zenith grail
ah ok thank you
#help-13
cedar kilnBOT
cedar kilnBOT
Available help channel!
dire minnow
Help me differentiate this
cedar kilnBOT
Help me differentiate this
sacred iron
Holy hideous…
mighty shuttle
I was going to suggest solving the ODE until I saw log(dy/dx)
drowsy rock
neon egret
Help me differentiate this
oh....
formal glacier
Help me differentiate this
there has to be some other way
ancient nova
Looks at y, $\frac{dy}{dx}=x+\sqrt{x^2+1}$
wraith daggerBOT
Fionna The Unemployed
ancient nova
can't be wrong
last plaza
Help me differentiate this
Put x = tan theta i guess
dire minnow
Put x = tan theta i guess
I have seen such substitutions before
What does the theta here mean?
meager prawn
Help me differentiate this
i'm getting dy/dx = x all the terms kind of cancel out or i'm wrong
dire minnow
I don't think so
meager prawn
hmmm
dire minnow
It wouldn't satisfy the end result
meager prawn
ye
dire minnow
I am trying the x=tan theta suggestion out
meager prawn
okk
last plaza
What does the theta here mean?
We're just changing variables, usually when there are terms like x^2 + 1, we put x = tan theta as it then becomes tan^2 theta + 1 = sec^2 theta
last plaza
i'm getting dy/dx = x all the terms kind of cancel out or i'm wrong
dy/dx should be x + root(x^2 +1)
dire minnow
dy/dx should be x + root(x^2 +1)
Can you show your steps?
last plaza
Sure wait
meager prawn
dy/dx should be x + root(x^2 +1)
oh ye mb
meager prawn
ye that's it
last plaza
Nice!
dire minnow
Thank you @last plaza
Thank you for keeping me company, everyone
and working, on solving the thing
last plaza
Some more substitutions like these... You can put x = sin theta or cos theta if you see 1-x^2
cedar kilnBOT
cedar kilnBOT
Available help channel!
proud barn
Can i ask to see your pen? I like it
cedar kilnBOT
Can i ask to see your pen? I like it
last plaza
Can i ask to see your pen? I like it
It's a normal ball point pen lol
proud barn
It's a normal ball point pen lol
Oh okay
jolly steeple
Hi, I hope y'all're doing well! Basically, I was solving for the domain of the function $f(x)=\sqrt{1-\frac{1}{x}}$ up until I realized that I might've been facing a misunderstanding regarding inequality manipulation . . . I first said that the domain of $f(x)$ is the intersection of the sets ${x \in \mathbb{R}| x \neq 0}$ and ${x \in \mathbb{R}| 1-\frac{1}{x} \qeq 0 }$, so I tried solving for $x$ in the second inequality and came up with the following:
$1-\frac{1}{x} \qeq 0$
$1-\frac{1}{x} \qeq 0$
oops . . . sorry, I wrote my question in the wrong place
patent belfry
cedar kilnBOT
floral arrow
The points A,B,C each have two possible positions if ABC is not necessarily inside DEF
cedar kilnBOT
@patent belfry Has your question been resolved?
wild belfry
cedar kilnBOT
cedar kilnBOT
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fallen yew
i am completely lost
cedar kilnBOT
i am completely lost
fallen yew
i know how to do the first one
i can squeeze that easy
no idea how to do the other ones
flint plinth
cerulean sail
For (7), if you look at the numerator for a while, and then look at the denominator for a bit, it may hint to you something you could try with them 
cedar kilnBOT
@fallen yew Has your question been resolved?
fallen yew
For (7), if you look at the numerator for a while, and then look at the denomina...
okay let me try
should i use a ln?
cerulean sail
<@272917285880987648> Has your question been resolved?
Could you react to the bot with ❌ first though, just so you don't lose your channel please 
cerulean sail
should i use a ln?
And you don't really need to, there's a more simpler example that you could use 
dusk goblet
the idea is that sums in the denominator are ugly
find a path that eliminates the sum
fallen yew
are u suggesting multiplying by a conjugate
fallen yew
then i must be able to factor it somehow
dusk goblet
from that remark i assume you don’t know about taking different paths for the limit
for example traveling along x = y
fallen yew
yeah i don’t know
dusk goblet
read your textbook then
fallen yew
.close
cedar kilnBOT
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compact trout
Let $I,J$ be ideals of a commutative ring $R$, let $f$ be a ring homomorphism from $R$ onto a commutative ring $R'$,
Prove that
$f(I \cap J) \subseteq f(I) \cap f(J)$
And equality holds if $ker(f) \subseteq I$ or $ker(f) \subseteq J$
I am asking is the last statement an if and only if condition?
That is, given the equality holds, does it necessarily imply $ker(f) \subseteq I$ or $ker(f) \subseteq J$ holds?
Can we get some counter example ? I have been stuck on this for weeks
wraith daggerBOT
Leno
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weak granite
so, reducing 6 p 3 is 2... where do we put the new 2 and why?
weak granite
I mean- do we put it where 3 was or do we put it where 6 was
and why?
(Ik it will replace 3 but i just need reasoning as what logic do we follow when we reduce resistances)
upper laurel
so, reducing 6 p 3 is 2... where do we put the new 2 and why?
parallel resistors are both connected to the same beginning and end
the 3 and the 6 share the same end
and they share the same beginning since the only difference is a wire with 0 resistance
so you place the 2 at the same beginning and end:
beginning is anywhere along the bottom wire, end is at the upper-left corner
to be clear, you are replacing the 3 and the 6 with the 2
weak granite
so you place the 2 at the same beginning and end:
beginning is anywhere along th...
doesnt the hypotenuse looking wire also have the same beginning and end
upper laurel
let me repeat what I said
the 3 and 6 share the same end
the 3 is the wire on the left
weak granite
yes
upper laurel
the 6 is the "hypotenuse looking wire"
so yes, the hypotenuse looking wire also has the same beginning and end as the 3 wire, and also the 2 wire that will replace them both
weak granite
the 6 is the "hypotenuse looking wire"
I'm sorry but... I dont understand?
yes ik 3 and 6 share the same beginning and end
yes ik 2 will replace the both of them
but I dont understand why did we choose bottom wire or upper left wire instead of hypotenuse looking wire
both hypotenuse and bottom and upper left all share the same beginning and end... So I dont quite understand your argument
this is the second time i struggle with you 😭 trauma from when you helped me find the domain of f(x)/g(x)
I relaly hope you dont remember that ❤️
weak granite
3-6 parallel so he replace them
okay... why didnt we put the new 2 here 😭
instead of here
ancient nova
Same thing bruh
weak granite
but...
ancient nova
It has the same start and end point
weak granite
how do you reduce this then (pretend the 6 is a 2)
none of them are p or s
but if the 2 is on 3 then its s with 8
meager prawn
so, reducing 6 p 3 is 2... where do we put the new 2 and why?
for easier understanding take the top left corner as C and bottom right corner as D potential at A is Va and potential at D is also Va assume potential at C as Vc then as you can see potantial differecnce accros 3ohm and 6 ohm is same we take them as parallel and then simplify the circuit the rest all resistors are in series
ancient nova
how do you reduce this then (pretend the 6 is a 2)
none of them are p or s
Huhhhhh
Okay hang on
meager prawn
but if the 2 is on 3 then its s with 8
even if the 2 was on 6 it'll still be s
ancient nova
weak granite
even if the 2 was on 6 it'll still be s
oh!
ancient nova
this's what you get after combine 3 adn 6
weak granite
even if the 2 was on 6 it'll still be s
how?
meager prawn
how?
it doesn't matter because pd across them is same across 6 and 3 is same so pd across 2 will also be the same so even if you remove 6 and write 2 or remove 3 and write 2 they'll be in s
ancient nova
don't say the 2 was one 6 
, if 3 and 6 has start and end point A,B then its replacement also has to have start/end point A and B
man my brain is fried
meager prawn
lolll
weak granite
it doesn't matter because pd across them is same across 6 and 3 is same so pd ac...
wait let me draw
meager prawn
to better understand it write the resultant resitance 2 on 6 and remove 3 then compare it by keeping the resistance 2 on 3 and remove 6
weak granite
meager prawn
ye that's it
weak granite
left diag
meager prawn
both are the same
weak granite
current wouldnt go thru 2
bc from D to D
Right diag is from D to C so- YEAH LIKE HOW
ancient nova
ye that's it
The diagram's hurting my eyes how did you even read that
meager prawn
since you removed diagonal in right also remove the extra wire in the left the left vertical line where 3 was
weak granite
The diagram's hurting my eyes how did you even read that <:cat_happycry:63640781...
name me a warmer color combo 😭
ancient nova
Just use a website to draw like I did
weak granite
since you removed diagonal in right also remove the extra wire in the left the l...
oh!
meager prawn
The diagram's hurting my eyes how did you even read that <:cat_happycry:63640781...
my diagram skills are the worst so ye
ancient nova
Ehhh is that D or O or both appear in the diagram
weak granite
Ehhh is that D or O or both appear in the diagram
fionna dont be rude 😭
my D's are amazing
weak granite
my diagram skills are the worst so ye
excuse me? my diagram skills are amazing
ancient nova
my D's are amazing
wut
weak granite
<:fern_done:780525405006200873> wut
what 
weak granite
🤩 atleast yk how to reduce resistances
my ass has been taking this for 3 weeks and i didnt know that im supposed to remove the 3 wire
ancient nova
I always draw diagrams like this even in my note
weak granite
I always draw diagrams like this even in my note
back in my days the internet didnt exist. we use hands! (im like 17)
meager prawn
I always draw diagrams like this even in my note
oh wow respecttt
ancient nova
Yk while everyone doing the second part of the problem that's when I finish my diagram
Ruler, I even use the scale
weak granite
we're required to solve questions as simple as these with our eyes
bc of the 3 minute rule
weak granite
Ruler, I even use the scale
fionna.... you're 30x more capable to imagine the whole process than iam
ancient nova
fionna.... you're 30x more capable to imagine the whole process than iam
Nahh, I'm pretty dumb
That's why I'm unemployed
ancient nova
ancient nova
weak granite
right after i close this channel before moderators appear (please if you see this im sorry dont reply ill die from panick)
.close
cedar kilnBOT
ancient nova
I think at least a mod is watching us haha
fossil dawn
👀
cedar kilnBOT
Available help channel!
buoyant latch
is this a typo
cedar kilnBOT
is this a typo
buoyant latch
why is there a ds
the left hand side writes e^-ks^2t if u integrate the s you wont have any s' left
cedar kilnBOT
@buoyant latch Has your question been resolved?
slate lintel
you need dsomething if it's an integral
cedar kilnBOT
@buoyant latch Has your question been resolved?
buoyant latch
you need dsomething if it's an integral
yeah my point is shouldn't it be dx?
dreamy void
yeah my point is shouldn't it be dx?
Wouldn't it diverge that way then?
hollow trail
the left side of the equation with the ds integral is the (?) function
it's saying that if e^(-ks^2 t) is the fourier transform of mystery function (?) then solving for (?) you get the inverse fourier transform of e^(-ks^2 t)
cedar kilnBOT
@buoyant latch Has your question been resolved?
tulip lynx
Let M and N be finite sets with m and n elements. Determine under suitable conditions on m and n how many functions $f:M \to N$ there are that are surjective.
wraith daggerBOT
Goofball
tulip lynx
”Suitable conditions” are probably just $m \ge n$
wraith daggerBOT
Goofball
tulip lynx
But I don’t know how to formulate ”the number of surjective functions”.
crimson delta
for simplicity lets say the sets are {1,...,m} and {1,...,n}
for j in {1,...,n} consider the sets A_j = {f: M->N\{j}}. how big is A_j. use inclusion exclusion
tulip lynx
Never heard of inclusion exclusion, I’ll read up on that rq
tulip lynx
for j in {1,...,n} consider the sets A_j = {f: M->N\\{j\}\}. how big is A_j. use...
@crimson delta thx for reply
cedar kilnBOT
@tulip lynx Has your question been resolved?
cedar kilnBOT
@tulip lynx Has your question been resolved?
cedar kilnBOT
@tulip lynx Has your question been resolved?
versed jasper
start by taking small m >= n and see if you can derive a recurrence relation
,texsp ||In a way, if you can reduce the problem to arranging $m$ objects into $n$ non-empty subsets, by definition, the answer is the Stirling number of the second kind $S(m,,n)$, which has both a recurrence formula and a direct formula by Inclusion-Exclusion||
wraith daggerBOT
@versed jasper
cedar kilnBOT
@tulip lynx Has your question been resolved?
cerulean creek
I need help with a question on divergence! The question asks you to calculate the divergence, then convert to spherical coordinates, then do it the other way around. I’ve done the first half fine, but I can’t figure out where the second one is going wrong. In this attempt, I’ve set the “new” variables as r_1, theta_1, etc and solved for them
cerulean creek
The correct answer is 2r^3(sin(theta)sin(phi)cos^2(theta) which my answer is annoyingly similar to
cedar kilnBOT
@cerulean creek Has your question been resolved?
zealous plinth
what's the original question?
cerulean creek
Calculate the divergence of F(x, y, z) = (2xy(z^2), −2(x^2)(z^2), 0) and then transform the result into
spherical coordinates. Compare this answer to the result you get if you switch to spherical
coordinates and then take the divergence
primal wigeon
how can these 2 have the same equation
cedar kilnBOT
how can these 2 have the same equation
primal wigeon
when they're going opposite ways
half ibex
What lang us this
primal wigeon
french
whole nexus
Well it's |x - 3|
primal wigeon
yes
whole nexus
And -|x - 3|
half ibex
Do u understand the modulus functions?
primal wigeon
alright
primal wigeon
Do u understand the modulus functions?
i dont know what that is because i learned the stuff in french
probably called something else in french
yeah no clue what that is
half ibex
^
primal wigeon
never saw that
half ibex
It's ok
minor yoke
fonctions de module
fluid pendant
bad translated i think, i'am also franch student i never heared that
primal wigeon
fonctions de module
explain it
minor yoke
yeah that
primal wigeon
well yeah i know what absolute function is
whole nexus
And what's the graph of an absolute function?
dire geode
is this rational
do you mean rational function
primal wigeon
yeah
dire geode
yes
primal wigeon
thanks
edgy kindle
how can these 2 have the same equation
g(x)=-0.4|x-2.5|+4.5
it is very simple
send me more difficult problem
primal wigeon
what is that equation from
primal wigeon
g(x)=-0.4|x-2.5|+4.5
it is very simple
send me more difficult problem
this is my first problem dude chill
i been solving basic equations before
whole nexus
You're fine man, you can ask anything here, they're just being a bit rude
primal wigeon
also why is the answer an equation
the question is
the total cost to cover the wooden wall
its a price
edgy kindle
also why is the answer an equation
so you mean: solve the second problem?
primal wigeon
g(x)=-0.4|x-2.5|+4.5
it is very simple
send me more difficult problem
wait did u replace
the absolute function
like the variables
primal wigeon
so you mean: solve the second problem?
no just help me
g(x)=-0.4|x-2.5|+4.5 is this
?
edgy kindle
okay
edgy kindle
the line include the G and H.
so (4, 3.9)in right line.
and then x=(4+1)/2=2.5
not x, it is h1
and k1= 4.3+(3-2.5)*(4.3-3.9)=4.5
and then insert F in this fancution:
a=-0.4
primal wigeon
the line include the G and H.
so (4, 3.9)in right line.
my question is why did u want to find this
to find the h?
ohh
i get it
i see what u did
edgy kindle
okay'
primal wigeon
ok so that side
is (4,3.9)
now to find h
u do 4-1
h is 3
wait no
its 2.5
edgy kindle
(1, 3.9) and (4, 3.9) are in g(x). -> h=(1+4)/2=2.5
cedar kilnBOT
@primal wigeon Has your question been resolved?
edgy kindle
@primal wigeon
r u student?
im teacher of university and AI developer for my company
primal wigeon
<@723362224717955123>
r u student?
im teacher of university and AI developer fo...
sorry back
yes imn a student
primal wigeon
<@723362224717955123>
r u student?
im teacher of university and AI developer fo...
wow ur a uni teacher?
yeah im in a last year of hs
edgy kindle
yes
primal wigeon
thats cool
edgy kindle
where r u from?
primal wigeon
canada
primal wigeon
yeah i understand
edgy kindle
so your age is 17 or 16?
primal wigeon
16
edgy kindle
im from japan
edgy kindle
let's contact with DM
please send me ''ADD Friend"
tight widget
How to solve this manually in an exam? I know its Pythagoras theorem but man do I have to square then add then find square root of these fat numbers manually? There should be a better way. But I don't know it.
tropic oxide
these look like they're in the ratio 3:4
worn brook
How to solve this manually in an exam? I know its Pythagoras theorem but man do ...
Check whether the legs are in a 3:4 ratio if they are the triangle is a 3-4-5 scaled one so just divide a leg by 3 (or 4) to get the scale and multiply by 5 for the hypotenuse.
tight widget
Damn! Getting the ratio then applying pythagoras then scaling it back is fast and easy.
Thank you @worn brook and @tropic oxide
.close
cedar kilnBOT
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Available help channel!
vital knoll
Yo guys
Is there difference between proving an implication statement and deducing a statement from implication statement
vital knoll
I know the answer might be obvious but i need a affirmation
worn brook
Yes
vital knoll
And what Modus ponens does mean?
worn brook
It’s just the rule: if you know P ⇒ Q and P is true then you can conclude Q.
vital knoll
So there when we conclude Q
We don't make it out of empty, it's just deuced?
worn brook
Yep basically you’re just reading Q off what’s already there not making it up.
cedar kilnBOT
@vital knoll Has your question been resolved?
hasty path
cedar kilnBOT
abstract breach
$\cos \frac{2 \pi}{3} = \cos \frac{4 \pi}{3}$ but $\cos( \frac{2 \pi}{3} + \theta) \neq \cos( \frac{4 \pi}{3} + \theta)$ usually
wraith daggerBOT
bloubbloub
cedar kilnBOT
@hasty path Has your question been resolved?
primal wigeon
need help
proper palm
regarde sur le graphique t’as deux points dont tu peux te servir
primal wigeon
regarde sur le graphique t’as deux points dont tu peux te servir
oui
proper palm
si t’évalues c en 10 ça te donne 14, en 35 ça te donnera 13
ça te fera deux équations
avec deux inconnues
h et k
primal wigeon
mais il faut pas convertir le 10 et le 35 en metre carree?
proper palm
ah jsp du tout 😭
primal wigeon
vu que tout les autres sont en metre
primal wigeon
ah jsp du tout 😭
pas grave c'est correcte
proper palm
mais il faut pas convertir le 10 et le 35 en metre carree?
j’pense ouais
primal wigeon
jai une autre question
proper palm
oui
primal wigeon
comment je converti un fonction absolue a racine caree
proper palm
oula c’est a dire
primal wigeon
j'ai pas d'exemples
primal wigeon
d'accord
proper palm
$|x|=\sqrt{x^2}$
wraith daggerBOT
tm
proper palm
tu parles de ça
proper palm
ça fait $-0.6 \sqrt{(x-3)^2}+6.5$ ducoup
wraith daggerBOT
tm
primal wigeon
ah
primal wigeon
equation de racine carre c'est a racinecaree (x-h) + k?
proper palm
l’équation d’une racine carrée ?
primal wigeon
oui
proper palm
c’est dans ton cours ?
primal wigeon
oui
proper palm
tu peux me montrer stp mdr
primal wigeon
j'ai pas de image
mais je dois connaitre fonction value absolue. racine caree
et rationelle
rationelle, lui qu'on a fait en haut
proper palm
ah j’ai trouvé ça $f(x)=a\sqrt{x-b}+c$
c’est le modèle de la fonction racine carree apparemment
wraith daggerBOT
tm
primal wigeon
b c'est h c 'est k
proper palm
tu peux écrire que $|x|=\frac{x^2}{|x|}$
wraith daggerBOT
tm
proper palm
pour passer d’absolue a rationnelle
wraith daggerBOT
tm
proper palm
c’est la même chose
primal wigeon
ah ok
primal wigeon
c’est la même chose
je vais trouver plus de exemples
proper palm
vas-y
primal wigeon
attend je comprend pas c'est quoi
le valeur absolue de x est egale a x^2/racine x^2
c'est quelle equation le x^2 / racinex^2
racine caree?
|x-5| = racine(x-5)^2
proper palm
|x-5| = racine(x-5)^2
oui
cedar kilnBOT
@primal wigeon Has your question been resolved?
cedar kilnBOT
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Available help channel!
patent prism
Hii! I don't know how to solve this problem: An even number N has 16 positive integer divisors. If one of the divisors is chosen at random, the probability that it is even is 3/4. What is the least possible value of N?
whole nexus
Okay so the probability of the divisor being even is 3/4
And total number of divisors are 16
So how many even and odd divisors are there?
patent prism
12 even and 4 odd
patent prism
I'm not sure, but I know the answer is 120 I just don't know how to get there
whole nexus
Alright, I gotta think then
patent prism
Okay
whole nexus
Wait though how is it 120
120 = 2,2,2,3,5
that's like 5 divisors
The probability also doesn't work here
whole nexus
Well that's odd, you sure about the answer and the question, like there's no error in them?
patent prism
Yeah i'm sure!
whole nexus
Alright then, I'm not exactly sure how to proceed with it
Apologies
You can wait for another helper
full quartz
Are you given the answer since you know its 120
patent prism
Oh it has 12 even divisors and 4 odd, the even are: 2,4,6,8,10,12,20,24,30,40,60,120 and the odd are 1,3,5,15
patent prism
Are you given the answer since you know its 120
Yeah
whole nexus
oh wow that changes things, let me think a bit now
Okay see
So we know that 4 are odd
and 12 are even
patent prism
Okay
whole nexus
For it to be the shortest value of N, there has to be 1,2,3,5 as primes of it
from that we get 3 odds
the 4th odd is 3*5 = 15
We got out odds - 1,3,5 as for N to be the smallest, it must have the smallest primes, and 15 as it is a product of two of those primes
patent prism
Okay
whole nexus
for evens we know 2,6,10,30 are divisors, as they're products of 2 with 1,3,5,15
patent prism
Okay
whole nexus
now for N to be the smallest, we must include 4, otherwise the 4 even remaining divisors would be pretty big compared to if we just include 4 as a divisor
patent prism
Ohh alr
ancient lodge
Wait though how is it 120
There's 4 odd divisors, so the "odd" part of the prime factorisation is p^3 or pq.
whole nexus
Ahhh yes, I got confused with whether it has 12 distinct PRIMES
Which TBH isn't even possible, as there are 8 even numbers
ancient lodge
Ahhh yes, I got confused with whether it has 12 distinct PRIMES
rip
alright I'll leave ygs alone again now
whole nexus
alright I'll leave ygs alone again now
Alright thanks man
patent prism
what does the p and the q mean?
whole nexus
Primes
patent prism
Oh I get the problem now!
whole nexus
Nice!
patent prism
Tysm!!
whole nexus
So like do you still want me to help you?
patent prism
Nah it's fine!
whole nexus
Alright then, glad then you get it🫡
cedar kilnBOT
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Available help channel!
normal hedge
What is 1+1?
cedar kilnBOT
What is 1+1?
cedar kilnBOT
sacred iron
nah i shouldnt troll
bro had a change of heart 💀
cedar kilnBOT
Available help channel!
spice grail
Hey! I'm trying to prove this using induction, but I'm kinda stuck
cedar kilnBOT
@spice grail Has your question been resolved?
spice grail
late wadi
Hey! I'm trying to prove this using induction, but I'm kinda stuck
do you have to use induction?
spice grail
yes
cedar kilnBOT
@spice grail Has your question been resolved?
spice grail
chrome elk
I'll get to this in about an hour and a half if no one else does
edgy kindle
hello, @here. im university teacher.
if you have problem, please ask me.
unique copper
hello, @here. im university teacher.
if you have problem, please ask me.
you don't have permission to ping everyone. If you want to help, go to help channels, check pinned message to get the problem and explain how to do it to the helpee.
edgy kindle
you don't have permission to ping everyone. If you want to help, go to help chan...
okya shoubh
edgy kindle
you don't have permission to ping everyone. If you want to help, go to help chan...
r u india
unique copper
yes, if you wanna talk ping me in #discussion
cedar kilnBOT
@spice grail Has your question been resolved?
spice grail
replace j = -1. you’ll see it’s also 0
pastel vault
Hey! I'm trying to prove this using induction, but I'm kinda stuck
you still haven't used the inductive hypothesis! $2 \sum_{k = 0}^n {n \choose k}^2 = 2 {{2n} \choose n}$
wraith daggerBOT
south
pastel vault
but then $2 {{2n} \choose n} + 2 \cdot 2^{n + 1}$ does not equal ${{2n + 2} \choose {n + 1}}$
so you've made a mistake somewhere
don't know where
wraith daggerBOT
south
cedar kilnBOT
@spice grail Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
lost aurora
a particle moves along the x-axis so that at time t> 0 its position is given by x(t) cos (root t)
what is the position of the particle at the first instnace the particle is at rest
lost aurora
i found that
v(t)=-sin(root t)/2(root t)
and if I set the numerator = o
idk what to do from there
wraith daggerBOT
〈 kitten | teacup 〉
cedar kilnBOT
@lost aurora Has your question been resolved?
torn marsh
cedar kilnBOT
torn marsh
hey I just want to check my answer
my answer key is giving me a different answer
Idk why
wait I messed it up, ill redo this
.close
vapid grotto
I don’t understand why for one the negative is inside the () but for the other it is outside even if they are the same step
tropic oxide
they're inside in both...?
vapid grotto
For the first one it always stays inside the () like this (-X) but the second one becomes -(X)
tropic oxide
yeah that's because of a subsequent horizontal transformation...
vapid grotto
And for this one I did a vertical stretch by -1/3 but on the answer key they did not do this is my version also correct ?
tropic oxide
no, yours is wrong
vapid grotto
yeah that's because of a subsequent horizontal transformation...
Yea but the other one also has a horizontal transformation but goes to the outside
tropic oxide
vertical stretch by k takes you from y=f(x) to y=kf(x)
not 1/k f(x)
vertical transformations are applied in the "expected" way
vapid grotto
no, yours is wrong
So if I just replaced the negative 1/3 with a positive and add a step at the end saying reflect over the y axis would that still be correct ? Or is that the wrong way
tropic oxide
Yea but the other one also has a horizontal transformation but goes to the outsi...
no, the one with x^3 has no horizontal stuff after the one you highlighted
tropic oxide
So if I just replaced the negative 1/3 with a positive and add a step at the end...
you should replace the 1/3 with just 3.
vapid grotto
Oh wait yea because it’s vortices and not horizontal
So I don’t really need to worry about order to much here rigjt since there is only one horizontal transformation?
umbral osprey
hi
vapid grotto
So I don’t really need to worry about order to much here rigjt since there is on...
I’m really confused now because it was the wrong order but why I thought order only matters if you have both a horizontal translation like left two or right two and a horizontal shrink or stretch b
Would mine also be correct I’m getting really confused now
cedar kilnBOT
@vapid grotto Has your question been resolved?
vapid grotto
<@&286206848099549185>
frosty creek
<@&286206848099549185>
Yes?
vapid grotto
Yes?
For my most recent message the order I did is different from the answer key but is it still correct because I know there can be multiple answers
frosty creek
For my most recent message the order I did is different from the answer key but ...
I think shifting, reflecting, stretching and shifting is the sequence
vapid grotto
So is it wrong ?
frosty creek
So is it wrong ?
It should be right 3 units right?
@vapid grotto the problem is 2nd and 3rd transformation
Horizontal shift and reflection is important
cedar kilnBOT
@vapid grotto Has your question been resolved?
weary ingot
Define $t:= \tan a$ s.t. $(\sqrt{\tan x})'$ evaluated at $x=a$ equals to 1, and $t\neq \frac{\pi}{4}$.
Show that $$t^3 + t^2 + 3t - 1 = 0$$
I've shown that:
$$t^4 + 2t^2 - 4t + 1 = 0$$
which is correct.
I am now stuck and as per the marking scheme i should divide by $t-1$.
How am i supposed to come up with the idea to, out of all things, divide this polynomial specifically by $t-1$?
wraith daggerBOT
woomy
weary ingot
Like i realise that 1 is a root but is there anything more to it?
Is it just lots of practice with these types of questions?
weary ingot
Because personally i reached that point and my first thought was that i made a mistake due to the fact that i dont have a term of t³
cyan whale
Because the t^4 and constant coefficients of the quartic are 1 and -1, and the t^3 and constant coefficients of the cubic are 1 and 1, (t-1) is the only thing that could work
frail edge
@primal wigeon
My account star053511 got a 7-day timeout, so let’s reach out to star__1226 instead.
weary ingot
sorry im back
weary ingot
Because the t^4 and constant coefficients of the quartic are 1 and -1, and the t...
okay makes sense
thanks!
.close
cedar kilnBOT
fossil dawn
<@723362224717955123>
My account star053511 got a 7-day timeout, so let’s reach...
<@&268886789983436800> admission to ban evading
cerulean sail
<@&268886789983436800> admission to ban evading
That's their original account that was timed out, the original timeout expired not too long ago 
cedar kilnBOT
Available help channel!
rare grail
Can someone PLS help me with tbis
cedar kilnBOT
Can someone PLS help me with tbis
floral arrow
,rccw
crimson sedge
may i can help u? @rare grail
wraith daggerBOT
rare grail
may i can help u? <@1060886328843186238>
Ye
crimson sedge
you mean: the count of all number as posible?
floral arrow
If you have a number abc where a,b,c are its digits, you can rewrite it as a*100 + b*10 + c
What part of the question do you not understand?
floral arrow
Where did u even get that from
I don't know you mean
formal glacier
I been staring at this for like
to find the least value of n just maximise the term your subtracting and minimise the term your adding
ezz
rare grail
to find the least value of n just maximise the term your subtracting and minimis...
I did 😭
But answer says 976
I have no idea how it even got 976
rare grail
97
floral arrow
First you say you don't understand the question, then you say you did something to answer it... Which one is it
formal glacier
and the second largest
rare grail
and the second largest
65
rare grail
First you say you don't understand the question, then you say you did something ...
No like i dont understand the question so i just tried guessing
crimson sedge
35+124+(97+86)+1000=976 and 976 is least number
formal glacier
we will use 95 and 76
formal glacier
35+124+(97+86)+1000=976 and 976 is least number
no 8 tho 
crimson sedge
yes, in this problem, you have to use number (1-9) for only once
rare grail
35+124+(97+86)+1000=976 and 976 is least number
Where u get the 8 from 😭
formal glacier
hmm but it says each of the seven
crimson sedge
read the problem deeply
rare grail
Thats why im so confused
floral arrow
If the answer really is 976, I'm pretty sure they meant to say "each of the nine digits from 1 to 9"
Otherwise I have no clue what they expect
rare grail
Yea but sadly the question says each of the "seven digits"
floral arrow
My only advice is to solve the question as if they said "each of the nine digits from 1 to 9" and to contact your teacher, explaining the situation (namely that there are 9 boxes to fill but only 7 given digits, and that you can get 976 if you use all 9 non-zero digits instead)
rare grail
😭😭😭
Sad thing is
This is a competiton question
So theres no "teacher"
Just me
And some assholes who js want money
floral arrow
Not sure I understand. If this is a competition question, why do you have the answer? Did you attend the competition and get a correction afterward? If so, are you asking why the answer you were given is 976?
@rare grail ?
floral arrow
So... what exactly is your question?
cedar kilnBOT
floral arrow
Ok then
cedar kilnBOT
Available help channel!
rare grail
Help this is one of the last questions i got
cedar kilnBOT
Help this is one of the last questions i got
tropic oxide
,rccw
wraith daggerBOT
tropic oxide
!status
cedar kilnBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
aight
by the looks of it, the 4 is just constant across all the equations, while the other terms increase each in their own arithmetic progression.
rare grail
Yea
Like idk how to find the other numbers
The pattern is 4
But then how to find the other number
Trial and error would yake too lonb
formal glacier
this and the previous one appear to be from the same question sheet hmm
rare grail
👍
formal glacier
Like idk how to find the other numbers
they appear to be in an ap
so they are increasing or decreasing with a constant rate
find that constant rate and use it to find the next term
An = Ao + (n-1)d
formal glacier
ye
cedar kilnBOT
cedar kilnBOT
Available help channel!
hexed vortex
is elements of order 10 the only ones they cant have in common
hexed vortex
I think I see why they cant have elements of order 10 in common since ifthey did then that element would generate both cyclic groups and so they would be equal
but im not sure about any other orders
cedar kilnBOT
Available help channel!
idle lagoon
don't know how to go about this at all
cedar kilnBOT
don't know how to go about this at all
hollow trail
do you know the criteria for a subset of some vector space to be a subspace?
idle lagoon
do you know the criteria for a subset of some vector space to be a subspace?
closed under addition and scalar multiplication?
hollow trail
that's 2/3
hollow trail
is not empty, or contains the 0 vector (take your pick but the second is usually better)
chrome quail
third is sometimes not stated so you might not know it. sometimes its omitted and "the empty set is not a subspace" is given as a remark
idle lagoon
wait so it's just a subspace bc 1) 0∈U for all the parts under the main diagonal 2) if there are two matrices ∈U 0+0 would be 0 anwyays 3) 0* scalar = 0 so still upper triangular?
like im so confused 💀 i don't think i undersatnd the first condition
hollow trail
that's pretty much it
idle lagoon
oh lmfao gotchu
hollow trail
by "0 vector" here we are referring to the matrix with all 0's, which is upper triangular according to the definition
idle lagoon
so that just proves it isn't empty right?
hollow trail
yes, although "contains 0 vector" is a more useful condition to start with than "isn't empty" because even if it's nonempty, it would not be closed under scalar multiplication if it didn't have 0
cedar kilnBOT
cedar kilnBOT
Available help channel!
paper gale
Sorry for the bad picture.
This is the only question I haven't been able to complete today. I keep getting an answer that is not up there to select.
I keep getting y+.24=12 for point slope form
And y=12x+1.56 for slope intercept form.
I used the rule to do it. Do you think it may be a problem with the answer provided or maybe with my process? If possible could you show me how to do it?
floral trout
find slope using y2-y1/x2-x1
the point slope form is
y-y1=m(x-x1)
find intercepts from the above form
then put those intercepts in intercept slope form
paper gale
Ok thanks
last plaza
Sorry for the bad picture.
This is the only question I haven't been able to com...
question is correct
cedar kilnBOT
paper gale
should be c and b respectively
I appreciate it. Now I am going to work those backwards so I can see what I did wrong 😅
paper gale
.close
cedar kilnBOT
Available help channel!
small willow
So I want someone to tell me if my answer is at all valid and if so how on earth can it be interpreted to make any sense. So I started with:
1^x = 2
=> 1 = 2^1/x
e^i2πn = e^(1/x) ln2
(n is an element of Z)
=> i2πn=1/x ln2
=> x=ln2/i2πn= - iln2/2πn
Okay and verifying this:
e^i2πn * (-i ln(2)/2πk)
(As far as I understand n and k are independent, I tried to verify this with some specific proof with complex valued logarithms but I couldn't show it rigorously, though I'm not too bothered)
e^ln(2) * (n/k)
2^n/k = 2
Holds for all n=k elements of Z ^ n,k don't equal 0
I don't understand how this is possible when taking 1^x = 2
I can get:
ln(1^x) = ln(2)
xln(1) = ln2
0= ln2 which is nonsense
Or is there some reason this only proves no solutions for x element of R
small willow
I tried to prove this otherwise with Taylor series expansions of ln but they didn't help me anyhow, I don't have the programming skills to graph 1^x in complex numbers in desmos :(
My only thought is because logs of complex numbers are multi valued that I'm somehow in some sleight of hand not taking the PV but idk
cedar kilnBOT
@small willow Has your question been resolved?
small willow
I'm sure my question is stupid but like ¯_(ツ)_/¯ I'm too stupid to answer it
<@&286206848099549185> sorry for the bother but ye
cedar kilnBOT
@small willow Has your question been resolved?
chilly warren
.close
cedar kilnBOT
small willow
.close
chilly warren
or .solved
cedar kilnBOT
Available help channel!
covert void
“Find the equations of ALL LINES through the point (1,-5) that are tangent to the graph of y=x^2-3x+1.
covert void
I’m at a loss of what to do because in our derivatives unit, we only ever focused on points which were actually ON the graph
But this one is off the graph since (1,-5) isn’t a point in the graph
analog pumice
the question doesn't require the lines to be tangent to the curve at exactly (1, -5). they're two separate requirements
you just have to construct lines that pass through the point (1, -5) and are also tangent to y=x^2 -3x + 1, but the tangency of the line can be at any point of the curve
covert void
you just have to construct lines that pass through the point (1, -5) and are als...
So shit what do I have to do then
Like do I just choose ANY point?
regal yacht
you just have to construct lines that pass through the point (1, -5) and are als...
how are you so mathematically gifted
analog pumice
how are you so mathematically gifted
???
covert void
I get what he means
But like I’m still confused
What do I do in order to get the line equations
loud gyro
Like do I just choose ANY point?
yea, you know the slope of tangent at some random point on the curve, so you can find the equation of the line. You can check for what values of (x,f(x)) the line passes through (1,-5)
covert void
yea, you know the slope of tangent at some random point on the curve, so you can...
I think not all values would work tho
Wouldn’t only a specific tan line work?
analog pumice
if you want a line that is tangent to a curve, what property must this line have?
covert void
if you want a line that is tangent to a curve, what property must this line have...
It must have uh
Be perpendicular?
Have only one point
That intersects
analog pumice
no thats the opposite of tangent. tangent means same slope. so the line meets the curve at a point, and at that point the slope of the line and curve is the same. so the derivative of the curve at that point is equal to the slope of the line. does this make sense?
covert void
I alr know the derivative to the equation
covert void
no thats the opposite of tangent. tangent means same slope. so the line meets th...
Yeah
The derivative is 2x-3
What can I do with that to solve for which point on the graph of y to use
analog pumice
What can I do with that to solve for which point on the graph of y to use
if I have to tell you how to draw a straight line, I need to either give you any two points on the line, or a single point and the slope of the line. if you notice, this question gives you enough information for the second approach
since you have to do this for any general point on the curve
let x=a be some point
then $\frac{dy(a)}{dx} = 2a - 3$
wraith daggerBOT
snooze-fest
analog pumice
so for the line we are trying to construct, we know its slope, 2a-3, where a is any point on the curve. so far so good?
covert void
so for the line we are trying to construct, we know its slope, 2a-3, where a is ...
Yeah
analog pumice
ok so you're told that (1, -5) is a point on the line. how do you write the eqn of a line using the slope and a single point?
$y - y_1 = m(x - x_1)$
wraith daggerBOT
snooze-fest
analog pumice
so can you see what x1, y1 and m would be here?
lean oracle
$y+5=m(x-1)$
wraith daggerBOT
NotYourAverage_3CL1P53
covert void
Literally what I said bru
lean oracle
$= x_1, y_1$
wraith daggerBOT
NotYourAverage_3CL1P53
analog pumice
Y+5=m(x-1)
sure but now we're doing this in terms of any general point a. so you have some point (a, a^2 - 3a + 1)
lean oracle
$(a,a^2-3a+1)$
wraith daggerBOT
NotYourAverage_3CL1P53
covert void
wtf
Ok this took a sharp turn
We did NOT establish this in class
Wait it makes sense tho
analog pumice
all I did was use a instead of x. instead of (x, y(x)), I'm writing (a, y(a))
covert void
all I did was use a instead of x. instead of (x, y(x)), I'm writing (a, y(a))
Yeah
What now?
analog pumice
<@&268886789983436800> spammer in help channel
covert void
so that's (a, a^2 - 3a + 1)
Yeah
What rhat gonna do with anything tho
Like what do I gotta do now
analog pumice
so now use that same formula as before, with x1 = a, and y1 = a^2 -3a + 1
what do you get?
analog pumice
**snooze\-fest**
this formula. just set x1 = a and y1 = a^2 - 3a + 1. since these are our two coordinates
covert void
this formula. just set x1 = a and y1 = a^2 - 3a + 1. since these are our two coo...
Oh whaaaa
Ok yeah we didn’t go over ts in calc class
analog pumice
this has nothing to do with calculus.. this is just the equation of a straight line
covert void
If there’s any problem asking for the derivative that’s not in the og equation I’m crashing out fr
covert void
this formula. just set x1 = a and y1 = a^2 - 3a + 1. since these are our two coo...
Ik but it feels weird asf setting a whole ass equation equal to the y1
I would have NEVER THOUHHR OF THAT
analog pumice
Ik but it feels weird asf setting a whole ass equation equal to the y1
you're not setting an equation to y1. that is the definition of y1. you're given the curve y = x^3 -3x + 1. this means a general point will be:
$(x_1, x_1^2 - 3x_1 + 1)$
wraith daggerBOT
snooze-fest
analog pumice
no?
a is some just x-coordinate of a point on the curve y=x^2 -3x + 1
so its y-coordinate is a^2 - 3a + 1
so when you plug this into the slope intercept form, you get:
$y - (a^2 -3a + 1) = m(x-a)$
wraith daggerBOT
snooze-fest
covert void
Yes that makes sense
analog pumice
but we know that m = 2a - 3
so plug that in, and then use the one point you haven't used till now, i.e. (1, -5), to find the value of a
I'll have to leave, <@&286206848099549185> in case someone else can take over
covert void
so plug that in, and then use the one point you haven't used till now, i.e. (1, ...
Set that to x and y?
PLEASE
NOOOOO
winter scarab
shrewd condor
I'll have to leave, <@&286206848099549185> in case someone else can take over
why why
loud gyro
Set that to x and y?
yes
put x and y as 1 and -5 in the equation, and solve for a to satisfy the equality condition
covert void
put x and y as 1 and -5 in the equation, and solve for a to satisfy the equality...
Ok this seems like a very overall fucked up provlem
Ngl
Like
Not enough calculus
Too much conceptual stuff going on
I don’t like it
loud gyro
all the solutions of a that you find would be the points on the curve where the tangent passes thru (1,-5)
covert void
At all
loud gyro
Not enough calculus
generally, this is kind of a problem is not given in calc
you should encounter it when you study conic sections
loud gyro
https://tenor.com/view/sponge-bob-yikes-cartoon-gif-13894010
wdym lol, you are supposed to study conics before studying calc
loud gyro
isnt conics a part of precalc?
covert void
isnt conics a part of precalc?
No
loud gyro
idk, I didnt study american, but khan academy sure thinks so
covert void
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
quasi heath
Can you guys help with seventh grade math?
cedar kilnBOT
Can you guys help with seventh grade math?
cedar kilnBOT
wicked mantle
Why?
quasi heath
.reopen
cedar kilnBOT
✅ Original question: #help-13 message
wicked mantle
You can ask here tho
quasi heath
So you can help middle school math?
wicked mantle
Just post it here and people may help you
quasi heath
Ok
wicked mantle
We don’t know if we’re capable of assisting you if you don’t post it in the first place
fossil dawn
,rccw
wraith daggerBOT
livid dirge
May we know what you've tried, or what you understand about this?
livid dirge
If it helps you understand this particular question, sure. But if you could do other questions like this one, what about this one is confusing you?
quasi heath
Let me give it another try?
If I still don’t understand I will open a channel
.close
cedar kilnBOT
livid dirge
You can leave this open I think?
quasi heath
It’s ok I closed it
cedar kilnBOT
Available help channel!
empty fable
cedar kilnBOT
mighty shuttle
Yws
empty fable
Yws
i got
y = 1
and
y = 7
and
im unsure what to do now
do i just say
x = 1 and x = 7
but i reject 1
anyone?
idk what to do
cedar kilnBOT
@empty fable Has your question been resolved?
livid dirge
You should have gotten a function statement, not two values, though.
neon fox
cedar kilnBOT
fossil dawn
true bearings are from north if im not mistaken
correct. bearings are measured from due north, clockwise.
neon fox
correct. bearings are measured from due north, **clockwise**.
so would a) be 110
degrees
fossil dawn
so would a) be 110
right
neon fox
alright thank you so much
twilit mirage
x = y^2 - 8y + 7
Yes, you find the reciprocal first before you state the domain and rance.
Wait crap that's old
Sorry
neon fox
!done
cedar kilnBOT
If you are done with this channel, please mark your problem as solved by typing .close
neon fox
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
carmine cloud
Can anyone help me with that
cedar kilnBOT
Can anyone help me with that
inland ether
Can anyone help me with that
can u translate the stement given in the qn to english mate?
carmine cloud
It says, a, b, c, d positive real numbers, prove for :
inland ether
this property of all real nos is known as arithematic geometric mean ineuality first of all
carmine cloud
Okay?