drutus
#help-39
jolly parrotBOT
versed mica
1/(4pi e0)?
yes
frail summit
9x10^9
regal herald
alrighty, so, you need to solve for r, such that 'r' away from the charged particle, the field is 3N/C
frail summit
same thing
yeah but I use that so it's less complicated
regal herald
if i say the particle is at d along the x axis, then the field is 3 at d+r along said axis, or d-r due to symmetry
frail summit
alrighty, so, you need to solve for r, such that 'r' away from the charged parti...
$r=\sqrt{K\frac{q} {E}}$
regal herald
oh dear
frail summit
Wtf
jolly parrotBOT
drutus
regal herald
missing a + or -
frail summit
if i say the particle is at d along the x axis, then the field is 3 at d+r along...
I dont think I understood anything you just said
I should probably look for videos about this first before asking for help
brb
Is it similar to this one
regal herald
kinda but not really
the above is like the sum of electric fields
you can model it the same though
in terms of a diagram
regal herald
draw a straight line, draw your charge of 6nC at some point on that line
call it the point with x coordinate d or something
at a point further along the line, draw a dot signifying your test charge a distance r away from the main one
frail summit
what's d
regal herald
just an arbitrary value
you could model it as being on the origin if you want
its just kind of unspecific in the question
frail summit
prob not
frail summit
unkempt yacht
the charge is 6nC, we want to find where the field is 3N/C
electric field afaik is measured in V/m
or whatever the hell this is
never heard of newton per coulomb
frail summit
at a point further along the line, draw a dot signifying your test charge a dist...
is the test charge the 3N/C one?
unkempt yacht
oh wait
The SI unit for the electric field is the volt per meter (V/m), which is equal to the newton per coulomb (N/C).
my bad, keep going
regal herald
si lol
frail summit
bro is spanish
regal herald
is the test charge the 3N/C one?
the test charge just has charge of magnitude 1
you can pretty much ignore it
frail summit
okay
regal herald
we're just using it to see what the field is at some point
frail summit
what do I do with this, or did I miss something
regal herald
at a point further along the line, draw a dot, mark it as being r away from the main charge
you may also want to write that the field is 3N/C there
regal herald
yeah, close enough ig
regal herald
**drutus**
you already have the set up to solve for r, albeit missing a +-
frail summit
oh wait I think I get it
regal herald
you square rooted, you have a positive and negative solution
regal herald
$\pm$
jolly parrotBOT
AℤØ
regal herald
you could, usually it goes in front of the root
frail summit
I meant here
regal herald
no, youll just find r can also be negative, then itll be on the other side of the charge
frail summit
$r=\pm\sqrt{K\frac{q} {E}}$
jolly parrotBOT
drutus
regal herald
two solutions
frail summit
like that?
regal herald
yeah
frail summit
so can I proceed to solving now
regal herald
you can
frail summit
does it equal to plus and minus 4.24m
pearl pondBOT
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pearl pondBOT
@frail summit Has your question been resolved?
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charred herald
help please
pearl pondBOT
@charred herald Has your question been resolved?
sand robin
pearl pondBOT
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misty stump
i would probably write tanh in terms of e first
unless you have some nice things about tanh you can use
yea
i think it will be pretty clear what happens as x goes to infinity when you do that (i know you said we need an epsilon delta proof but at least we’ll know the answer first)
well hold on
yea
can you post the question?
jolly parrotBOT
snow
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misty stump
also i think you mean |f(x) - 1/2|
what
limits involving infinity have a different definition
lim x to infinity f(x) = L means for all epsilon > 0, there is an M such that for all x >= M, |f(x) - L| < epsilon
yea probably
well first thing is we can kill the absolute value
sqrt(1+x^2) - 1 is nonnegative for every x
then just do some manipulation for x < something
and that will tell you what delta to pick
then you can go back and write everything in the correct order
ummm
this stuff should be done on the side before you write the proof
wdym
o well if this isn’t supposed to be the final proof then ok
your <‘s became =‘s randomly though
for x >= 0 that is true but idk what it has to do with < and =
ok one little note
x^2 < a is equivalent to |x| < sqrt(a)
at the end, rather than x, you can put |x|
you mean delta?
what do you think
not sure what delta = x means but sure to the last thing
what? no
just suppose |x| < delta
pretty much just what you did before to find what delta to use, but backwards
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sacred bolt
I'm kinda confused with this question what I tried to do is to get the integral from 0 to 1 for the square root of x and then the integral between 1 and 2 for 1/x^2 but I'll have to divide by zero for the first integral ?? which is confusing
sacred bolt
real palm
if those are integral signs. im pretty sure your did not find the antiderivative
brittle tinsel
next kindle
yeah that's right, the integral of sqrt(x) is 3/2(x)^(3/2)
sacred bolt
thx thx everyone
next kindle
2/3*
sacred bolt
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midnight haven
pearl pondBOT
midnight haven
I feel like I am missing something
timber void
midnight haven
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pearl pondBOT
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smoky saffron
whatd i do wrong
pearl pondBOT
whatd i do wrong
worthy lance
limit when x->1?
smoky saffron
limit when x->1?
Yeah
worthy lance
so what are you doing in the right?
worthy lance
what do u get if u put 1 into the x to get the limit?
smoky saffron
oh i forgot i had to do that
Do i have to do it for every question?
Before i factor out
worthy lance
i'm not sure what's the original question, but you don't need to factor if u get the limit by plugging the number
if u put 1 there u get the limit right away
smoky saffron
Oh ok
worthy lance
maybe you copied wrong the fraction?
smoky saffron
No thats the question i was just sovling it wrong
feral leaf
Do i have to do it for every question?
You should test the limit first to see if you need to do any extra math
smoky saffron
You should test the limit first to see if you need to do any extra math
Oh ok
feral leaf
If it's an indeterminate form, then you need to do extra manipulation
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smoky saffron
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knotty roost
Yea looks good
knotty roost
They both end up being the same thing
smoky saffron
Am I supposed to know this method ?
Cuz I dont know how to figure out the lim x > 0- unless its the same thing
knotty roost
You can also input numbers close to 0
smoky saffron
oh
wth the answer for lim x > 0- is negative infinity ???
I dont understands
how they got there
my answer was 1
worthy lance
post a picture of the original question if possible
smoky saffron
Ok one sec
smoky saffron
post a picture of the original question if possible
But i dont understand my sisters way of solving it this is the method i used
smoky saffron
smoky saffron
the teacher said its negative infinity
worthy lance
You have to just split in 2 fractions.
(A+B)/C = A/C + B/C
and solve each limit
you will get 1
smoky saffron
(A+B)/C = A/C + B/C
Ohh ok
tawdry hound
how would I do this proof? Prove that one half of the sum of two consecutive odd prime numbers is a composite number.
tawdry hound
I assume that two consecutive odd prime numbers
But I dont know how would I express that
if I say p is a prime number and p+2 is prime, then it wouldn't work since if p = 13 then p+2 = 15 which is not prime so I am not sure
midnight haven
think of a way to express this algebraically
tawdry hound
im trying to do that but I dont think my brain is working
if p = 2n -1 or something
i think i know how to do the rest but not sure how to express the prime numebrs
<@&286206848099549185>
candid spire
Ok I mean
@tawdry hound do you know modular arithmetic or nah
Oh I’m a dumbass
Consecutive odd primes, so could be 31 and 37
I’m stupid
Just tried out some examples
Doing this process with actual numbers
I always get an even number, which is composite
Seems like the sum of consecutive primes is always divisible by 4
@tawdry hound are you following all this? Lol
gritty star
Seems like the sum of consecutive primes is always divisible by 4
43 + 47 not though
royal shuttle
and 2+3
candid spire
Odd primes
royal shuttle
oh didnt read that
gritty star
I'd say those odd numbers can be expressed as anything like (2n-1) + (2n+k) for any odd k which depends on the length of the consecutive odd primes, which then can be expressed as 4n + k-1 and k-1 is even so it can factored by 2
royal shuttle
noo
candid spire
Where’s the “prime” part coming in, anyway
royal shuttle
say p1= 2k+1 and p2= 2l-1 then (p1+p2)/2 is simply k+l and if you say that every comp. number then you have k+l=n, and n is a naturally a composite number
candid spire
What
gritty star
Where’s the “prime” part coming in, anyway
Prime is just a subset of odd numbers, so if we can prove that it works for any odd then it works with prime
candid spire
It doesn’t work for any odd pair
(5 + 21)/2 = 13, which is prime
candid spire
Yes I know
But I’m asking where in ur proof do you use the hypothesis that the original pair is prime numbers
royal shuttle
I know what you mean, but if you say that 2 prime numbers are already given, then we can define them as p1 and p2, so mathematically:
∀p ∈ P : ∃n ∈ N : p=2n-1
with 2n-1 you can of course use for odd numbers, but for certain n, it is a prime
and if you take p1,p2 ∈ P, then there are certain k,l ∈ N where you can define p1= 2k-1 and p2=2l-1
P: prime numbers, N: natural numbers
does it make sense?
candid spire
I know what you’re saying
You’re merely saying
p1, p2 prime => p1, p2 odd => (p1+p2)/2 composite
But the second implication is False
royal shuttle
how?
candid spire
That changes nothing, you’re still not using the full power of the prime condition
royal shuttle
wait, why again are we using 21? I mean it's not prime
or whats the idea
because the task is adding 2 prime numbers and then dividing them by 2, or do i get it wrong
candid spire
Claim:
(p1,p2 odd => (p1+p2)/2 composite) is False
Proof:
5,21 odd, but (5 + 21)/2 = 13 is not composite
candid spire
Claim:
> (p1,p2 odd => (p1+p2)/2 composite) is False
Proof:
> 5,21 odd, but (5 +...
Read this
royal shuttle
Ohh
candid spire
You’re merely saying
p1, p2 prime => p1, p2 odd => (p1+p2)/2 composite
Therefore this proof method is invalid
Because it’s impossible to prove the second arrow
(Since it’s false)
gritty star
Maybe it meant twin prime?
candid spire
Press X to doubt
The claim seems to hold true in all our test cases
(43 + 47)/2 = 45 is composite
That’s the most remarkable
It has nothing to do with odd/even
pearl pondBOT
@tawdry hound Has your question been resolved?
candid spire
And wtf with “consecutive primes”? How do you even talk about that? They get spread out more and more as their size increases
I mean, the claim is certainly not true for any pair of primes. We have (7+19)/2 = 13 which is not composite
gritty star
I think modulo is the way to go
blazing pendant
There are two possible meanings of consecutive odd primes: either the problem statement really meant to say twin primes, or the problem statement means to say an odd prime and then the immediate next odd prime
gritty star
There are two possible meanings of consecutive odd primes: either the problem st...
Twin primes just 2n-1, 2n+1 yah
The other one is modulo
blazing pendant
But the first case is a subset of the second, and the claim in the problem statement is true for the latter
candid spire
The latter claim is true? Shit yeah
That’s what’s so difficult
Consecutive primes…
Here I am thinking about cyclic groups and shit
blazing pendant
I think y’all are getting way too lost in the formalism
What do you call half the sum of two numbers
candid spire
Average
blazing pendant
And what do you know about the average of two unequal numbers?
candid spire
So like, the middle number between two consecutive primes is composite?
candid spire
And what do you know about the average of two unequal numbers?
It’s halfway between them
blazing pendant
Which importantly implies that it’s strictly between them
candid spire
Oh my god……….
blazing pendant
But the two primes were consecutive, so their average can’t be an odd prime
blazing pendant
So you just need to check that you’re looking at a positive integer greater than 2
Hence why only odd primes
candid spire
That’s so
That’s such a bruh moment
It’s literally like
Tautological
It’s true by Definition
Goddamnit bruh
gritty star
But the two primes were consecutive, so their average can’t be an odd prime
Damn
No modulo needed
blazing pendant
Not entirely. You’ll still need to prove that the average is strictly between the two numbers, and then show it’s a positive integer greater than 2
blazing pendant
No modulo needed
Something like this could be used to show that the average is an integer
Anyway y’all have fun ironing out the formal proof
gritty star
Not entirely. You’ll still need to prove that the average is strictly between th...
I mean they are distinct so it has to be between?
lucid hazel
pearl pondBOT
blazing pendant
I think it’s only asking for the area between a single curve and the x-axis, not the area between both curves
unkempt yacht
can you show figure 5.21
lucid hazel
can you show figure 5.21
lucid hazel
I think it’s only asking for the area between a single curve and the x-axis, not...
probably
i was just making sure
can you help me with this, i do not know how to setup the intergrand
unkempt yacht
shouldnt the area here be 2(32/3)
it is asking the area confined by x axis and one of the graphs
unkempt yacht
can you help me with this, i do not know how to setup the intergrand
did they mean around the line y = 1?
unkempt yacht
bounds
if they didnt specify one of the bounds, you have to find it yourself
find the point where the 2 graphs intersect
unkempt yacht
y = 1 and y = sqrtx
but here, they revolve it around y=1 instead
so you have to shift the graph 1 unit downward in order for y=1 to match with the x axis
then, find where they intersect and apply the formula for rotating 1 graph around x axis
lucid hazel
so they intersect at x = 1?
unkempt yacht
so you have to shift the graph 1 unit downward in order for y=1 to match with th...
shift sqrt(x)
in other word, your problem can be reworded as: find the volume of the solid created by rotating sqrt(x)-1 around x axis
where the bounds are, as you said, 1 and 4
this shouod be enough hint to you
lucid hazel
got it thanks
in this ( sorry if i am asking to many questions )
how did we get 1/2 x sin2x
i did u = 2x
1/2 du = dx
unkempt yacht
well theres a fast way to integrate composite functions where g is a linear func
no need to do u sub
lucid hazel
so i took 1/2 outside the interval times another 1/2 = 1/4 integral of 1-cosu
unkempt yacht
$\int f(ax+b)dx = \frac1a F(ax+b)$
jolly parrotBOT
FungusDesu
unkempt yacht
in this ( sorry if i am asking to many questions )
so try it here
lucid hazel
1/2 sin (2x)?
unkempt yacht
thats right
lucid hazel
the book says sin2x/4
pearl pondBOT
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harsh apex
Any tips on classifying a quadrilateral by 4 points. I can’t just say “because it looks like a ___”
near echo
review the definitions
harsh apex
review the definitions
I know but i wanted to know if there were any tricks
near echo
the best way to classify them is to know the definitions and apply them
you should be able to make a mental image of each of the shapes quickly if someone said their name thought
that way you know what sort of shape you are looking for
meager vector
Hi I need help with c and d
pearl pondBOT
Hi I need help with c and d
indigo pewter
For c, try making all three terms into one fraction with the same denominator
I'm assuming you're using vietas?
midnight haven
Hi
I think for c, you can add (+3-3)
it means F(x) = F(x) + 3 - 3
and then you can add 1 for each section
you can get
this function
(a+b+c)/a + (a+b+c)/b + (a+b+c)/c -3
I think you can calculate it
indigo pewter
for that you would have to know the individual values of a, b, and c, right?
midnight haven
no dont need
indigo pewter
how would you find it then?
acoustic path
by factoring out the (a + b + c)
indigo pewter
yea ig
acoustic path
I think for c, you can add (+3-3)
this is good approach
midnight haven
(a+b+c)/a + (a+b+c)/b + (a+b+c)/c -3
it converts to (a+b+c)(1/a+1/b+1/c) -3
indigo pewter
solid
acoustic path
in general, when you see sum of (n - 1) roots when n roots are present…
this demands the substitution (sum of roots) - 1 term… or something similar
indigo pewter
honestly i would just multiply and pray to god that its simplifiable lol
midnight haven
it converts to (a+b+c)(1/a+1/b+1/c) -3
it also can be (a+b+c)(ab+bc+ca/abc) - 3
I think you know a+b+c, ab+bc+ca, abc
midnight haven
oh okay
indigo pewter
For part D, you can multiply each fraction to get a denominator of abc, and you'll get (a^2+b^2+c^2)/abc, which you can obviously do.
midnight haven
from (a^2+b^2+c^2), you can get (a+b+c)^2 - 2(ab+bc+ac)
indigo pewter
in part a you can see he already solved it
lyric basin
pearl pondBOT
lyric basin
i dont understand this
this is using the nth term test for divergence right?
so since it doesnt equal 0, it should diverge
merry carbon
!original
pearl pondBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
snow sail
was the original $\lim \qty( (0.3)^n - 1 )= ?$
jolly parrotBOT
jan Niku
lyric basin
is it because its a sequence?
pls someone help i dont understand this at all
<@&286206848099549185>
anyone who responds pls @ me
pearl ice
anyone who responds pls @ me
hello
lyric basin
hm
pearl ice
it converges because it's a sequence; you're not summing it
lyric basin
does the nth term test also work for sequences?
pearl ice
not really
lyric basin
also what does it mean for a sequence to diverge/converge
pearl ice
a convergent sequence gets closer and closer to some specific value
it "converges" to that value
a divergent sequence does not
lyric basin
so the infinite term of the sequence is some nunber
pearl ice
it has a limit, yes
lyric basin
divergent is just infinity?
pearl ice
there is no "infinite term"
a divergent sequence doesn't necessarily go to infinity
for instance a sequence that goes 1, -1, 1, -1.... is divergent but it doesn't go to infinity
it just doesn't get any closer to a specific value
lyric basin
okay
pearl ice
however the sequence 1, 1/2, 1/4, 1/8...... converges because its always getting closer to 0
its limit is 0
lyric basin
if a question says An, does that mean sequence
pearl ice
yes
lyric basin
and sum of An is series
lyric basin
okay thank you
pearl ice
is that all you needed
lyric basin
yes for now
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frail summit
pearl pondBOT
frail summit
I'm not familiar with solving problems with these kind of positions
prime bramble
draw a picture
as in, draw the x and y axes, place the charge at (4m, 0m) and then place the point (2m, 2m)
from there, you should be able to calculate the distance between the charge and the point using the picture
pearl pondBOT
@frail summit Has your question been resolved?
frosty frigate
do uk the formula for electric field
frosty frigate
I'm not familiar with solving problems with these kind of positions
bro these are coordinate cartesian systems...
how tf are u not familiar
pearl pondBOT
frail summit
.reopen
pearl pondBOT
✅
frail summit
how tf are u not familiar
ik the cartesian plane but how do i use it on this topic 😭
modest badge
ik the cartesian plane but how do i use it on this topic 😭
distance formula
frosty frigate
ik the cartesian plane but how do i use it on this topic 😭
what is the formula for electric field
modest badge
let me recall
r= sqrt(dx^2+dy^2)
frail summit
$d=\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 }$
modest badge
$d=\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 }$
Yep
frail summit
MY GOD
jolly parrotBOT
drutus
frail summit
there
modest badge
And the formula for the electric field
frosty frigate
lol chill out
frail summit
what is the formula for electric field
E=kq/r²?
frosty frigate
yes
frail summit
Im done using latex
frosty frigate
use that now
XD
plug r = the distance u found
using distance formula
q is given
frail summit
ohh okayy
prime bramble
missing units
prime bramble
mhm
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rapid plume
I haven't done probability in a long time, could someone check my answer for b please.
pearl pondBOT
I haven't done probability in a long time, could someone check my answer for b p...
@rapid plume Has your question been resolved?
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@rapid plume Has your question been resolved?
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shadow knoll
pearl pondBOT
shadow knoll
for number 2 i calculated that f isnt self adjugated in respect to s
i did it by calculating if <Av,w> = <v,Aw> and it wasnt the case here, is this the right way to show it?
because <Av,w> =/= <v,Aw> in respect to s
autumn narwhal
Can you translate the question...?
shadow knoll
i did it by calculating if <Av,w> = <v,Aw> and it wasnt the case here, is this t...
i think the reaction on my message here is enough but thanks for offering help! i just wanted to make sure i got it right
.close
pearl pondBOT
merry carbon
i think the reaction on my message here is enough but thanks for offering help!...
.(you could e.g. also compute the conjugate transpose and check if it's the same as the original matrix, which here it isn't, and is probably quicker)
shadow knoll
.(you could e.g. also compute the conjugate transpose and check if it's the same...
its a lot quicker but i wasnt sure if i can simply do this here tysm!
.close
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round tide
In order to factorize by grouping, there is a method that consists in comparing the ratios of both groups and if they are equal we can factorize by grouping, like in the example seen in the image. Now, how do I choose these ratios, do I choose the bigger coefficient to smaller coefficient for both groups, do I choose the bigger degree coefficient to smaller degree coefficient for both groups? I dont know if it matters or not
pseudo oxide
!15m
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round tide
<@&286206848099549185>
round tide
yes
Consider this expression: 4x^3 + 1x^2 - 5x - 20
If I divide the biggest coefficient with the smaller coefficient it does result in unequal ratios, meaning I cannot factor by grouping.
is this correct or was it just a coincidence?
basically
the video says the ratios should be the same
but this is a vague statement
since, with the same values, I can make many different ratios
I want to know which are the ones that work
you get it?
round tide
What is the "Bigger" and "Smaller" coefficients.
in the example (4x^3 + 1x^2) (- 5x - 20) for the first parenthesis the biggger coefficient is the biggest number, 4. And in the second one is -5 (-5 > -20)
inner granite
Why would you divide them?
round tide
what do you mean?
inner granite
What do you get by dividing them?
round tide
that their ratios are equal
which is a mistake
since the polynomial isnt factorable
inner granite
$\frac{1}{4} \neq \frac{-20}{-5}$
jolly parrotBOT
Roman_Garland
pearl pondBOT
@round tide Has your question been resolved?
torn willow
can someone help me with this question
pearl pondBOT
can someone help me with this question
cunning comet
been there, done that. #help-36 message
torn willow
ye before i ask my question the channel closed
cunning comet
so: whats your question?
torn willow
i have some question in this solution
i still don't understand the 3^(2n+1) and 5^(3m+2)
cunning comet
i explained it. what is unclear?
torn willow
i still don't get how they prime factorized r
cunning comet
should i repost everything again or can you explain which step is unclear?
torn willow
i get how 3r=n^2 and 5r=n^3, but don't understand anything after that
cunning comet
3r is a perfect square, so it is something like c times c.every primefactor whch divides c apears twice.
25 = 5 times 5. so it appears twice.
144 = 12 times 12 = 3^2 times 2^4
-> every prime factor which divides a perfect square has to appear in a even count.
do you understand this?
torn willow
yes
cunning comet
thats all.
3 divides (3r), (3r) is a perfect square, so 3 must appear in a even count. one have you in 3, so r must have 3 as prime factor in an odd count.
so there exists some n such that 3^(2n+1) divides r.
pearl pondBOT
@torn willow Has your question been resolved?
cunning comet
@torn willow are you gone again?
torn willow
Sry was away
torn willow
thats all.
3 divides (3r), (3r) is a perfect square, so 3 must appear in a even ...
WDYM by “one have you in 3”
cunning comet
assume 324 as perfect square, this is - written in prime factors - 3 x 3 x 3 x 3 x 2 x 2 (3 appears 4 times, 2 appears 2 times - each in an even count)
if you write 324 as 3r, this is 3 x (3 x 3 x 3 x 2 x 2)
torn willow
assume 324 as perfect square, this is - written in prime factors - 3 x 3 x 3 x 3...
yes i understand this
cunning comet
so are we done now?
cunning comet
yes. for the 5 its the same logic.(but keep in mind we need there a perfect cube, not a perfect square)
cunning comet
and i also don't understand this part
you need the smallest r. so - for example - you wont take 324 as perfect square, you would take 81. (so you would drop the 2^2).
torn willow
yes. for the 5 its the same logic.(but keep in mind we need there a perfect cube...
so the prime factors which divides the perfect cube must appear 3 times right?
cunning comet
so the prime factors which divides the perfect cube must appear 3 times right?
yes. therefore 3m+2
torn willow
but why is it +2
cunning comet
you need 5 to appear in a multiply be 3, so you can write it as 3m+3 (for the perfect cube) and again you have one factor in front so you have 3m+2 für r.
cunning comet
so are we done now, @torn willow ?
cunning comet
then you can type .close
torn willow
.close
fringe cypress
does anybody have any resourse for a question bank on mathematical foundations for machine learning
distant plinth
How do I find the turning points of something like this without calculus?
distant plinth
I used this sheet to find everything from a to f but I don't know what to do for g)
edgy stone
How do I find the turning points of something like this without calculus?
define turning point
distant plinth
when the curve changes direction
cunning comet
when the curve changes direction
This sounds more like extreme values than a turning point.
edgy stone
I used this sheet to find everything from a to f but I don't know what to do for...
what do you have for S(x), R(x), Q(x)?
distant plinth
This sounds more like extreme values than a turning point.
what's extreme values?
edgy stone
ok
cunning comet
what's extreme values?
local minima, local maxima.
edgy stone
this seems annoying tbh
i don't immediately see how to get the turning point without calculus...
distant plinth
I think AM-GM was used somehow to find the point when x>0
and then a quadratic was made and vieta was used to find the other one
I forgot how most of it worked
midnight haven
i think you should express it as S(x) + R(x)/Q(x)
edgy stone
I think AM-GM was used somehow to find the point when x>0
oh that's clever
midnight haven
and find the intersection points of S(x) and R(x)/Q(x)
youre adding those 2 functions so the intersection points are gonna be the turning point
edgy stone
i don't quite understand it but i can see how it could work
edgy stone
youre adding those 2 functions so the intersection points are gonna be the turni...
??
since when?
midnight haven
it works in this case i think
distant plinth
doesn't really work
edgy stone
turning points of x^2 + 1 are the intersection of x^2 and 1?
midnight haven
But in this case its x + 1/x form
so i thought it would work but nvm i guess lol
wait try -x and -6/x-2
midnight haven
But in this case its x + 1/x form
so i think you have to match the x
so (-x+2) + 6/(-x+2) - 7
so you have to find the intersection points between -x+2 and 6/(-x+2)
i think that would match the turning points
ive rarely used this method so sorry for making some mistakes
pearl pondBOT
@distant plinth Has your question been resolved?
distant plinth
so i think you have to match the x
I think that's similar to something my teacher did
hmm
distant plinth
so you have to find the intersection points between -x+2 and 6/(-x+2)
Could you explain this part again?
midnight haven
when youre dealing with something like x + 1/x you can solve x = 1/x to get the turning points (graph)
you can prove this by using AM - GM
i think
since AM - GM is related to min/max
distant plinth
What is the next step after I get to (-x+2)+6/(-x+2)-7?
distant plinth
when youre dealing with something like x + 1/x you can solve x = 1/x to get the ...
how does this work?
midnight haven
x + 1/x >= 2sqrt(1) using am - gm
and the = is satisfied when x = 1/x
thats my reasoning
distant plinth
oh
I sorta get it now
(-x+2)+(-6/x-2)>=2sqrt6
so the function is >=2sqrt6-7 when x<2
distant plinth
you apply the same logic
solve (-x+2) = 6/(-x+2)
Is there another way to find the other turning point without this?
midnight haven
without AM - GM?
distant plinth
wait nvm
distant plinth
without AM - GM?
is there another way?
midnight haven
i dont think so
distant plinth
.close
pearl pondBOT
unborn abyss
i guess just like
keep trying to find new angles and side lengths
there's a 30-60-90 triangle that i can see
indigo pewter
Yea just chase side lengths
unborn abyss
there's a 30-60-90 triangle that i can see
^
pearl pondBOT
pearl pondBOT
Available help channel!
hazy radish
can someone explain to me how you find out that k^4 + 6k^3 + 13k^2 +12k +4 can become (k^2 + 3k + 2) ^2
hazy radish
$k^4 + 6k^3 + 13k^2 +12k +4 = (k^2 + 3k + 2) ^2$
jolly parrotBOT
TheKingPin
hazy radish
its true, its just a little ridiculous, I would have no idea this would be true unless someone tells me.
So I want to know, just from looking at the LHS, how do you know it can be simplified?
acoustic path
can someone explain to me how you find out that k^4 + 6k^3 + 13k^2 +12k +4 can b...
consider plugging in x = -1
worldly glacier
can someone explain to me how you find out that k^4 + 6k^3 + 13k^2 +12k +4 can b...
well the key realization here is we have a k^4 term and a 4 term
acoustic path
then, you know x + 1 divides the quartic, and you can factor it... etc....
versed mica
well the key realization here is we have a k^4 term and a 4 term
yea
hazy radish
well the key realization here is we have a k^4 term and a 4 term
how is that key? is there an algebra concept that explains this?
versed mica
last two terms r perfect squarws
hazy radish
if im dealing with squares then i would have no problem seeing patterns
right
i can see that
versed mica
or first and last ig
worldly glacier
how is that key? is there an algebra concept that explains this?
okay if we have (x + y + z)^2, we know we will get x^2 and z^2 as a term
hazy radish
yes
acoustic path
want to note that's not how you normally factor, since you're assuming that the factorization conforms to a specific form (i.e. why assume it's a perfect square?)
guessing polynomial roots is how you typically see that a polynomial is factorable
acoustic path
want to note that's not how you normally factor, since you're assuming that the ...
in particular, it helps to be familiar with the "Rational Root Theorem"
worldly glacier
want to note that's not how you normally factor, since you're assuming that the ...
yes but you see 3 terms that match up to what you would expect
and I think it's a reaasonable guess no
but I agree with Manic in the general case
it is def better to guess the roots
hazy radish
in particular, it helps to be familiar with the "Rational Root Theorem"
ill make sure too look into that
i thought this was a pascals triangle thing the whole time
worldly glacier
i thought this was a pascals triangle thing the whole time
well you can use the multinomial thm sure to break this up
misty stump
ok to be fair though, if you take two quadratics with integer coefficients and irrational roots and multiply them together and give someone the quartic, it's totally hopeless for them to factor it
worldly glacier
do we learn this in grade school?
i did idk if its common
hazy radish
i did idk if its common
maybe, i went to a not so good HS
worldly glacier
maybe, i went to a not so good HS
all good you can learn it rn
shouldn't take you long
hazy radish
it makes me upset that my math is failiing cause of years of bad edcation
misty stump
the fact that that one you posted has integer (or rational) roots is what makes it possible to easily factor
hazy radish
but ill have no problem looking into those two thm
worldly glacier
it makes me upset that my math is failiing cause of years of bad edcation
you have a long way ahead of you
just be passionate about mathematics
and you will go a long way
hazy radish
just be passionate about mathematics
thanks man, i needed to hear that
ill look at the two thm and come back if i have any other questions. I dont want to hold the room from other questions
.close
pearl pondBOT
pearl pondBOT
Available help channel!
worldly rampart
Can anyone please help me see where I went wrong?
pearl pondBOT
Can anyone please help me see where I went wrong?
worldly rampart
plush bramble
,rotate
jolly parrotBOT
pearl pondBOT
@worldly rampart Has your question been resolved?
worldly rampart
.close
pearl pondBOT
pearl pondBOT
Available help channel!
smoky saffron
pearl pondBOT
smoky saffron
i dont get it?
hallow cedar
Use the definition of the derivative maybe
unkempt yacht
$f(x)$ is differentiable on $\mathbb{R}$
pearl pondBOT
$f(x)$ is differentiable on $\mathbb{R}$
jolly parrotBOT
FungusDesu
unkempt yacht
$f'(x) = f(x) + e^x\cos2021x$ and $f(0) = 0$
jolly parrotBOT
FungusDesu
unkempt yacht
How many intersections does f(x) make with the x-axis in the domain [-1; 1]?
i would like to check my answer, which i got 1
however my answer key gave 1287, where did i go wrong?
pearl ice
what did you get for the function f(x)?
unkempt yacht
**FungusDesu**
for reference, solving this differential equation gets me
$f(x) = \frac{e^x}{2021}\sin x$
jolly parrotBOT
FungusDesu
unkempt yacht
according to my calculation, it should only intersects with the x-axis right at the origin
not 1287 intersections?
pearl ice
it should be $\frac{e^x}{2021}\sin{2021x}$
jolly parrotBOT
The Hat of DMing
unkempt yacht
ah.
but even then, how would i use calculus to find how many intersections in [-1; 1]?
unkempt yacht
drawing variation table would not be practical
pearl ice
$\frac{e^x}{2021}\sin{2021x} = 0$ implies $\sin{2021x} = 0$
jolly parrotBOT
The Hat of DMing
unkempt yacht
so differentiating this gets me an equation
pearl ice
sin(2021x) = 0 at x = πk/2021 for k in Z
unkempt yacht
and after some transformations, my goal is to practically solve
$\sin2021x + 2021\cos2021x = 0$
jolly parrotBOT
FungusDesu
pearl pondBOT
pearl ice
@unkempt yacht out of curiosity where's the problem from
it looks like competition math
unkempt yacht
it looks like competition math
asian math homework
if you say that im flattered lol
pearl ice
it's the "2021"
a lot of competition math sticks the year into it for some reason, probably just to cause more pain for the people going into the archives and studying the problems
at least when you're doing it for real you only have to deal with one irritating arbitrary large number
unkempt yacht
eh its common across all of my homework
usually i just treat it as another variable
pearl pondBOT
Available help channel!
near echo
i have a diffeq
[
a(t)x(t)^2 +2b(t)x'(t) x(t) = f(t)
]
can i write the LHS as a derivative of (t)? i imagine i want (b'(t) = a(t))
near echo
just need some confirmation
or i think it should be a(t) = b'(t)
let me rewrite the original message
jolly parrotBOT
maximo
near echo
i feel like im going insane
snow sail
then you can write $\dv t \qty(bx^2) = LHS$
jolly parrotBOT
jan Niku
near echo
so id want a to be the derivative of b
snow sail
because this would be $x^2b' + 2bxx'$
jolly parrotBOT
jan Niku
inland ivy
Yeah, so b’=a right?
snow sail
so if b'=a, you recover what you had before
near echo
right so b' = a
near echo
that's like the exact thought process i went through
ok great. im gonna keep this open cause i might need help tweaking my ode
autumn trellis
snow sail
its fast to check fortunately 
near echo
my specific ode is
[
3\omega^2 + 8\omega\dot\omega t = f(x,t)
]
where (\omega = \omega(t)). i am trying to write the LHS as a derivative on (t), but don't know what my integrating factor should be. we can basically ignore (x) (which is a function of (t))
jolly parrotBOT
maximo
near echo
i am not able to do this for some reason so i would appreciate any help whatsoever
snow sail
thats an extra factor of t right
i wanna try even though i will probably not win
okay les go
jolly parrotBOT
jan Niku
snow sail
i still have to check
near echo
let me try that
snow sail
but i wanted to be first if its right 
potent wind
my specific ode is
\[
3\omega^2 + 8\omega\dot\omega t = f(x,t)
\]
where \(\omega...
This might be super wrong, but to solve this for omega(t), what if you take the derivative with respect to omega of both sides?
Then you get a simple ODE for omega
near echo
This might be super wrong, but to solve this for omega(t), what if you take the ...
the thing is the derivative wrt omega would require knowing what the derivative of t and x are wrt omega
snow sail
so, you end up with $\dv t \qty( t^{\frac34} \omega ^2 )$
jolly parrotBOT
jan Niku
near echo
the thing is the derivative wrt omega would require knowing what the derivative ...
and since omega and x are unkown and dependent on t, would become an unsolvable (basically) ode
snow sail
is that right 
potent wind
and since omega and x are unkown and dependent on t, would become an unsolvable ...
That's true
snow sail
,w D[ t^(3/4) * (w(t))^2, t ]
jolly parrotBOT
snow sail
near echo
is that not it
snow sail
pearl pondBOT
near echo
i figured as much, i just am not in the right headspace
near echo
i think expecting t^m was clear
pearl pondBOT
Available help channel!
edgy scaffold
please help with this question, I know i am supposed to substitute a_n into the sequence but in the formula do we just ignore the n-1? or do we do: a_n = -3(0-1) + 4(0-2) or do we just replace a_(n-1) with 0
pine moat
if you wanted to verify, say c, and check if that works
you would replace a_n with (-4)^n, a_(n-1) with (-4)^(n-1)
edgy scaffold
but how come we dont ignore the n-1 if we need to replace it with a constant?
like a_n = 0
we would do
0 = -3(0) + 4(0)
why do we ignore the n-1 here?
pearl pondBOT
@edgy scaffold Has your question been resolved?
slender atlas
pearl pondBOT
pearl pondBOT
@slender atlas Has your question been resolved?
slender atlas
<@&286206848099549185>
static fossil
how to do this q in time constraint
There is no shortcut , just get the matrix there and make the equations and check for every condition.
( I remember this question, is it from JEE adv 2023)
slender atlas
There is no shortcut , just get the matrix there and make the equations and chec...
hmm
wouldnt that be sooo long
even if i check 2 options
static fossil
Nope, I did it too when I gave advanced, it was very easy
Your calculations should be fast enough
Making a matrix is not hard, there is generally no shortcut to solve a matrix question.
slender atlas
i havent done matrix
static fossil
It'll be easy when you do it.
slender atlas
It'll be easy when you do it.
i was doing this with only determinant
static fossil
There are certain conditions for equations in matrix where you can compare for no solution , infinite solution and all.
pearl pondBOT
static fossil
ok ig thanks for now , will do it when i do matrix
Do you know crammer's rule ?
pearl pondBOT
✅
static fossil
Use it then, that's the only way to solve it efficiently
Practice a few more problems using the rule, once you get the hang of it, it is pretty simple to solve it.
pearl pondBOT
pale juniper
yes
regal herald
5.375%
pearl pondBOT
west sapphire
easiest to start with the LHS
just write everything in terms of sin and cos and then put over a common denominator
then use a trig identity in the numerator
swift lodge
Ok lemme try
west sapphire
sure, if you get stuck let me know and i'll give another hint
west sapphire
if i write the following, does it ring a bell?
sin(a)cos(b) - cos(a)sin(b)
west sapphire
nicely done
swift lodge
We can subtract the donomi right
west sapphire
what do you mean, can you write out what you're proposing?
swift lodge
west sapphire
tan(3a) - tan(a) isn't the same as tan(2a)
swift lodge
Ok
west sapphire
ah i guess that's part vii, looks grungy
wait, why are the LHS of vii and viii the same but their RHS are different
swift lodge
Let's see
west sapphire
my brain is too tired to attempt it, it's like 3:30am here
west sapphire
yea i'm gonna head to bed
gl with the rest of these!
might want to open a new help channel to get a better chance of attracting other helpers
swift lodge
It can be done like this right
west sapphire
yea that's legal
swift lodge
.close
naive dirge
a
hearty junco
yo help me out
i cant solve this geometic series question
im using the formula Sn= (a(1-r^n))/1-r but i keep getting 2915=3^n
pearl pondBOT
rustic gate
rustic gate
.reopen
midnight haven
uh oh
rustic gate
vocal dove
pearl pondBOT
rustic gate
midnight haven
rustic gate
.reopen
pearl pondBOT
✅
rustic gate
whos channel is this 
midnight haven
its in limbo
rustic gate
