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#help-42
viral isle
karmic willow
wouldnt it be -2.75cos((pi/6)t) + 12.25
viral isle
wouldnt it be -2.75cos((pi/6)t) + 12.25
It tells u to select a sin function?
Idk I was a bit uncertain about my answer
Cuz it includes cos functions
karmic willow
oh is that what sinusidal means?
karmic willow
i thought that just meant like periodic
viral isle
i thought that just meant like periodic
Oh
karmic willow
yeah that was wrong
viral isle
Ok nvm
karmic willow
its actually schizo
look
ohhhh nvm
apperently i was supposed to click 2 and the last one
didnt know you could pick 2
karmic willow
yeah thats the point
viral isle
But the question is asking for a sin function
karmic willow
they are both "the same" it wanted me to pick both TT
viral isle
they are both "the same" it wanted me to pick both TT
Anything else u need help with?
calm coralBOT
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strong owl
I am a little confused on number 12. mostly the middle 6 sub questions
leaden thunder
!ss
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strong owl
sorry
Its asking for the name and equation
i beleve the top ones are inner loops, and the bottom ones are dimples
i just am having trouble finding the equations
<@&286206848099549185>
<@&286206848099549185>
😦
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floral mango
Does this look right?
calm coralBOT
Does this look right?
floral mango
breaking it down
mortal orbit
breaking it down
this looks correct
I would just switch in the end to (r-p)(s-q)/...
to do that, you multiply by (-1) * (-1)/ [(-1) * (-1)] = 1
so then you get the exact definition of [p,q;r,s]
but that's just my extreme rigor talking
your proof is fine
calm coralBOT
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lyric ore
any ideas?
calm coralBOT
any ideas?
mortal orbit
any ideas?
comparison test?
mortal orbit
(X_n) is almost surely a sequence of non-negative terms
mortal orbit
uh
mortal orbit
it is just _surely_ that
not really tho
velvet osprey
X_n takes only two values: 0 and 2^-n
mortal orbit
it's never said that X_n(Omega) is a subset of {0,2^(-n)}
mortal orbit
anyways we're only after the probability
so no matter whether X_n = 2^(-n) or X_n = 0, you have 0 <= X_n <= 2^(-n) for those two configurations
since they amount to (probability wise) all the cases
(almost surely) sum(X_n) converges by comparison
calm coralBOT
teal drift
???
mortal orbit
hekkkkkkkkkkkkkkkkkooooooooooooooo
If you have a math question you need help for, go to #❓how-to-get-help for clarification
violet cosmos
If you have a math question you need help for, go to <#488120190538743810> for c...
sorry, it's my first time using discord and i don't really understand the UI of it, makes me overwhelming
teal drift
Mmh in the description it says you joined Discord in 2023
mortal orbit
sorry, it's my first time using discord and i don't really understand the UI of ...
no worries, take your time to look around. This category of channels you're in is currently "occupied", meaning already assigned to another person
mortal orbit
If you have a math question you need help for, go to <#488120190538743810> for c...
go to the channel I linked for more info
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violet cosmos
Mmh in the description it says you joined Discord in 2023
yup, made the account along time ago but never used it and today someone from my university asked me to join his discord, that's why i am here
teal drift
<@&268886789983436800>
dreamy lance
Don't troll here
violet cosmos
<@&268886789983436800>
So, every server has many channels?
teal drift
Usually yes
But if you don't have a maths question, please go to the #discussion or #serious-discussion or #chill channel
calm coralBOT
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floral mango
Please let me know if you need help understanding my scribble..
floral mango
Does this look close enough?
calm coralBOT
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unique juniper
calm coralBOT
unique juniper
anyone explain please
covert scroll
Idk maybe you can try this
If it's true than you can say triangles similar by shred side and twi angles
And therefore ba=bc
But maybe I'm lying
And we can't do it
marsh bison
Ok so I made a rough sketch
If you draw like the diameter from B to the center O then it would extend downward to a point
If you draw a line from A and C to that point then that angle has to be 90° I think since any angle opening to the diameter is 90°
To prove that the 2 sides A and C are the same you gotta prove the 2 triangles are the same
So congruent right?
unique juniper
yea I think so
marsh bison
So if the angle to the point is 90° for both sides that means that the angle to the other point B is also 90°
So you prove that the 2 angles are the same
Now the side from A to the point I made should be same I think
When you compare it to the other side from C to point
late jasper
since bo bisects abc, if there were a line segment ac then it would bisect ac as well
this means the "triangle" is isoceles and therefore ab = bc
marsh bison
And then you got 2 angles and a side so you can prove the 2 triangles are congruent and as such the hypotneuse should be same on AB and bc
Idk I'm not that good
late jasper
since bo bisects abc, if there were a line segment ac then it would bisect ac as...
you can use more thorough proofs but this is the quickest way to say it
asssuming line segment ac exists, either ab = bc or ab = bc = ac
mellow elm
consider the two triangles BOA and BOC (draw the sides)
both are isosceles because two sides are radii, which are congruent
the angle ABO is equal to BAO. The same follows for OBC and BCO, but ABO and OBC are congruent since OB bisects ABC
This should be helpful enough to help you find the solution
unique juniper
alright thank you very much everyone
quick talon
quick talon
What can you say about these 2 triangles ?
calm coralBOT
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unique juniper
What can you say about these 2 triangles ?
conqurent
quick talon
They’re identical, explain Why and you got your answer
unique juniper
alright
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gusty lance
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gusty lance
Idk how to solve for r after where I got
surreal rampart
Idk how to solve for r after where I got
they didnt ask to solve they asked for the smallest value
use the condition
g(x)>7
means g0>7 means r>7
gusty lance
winged basalt
hello i need help with this problem
A group of 4 friends, Aaron, Billy, carl and dany are playing a video game and betting 10$ per game. In each game, the winner gets 25$, the second place gets 10$ and the third place gets 5$
Based on many past games, they've come to the following conclusions:
Aaron has a .4 probability of winning
Danny has a .3 probability of winning
Carl has a .1 probability of winning
Billy has a .2 probability of winning
When Aaron wins, carl has a .6 probability of winning second place
When Danny wins, aaron has a .4 probability of ending in last place
When Carl wins, Danny has a .6 probability of getting 3rd place
The rest of the probabilities are evenly distributed as long as they've been observed
Given the available info, what is the expected value for Danny after 5 games?
potent lotusBOT
Charlotte
gusty lance
expected value is just n(p) but can you also type this in a available channel
surreal rampart
g(0)=r>7 means 4sin(-3pi/2)+2.5+q=r =6.5+q =r however we know q>0 so q+6.5>6.5 r>6.5 then the other condition g(0)=r>7 intersect?
surreal rampart
this is calculations
just like u did
but i used the condition from the question before too
the intersection because both are conditions
gusty lance
oh
so where r we getting 6.5r > 6.5 from? im a bit confused on this
or wait
is that saying q + 6.5 > 6.5
and that r > 6.5
if its the latter then i understand
wait doesn't r >7
surreal rampart
and that r > 6.5
yes
exactly
so intersect them
the smallest value is 7 but i dont understand why they asked that question
just by doing g0 ull find that....
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knotty saddle
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knotty saddle
i m not sure how to approach this
ik the vectors would be perpendicular
would they form a crosshair almost on the circle
granite dust
try drawing a graph
potent smelt
@knotty saddle if you think about this geometrically, it may help to recall the central angle theorem.
(This will give you one crucial fact that will allow you to verify 2 of the 4 answers quickly)
(The final one you should have eliminated already, leaving you with just one answer remaining)
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slender crescent
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slender crescent
find area of OBD
B (2,1)
equation of straight line is y=-x+3
this is my working and i get a negative number
can anyone tell my what i did wrong tysm
fyi answer is 115/6
velvet osprey
the bottom half of the orange curve has equation y = -2 sqrt(x) but you're subtracting that
so both of the -2sqrt(x) under the integral should become +2sqrt(x)
calm coralBOT
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ivory lion
why can i break the seconf line as I5I IAdjAI = 5
calm coralBOT
why can i break the seconf line as I5I IAdjAI = 5
ivory lion
oh because its a number
velvet osprey
did you mean can't when you typed can?
ivory lion
cant yes im meant cant
velvet osprey
also use | not capital letter i for vertical bars
ivory lion
ahh i coulnt find the symbol :_)
velvet osprey
oh because its a number
yes, because $|cA| = c^n |A| \neq c |A|$
potent lotusBOT
Ann
calm coralBOT
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spark steeple
Hello, I made this graph theory problem and was wondering if i got the cheapest total ($4,920 without Jacksonville) and $6,600 with Jacksonville added. I said it's not possible to travel each route exactly once, and if I could remove an airport I'd remove ATL Atlanta. I'm wondering if anyone could get cheaper flights and better solutions to questions. I can also put out my route if it would help
spark steeple
<@&286206848099549185>
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potent smelt
@spark steeple if you count the number of edges terminating in every node, unless every node but two has an even number, it's not possible to cover them all except by backtracking. By my count, though it's not completely clear reading the map, there seem to be 4 nodes with an odd number of edges. So you would be correct that it's not possible.
spark steeple
<@637288977505714192> if you count the number of edges terminating in every node...
yeah
I was wondering if the paths i got were the best options
potent smelt
Assuming that all flights cost the same amount, as long as you didn't double up on the more expensive flights and only did 1 flight worth of backtracking then you have an optimal solution.
according to my math, you did a total of 17 flights, and only did the expensive flights once
so you're all good.
calm coralBOT
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rough ferry
are my calculations right can someone please check
calm coralBOT
are my calculations right can someone please check
rough ferry
if the intersection point is X
I want to get angle PXQ (this is what part b asks for right?)
so my plan is to use the cosine law with the a and b as the diagonals halved
am I on the right track
cedar rose
you dont need to take halfs just calculate angle between OQ and RP (we dont care if they dont come from same point they are vectors anyway)
but your way is also should give right answer
cedar rose
if the intersection point is X
I want to get angle PXQ (this is what part b asks...
Just noticed, did you do first one the same way?
There is formula for cos of angle between vectors. Its related to vectors dot product
rough ferry
yeah I did with the cosine law
I got an answer for b
but it isnt right according to the answer key
not sure whats wrong
cedar rose
Search for Angle Between Two Vectors. If you already learned it, its easier to use
rough ferry
i didnt learn it
cedar rose
Okay then can you show your result(calculations) and answer key
rough ferry
this is the answer key
|OR| = sqrt(65)
|OP| = 25
angle POR = 80.8
angle QPO = 99.2
|PR|^2 = |PO|^2 + |RO|^2 - 2|PO| * |RO| * cos 80.8
|PR| = 25
same reasoning to find |OQ|
|OQ| = 27.64
finally, use cos law to find angle between PR and OQ
RO^2 = |PR|^2 + |OQ|^2 - 2|PR| * |OQ| * cos(x)
65 = 1379.1 - 1362 cos x
x ~= 18 degrees
last question in my hw and my brain is fried
so help appreciated 🙏
cedar rose
|OR| = sqrt(65)
|OP| = 25
angle POR = 80.8
angle QPO = 99.2
|PR|^2 = |PO|^2 + ...
you cant use RO here since PR and OQ dont create triangle naturally. Its actually should be RP - OQ its v in answer key
And also OQ and PR can be find with sum of vectors. You used cos law which is technically correct but you will have measurement error (angles are not exact + cos also not exact)
rough ferry
you cant use RO here since PR and OQ dont create triangle naturally. Its actuall...
isnt |RP - OQ| = |QP|
this is what im seeing
cedar rose
this will work only if vectors start from same point (Triangle Law of Vector Addition)
thats why RP - OQ = v in answer key, since it cannot be showed directly (fortunately its not nessesary to see it to calculate it)
rough ferry
thats why RP - OQ = v in answer key, since it cannot be showed directly (fortuna...
i have a question, how do u know its RP - OQ, not OQ - PR, i face this problem a lot, so I have to visualize negating one of the vectors and adding it the other and it kinda takes time
cedar rose
in problem statement there is vectors OQ and RP
so we calculate RP - OQ, calculating OQ - RP will give same result
but OQ - PR will give adjustment angle
if you imagine vectors a and b from one point there is no difference between angle from a to b and from b to a, but when you change RP to PR that means you change vector direction to opposite, which results into adjustment angle (in this case its same as changing b to -b)
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still terrace
yo can someone help
calm coralBOT
yo can someone help
tranquil wasp
this is a google translation but i dont fully understand this
still terrace
this is a google translation but i dont fully understand this
what do u not understand
hot prawn
this is a google translation but i dont fully understand this
not very legible
tranquil wasp
describe the position of the line ga
maybe you could say it passes through (2,4,2) at r=0 and the line kinda rotates around the point as you change the value of a
still terrace
maybe you could say it passes through (2,4,2) at r=0 and the line kinda rotates ...
could i say that its star shaped
tranquil wasp
could i say that its star shaped
wait star?
tranquil wasp
the different values for a
i dont know how you see a star
still terrace
i dont know how you see a star
ok
still terrace
https://tenor.com/view/baffling-gif-24471655
wait
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tranquil wasp
how do i sketch the like
i know its 3 dimensional so its probably pretty hard to do that i dont really know
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patent phoenix
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hasty fiber
you can use these two equations to write your expression for V in terms of only one of the variables
patent phoenix
you can use these two equations to write your expression for V in terms of only ...
how?
there's h l and w
hasty fiber
from the top equation you have h = 2-2w
patent phoenix
Ya
hasty fiber
you can sub that expression for h into your expression for V
hasty fiber
indeed
hasty fiber
patent phoenix
Did i do this wrong omg 😭
hasty fiber
why do you think so?
potent lotusBOT
hasty fiber
ok i guess you did do something wrong
patent phoenix
hasty fiber
why did the + become a -
hasty fiber
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limpid mulch
how to do b using conditional probability formula
calm coralBOT
how to do b using conditional probability formula
limpid mulch
.close
calm coralBOT
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brittle sail
0 to 1 integration ( \sqrt{\frac{x^3}{1-x}} )
calm coralBOT
0 to 1 integration \( \sqrt{\frac{x^3}{1-x}} \)
potent lotusBOT
Andy
polar bison
0 to 1 integration \( \sqrt{\frac{x^3}{1-x}} \)
$\int_{0}^{1} \sqrt\frac{x^3}{1-x}$
potent lotusBOT
devthemasked
polar bison
?
remote mural
0 to 1 integration \( \sqrt{\frac{x^3}{1-x}} \)
Beta function?
remote mural
too complicated
K
mellow harbor
Just use u-substitution $u = 1 -x$
potent lotusBOT
HitenTandon
potent lotusBOT
What a wonderful world !
potent lotusBOT
HitenTandon
brittle sail
King's rule?
potent lotusBOT
HitenTandon
mellow harbor
That's what the negative sign effectively does
brittle sail
You have to put it 1 to 0 if you are having negative sign
After removing negative sign we can have limit 0 to 1
brittle sail
Bro
u--->1-x
du= -dx
and we have I= 0 to 1 √(x^3/(1-x))
so here our limit for x is 0 to 1
So for u substitution it will be 1 to 0 no?
@mellow harbor
1 to 0 -(√(1-u)^3/u) du
$$
\int_1^0 -\frac{\sqrt{((1-u)^3}}{u}) , du
$$
brittle sail
**HitenTandon**
But you are writing this one check it again
mellow harbor
Oh yea mb
brittle sail
Then why were you arguing?
mellow harbor
Then why were you arguing?
I'm sowwy
brittle sail
Okay so what will be our next step
potent lotusBOT
Andy
mellow harbor
FOIL, distribute integrate
blazing coyote
You can take (1-u)^2 outside first
remote mural
But condition is mn>0
Isn't it 5/2 and 1/2 though?
blazing coyote
You can take (1-u)^2 outside first
then IBP
brittle sail
$$
\int_0^1 \sqrt{\frac{(1-u)^3}{u}} , du
$$
$$
\int_0^1 (1-u)\sqrt{\frac{1-u}{u}} , du
$$
potent lotusBOT
Andy
remote mural
0 to 1 integration \( \sqrt{\frac{x^3}{1-x}} \)
Is it 3pi/8
brittle sail
Is it 3pi/8
Absolutely
west horizon
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calm coralBOT
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west horizon
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velvet osprey
west horizon
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tidal grotto
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do you know the form of a taylor polynomial?
west horizon
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west horizon
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west horizon
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tidal grotto
the best thing to do is to break it into parts
west horizon
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tidal grotto
you can do this :)
basically what f^(n)(a) is saying is the nth derivative of f at a
west horizon
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tidal grotto
so you do know that notation :)
west horizon
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tidal grotto
so what don't you understand?
west horizon
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tidal grotto
you're given f(-3), f'(-3), f''(-3) and so on
west horizon
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tidal grotto
factorial is just n(n-1)(n-2)...1
you know third degree means that it will be a cubic polynomial
so just first write out the form it will take
west horizon
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west horizon
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tidal grotto
yes
0! and 1! technically on the first terms but those are both 1
that is also part of definition of factorial, that 0!=1!=1
west horizon
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potent lotusBOT
west horizon
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frail drift
calm coralBOT
frail drift
i dont understand this question
calm coralBOT
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leaden thunder
i dont understand this question
Either use derivatives or just compute all F(1), ..., F(8) and find which one is the maximum
frail drift
ok
calm coralBOT
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prime topaz
Can someone explain for b, what the r-(3i - j) is supposed to represent? Like what's the r? Is it just a random vector?
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prime topaz
<@&286206848099549185>
shy swallow
Can someone explain for b, what the r-(3i - j) is supposed to represent? Like wh...
i believe so
prime topaz
i believe so
ah ok, but what's that entire expression representing?
shy swallow
ah ok, but what's that entire expression representing?
equation for tangency i presume?
it just means that either tangent vector r is
obviously tangent to a
or is zero
prime topaz
equation for tangency i presume?
oh sorry i meant the r-(3i-j)
wait i dont get how i would explain this
shy swallow
just try to make a vector diagram first
prime topaz
yeah i dont get how to make the r-(3i-j) vector
do i just draw a random point and minus it from a
shy swallow
take the inverse of a vector
inverse as in
additive inverse vector
$\vec{a}=\vec{OA}$
potent lotusBOT
parabolicinsanity
shy swallow
so $-\vec{a}=\vec{AO}$
potent lotusBOT
parabolicinsanity
shy swallow
i'm not sure if r is a position vector or is just an arbitrary vector
so assume the latter
$\vec{r}=\vec{AR}$
so use that
potent lotusBOT
parabolicinsanity
shy swallow
now, $\vec{AR}+\vec{AO}$ is what?
potent lotusBOT
parabolicinsanity
prime topaz
one sec
prime topaz
now, $\vec{AR}+\vec{AO}$ is what?
is this diagram right
shy swallow
yes
this problem in general is kinda weird because $\vec{R}\cdot\vec{a}=0$ is sufficient maybe
potent lotusBOT
parabolicinsanity
shy swallow
this implies tangency so we'd be done
i'm not sure what the signficance of $\vec{r}-\vec{a}=0$ is though...
potent lotusBOT
parabolicinsanity
prime topaz
isnt AR + AO just like idk some random other vector pointing into the centre
prime topaz
oh
shy swallow
at least that is what it seems like the equation is leading us to believe
that this middle vector is orthogonal to the position vector of A
which is just
the tangent
oh wait
that's it
$\vec{t}=(\vec{r}-\vec{a})$
potent lotusBOT
parabolicinsanity
shy swallow
$\vec{t}$ is the tangent vector!
potent lotusBOT
parabolicinsanity
shy swallow
so we have to find r instead
the problem was a bit unintuitive because it didn't really define much but
find r that's all
$\vec{r}\cdot a = \vec{a}^2$
prime topaz
$\vec{r}\cdot a = \vec{a}^2$
help i need clarification so how did u get that last equation
shy swallow
oopsies
just expand out the
dot product
$(\vec{r}-\vec{a})\cdot\vec{a}=\vec{r}\cdot\vec{a}-\vec{a}^2=0$
potent lotusBOT
parabolicinsanity
prime topaz
soo how does that show that its a tangent..
prime topaz
$(\vec{r}-\vec{a})\cdot\vec{a}=\vec{r}\cdot\vec{a}-\vec{a}^2=0$
wait dont u already show that its a tangent by saying t= r - a which is the tangent vector
shy swallow
$\vec{r}-\vec{a}$ itself is the tangent vector
prime topaz
actually nvm its not rly showing
potent lotusBOT
parabolicinsanity
shy swallow
not r
prime topaz
**parabolicinsanity**
wait what are you trying to do here? Im kinda confused
shy swallow
wait what are you trying to do here? Im kinda confused
finding r?
prime topaz
finding r?
ohh ok
shy swallow
that leads us to two cases
prime topaz
since r - a = t is orthogonal to a
o yep
shy swallow
just try to do it manually by assigning $\vec{r}= x\hat{i}+y\hat{j}$
potent lotusBOT
parabolicinsanity
shy swallow
like r-a and a?
yes
calm coralBOT
shy swallow
try it and open another channel if you face any problems
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wide vine
Neend help with 18 and 22
calm coralBOT
Neend help with 18 and 22
wide vine
I got 19 ans a1 wanted to recheck that
unkempt drift
I got 19 ans a1 wanted to recheck that
for q18, use Taylor series
write out the Taylor series centred at x = 2
the denominators go 1!, 2!, 3!, 4!...
wide vine
for q18, use Taylor series
Yeah taylor series is not going to be taught for another 1-2 years
out of syllabus currently
unkempt drift
but yeah u'(x) = 7 v'(x) implying p = 7 and u(x) / v(x) = qx + c, so that forces q = 0
unkempt drift
out of syllabus currently
that really sucks cause it's such a easy way for that q
wide vine
Any way to do in with basics? I'm ending 11th grade as of now
unkempt drift
Any way to do in with basics? I'm ending 11th grade as of now
let p(x) = ax^4 + bx^3 + cx^2 + dx + e
wide vine
but yeah u'(x) = 7 v'(x) implying p = 7 and u(x) / v(x) = qx + c, so that forces...
Yeah then p/p=1
unkempt drift
then start from the information that 4th derivative of p(x) at x = 2 equals 24
wide vine
Ohh
unkempt drift
so you would get (4 * 3 * 2 * 1) a at x = 2 equals 24
wide vine
And then solve for a b c d then e
unkempt drift
then similarly yep!
wide vine
E you took for any constants present right?
unkempt drift
yeah the last piece you need is p(2) = -1
wide vine
then similarly yep!
That's not as complicated as I thought
unkempt drift
That's not as complicated as I thought
that's the derivation behind Taylor series, congrats
if you understand the (4 * 3 * 2 * 1) bit for the 4th derivative of x^4
wide vine
if you understand the (4 * 3 * 2 * 1) bit for the 4th derivative of x^4
Yeah I got that
But how is that related to taylor series?
I thought taylor series was x/1! +x²/2! + x³/3! ....
unkempt drift
But how is that related to taylor series?
well, you want to make the best polynomial of a function centred at a specific point
the way to do that is to make sure all the derivatives match
the 0th derivative (value of y), the 1st derivative, the 2nd, 3rd, and so on
unkempt drift
I thought taylor series was x/1! +x²/2! + x³/3! ....
I'll show you the correct expression
https://www.youtube.com/watch?v=3d6DsjIBzJ4
also this video is really good
wide vine
Does it go on until infinity?
So infinith derivative of f(a)/infinity! (X-a)^infinity
?
unkempt drift
Does it go on until infinity?
indeed, it's an infinite series
calm coralBOT
@wide vine Has your question been resolved?
wide vine
indeed, it's an infinite series
ohh
then if its not specified then its not possible to get a definate answer right?
unkempt drift
then if its not specified then its not possible to get a definate answer right?
wdym
infinite series are well-defined as long as they converge
oh boy this is a whole other story
wide vine
oh
i dont get why in that video cosx was being represented only by an quadratic?why not cubic or why not any other degree polynomial?
while approximaitng cosx
unkempt drift
i dont get why in that video cosx was being represented only by an quadratic?why...
it just so happens that at x = 0
the third derivative of cos(x) is sin(x)
and so sin(0) = 0, so that means that the Taylor series will have +0x^3
the next nonzero term is the x^4 term
so yes, cos(x) only has even-powered terms in the Taylor series at x = 0, because all even-powered terms will have either sin(0) or -sin(0) = 0
wide vine
the third derivative of cos(x) is sin(x)
third is +sin right?
unkempt drift
third is +sin right?
corrected
wide vine
so yes, cos(x) only has even-powered terms in the Taylor series at x = 0, becaus...
so then why stop at power 2? because its already good enough approximation?
unkempt drift
so then why stop at power 2? because its already good enough approximation?
yes basically
there's always some subjective parts to this
wide vine
but how are we supposed to know that if we do not have an graphing calculator or smth?
unkempt drift
but how are we supposed to know that if we do not have an graphing calculator or...
ah, there are formulae for the max error of a Taylor series
search up 'Lagrange error bound'
here we can use the fact that the max absolute value of all derivatives, of plusminus sin(x) and cos(x), is 1
wide vine
by this there could have been an 4th term C4x^4 and 5th C5x^6 and so on how do we figure out than power 2 is enough
unkempt drift
so the max error for the quadratic will be a^3 / 6 for x = a, well in the radius of convergence
unkempt drift
by this there could have been an 4th term C4x^4 and 5th C5x^6 and so on how do w...
as I told you it's subjective
it depends how much error you're willing to tolerate with the actual function
pretty incredible right
similarly, here are the bounds for the Taylor series truncated at x^4
wide vine
https://www.desmos.com/calculator/st0oqggaax
woahhh\
wide vine
howd they figure this out? just by taking the derivatives and checking the slope and adding/substracting stuff to make it fir the graph of cosx the best?
unkempt drift
search up 'Lagrange error bound'
there's a systematic way
wide vine
https://www.desmos.com/calculator/uasgaev9l3
changing the sign of the last term for all the graphs just made a perfectly mirror image of itself?
wide vine
there's a systematic way
yeah i got that video im rewatching the 3blue1brown just to get a better grasp of things
so the more terms there are the more insignificant change they do to our current approximation?
not insignificant but very very very small
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tribal ether
hi
calm coralBOT
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cedar rose
in this question why cant we do 4c1 X 9c4
because you cant make first picked woman special. you can have same set if first woman was different
tribal ether
that profile of yours is sus
lol
tribal ether
because you cant make first picked woman special. you can have same set if first...
oh right right thank you
calm coralBOT
@tribal ether Has your question been resolved?
tribal ether
Yezzir
icy galleon
given two points in the open unit disc in C, construct a homeomorphism from said shape to itself that sends the two points to each other but doesnt move any points on the boundary
icy galleon
this solution is confusing me. someone mind explaining?
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@icy galleon Has your question been resolved?
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@icy galleon Has your question been resolved?
icy galleon
or more realistically, explain the sentences "Also, f(0)=-1" to "that takes C to C"
night narwhal
Bro no joke i think ur question is so hard that u wont het answers anytime soon
Good luck tho
May i ask what it is that u study?
Like major or whatever
high palm
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@icy galleon Has your question been resolved?
brittle sail
calm coralBOT
brittle sail
Can anybody help me with this question?
calm coralBOT
@brittle sail Has your question been resolved?
brittle sail
.close
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paper zealot
Who can help me resolve this integral with a yellow sheet formula?
last zephyr
Take 2 common in deno first
Then substitute 10 - t = k^2 (say)
Now diff both sides
So u get
-dt = 2kdk
Now use these both equation and u can do it
paper zealot
Ok ok thank you
blazing coyote
Then substitute 10 - t = k^2 (say)
honestly here, 10-t=k works too
fickle sedge
calm coralBOT
fickle sedge
I don't even know where to start
If I don't know the function, how do I use simpson's rule?
velvet osprey
can you state simpson's rule anyway?
velvet osprey
the thing about Simpson's rule, or in fact all numerical integration rules, is that it does not actually require you to know the formula for the function -- only to sample it at specific points.
velvet osprey
well again can you state the rule
fickle sedge
I actually ended up solving it 😅
fickle sedge
the thing about Simpson's rule, or in fact all numerical integration rules, is t...
I realized it when you said this
Thank you!
white mountain
Question 29, id like to use polar form for this but I don’t remember how to work with something like this, any hints?
potent smelt
Start by substituting in u = x+2 and v = y+3
Now you have a circle centered on the origin in u and v
And you can convert to polar form in the standard way
calm coralBOT
@white mountain Has your question been resolved?
white mountain
And you can convert to polar form in the standard way
Do I have to do Jacobian stuff
potent smelt
Do I have to do Jacobian stuff
Unless you already know what the proper differential elements are, yes
white mountain
Okay 👍
also I have an additional question
Why does the contour have a negative?
In that derivation bit
Cause I’d think it would be Mdx+Ndy
potent smelt
Why does the contour have a negative?
I don't know of an intuitive explanation for that.
white mountain
But it can be either cause of part one and part two
white mountain
I don't know of an intuitive explanation for that.
Alr is it hard to find intuition for?
potent smelt
I just never tried.
potent smelt
I know that 3b1b did Khan academy's multivariate calculus module
So if there is an intuitive explanation, that's likely a good starting point
swift laurel
Why does the contour have a negative?
it is the line integral of 1/2(-y, x)
calm coralBOT
@white mountain Has your question been resolved?
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potent lotusBOT
Kenzo
tranquil wasp
i think bro is trying to write the chain rule but this is worrying?
formal pulsar
ikr
west horizon
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formal pulsar
but yeah, just y''/x''
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formal pulsar
i don't think that works
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tranquil wasp
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what is dy/dt divided dx/dt (pretend they are fractions)
formal pulsar
$\frac{\frac{d}{dt}\frac{dy}{dt}}{\frac{d}{dt}\frac{dx}{dt}}$
potent lotusBOT
theaveragejoe6029
formal pulsar
goofy ass looking fraction
west horizon
what is dy/dt divided dx/dt (pretend they are fractions)
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tranquil wasp
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how would you do 1/3 divided by 1/2 without a calculator?
west horizon
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potent lotusBOT
Kenzo
west horizon
how would you do 1/3 divided by 1/2 without a calculator?
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tranquil wasp
yeah and how did you do it?
west horizon
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tranquil wasp
like what do you do to the 1/2
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halcyon ravine
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This is correct
west horizon
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west horizon
This is correct
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tranquil wasp
what is dy/dt divided dx/dt (pretend they are fractions)
yeah alright now go back and do this one
stoic pagoda
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pmo 🥀
west horizon
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stoic pagoda
br thnk h shkpr 🥀
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potent lotusBOT
Kenzo
west horizon
br thnk h shkpr 🥀
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stoic pagoda
then diff
west horizon
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stoic pagoda
carti did not drop for this 💔
west horizon
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stoic pagoda
❓ ❓ ❓
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potent lotusBOT
Kenzo
stoic pagoda
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no
denom is 3t^2
get reid of t^2
so ontop you now have t^2(t^3-2)
and denom is 3
then jus expand
west horizon
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potent lotusBOT
Kenzo
stoic pagoda
foil
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potent lotusBOT
Kenzo
tranquil wasp
there are no brackets
west horizon
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stoic pagoda
bro
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stoic pagoda
(1/3)t^5-(2/3)t^2
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potent lotusBOT
Kenzo
west horizon
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stoic pagoda
yuhh
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stoic pagoda
t^5
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stoic pagoda
oh yujhh u got it
stoic pagoda
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nah
west horizon
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stoic pagoda
remb ur finding
west horizon
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stoic pagoda
d^2/dx^2
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stoic pagoda
d/dx (dy/dx) = (d/dt [dy/dx]) * (dt/dx)
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stoic pagoda
dt/dx = 1 / (dx/dt)
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stoic pagoda
d2y/dx2 = (d/dt [dy/dx]) / (dx/dt)
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stoic pagoda
when we find the derivtive of this, we do not get d2y/dx2
why?
because we diffed in terms of t, not x
west horizon
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potent lotusBOT
Kenzo
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stoic pagoda
gng what
west horizon
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stoic pagoda
ok
do you udnerstand
that we have this atm d/dt(dy/dx)
and not thes second deriv
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stoic pagoda
thinking like algebra
what do we need
to multiply/divide this by
to arrive at the second deriv
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sharp narwhal
no
stoic pagoda
what does the deritive of x tell you 😭
west horizon
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stoic pagoda
we dont have x rite
but we do have
dx/dt
so what can we do to dx/dt to arrive at dt/dx
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stoic pagoda
what
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stoic pagoda
bro 2hollis did not drop aoty for this
dont overcomplicate
if you have 1/2
and you want to get to 2
what can you do
west horizon
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stoic pagoda
rite
west horizon
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stoic pagoda
yes
stoic pagoda
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remember
west horizon
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stoic pagoda
that
west horizon
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stoic pagoda
and when i wrote divide
i liek already simplified it
its basicallt
d2y/dx2 = (d/dt [dy/dx]) * (dt/dx)
which we now know
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stoic pagoda
is
potent lotusBOT
Kenzo
stoic pagoda
(d/dt [dy/dx]) * (1/dx/dt)
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stoic pagoda
i simplified without showing how
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potent lotusBOT
Kenzo
stoic pagoda
[(5/3)t⁴ - (4/3)t] / (3t²)
west horizon
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stoic pagoda
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same as what you did
west horizon
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calm coralBOT
stoic pagoda
seeyuh
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