#help-23
wind laurel
this seems like a very annoying question 😭, ill try to see if i can solve it
sand oyster
Ok
alpine aurora
this seems like a very annoying question 😭, ill try to see if i can solve it
It seems like rly annoying algebra and analysis 
zealous ingot
is this thing a differential equation?
sand oyster
Yes
wind laurel
$$f(a) = 0 \implies \sqrt{\lim_{r \to a}\left(\frac{2r^2\left(f(r)^2\right)}{r^2}-r^3 e^{\frac{f(r)}{r}}\right)} = 0$$
main mural
do the curly brackets and the square brackets mean anything
wind laurel
pretty sure its just paranthesis
main mural
ok good
main mural
$$f(a) = 0 \implies \sqrt{\lim_{r \to a}\left(\frac{2r^2\left(f(r)^2\right)}{r^2...
r->a, not 0
i am trying the same approach lol
flat frigateBOT
woomy
wind laurel
oopsies
then i'd try to solve this limit
so that we get g(ea) = 0 and solve for ea
main mural
the square root isn't even necessary here
wind laurel
first term tends to 0 since f(r) tends to f(a) = 0
main mural
a can't be zero from the question
wind laurel
huh
main mural
or it actually can..
wind laurel
i mean it can but then why word the question like that?
why ask us to find the value of e*a and not just a
main mural
f(r)/r causes issues if that's the case ig
main mural
why ask us to find the value of e*a and not just a
true
wind laurel
let me try evaluating f(1) since that is given in the question
zealous ingot
$\lim_{r \to x}\left(\frac{2r^2\left(f(r)^2-f(x)f(r)\right}{r^2 - x^2}) = xf(x)f'(x)$
flat frigateBOT
Donkey
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
wind laurel
$$f(a) = 1 \implies \sqrt{\lim_{r \to 1}\left(\frac{2r^2\left(f(r)^2 - f(r)\right)}{r^2 - 1}-r^3 e^{\frac{1}{r}}\right)} = 1$$
flat frigateBOT
woomy
sand oyster
Guys this question is from previous jee mains exam
wind laurel
**Donkey**
Compile Error! Click the <:errors:504266556054962196> reaction for mo...
thats smart yea
it seems right to me
flat frigateBOT
Donkey
zealous ingot
yeah, bangalore
sand oyster
Ok nice wt r u studying rn
zealous ingot
I mean that
sand oyster
I am in narayana
zealous ingot
rest is integration by separation of variables
and that should be problem complete
sand oyster
BTW how many marks u get in the Allen exams out of 180
zealous ingot
BTW how many marks u get in the Allen exams out of 180
advanced ones?
sand oyster
advanced ones?
Yah
zealous ingot
usually split is smn like 50+, 40+, 50+ in pcm
zealous ingot
@wind laurel review?
zealous ingot
Can we like bcome friends
yeah bet
sand oyster
@zealous ingot i sent u friend request
wind laurel
can i ask whats v?
zealous ingot
hell yeahhh
wind laurel
just need to use the boundary conditions f(1) = 1 and f(a) = 0
safe radishBOT
@sand oyster Has your question been resolved?
runic ruin
Hii!! I wanted to ask anyone please if you could explain what they did for parts b and c of the question as I'm a bit lost for part b, and for part c I don't understand why the guy set (2-3/2 lambda = 0). Help would be very appreciated thanks!
safe radishBOT
Hii!! I wanted to ask anyone please if you could explain what they did for parts...
lost jewel
https://youtu.be/HsJiw62ErUU?si=V4041RNCCDom4LNA
A- Level !! 
There's a concept that you need to know
When a vector is multiplied by a scalar, it length increase
So in this case when we multiply vector AB by the right scalar it will become vector AC because AC is just vector AB but different in size
AC is just vector AB but different in size
This's only true if A,B,C are collinear tho
runic ruin
ahh I see I think I understood part b thanks
but could u pls explain also part c cus why did they set the coefficient of a to 0 in ON?
lost jewel
Sure just gimme a min to watch what they do
runic ruin
thank u so much!
lost jewel
Oh that's clever
lost jewel
thank u so much!
So as you know a vector can be written in term of two other non parallel vectors right?
Like how you wrote CN in term of vector a and b with coefficients
runic ruin
ah yeah
lost jewel
So you can write vector AB in term of AC and here
Can you write AB in term of AM and another vector?
runic ruin
idk isnt AM = Lambda of AB
runic ruin
ah yess
lost jewel
But MB is just a smaller AM
let say it's a time AM
So AB= aAM + AM
= (a+1)AM
Let go back to your problem
ON is just a smaller OB which is B right?
runic ruin
yeah
lost jewel
So it can be equal to b multiplied by some scalar
ON= kb
But vector a
vector a isn't a different size vector b
It has different direction
lost jewel
= (a+1)AM
So you can't add them up like this
And it also make no sense that ON= k*vec(b) but also ON= (...)*a + (....)*b
Cuz vector a have different direction it will change direction of ON
So ON won't be the same direction with b anymore
Unless
There're actually no vector a!
So that mean a has to be multiplied with 0 for it to disappear
runic ruin
ahhh so we remove vector a so that the vectors in the same direction will remain? as in those that are parallel?
lost jewel
ahhh so we remove vector a so that the vectors in the same direction will remain...
yeah
runic ruin
ohhh ok that makes more sense ty, btw thx for the visuals it helps a lot
lost jewel
ohhh ok that makes more sense ty, btw thx for the visuals it helps a lot
np
Given a=m*b+n*c ( vector )
the coefficients of b and c which are m and n determine the direction of a
if m=0 then a has direction of c
and the same for n
btw, this's outside the program
But this can be solved with menelaus theorem
runic ruin
i'll look into that thanks a-levels r a nightmare already tho
lost jewel
i'll look into that thanks a-levels r a nightmare already tho
No problem, my friend also took A-level
actually he's taking it
lost jewel
Hm Im not sure,I'll ask him. Btw this isn't 3d vector lmao
Why the thumbnail looks like that
runic ruin
haha idk but it covers both year 1 and 2 content
lost jewel
haha idk but it covers both year 1 and 2 content
wait what both years!!?
Are you speedruning A-level
runic ruin
ah no i'm in second year doing revision cus i forgot most of this lmao
lost jewel
ah no i'm in second year doing revision cus i forgot most of this lmao
Vector ain't that hard so dw, there're a some tricks and formulas too
You'll get it soon enough
runic ruin
thank uu i'm making method sheets for some of the harder problems
lost jewel
thank uu i'm making method sheets for some of the harder problems
ehh
You should really just understand the concept
That should be good enough
runic ruin
ah yeah i first usually do textbook problems to undersatnd the concepts
and then for the harder more repetitive problems i do a few of the method sheets and then i do like some harder ones
lost jewel
ngl, it's weird to see harder and repetitive in the same sentence
A hard problem would be unique
runic ruin
ah no for some of the extra hard ones i dont make the method sheets
but some questions r rlly repetitive with just diff numbers so idk its a way for me to guarantee marks
lost jewel
but some questions r rlly repetitive with just diff numbers so idk its a way for...
ah I see
Well good luck
runic ruin
ohh me too
lost jewel
Yeah I know I took a look at your bio
lost jewel
idk how to close this btw do u know how
type .close
safe radishBOT
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sage ravine
Help my answer is N = 0,-1,7,6
safe radishBOT
Help my answer is N = 0,-1,7,6
sage ravine
But theres 12 total possible answerr
And also the signs are wrong
Its 5 > 10/|N-3| > 2
stoic saddle
2<|N-3|<5
yeah you're right
just add them
the answer wanted the sum not the number of solutions
0-1+7+6 = 12
safe radishBOT
@sage ravine Has your question been resolved?
sage ravine
the answer wanted the sum not the number of solutions
Tyty
thorn epoch
safe radishBOT
last wren
!status
safe radishBOT
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
uhh so i did x = 1,2,3,4 and y = 3,4,5,6
then 4 x 4 = 16 total possible outcomes
then 10 outcomes give above 3 but below 8
5/8
but answer was 66
last wren
so the problem here is that it specifies X and Y are real numbers
do you know what that means
thorn epoch
yea i think? js that arent imaginary numbers
last wren
yeah, so if X is a real number between 0 and 5 it could be like 2.3 or π
so you can't just count, you need to use area
thorn epoch
oh
last wren
have you done that before
thorn epoch
ohhhh my bad i assumed it was integer number only
last wren
we've all done it lol, all good
thorn epoch
have you done that before
js integration?
last wren
you can use integration but that would make it harder tbh
since X and Y are randomly chosen, it means uniformly chosen
so you can use the area method, have you done it before
if not I can write out the steps for you (or you can just integrate if you're more comfortable)
thorn epoch
if not I can write out the steps for you (or you can just integrate if you're mo...
ye
last wren
alright
- draw out the region in the X Y plane defined by 0 < X < 5 and 2 < Y < 7. this will give you a rectangle
- shade the area in the rectangle corresponding to 3 < X+Y < 8
- find the area of this region and divide it by the area of the rectangle. that's the answer
if you do that it's just a bit of geometry instead of calculus
thorn epoch
alright gimme a sec to do that
alright tyty i think i got it
i needa sleep now
2:23 am
.close
safe radishBOT
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golden forge
it is not possible to calculate the square root of negative numbers (when not considering the complex numbers). i was curious if the super square root (inverse function of tetration) also has the same or even another limitation
safe radishBOT
it is not possible to calculate the square root of negative numbers (when not co...
golden forge
i know very little about tetration/super root tho
kind acorn
Hmmmm. I think it's been studied before according to google
Although I always thought it only works for positives
flint vessel
it is not possible to calculate the square root of negative numbers (when not co...
ye
flint vessel
Although I always thought it only works for positives
well you can take it you will just get a complex response
austere panther
can someone explain the solution?
safe radishBOT
can someone explain the solution?
plucky elk
can someone explain the solution?
which part do you get lost first
austere panther
2nd step
austere panther
what do they mean keep degree equal to or less than 4
wouldnt this be larger than 4th degree?
plucky elk
plucky elk
wouldnt this be larger than 4th degree?
yes you don't need to keep that term
shell horizon
Hi can someone help me with these type of questions
safe radishBOT
Hi can someone help me with these type of questions
plucky elk
what's the question
shell horizon
the solutions group of this is a Union between 2 Foreign sections
i translated it its in a different language
plucky elk
are you looking for what x satisfies that inequality?
north raven
Hi can someone help me with these type of questions
factorise the cubic first
here's a neat trick: if the sum of coefficients is 0, the polynomial has a factor of (x - 1)
-# reason this works is because of remainder theorem
I would assume you're finding the range of values of x for which that inequality is true?
shell horizon
you guys are right thank you
north raven
do you know how to factorise the cubic?
shell horizon
i went back to the vods
safe radishBOT
@shell horizon Has your question been resolved?
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strong pike
Question and solution. I don't get how they take O'P = 2 - r
where O is center of bigger circle of radius 2
O' is center of smaller circle with radius r
safe radishBOT
Question and solution. I don't get how they take O'P = 2 - r
where O is center o...
glacial cairn
OP = O'P, that's an isosceles right triangle
lost jewel
why the diagram looks so off
strong pike
Thus is what I have done.
- Form a square with radius of bigger circle and coordinate axis and find its diagonal.
- Subtract radius of bigger circle from diagonal to get diameter of smaller circle. Then divide by 2 to get radius.
- I got r = root(2) - 1
strong pike
OP = O'P, that's an isosceles right triangle
How?
glacial cairn
Subtract radius of bigger circle from diagonal to get diameter of smaller circle.
You're getting more than the diameter
strong pike
> Subtract radius of bigger circle from diagonal to get diameter of smaller circ...
Huh?
lost jewel
there's a tiny part at the corner
strong pike
> Subtract radius of bigger circle from diagonal to get diameter of smaller circ...
Ok, got my mistake 
Thank you both
.close
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severe pond
have you tried anything?
🥪
well, upon substituting youd find that you have 0 times something that oscillates between -1 and 1
cos(infty) is just a bunch of oscillations between -1 and 1
its effectively like multiplying by a constant
wdym?
yea
the input of cos goes to infinity
so it keeps oscillating
doesn’t approach anything
torpid girder
uhhh
severe pond
but the x^4 dominates it when it goes to 0
rendering its contribution useless
🤔🤔🤔
sure
but the input is 3/x
not x
torpid girder
yes
severe pond
if the input was x youd just substitute and move on with your life
,w plot x^4 cos(3/x)
flat frigateBOT
severe pond
notice how the x^4 going to zero makes it hug around 0
torpid girder
uhhhh
severe pond
this question is designed for squeeze theorem
flint atlas
could someone explain how odds ratios works intuitively
cause man I am really struggling w understanding it 💀
severe pond
if you’re dealing with trig functions it should always be in the back of your mind
i’m not sure what answer youd find to be satisfactory
no this isn’t how math works
a lot of pattern recognition
and creativity
i mean
i came in here and solved it in under 5 seconds
no
first thing i always do is substitute
really the only case where having 0 times something and not getting 0 is if you have 0 times infinity
and we don’t here
so i thought of how we might prove it
cos is bounded
so it’s contributions are essentially nothing
what?
wdym it doesn’t work
3/x —> inf
ok but what’s your point
i mean
sure you can’t just get a number out of substituting
but you know cos is bounded
torpid girder
?
severe pond
yea
torpid girder
uh ya
severe pond
because it means the 0 dominates
as i said before
the only case where it’s going to be an issue is if we multiply by something unbounded
yea
rough storm
are you familiar with squeeze theorem :3
torpid girder
noT really bro
severe pond
rough storm
usually one of the form x^4sin(1/x) or x^2cos(1/x^2), those sorts are squeeze theorem
its using the fact that sin(x) and cos(x) are both bound between 1 and -1
so, if you know -1<=sin(x)<=1, then that means -1<=sin(3/x)<=1 is too
split kayak
Assume:
$-1\leq \cos x \leq 1$
flat frigateBOT
∫ᴄ 𝐅·𝑑𝑟 = ∬ʀ ∇⨯𝐅 𝑑𝐴
split kayak
Multiply all parts by x^4
rough storm
it will be 0
split kayak
Yes, when you take the limit, both sides of the inequality limit to 0
split kayak
So the inside must also limit 0
split kayak
the bounds would limit to
$-3^4 \leq 3^4\cos x \leq 3^4$
flat frigateBOT
∫ᴄ 𝐅·𝑑𝑟 = ∬ʀ ∇⨯𝐅 𝑑𝐴
split kayak
So you actually are stretching the interval
torpid girder
ohh ok
split kayak
Yeah, the squeeze theorem works to show that if an inequality holds on both sides of an expression
And if both bounds limit to the same value, then the center expression must always remain between each other, therefore, it limits to the same value
There you cant apply squeeze
Since the bounds dont limit to the same number
yes, youd have to find it other way
Squeeze theorem is usually used when computing the actual limit isnt possible, but you can find some sense for a lower and upper bound
for limx->3 of our original expression, you can just crunch the numbers yourself
safe radishBOT
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trim carbon
safe radishBOT
trim carbon
what like negeative abs func and positive abs func?
then i say the lim of those two is 0 close to x=0
light shoal
$\left|x^2 \sin(1/x)\right| \leq \cdots$
flat frigateBOT
Bungo
light shoal
any bound that goes to zero as x->0 will work
light shoal
do you know how the squeeze theorem works?
trim carbon
if a function is a bounded by two other functions
and the lim of those two functions are same
then the middle function has the same lim
light shoal
yea in this case, 0 will be one of the functions
trim carbon
that is my basic understanding
trim carbon
what is the middle function here that we're trying to find
light shoal
we want to show that this goes to zero as x->0
(this will imply that the same quantity without the abs val also goes to zero)
light shoal
yea that's the right idea
safe radishBOT
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upper ocean
!help
safe radishBOT
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
upper ocean
$$Prove that 2903^n - 803^n - 464^n +261^n is divisible by 1897 for every natural number n.
zealous ingot
$$Prove that 2903^n - 803^n - 464^n +261^n is divisible by 1897 for every n...
!status
safe radishBOT
$$Prove that 2903^n - 803^n - 464^n +261^n is divisible by 1897 for every n...
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
zealous ingot
ok, what do you think we shd do
upper ocean
1897 =7 x 271 , i proved that the given expression is 0 mod 7 by the property that a^n - b^n is always dividibe by (a-b) now what should i do to prove it for 271 .that the given expression is divisible by 271
zealous ingot
Perfect so far actually
you use the same property to prove that its divisible by 271
but instead of taking (a,b) = (2903,803) & (464,261), take (2903,464)&(803,261)
upper ocean
wait , let me try for myself
zealous ingot
mhm
safe radishBOT
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torn glacier
hello!
torn glacier
any tips to improve math calculating speed?
magic junco
Practice.
velvet nebula
practice the things you want to calculate faster
but also sometimes it's technique as well
safe radishBOT
@torn glacier Has your question been resolved?
flint vessel
any tips to improve math calculating speed?
learn squares uptil 41 and cubes uptil 25 and practice till you can do 2-digit operations mentally
that should be enough
safe radishBOT
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slender cloak
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slender cloak
Anyone up for this?
I am getting incredibly and frustratingly close to the last answer.
I am getting this:
Can anyone confirm or check anything to see if it somehow matches with the answer?
I keep tryring to swap and absorb with constants but i am not getting there, especially with the last term
The closest I get is the first two terms, then the last term always something like:
(k^2 + 4) / 4C
so idk
<@&286206848099549185>
is this too advanded for here?
I dont understand i dont get responses anymore past my A-level 😢
primal blaze
Can anyone confirm or check anything to see if it somehow matches with the answe...
it does
slender cloak
howww
did you replace k with c
I did that too i dont know what else to do I can't get the last term 😭
primal blaze
$K=C'$
flat frigateBOT
Spooki
primal blaze
$KC/2 = K'$
flat frigateBOT
Spooki
slender cloak
Ahhhhh
I see
I didn't absorb C with the original K
that makes sense because then you can
thank you
so this is what I had when I was trying to not simplify anything
primal blaze
yeah lol np
slender cloak
I see it
primal blaze
oh the coefficient of x had both constants so that shouldve been a clue
slender cloak
Exactly u see i didnt notice
Because I tend to take non-efficient steps
I opened everything immediately when I had the ^2
so i started simplifying too early and i didnot notice
primal blaze
i see
slender cloak
also
does ' denote the original term here?
Since it would be confusing to write something like KC/2 = K
Or is it the other way around
primal blaze
yeah use different symbols to simplify, it's not the original term
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outer bronze
help
vagrant ice
help
what have you tried so far?
for example, the first two terms are $\log \frac{a + 1}{a} + \log \frac{a + 2}{a + 1}$
how can you simplify that?
flat frigateBOT
south
outer bronze
log a+2/a?
i tried seeing if i could convert it into a series that i am familiar with like arithmetic or geometric but that didnt work
vagrant ice
log a+2/a?
yep!
so how about $\log \frac{a + 1}{a} + \log \frac{a + 2}{a + 1} + \log \frac{a + 3}{a + 2}$
flat frigateBOT
south
vagrant ice
just checking if you get the idea
vagrant ice
okay, so clearly there's a lot of cancellation: it's everything except the last numerator and the first denominator, in fact
outer bronze
so i am getting a=35/12
vagrant ice
for the last term, you sub in k = a + 35
... so k + 1 becomes a + 36
outer bronze
so a=3?
outer bronze
.close
safe radishBOT
south sparrow
If A is this matrix, then subdeterminant of |A|_23 = adjungated subdeterminant |A|_23
fresh perch
Hi guys I must be stupid because I can't make the connection to prove this (or reason up a way/find a counterexample for why this need not be true). The first question is proved by just saying by rank nullity theorem there exists a nonzero vector x for which (A- λI)x = 0.
So far I've tried to tackle the second question BWOC. We know then that the derivative of the characteristic polynomial evaluated at λ is 0. Alternatively, if the rank of A-λI is n-1 then we must have that rank(adj(A - λI))) = 1 and furthermore that the nonzero columns of adj(A-λI)) are all scalar multiples of one of the eigenvectors for λ. I'm not sure if there's a way to connect these two properties to reveal a contradiction.
safe radishBOT
Hi guys I must be stupid because I can't make the connection to prove this (or r...
fresh perch
For context M_n is shorthand for the vector space of n-by-n square matrices over the field of complex numbers, \sigma(A) refers to the set of eigenvalues of A
cedar widget
Hi guys I must be stupid because I can't make the connection to prove this (or r...
you get that the geometric multiplicity of lambda is 1
iirc this doesn't imply it has algebraic multiplicity 1
obsidian oracle
Hi guys I must be stupid because I can't make the connection to prove this (or r...
unclear whether multiplicity refers to algebraic or geometric one, but let's assume they mean geometric...?
fresh perch
unclear whether multiplicity refers to algebraic or geometric one, but let's ass...
They mean algebraic multiplicity here
fresh perch
I was actually trying to conjure up counterexamples now but my brain farted because it's been years since I did basic arithmetic
obsidian oracle
and rank(A-0I) = 2-1
fresh perch
here 0 has geometric multiplicity 1 but algebraic multiplicity 2
Is it possible to obtain any information about the rank of a matrix from just its characteristic polynomial?
obsidian oracle
Is it possible to obtain any information about the rank of a matrix from just it...
no, not really
Any matrix such that characteristic poly is X^n
can have any rank between 0 and n-1
(take matrices made of jordan blocks as examples)
fresh perch
Any matrix such that characteristic poly is X^n
Like as in the principle minors of degree 2 to n-1 might be nonzero but the sums for each respective degree all cancel out?
In the sense that the coefficients of the characteristic polynomial are sums of principle minors
It seems that way at least
Anyway my main question was answered thank you guys
.close
safe radishBOT
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merry stag
Currently trying to solve the following problem:
Prove that the remainder of dividing n ^ 2 by 4 is 0 if n is even
Prove that the remainder of dividing n ^ 2 by 4 is 1 if n is odd
Using
a ≡ b (mod m) <=> m | a - b <=> a - b = m . q with q ∈ Z
I've done
n ^ 2 = 4 . q + 0
4 | n ^ (2) - 0
n ^ 2 ≡ 0 (mod 4)
n ≡ 0 (mod 4)
In an attempt to simplify by getting rid of the power since i have 0 on one side, I've got a sheet with some definitions I think might be useful like
Let a ∈ Z, m ∈ Z>0, r = a + mq
Then
a ≡ r (mod m)
Let a, b ∈ Z, m ∈ Z>0
Then
a ≡ b (mod m) iff a and b have the same remainder in the division with m
I'm mostly looking for a general sense of direction since i'm unsure of what my goal is on paper here, and i'm not sure on how to solve for a remainder in this context. thanks in advance.
safe radishBOT
Currently trying to solve the following problem:
> Prove that the remainder of d...
merry stag
no, i have other things i could use, these are just the ones that seemed useful at a glance
merry stag
do you mean to write n ^ 2, 0 and 4 as 2k or 2k + 1?
what are we heading towards here?
merry stag
right, so i rewrite as 2k for even and i get 4 . k ^ 2, which i get should be obviously divisible by 4 with remainder 0, right?
astral glacier
Yes
merry stag
thanks, i still don't get the hang of generally useful forms to rewrite numbers in like this, will keep in mind when next dealing with evens and odds
i think i can finish up from here
.close
safe radishBOT
astral glacier
Sure, feel free to tag me if you need more help
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charred cedar
hello
charred cedar
Kinda weird question but I have to memorize the transformation of cylinderical coordinate to cartesian and spherical to cartesian ( and vice versa)
does anyone have any tips to memorize these ? Cuz Memorizing the matrix alone doesn't make sense to me
charred cedar
that's a good observation
does these transformations have some proofs or anything.. maybe it will make sense more ?
still surge
does these transformations have some proofs or anything.. maybe it will make sen...
do you know euler's identity
e^ix
do you want the proof of the matrix, or just a way to memorize it?
cause you can also notice the top matrix: col 2 is just the derivative of col 1
charred cedar
do you want the proof of the matrix, or just a way to memorize it?
Mainly a way to memorize it.. I thought the proof would help me to memorize
still surge
you can just look up the proof for the rotation matrix
charred cedar
cause you can also notice the top matrix: col 2 is just the derivative of col 1
I see
charred cedar
cause you can also notice the top matrix: col 2 is just the derivative of col 1
it also applies to spherical system right?
still surge
wdym ?
uh just ignore that
but you can simply look up the rotation matrix proof for spherical/cylindrical
charred cedar
but you can simply look up the rotation matrix proof for spherical/cylindrical
alr then
thanks for ur help you're a legend
bye
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soft spoke
Can someone tell me if this is wrong and how to fix it, I can see I forgot to add +c already
safe radishBOT
Can someone tell me if this is wrong and how to fix it, I can see I forgot to ad...
quasi bison
Can someone tell me if this is wrong and how to fix it, I can see I forgot to ad...
you multiplied by dx wrong too
soft spoke
It should be dy=(6-2y)dx
So does it have to be in the form dy/dx= … before you start moving the dx?
edgy breach
Dx is just treated as a term
So it follows the rules as if its a or k or beta or whatever
soft spoke
So it was just rearranged wrong ?
edgy breach
Yes
hidden grove
Hi
hidden grove
I need help
A rectangular garden has an area of 120 square meters. If its length is 5 meters more than its width, find the dimensions of the garden.
this is the question
quasi bison
ok, progress?
hidden grove
wdym?
quasi bison
how far did you get so far on this question?
hidden grove
ohk
quasi bison
if you have no progress then say you have no progress
no shame in that but we do need to know where you're at
quasi bison
ok... can you tell more specifically which part of the question stumps you
quasi bison
if you have €40 in your wallet and i have €5 more than you, how much is in my wallet?
hidden grove
45
rugged cave
quasi bison
45
yeah ok
"length is 5m more than width" can translate as L = W+5
(assuming L and W stand for length and width respectively, which they probably should)
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gloomy cairn
I'm very confused on how to complete my hw. i understand the concept of making the starting equation x^2(x+4), however I'm confused how to utilize multiplicity and complete the equation using F(x).
safe radishBOT
I'm very confused on how to complete my hw. i understand the concept of making t...
plucky elk
you need a constant out front
gloomy cairn
so would the constant be 1?
plucky elk
does (-1)^2(-1+4) = -6?
plucky elk
so the constant isn't 1
gloomy cairn
so where do i continue from when F(-1)=3. how do i find all things that will make it = 6
plucky elk
you need a constant out front
write f(x) with this constant
plucky elk
I'm very confused on how to complete my hw. i understand the concept of making t...
what you have is close but not correct because the constant in your answer is 1, which doesn't satisfy f(-1) = -6
gloomy cairn
so when i make the constant f(-1)=3 and when i make the constant f(3)=63. sorry but im confused where to go.
plucky elk
where does f(3) = 63 come from
gloomy cairn
when i use f(-1)=(x^2)(x+4) i get F(-1)=3 and i didnt know where to go from there so i plugged 3 into f(x)
plucky elk
what you have is close but not correct because the constant in your answer is 1,...
i already established that your f(x) was incorrect
using incorrect things further is not a good idea
gloomy cairn
so how does one obtain the correct f(x)
plucky elk
you need a constant out front
.
plucky elk
write f(x) with this constant
.
gloomy cairn
so any real number?
gloomy cairn
ohh so its the same as y=mx+b basically i think i understand thank you!
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exotic tundra
Can someone help me with this? I dont think I did it right i dont really get it
exotic tundra
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✅ Original question: #help-23 message
exotic tundra
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silver dune
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hallow ice
The value of the integral is (4) 0.
silver dune
The value of the integral is (4) 0.
its wrong
quasi bison
,rccw
flat frigateBOT
quasi bison
The value of the integral is (4) 0.
!nosols
safe radishBOT
The value of the integral is (4) 0.
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.
silver dune
!nosols
anyway i got the answer
thanks for the help everyone who tried
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valid mauve
If f is continuous and $\int_0^1 f^2 , dx = 0$ can we conclude that $f(x) = 0$ for all $x \in [0,1]$?
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If f is continuous and $\int_0^1 f^2 \, dx = 0$ can we conclude that $f(x) = 0$ ...
flat frigateBOT
Halex
peak estuary
assume f(y)>0 for some y in [0,1]
what can you say about a neighborhood around y due to continuity?
valid mauve
what can you say about a neighborhood around y due to continuity?
for all epsilon, there is a delta such that |x-y| < delta implies |f(x) - f(y)| < epsilon
main raven
severe pond
for all epsilon, there is a delta such that |x-y| < delta implies |f(x) - f(y)| ...
how about that it is > 0 for some neighborhood around y?
and then from there you can easily contradict the integral being 0
just take the minimum of f on that interval where its > 0 and then you know the integral is > the area of the rectangle with height of that minimum and width of the interval
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valid mauve
how about that it is > 0 for some neighborhood around y?
f > 0 or f(y) > 0 ?
severe pond
f > 0 or f(y) > 0 ?
f(x) > 0 for all x in some neighborhood around y
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mighty mango
the black is a rod which is (in equilibrium? idk how to say it) F , 1/2 F are forces acting on it "pulling force" and W is its weight
what is the ratio between AC and CB
i solved this in 2 seconds saying that "The ratio between the lengths is the inverse of the ratio between the forces" so 1 : 1/2 or 2 : 1
but my teacher used torque to determine that "1/2 AC= CB" so was his approach redundant or did i get it right by accident
safe radishBOT
the black is a rod which is (in equilibrium? idk how to say it) F , 1/2 F are fo...
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north raven
For two forces which act in opposite directions about a pivot, say $F_1$ and $F_2$ at distances $d_1$ and $d_2$ away from the pivot respectively, assuming the object is in equilibrium, then by the principle of moments,
$$F_1 \times d_1 = F_2 \times d_2 \implies \frac{d_1}{d_2} = \frac{F_2}{F_1} = \left(\frac{F_1}{F_2}\right)^{-1}$$
So yes, you are correct.
flat frigateBOT
north raven
For two forces which act in opposite directions about a pivot, say $F_1$ and $F_...
@mighty mango
mighty mango
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✅ Original question: #help-23 message
north raven
this trick wouldnt work if the forces act on the same side of the pivot, i.e. in the same direction
mighty mango
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✅ Original question: #help-23 message
mighty mango
this trick wouldnt work if the forces act on the same side of the pivot, i.e. in...
no i wanna discuss this
north raven
no i wanna discuss this
well it would be impossible to have the object in equilibrium if all the force was only on one side, first of all.
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mighty mango
BD is a rod, the black triangles are "holders". its in equilibrium. and there's a box on point A.
what do i benefit from knowing that "the pressure on A = the pressure on C"
safe radishBOT
BD is a rod, the black triangles are "holders". its in equilibrium. and there's ...
mighty mango
I had this information written on a question and- my teacher didnt really use it
mighty mango
BD is a rod, the black triangles are "holders". its in equilibrium. and there's ...
assuming that hte weight of the box is like 10
what does that say about point C
well I did something weird when I wanted to calculate the torque of the F thats acting on point C with pivot point being A
I said F-10 for the force of point C
assuming that theres some- idk invisible weight that's equivalent to the weight of hte box
hence why "the pressures are equal
split kayak
The box can be thought as a distributed load
For 2D systems, a pressure can also be seen as F/m, which is the formal magnitude of a distributed load.
From the diagram, you can figure out whats the force K based on the fact that C and the weight have the same force.
For this case, that doesnt make much difference as from a regular force
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rocky pond
can someone check if I did smth wrong cuz this feels weird
safe radishBOT
can someone check if I did smth wrong cuz this feels weird
tardy mango
can someone check if I did smth wrong cuz this feels weird
,w dM/dt = 1/2 + 1/4 sin t - M/50
flat frigateBOT
tardy mango
can someone check if I did smth wrong cuz this feels weird
you forgot about (reverse) chain rule when going from dv to v in your integration by parts
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If you are done with this channel, please mark your problem as solved by typing .close
@rocky pond Has your question been resolved?
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snow sky
help
mossy lotus
going from 2nd to 3rd line you ate the pi in 2nd term
snow sky
going from 2nd to 3rd line you ate the pi in 2nd term
still im getting 2609
snow sky
ohh
snow sky
also you were asked surface area
im getting 67.6
still wrong😭
oh no
im getting 727.5
mossy lotus
ok, lemme have a go at it and work it out
snow sky
ok, lemme have a go at it and work it out
alr
mossy lotus
did you add the flat surface area (the circle) of the hemisphere?
it should also be present in the total SA that the problem asks
mossy lotus
x = 5.378, and that means radius = 10.756
snow sky
i didnt attempt this yet because i dont understand how to do it
mossy lotus
factorize everything and bring everything that you can in terms of powers of 5
snow sky
how do we factorize it?
mossy lotus
and remember $\sqrt{5} = 5^{\frac{1}{2}}$
flat frigateBOT
βαχτϵρ10Φρ4γ
mossy lotus
how do we factorize it?
factorize 30 as 2*3*5 and same with 180
you will see some minor simplifications right away
snow sky
factorize 30 as 2\*3\*5 and same with 180
we write them as a product of prime factors?
mossy lotus
yea
that helsp
but if you feel like where its going and are confident enough, no need to go for prime factors, any factors would do
snow sky
yes
mossy lotus
well, your aim is to simplify, so you can try cancelling common factors from numerator and denominator
no need to combine them back what you have already split apart
thats just undoing your progress
snow sky
but then theres no common factors to cut off?
mossy lotus
or is it 2 * 3 * 5^8x+28
and please use parentheses whenever possible 
I can directly see a few
such as a 6 or a 5^(2x) and so on
snow sky
do we cut the enitre 5^(2x) from both denominator and numerator?
mossy lotus
yea? can't you?
your aim is to simplify
and that means you cut out everything you can
snow sky
what would happen to the +4.5 back there?
mossy lotus
there is also a sqrt5 there, combine those together
snow sky
so 5sqrt5 ^(2x+4.5) ??
mossy lotus
no...
mossy lotus
$\sqrt{5} \times 5^{4.5} = 5^{0.5} \times 5^{4.5}$
flat frigateBOT
βαχτϵρ10Φρ4γ
mossy lotus
this is not how to write it
the denominator is wrong
the powers are for 5, not sqrt5
sqrt5 just multiplies it
this is how you can do it
snow sky
yes so 4x+14 -2x+5?
snow sky
so answer is 5^( 2x+19) ?
mossy lotus
well, they ask for w
and this would be the exponent, you forgot the parentheses again: 4x+14 -(2x+5)
so that becomes 2x+9 not 19
mossy lotus
honestly, use it everywhere you need to, when you move more than a single term to other side (numerator to denominator, LHS to RHS etc.)
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half perch
can someone tell me the answer because i dont have the solutions
safe radishBOT
can someone tell me the answer because i dont have the solutions
@half perch Has your question been resolved?
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small shell
Anyone got a good way to calc a pot in
safe radishBOT
Anyone got a good way to calc a pot in
small shell
Poker
magic junco
Anyone got a good way to calc a pot in
wym by that?
magic junco
💀
small shell
Ur name
magic junco
Math-related ofc
small shell
Chess
LMAO
chess is math related
Core strategies
Can be mathematical
Is ur name a chess strategy
vagrant ice
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rich hull
,,Determine all three-digit numbers (n) having the property that (n) is divisible by (11) and
[
\frac{n}{11}=\text{(sum of the squares of the digits of }n).
safe radishBOT
,,Determine all three-digit numbers \(n\) having the property that \(n\) is divi...
flat frigateBOT
Ashrafisgood
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
quasi bison
you may wanna just post a picture
rich hull
safe radishBOT
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
n = [abc] = 100a + 10b + c
and
n = 11(a^2+b^2+c^2)
rich hull
n = [abc] = 100a + 10b + c
and
n = 11(a^2+b^2+c^2)
why only 3 digits??
quasi bison
question says so
rich hull
ok, let me try.
i used that emoji for myself.
quasi bison
yeah idk if this is gonna cook at all
i think you need to think about like, upper and lower bounds for a^2+b^2+c^2
rich hull
i think you need to think about like, upper and lower bounds for a^2+b^2+c^2
a-b+c=0 always
quasi bison
are you sure?
rich hull
,,0 = 2a^2 + 2ac + 2c^2 - 10a - c
flat frigateBOT
Ashrafisgood
quasi bison
i found a number that actually works but which does not have a-b+c=0
so you are definitely wrong
n = 803
a^2+b^2+c^2=64+9 = 73, and 11*73 = 803
rich hull
i found a number that actually works but which does not have a-b+c=0
or it can be 11
rich hull
n = 803
a^2+b^2+c^2=64+9 = 73, and 11*73 = 803
0 = 2a^2 + 2ac + 2c^2 - 10a - c 550 is also correct
and your answer works with my formulation as well. i only a-b+c=0 in context of mod 11 ,im sorry i could have phrase that better.
.close
winter knot
I reached the answer 1152, is it wrong? the question is kinda confusing.
wild copper
Sounds right to me, but how did you get to that answer?
obsidian oracle
Also maybe showing figure 4 can give more context
winter knot
winter knot
Sounds right to me, but how did you get to that answer?
well I just did as i said, 32 + 16 times 24 + 16 which gives us 1920
minus 32 * 24
which is 768
and gives us 1152
but I felt as if it was too easy and too confusing to be that straightforward.
wild copper
Well, it also seems to be a plug-n-play to me too.
safe radishBOT
@winter knot Has your question been resolved?
radiant matrix
?
austere goblet
yes? do you have a question?
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@radiant matrix Has your question been resolved?
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rich hull
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lost jewel
Is this in G.P topic?
rich hull
geometric progression idk
errant finch
<@&268886789983436800>
quasi timber
<@&268886789983436800> scam
rich hull
why
lost jewel
geometric progression idk
the last equation xy=z^2 can make it a G.P
rich hull
<@&268886789983436800> scam
lost jewel
They weren't talking about you
rich hull
the last equation xy=z^2 can make it a G.P
any hint
lost jewel
Well you can let x=a , y= a*r and z=a*r^2
Assuming x,y,z form a G.P base on the last equation
rich hull
Well you can let x=a , y= a*r and z=a\*r^2
then we will fail the 1st condition that x+y+z=a
because z,x,y are positive distinct integers
lost jewel
then we will fail the 1st condition that x+y+z=a
BRUHHHH, I didn't mean that a
I meant
You can make it a G.P with 2 unknow varibles m and r
Okay change a in what I said to m
rich hull
will that assure that x,y,z are distinct
lost jewel
will that assure that x,y,z are distinct
yeah, if r not equal 1 or 0
rich hull
<:hmmcat:831508801646755850> yeah, if r not equal 1 or 0
yes
r=r^4
which has no solution aside from 1 and 0
i think we need a different approach can you think of something
i figured it for z
now what
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grand tendon
Ok
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opaque fern
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opaque fern
im bugging but how did they get $\hat M(f)$
flat frigateBOT
fathom jewel
looks like -j = 1/j
opaque fern
okay sure
fathom jewel
or do you mean the last line?