrals where D is the tirangular region with vertices (0,0) (4,2) (6,0)
and we were given an unknown f(x,y) to set it up with, but i just put one for the time being
winged wave
try drawing out the region you're integrating over
and writing the borders in terms of x instead of y
winged wave
you might have to split it into two integrals then
one where x goes from 0 to 4 and the other from 4 to 5
winged wave
👍
celest parrot
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vast shale
Can someone tell me how I can minimize this?
vast shale
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kind fiber
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regal heron
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regal heron
how do we prove that it is equal?
tranquil trellis
Notice you can factor out (sinx - 1) from the numerator and denominator
high kettle
\begin{align*}\text{L.H.S.}&=\frac{\sin^{2}x-1}{\tan x\sin x-\tan x}\&=\frac{(\sin x-1)(\sin x + 1)}{\tan x(\sin x-1)}\&=\frac{\sin x+1}{\tan x}\&=\cos x+\cot x\end{align*} and \begin{align*}\text{R.H.S.}&=\frac{\sin x \cos x + \cos x}{\sin x}\&=\cos x+\frac{\cos x}{\sin x}\&=\cos x + \cot x\end{align*}
twin meteorBOT
如月あやみ Kisaragi Ayami
tranquil trellis
that works
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smoky sage
can someone explain what i did wrong ☠️ it's physics and im tryna prep for an exam with this practice quiz
vocal sleetBOT
can someone explain what i did wrong ☠️ it's physics and im tryna prep for an ex...
sly sierra
consider answer 3
if the momentum of each object is unchanged, did a collision even occur?
smoky sage
oh nah
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outer pendant
hi, anybody happen to know how to solve this?
vocal sleetBOT
hi, anybody happen to know how to solve this?
outer pendant
I feel like I've made a mistake already
vocal sleetBOT
@outer pendant Has your question been resolved?
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@outer pendant Has your question been resolved?
outer pendant
<@&286206848099549185>
half imp
how do we know that I_{n+1} is the derivative of I_{n+2}?
vast shale
i would approach it using integration by parts
try splitting $I_{n+2} = \int \frac{x^{n+2}}{\sqrt{1-x^2}} dx$ as $\int x^{n+1} \cdot \frac{x}{\sqrt{1-x^2}} dx$
twin meteorBOT
villegas_bozo
uncut holly
hi, anybody happen to know how to solve this?
where are these questions from?
vocal sleetBOT
@outer pendant Has your question been resolved?
steep crater
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steep crater
!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
my thought process when i saw this problem was first that condition (ii) has kind of a "dependency" relationship, where each element in either set must depend on another element. if you think about it, these dependency relationships must form only loops, for example:
Number A depends on Number B = A - b
Number B depends on Number C = B + a
Number C depends on Number D = ...
...
and then the last number in the loop must depend on number A.
Then, because we reached number A again, all the additions and subtractions must cancel out to 0.
severe flint
Why would they form loops
if they didnt form loops, there would be a dead end somewhere, there would be a number that doesnt depend on another number
steep crater
Because we can't minus b or add a right
severe flint
what do you mean
severe flint
well i mean suppose we started on the number 10 in the set B, and a=3 and b=2.
Then you can imagine that there are elements 13 and 16 in the set A, and elements 14 and 12 in the set B as well
And if you track how they're dependent to each other, it would look like:
10 -> 13 -> 16 -> 14 -> 12 -> 10
steep crater
Uhh okay if thats what you mean
Yea
A - pa + qb where pa=qb
How would we continue
severe flint
note that if pa=qb then q=a and p=b
steep crater
Btw tysm for taking the effort to help 🙂
severe flint
no problem :)
steep crater
note that if pa=qb then q=a and p=b
Only if a and b are coprime
steep crater
Ig we could do some gcd messing but that would be more cases
severe flint
it only really matters the ratio
steep crater
but q/p = a/b will always be true
Ok
steep crater
it only really matters the ratio
How would we continue
severe flint
Well in my example i gave, i have a=3 and b=2
and you could note that |A|=2 and |B|=3
steep crater
Ya
severe flint
its very clear that a|A| = b|B| in this scenario, and all you have to do is generalize it
for a single loop
severe flint
if you have A - pa + qb = A
Then you have q/p = a/b
where q is the amount of elements in set B, and p is the amount of elements in set A
So |B|/|A| = a/b
in fact you can just say A - |A|a + |B|b = A and simplify easily
steep crater
if you have A - pa + qb = A
Then you have q/p = a/b
where q is the amount of ele...
q is not necessarily |B| and vice versa tho
Wait
severe flint
q is not necessarily |B| and vice versa tho
in the case that there is only one loop, q is |B| because q is the amount of times which you subtract b to cancel it out, and every time you subtract b that means you're going to an element in B
steep crater
Shit my brain is fried from functional equations
Gimme a min sorry
Theyre disjoint
severe flint
Also, i think given the constraints, a and b are necessarily coprime, so dont worry about the case where they arent
because theyre disjoint and they have to "loop" in the way i said, they cant have common divisors
severe flint
i mean im not like totally confident in that cause i do think there are like edge cases where they can have common divisors but it really doesnt help to think about them
Like in the case where a=b and you have a loop with one element in A and one element in B where the element in B is greater than the element in A by a and vice versa
coral juniper
Hello! I was wondering if anyone could tell me what I need to know before learning Heine's limits. I'm really lost and I don't understand it so maybe I'm missing something hence why I'm asking. I know limits (I think?) so I don't get what else I'd need, when I try to do exercises I don't get where I'd apply the definition and I get it wrong usually.
vocal sleetBOT
Hello! I was wondering if anyone could tell me what I need to know before learni...
coral juniper
Damn I can't find Layla or else I'd ping her
bronze osprey
Hello! I was wondering if anyone could tell me what I need to know before learni...
maybe try asking in #book-recommendations or #math-discussion
coral juniper
Uh aren't i supposed to ask in a help channel
bronze osprey
Uh aren't i supposed to ask in a help channel
that's not a rule
coral juniper
Usually I'd ask in discussy but I don't wanna annoy them today lol
coral juniper
that's not a rule
Fun
bronze osprey
Usually I'd ask in discussy but I don't wanna annoy them today lol
oh bad idea discussy goes by very quickly
coral juniper
It does but it always works
bronze osprey
basically the rule is you have to be on-topic, so like
coral juniper
I always say Layla asked
bronze osprey
It does but it always works
most people in discussy do not have an analysis background
much less are reading your specific text
coral juniper
Usually it works and if it doesn't I just ask harper
Either way I shall ask in maths discuss
Discussy* grr autocorrect
See u!
.close
bronze osprey
fair enough then
hexed umbra
A man was 30 years of age when his daughter was born. The father’s age now
exceeds 3 times the daughter’s age by 6 years. How old is each at present?
im going insane wtf
vocal sleetBOT
A man was 30 years of age when his daughter was born. The father’s age now
excee...
lilac sluice
it's neither
try solve the first and the second
you won't get the correct ansmwer
hexed umbra
😭 😭 😭
hexed umbra
im assuming x is the daugters age here
yes it is
lilac sluice
these questions are slightly annoying but reading the question carefully makes things a whole ton easier
bronze osprey
A man was 30 years of age when his daughter was born. The father’s age now
excee...
let x number of years pass
after x years, how old is the man and how old is the daughter
great, now use the question
hexed umbra
so 30 + x = 3(x + 6) ??
lilac sluice
no
u add 6 to the 30 u were correct bfr
but in this question we only refer to the fathers age changing
cus it says by 6 years
do u get it?
sorry if it's not that clear
hexed umbra
do u get it?
yes
lilac sluice
okay
so essentially
on the RHS
you won't add the 6 to the x
which means it's just 3x
cus the question states 3 times the daughters age
plus another 6 years
hexed umbra
how do i know if i have to add in parenthesees or outside cuz i literally get them confused everytime
bronze osprey
how do i know if i have to add in parenthesees or outside cuz i literally get th...
when you have a compound term, like x - 5 or whatever
and you want to multiply that term by something, or divide by something
always use brackets
hexed umbra
compound term meaning same units or
bronze osprey
compound term meaning same units or
yeah it wouldn't make sense if the units were different
hexed umbra
ok
vocal sleetBOT
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ruby estuary
Hello, I need to determine the convergence of this series, I need some hints
ruby estuary
I should probably use some convergence criterion but idk which one
civic otter
Try to rewrite the inside of the log
ruby estuary
1+2/(n-1)
civic otter
we havent covered this sadly:(
Ah 😬
Have you maybe seen that $\log{(1 + x)} \sim x$, if x → 0 ?
ruby estuary
yes
twin meteorBOT
Alberto Z.
ruby estuary
but I cant use this ye
civic otter
That is indeed the Taylor expansion, actually
Just stopped at first order
civic otter
but I cant use this ye
Your x is 2/(n-1)
civic otter
Yep, I don't see many other (quick) ways
ruby estuary
my prof calls this approximation of log for the poor
thats good tho it works for me
thanks!
.close
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proper jackal
paper estuary
hmm
worthy crane
help
worthy crane
help me please number 7
tight totem
yes
tight totem
help me please number 7
Can you provide a clearer screenshot
tight totem
CAn you send clear screenshot of problem 5
worthy crane
this
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@worthy crane Has your question been resolved?
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@worthy crane Has your question been resolved?
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