ideal gas equation?
#help-0
lofty heart
native cloud
Chemistry isn't my jam
ebon sparrow
there's a chem server in #old-network
lofty heart
im not 100% thats just what im assumed to start with
tardy stag
i always just started with the ideal gas law because i couldn't bother memorizing three different laws
primal crag
$\frac{p_1 v_1}{T_1}=\frac{p_2 v_2}{T_2}$ I think this works.... equation of state.... thats what my chem teacher used to call it
keen prawn
Aren’t there 4?
ocean sealBOT
R(icky)
keen prawn
Wait lemme check
keen prawn
Huh?
zenith veldt
Does anyone here have a detailed explanation of art of problem solving's books ?
lofty heart
using ideal gas equation you get the moles
then you use the new numbers with the same moles for the new volume
keen prawn
using ideal gas equation you get the moles
Already tried it doesn’t work
lofty heart
how didnt it work for you
keen prawn
Idk even used a calculator
zenith veldt
Does anyone here have a detailed explanation of art of problem solving's books ?
Can you help me?
lofty heart
wrong chat bud
zenith veldt
Why
keen prawn
$\frac{p_1 v_1}{T_1}=\frac{p_2 v_2}{T_2}$ I think this works.... equation of sta...
Thank you this worked
primal crag
Thank you this worked
its a combination of boyle's and charles' laws
ebon sparrow
How can I get help
!help
lone heartBOT
How can I get help
Please read #❓how-to-get-help
keen prawn
its a combination of boyle's and charles' laws
Oh
keen prawn
what did you get out of curiosity
0.821 moles
zenith veldt
Thank you everyone
lofty heart
i meant for the volume of the second CO2
zenith veldt
Is this a chemistry group or math group?
zenith veldt
Ok
keen prawn
i meant for the volume of the second CO2
Nvm it’s changing everytimr
Idk why
But thank you guys
.close
alpine sable
Is there any notation to denote repeated function composition? Such as [
\nest{10}{\inline#1{\map f{#1}}}x
]
ocean sealBOT
pallid glade
💀
native cloud
Infinite series maybe..?
pallid glade
Infinite series maybe..?
it isnt infinite tho
native cloud
Partial sum maybe..?
alpine sable
It isn't a sum
pallid glade
i dont remember ever studying it either
vague coral
$f^{\circ n}$ ?
ocean sealBOT
Herels
echo socket
I think just f^n
pallid glade
I think just f^n
nope
pallid glade
f o denotes composite function
vague coral
we know
echo socket
That has nothing to do with what I said
vague coral
The thing I saw back then in abstract algebra class was that :
$$a^{n}$$ with $$ being a law of composition
ocean sealBOT
Herels
silk crystal
guys, how to use latex here?
lone heartBOT
guys, how to use latex here?
finite flax
guys, how to use latex here?
There's already a channel for help with LaTeX #latex-help
lone heartBOT
@silk crystal Has your question been resolved?
maiden glen
.close
alpine sable
slope of the line perpendicular to the line $y=\frac{4}{11}x+8$
echo socket
You mean $y = \frac4{11}x + 8$?
ocean sealBOT
A Lonely Bean
alpine sable
$x = \frac{11}{4}*(y-8), \frac{11y}{4} + \frac{-88}{4}, \frac{11y-88}{4}$
I tried this
alpine sable
You mean $y = \frac4{11}x + 8$?
yes
echo socket
Generally if the slope of a line is k, then the slope of the line perpendicular to it will be -1/k
Use this
alpine sable
Generally if the slope of a line is k, then the slope of the line perpendicular ...
can you explain why that's true
echo socket
There is a geometrical proof iirc
tardy tapir
there is another
echo socket
There is an algebraic one?
Oh there might be actually
Vectors and dot products could be helpful
ocean sealBOT
Dyssrupt
alpine sable
There is a geometrical proof iirc
is it easy to understand it? like how we know 1 + 1 = 2, we can imagine an apple with another apple equal 2 apples
echo socket
**Dyssrupt**
Makes sense
tardy tapir
**Dyssrupt**
with a mod*
echo socket
is it easy to understand it? like how we know 1 + 1 = 2, we can imagine an apple...
It involves drawing two perpendicular lines, say the intersection point is (a, b), then connecting the points (a + 1, b + m1) and (a + 1, b + m2) so that there is a right triangle forming
Then you draw a line which starts from the intersection point and is perpendicular to the first line draw you drew
And form two smaller right triangles
And after applying Pythagorean theorem 3 times you conclude that the product of the slopes of -1
I think I just came up with a proof involving vectors though
frigid mirage
This could be more intuitive
Draw any line (positive slope works best) other than a horizontal or a vertical. Choose any two points on the line, and let's say the rise between the two points is a and the run is b, so the slope of the line is a/b.
Now rotate your paper 90 degrees.
The same two points on the rotated line have rise b and run (-a), so the slope of the rotated line is -b/a.
Thus the product of the slopes, for the two perpendicular lines, is (a/b)*(-b/a) = -1.
https://math.stackexchange.com/questions/519620/explain-why-perpendicular-lines-have-negative-reciprocal-slopes
alpine sable
thank you guys
lone heartBOT
@alpine sable Has your question been resolved?
fervent ferry
hello!
i don't understand why they pick x(0) = 1 in the last line
in the exercise i hed to model those red underlined functions and then solve them.
fervent ferry
this is the exercise https://ocw.mit.edu/courses/18-03sc-differential-equations-fall-2011/resources/mit18_03scf11_ps1_ii_s4_5s/
it's second page
goshhh nevermind i found it written in the problem statement
.close
lone heartBOT
native cloud
Woah.. multivariable calculus
lone heartBOT
Available help channel!
vapid steppe
how to find total distance traveled using position vs time graph
tacit arch
<@&268886789983436800>
wild umbra
<@&268886789983436800>
tacit arch
how to find total distance traveled using position vs time graph
you got spammed, maybe just open a new channel
wary stream
<@&268886789983436800>
vapid steppe
bruh lmfao
tacit arch
.close
lone heartBOT
alpine sable
how to find total distance traveled using position vs time graph
The total distance at t would just be f(t)
vapid steppe
you got spammed, maybe just open a new channel
can’t you just ban them
wild umbra
he cant
median dirge
He did the right thing
tacit arch
Why did they close the channel <:ICANT:1012057045098311781>
to avoid spammer
oh blocked. very well then
median dirge
Hasn't the mod response time increased
Mods are becoming more sapiens than discordiens
naive valley
at least some of the mods are students, probably a busy time of year for them
karmic grove
The total distance at t would just be f(t)
Not if the direction of motion changes
tardy tapir
Mods are becoming more *sapiens* than *discordiens*
fact
tardy tapir
crushed
tacit arch
Imagine spamming
can you not
lone heartBOT
Available help channel!
alpine sable
Hry
dull dove
Send the question bruh
dull dove
What is this
dull dove
So you need to do all operations?
alpine sable
Yes
dull dove
To get 9?
alpine sable
() + - × ÷
You can use any of these
dull dove
For the first one just multiply the first 3 2s and put a bracket around the last 2 and divide them
stable berry
8÷8+8~8+8=9
alpine sable
I need help with
4 4 4 4 4
5 5 5 5 5
6 6 6 6 6
7 7 7 7 7
stable berry
For this one (7÷7)+7+(7÷7)
wary stream
Tbh google a solver... google something like " missing operations solver"
lone heartBOT
For this one (7÷7)+7+(7÷7)
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.
stable berry
Ok mb
dull dove
I need help with
4 4 4 4 4
5 5 5 5 5
6 6 6 6 6
7 7 7 7 7
Don’t you have an idea
From what we’ve said
stable berry
Told u an answer by accident
But u should still able to figure it out for the last 3
alpine sable
I need help with
4 4 4 4 4
5 5 5 5 5
6 6 6 6 6
7 7 7 7 7
Ive done these kind of math before but i get nothing from the ones i typed here
wary stream
dull dove
For most of them you don’t even have to go crazy just know how to utilize brackets
dull dove
Make a channel
stable berry
Make a channel
I did
xavier2024
Occupied
Mb number 9
Help number 9 not number 2
wary stream
Mb number 9
Please don't try to bring your channel attention
stable berry
Please don't try to bring your channel attention
Sorry :< 😞 😓
stable berry
Hmm?
wary stream
I have another question
Ask
alpine sable
Ive got in my math book
continue to use the first 6 digits of Kim Larsen's CPR number, so that the results constantly increase by 1. continue up to 10. Also try to do calculations where the result becomes negative
Didnt get this 🤔
dull dove
Snap the question
alpine sable
Idk how to do that lol
Im just gonna try my best
Theres a example up here
need help?
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
<@456226577798135808> Has your question been resolved?
Nope i still need help
alpine sable
need help?
Yeah
merry depot
what are you trying to do?
oak perch
What symbols are you allowed to add, name all of them
+,-,*, /, (, ). And ? Is that all? Or there are still symbols allowed
Like !, !!, ^,… what among them are allowed too?
alpine sable
continue to use the first 6 digits of Kim Larsen's CPR number, so that the resul...
Im doing this question right now
continue to use the first 6 digits of Kim Larsen's CPR number, so that the results constantly increase by 1. continue up to 10. Also try to do calculations where the result becomes negative
oak perch
Any reference, picture or something, showing what Kim Larsen’s CPR number is
alpine sable
23 10 45 - 06 37
oak perch
Doesn’t make any sense. I am not even sure whether you asked a math question, since those don’t look like math concepts
No any concept related to Kim Larsen I found. According to google he is a musician.
naive sorrel
lol cpr number
alpine sable
lol cpr number
?
naive sorrel
never heard ofi t it sounds funny
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
never heard ofi t it sounds funny
Oh
tribal valve
lone heartBOT
tribal valve
How can I start?
steady mantle
Use the chain rule
tribal valve
On F(s)?
tribal valve
Chain rule = $f'(g(x))(g'(x))$
ocean sealBOT
dabbingpotato
tribal valve
$f(x) = 6e^x$
ocean sealBOT
dabbingpotato
tribal valve
$g(x) = \frac{s}{20} - \frac{s^2}{2400}$
ocean sealBOT
dabbingpotato
tribal valve
right?
steady mantle
Yes, thats fine, but not the chain rule I was talking about
last ether
Wouldn't this be better as a differential
steady mantle
s changes with time, so we have s = s(t). We want d/dt F(s(t))
steady mantle
the relevant s(t) is given in the question
tribal valve
s(t) = 20t + 50?
steady mantle
Sure, I guess that works, though you should probably think of it as s(t) = 50, d/dt s(t) = 20
(maybe it's better to rename t)
steady mantle
if s depends on t, F also depends on t. use the chain rule to figure out what d/dt F(s(t)) is
steady mantle
yes
tribal valve
So s(t) = 50
s'(t) = 20
Would we have to use chain rule twice
To find the derivative of f(s)
steady mantle
We've used the chain rule once to find d/dt F(s(t)) = F'(s) * s'(t)
tribal valve
But we don't know what F'(S) is
steady mantle
**dabbingpotato**
Then to differentiate F(s), we would have to use the chain rule like here ^
tribal valve
So we do have to use the chain rule to find F'(s)
steady mantle
yes
tribal valve
$f(x) = 6e^x$ and $g(x) = \frac{s}{20} - \frac{s^2}{2400}$
ocean sealBOT
dabbingpotato
tribal valve
$f'(x) = 6e^x$ and $g'(x) =400s' - 2400^2s'^2$
ocean sealBOT
dabbingpotato
tribal valve
am i doing this right?
steady mantle
g'(s) is a derivative with respect to s, no t's should be involved
ocean sealBOT
dabbingpotato
tribal valve
is that better
steady mantle
I get $g'(s) = \frac{1}{20} - \frac{2s}{2400}$
ocean sealBOT
Toblerone
tribal valve
dont we have to use the quotient rule?
steady mantle
the denominators are constants
tribal valve
**dabbingpotato**
.
steady mantle
yes
tribal valve
now we get a pretty big clump of stuff
$6e^{\frac{s}{20} - \frac{s^2}{2400}} \times \frac{1}{20} - \frac{2s}{2400}$
ocean sealBOT
dabbingpotato
tribal valve
now do we just input 50 for s?
steady mantle
yes
steady mantle
We've used the chain rule once to find d/dt F(s(t)) = F'(s) * s'(t)
then substitute into this ^
tribal valve
oh lmao i forgot this was just f'(s)
s(t) = 50
s'(t) = 20
if we input 50 in for s
1.24797000523
thats what we get
and then multiply by 20
24.9594001046
thats not an answer choice 
what did i do wrong
steady mantle
**dabbingpotato**
put parenthesis around the second part
tribal valve
oh wait
you're right
it was 4.2987889063
so B
damn that took long
thanks so much 🙏
steady mantle
you're welcome
tribal valve
.close
lime bobcat
Consider the hyperbola
x²+y²+4xy-8x-4y-2=0.
Calculate the conjugate diameter in the direction of y=4x.
The worked solution says if p, q are the slopes of conjugate diameters, then pq+2(p+q)+1=0. Since p=4, then q=-3/2 so the conjugate diameter is y-2=-3/2x.
My question is where "pq+2(p+q)+1=0" comes from.
I haven't found that formula anywhere outside this solution I looked a lot round the internet. Everything I find is related to equilateral hyperbolas.
The worked solution also uses a similar formula (p-q)/(1+pq)=1 which holds when two conjugate diameters form a 45° angle; and the formula 2m²+0m-2=0 for calculating the slopes of the axes.
Where all these formulas relating slopes come from? I can't find them anywhere I tried everything.
lone heartBOT
Consider the hyperbola
x²+y²+4xy-8x-4y-2=0.
Calculate the conjugate diameter i...
@lime bobcat Has your question been resolved?
lime bobcat
<@&286206848099549185>
lime bobcat
<@&286206848099549185>
lone heartBOT
@lime bobcat Has your question been resolved?
lime bobcat
The use of pq+2(p+q)+1=0 is on pic 2 part f) and the use of (p-q)/(1+pq)=1 is on pic 2 part g).
lime bobcat
Sad. Thanks for your feedback anyway! I'm considering looking for books exclusively on conics.
lone heartBOT
@lime bobcat Has your question been resolved?
daring creek
lone heartBOT
daring creek
I tried solving this using L'hopital
the answer is supposed to be 6 * sq root (3)
Here is how I worked it out:
bitter kestrel
lilac knot
lone heartBOT
@lilac knot Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
mint oxide
Help I don't understand a lot of these...
lone heartBOT
Help I don't understand a lot of these...
mint oxide
My teacher let us review our paper, I am mostly struggling on the a and b since I wasnt able to take note during the lesson
sour harbor
Hello can someone help me with 4 Questions i have left, this is 1st with answer but noy sure
Q
Not sure
lone heartBOT
@mint oxide Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
karmic fossil
hey can i have some help with measurements, im planning to build a reptile enclosure and im wondering if my measurements are ok \
alpine sable
hey can i have some help with measurements, im planning to build a reptile enclo...
I can help you
What exactly do you need
karmic fossil
i just need someone to check if my measurements are correct
because when i was measuring the air vents the measurements just didnty= fit
lone heartBOT
@karmic fossil Has your question been resolved?
lone heartBOT
@karmic fossil Has your question been resolved?
lone heartBOT
@karmic fossil Has your question been resolved?
lone heartBOT
@karmic fossil Has your question been resolved?
drifting seal
maiden glen
the text in the picture is illegible at that resolution
and we can't help check, because that's to do with the physical process of actually measuring
silk haven
lone heartBOT
silk haven
how do I do this
steady mantle
take logs and solve a linear system for log(a) and b
(alternatively, its also ok to work with the exponential form)
wanton pebble
native cloud
And then substitution!
amber tusk
yow can someone dm me their solving steps (asking for a friend)
lone heartBOT
yow can someone dm me their solving steps (asking for a friend)
Please read #❓how-to-get-help
tardy tapir
This channel is already occupied, please find yourself a new one! @amber tusk
amber tusk
okayyeye
lone heartBOT
@silk haven Has your question been resolved?
somber steppe
Hey so I'm stuck at this question, I really don't know how to start: Let $M$ be a matrix in $Mat(n × n, K)$ such that
$M^2 = 5M + I$
where I denotes the identity matrix. Show that M is necessarily invertible.
What is its inverse?
ocean sealBOT
froud
alpine sable
what have you tried so far
somber steppe
I know I have to show that M times something else is equal to I, so I tried doing $M^2 - 5M = I$, then I factored out M but I'm not even sure its legal $M(M-5I) = I$ and then I dont really know what to do
ocean sealBOT
froud
pallid scarab
Well you can do it in reverse to check but yes
somber steppe
like what kind of operations can you do? distributivity, additivity? because I know the order counts
pallid scarab
you can check that M(M-5I) = M*M - 5M = M^2 - 5M
and yes distributivity is allowed for matrices
somber steppe
but isn't the order important for matrix multiplication?
pallid scarab
just don't forget that when factoring, the "1" for matrices is "I"!
pallid scarab
but isn't the order important for matrix multiplication?
it is
however, when only dealing with powers of M, you have commutativity
lone heartBOT
lone heartBOT
Available help channel!
charred pier
lone heartBOT
charred pier
.close
flat roost
How would i do d/dt (r^2h)? is it 2r dr/dt h + r^2 dh/dt?
lone heartBOT
How would i do d/dt (r^2h)? is it 2r dr/dt h + r^2 dh/dt?
tardy tapir
correct.
turbid stratus
lone heartBOT
turbid stratus
may i ask what the equations on top are for?
i dont really understand how they're related to the question
wind cloak
Well how else are you gonna find f(x - 3) and the others
lethal belfry
i dont really understand how they're related to the question
They are functions
turbid stratus
ohh icic
lethal belfry
Treat the x-3 for instance as a variable u and try to solve it
turbid stratus
ohh
lethal belfry
I also suggest you revise compositions (in maths), doens't seem like you're very good at it yet
flat roost
lone heartBOT
flat roost
for q9, do i set V = 1/3 pir^2h
dV/dt = 3
dh/dt = dh/dV x dV/dt or is there a better way
tardy tapir
why are you differentiating h with respect to V?
flat roost
to get dh/dt
tardy tapir
for q9, do i set V = 1/3 pir^2h
but cant you just differentitate this w.r.t time?
tardy tapir
yeah you can also do that, but you know dr/dt not dr/dv
tardy tapir
ok, try with your approach and show
flat roost
to the problem is i dont know how to find dh/dV
tardy tapir
now try differentiating the equation with respect to t
flat roost
1/3 pi r^2h?
tardy tapir
yeah
flat roost
2r dr/dt h + r^2 dh/dt
tardy tapir
now put the values in
flat roost
but what is dr/dt
tardy tapir
where R and H are radius and height of cone
and r and h are radius and height of cone formed by water
(by similar triangles or tan(theta))
tardy tapir
r = Rh/H
flat roost
yep
tardy tapir
i dont think you can do anything if the dimensions are not given.
you need to express r in terms of h to find dr/dt
<@&286206848099549185> what do you guys think?
hey, this channel is occupied, please pick a new channel. refer #❓how-to-get-help
tacit arch
you need to express r in terms of h to find dr/dt
i think you can assume the cone is 45 degrees
flat roost
i think you can assume the cone is 45 degrees
why?
tacit arch
usually given in your book. look for a worked example in this chapter with cones
flat roost
i'm not sure which chapter has cones
tacit arch
first check the same chapter as the problem
flat roost
this is the IB AA HL book and doesnt cover much about geometry
ok the only cone problem i found
tardy tapir
i think you can assume the cone is 45 degrees
is it right conical?
tacit arch
yea it looks that way from example 38
i was wrong about the 45 degree cone
it's this as dyssrupt said
tardy tapir
if the upper angle is 90 then you can find r in terms of h
flat roost
how do i continue frm that though
tardy tapir
tan(45) = r/h
flat roost
= 1?
tardy tapir
yeah
flat roost
so r = h..?
tacit arch
i havent learnt about cones yet so i dont know much about them sorry
if you don't understand something in a problem, the first thing to do before even the problem itself is to learn about that something
in this case cones
math books assume you learned a lot of things before
flat roost
math books assume you learned a lot of things before
yeah
tacit arch
<https://www.cuemath.com/geometry/right-circular-cone/>
learn about cones here
flat roost
<https://www.cuemath.com/geometry/right-circular-cone/>
wait so this question assumes a right circular cone?
tacit arch
yea it looks that way from example 38
.
flat roost
But i dont know if one example can justify another
tacit arch
then you can ask your teacher if you don't trust us
flat roost
then you can ask your teacher if you don't trust us
i'm self learning this unfortunately
so conclusively, this question assumes certain conditions..?
tacit arch
i don't know what more you want from us
we already told you everything you need to know, but just won't trust us
so i don't know how else i can help
good luck
glossy hill
How do i make the point A in (-14 ; 11 )
lone heartBOT
How do i make the point A in (-14 ; 11 )
glossy hill
I m mean wich transformation ?
lone heartBOT
@glossy hill Has your question been resolved?
lone heartBOT
@glossy hill Has your question been resolved?
lone heartBOT
@glossy hill Has your question been resolved?
ebon sparrow
How do i make the point A in (-14 ; 11 )
Can you be more specific on what are you trying to do?
ebon sparrow
I m mean wich transformation ?
do you mean transformation rules?
gloomy ferry
friend of an opp is an opp
lone heartBOT
friend of an opp is an opp
ebon sparrow
?
lofty heart
friend of an opp is an opp
smart words
wary stream
friend of an opp is an opp
One what does this mean
Two, don't open a help channel for non math related things
.close
lone heartBOT
gloomy ferry
can i get general life advice here? or even general math help? sorry im new here
echo socket
Friend of an opponent is an opponent? 
echo socket
can i get general life advice here? or even general math help? sorry im new here
#❓how-to-get-help Clearly states that you can ask only math-related questions in help channels
gloomy ferry
oh oken thanks
wary stream
can i get general life advice here? or even general math help? sorry im new here
Not in a help channel
ebon sparrow
it's closed already
gloomy ferry
oh
wary stream
can i get general life advice here? or even general math help? sorry im new here
.... You're new but joined the server in Dec 2022?
gloomy ferry
ill get anti as ever
echo socket
You will get what?
gloomy ferry
listen i dont deal with disheartening speeches
under what channel is ergodic theory?
echo socket
Well there is #dynamical-systems channel
lone heartBOT
Available help channel!
foggy current
lone heartBOT
remote heron
I'm not sure how angles are adding up
please delete your messages and open your own channel
boreal plaza
please delete your messages and open your own channel
oh sorry the channel said to open my question here
remote heron
oh sorry the channel said to open my question here
yea, its been a discussion for some reason that help-0 is shown there
honest mistake
boreal plaza
oh
pallid scarab
You will need to reindex your sum at some point so all terms are regrouped under the same power of x
foggy current
You will need to reindex your sum at some point so all terms are regrouped under...
Ok take 2
ocean sealBOT
jan Niku
$J_1 ' (x) = \sum _1 \frac{ (-1)^{n+1} x^{2n} (2n+1) }{ n! (n+1)! 2^{2n+1} }$
remote heron
yea?
foggy current
**jan Niku**
```latex
$J_1 ' (x) = \sum _1 \frac{ (-1)^{n+1} x^{2n} (2n+1) }{ n!...
Yeah
ocean sealBOT
jan Niku
so $J_1 ' (x) = \sum _0 \frac{ (-1)^{(n+1)} x^{2(n+1)} (2(n+1)+1) }{ (n+1)! \qty((n+1)+1)! 2^{2(n+1)+1} }$
foggy current
**jan Niku**
```latex
$J_1 ' (x) = \sum _1 \frac{ (-1)^{n+1} x^{2n} (2n+1) }{ n!...
Wait why's the power of -1 n+1 instead of just n?
remote heron
I re-indexed
hopefully correctly 
change the starting index of the sum to 1 less
and just add 1 to each index
so everywhere you had an n, goes n+1
foggy current
But the power of the -1 stayed as n+1 after reindexing
remote heron
oh, my bad, i wrote the original wrong 
remote heron
**jan Niku**
```latex
$J_1 ' (x) = \sum _1 \frac{ (-1)^{n+1} x^{2n} (2n+1) }{ n!...
sorry, this should just be (-1)^n
youre right
foggy current
Ok I was a bit confused there
remote heron
**jan Niku**
```latex
so $J_1 ' (x) = \sum _0 \frac{ (-1)^{(n+1)} x^{2(n+1)} (2(...
okay so back here
foggy current
**jan Niku**
```latex
so $J_1 ' (x) = \sum _0 \frac{ (-1)^{(n+1)} x^{2(n+1)} (2(...
Makes sense to me
remote heron
$J_1 ' (x) = \sum _0 \frac{ (-1)^{(n+1)} x^{2n+2} (2n+3) }{ (n+1)! (n+2)! 2^{2n+3} }$
ocean sealBOT
jan Niku
remote heron
man i wish we just had the one differentiation huh
ocean sealBOT
jan Niku
$J_1 '' (x) = \sum _2 \frac{ (-1)^n x^{2n-1} (2n+1) (2n) }{ n! (n+1)! 2^{2n+1} }$
remote heron
$J_1 '' (x) = \sum _0 \frac{ (-1)^{(n+2)} x^{2(n+2)-1} (2(n+2)+1) (2(n+2)) }{ (n+2)! ((n+2)+1)! 2^{2(n+2)+1} }$
foggy current
Wait shouldn't the starting number of J_1'' be 1?
remote heron
sorry i guess i should say youve probably already done this but i want to try to help with the problem as review for my own classes 
remote heron
Wait shouldn't the starting number of J_1'' be 1?
nah
remote heron
**jan Niku**
```latex
$J_1 ' (x) = \sum _1 \frac{ (-1)^{n+1} x^{2n} (2n+1) }{ n!...
im differentiating this
ocean sealBOT
jan Niku
$J_1 '' (x) = \sum _0 \frac{ (-1)^{(n+2)} x^{2(n+2)-1} (2(n+2)+1) (2(n+2)) }{ (n+2)! ((n+2)+1)! 2^{2(n+2)+1} }$
foggy current
Ok I got to go for a bit hope this channel doesn't close
remote heron
how longs a bit
$J_1 '' (x) = \sum _0 \frac{ (-1)^{n} x^{2n+3} (2n+5) (2n+4) }{ (n+2)! (n+3)! 2^{2n+5} }$
ocean sealBOT
jan Niku
$J_1 '' (x) = \sum _0 \frac{ (-1)^{n} x^{2n+3} (2n+5) (2n+4) }{ (n+2)! (n+3)! 2^{2n+5} }$
lone heartBOT
@foggy current Has your question been resolved?
foggy current
how longs a bit
Half an hour
Wait I think I have just stumbled upon a solution
I've confirmed it's a valid solution
foggy current
You will need to reindex your sum at some point so all terms are regrouped under...
@pallid scarab Thanks a lot for the suggestion!
.close
spiral pumice
"Now consider the function h(x) = abs(x+2)+1 and try zooming in on the point (-2,1) by using the following windows:
What do you notice? This is an example of a function that is NOT “locally linear” at the point (-2,1)."
spiral pumice
how do i put that into a graphing calc? i have never seen "abs" before
pallid scarab
abs(x) = max(x,-x)
if x is positive, you take abs(x) = x
otherwise, you take abs(x) = -x
Another notation is |x|
dull dove
Absolute value
lone heartBOT
lone heartBOT
Available help channel!
keen elk
what is reference angle of -10pi/3
lone heartBOT
what is reference angle of -10pi/3
keen elk
is it pi/3 or am i trippin
spiral pumice
that seems fr
somber eagle
yeah
feral pebble
yes
fossil mulch
could someone help me moved this logaritham equation to the arrow
wary stream
could someone help me moved this logaritham equation to the arrow
The log connects to the end of the red line?
wary stream
First, I suggest removing the bounds
fossil mulch
whats bounds
wary stream
The -4 <= x <= 2 part, that restricts the graph between those two x values
If you are trying to translate that green line, having that restriction isn't going to help
fossil mulch
but restriction can help to make it small i removed it them
wary stream
If you're trying to translate that line, your translated line will still be in between -4 and 2 because of that restrictions
fossil mulch
.close
gleaming steeple
Hello, in Richard Hammack's "Book of Proofs" can't understand intersections with all sets on xy-plane. I know there is written the reason, but could someone explain, because I still don't get it:
1)How and why is the point (2,0) the only one intersection for these sets?
2) Why any other point, for example (1,0) on x-axis is not intersection as well?
gleaming steeple
lone heartBOT
@gleaming steeple Has your question been resolved?
lone heartBOT
@gleaming steeple Has your question been resolved?
gleaming steeple
.close
native sierra
Can someone explain how to do this
lone heartBOT
Can someone explain how to do this
alpine sable
Can someone explain how to do this
Do you know how to do subtraction
green shoal
can someone help me with taylor series please? I understand like how it's an infinite polynomial to approximate a function, but I don't understand like how you make one, or why f(x) ≈ f(a) + f'(a)(x - a)/1! + f''(a)(x - a)^2/2! + f'''(a)(x - a)^3/3! + ...
naive valley
"why you make one" - there can be many reasons, but a major one in math and in physics and other sciences, is to get a polynomial that approximates your function
polynomials are easier to work with than general functions
the taylor series is an "infinite" polynomial, but if you cut it off at some point, it becomes an ordinary polynomial
and the more terms you use, the better your approximation is
green shoal
"why you make one" - there can be many reasons, but a major one in math and in p...
how you make one not why
naive valley
ah, i saw how and why and misinterpreted what you were asking haha
proven leaf
you mean how do you derive the formula or how to create a polynomial given a function?
naive valley
well, the "how" is right there in the formula
the n'th term is (x-a)^n times a coefficient, and that coefficient is the n'th derivative of the function, evaulated at a, and then divided by n!
as far as why that's the formula, that's maybe beyond the scope of help channels, but it is explained in pretty much any calculus book
green shoal
Is it multiplied by n! because of the power rule
proven leaf
Is it multiplied by n! because of the power rule
1/n!
this cancels out when you iteratively apply the power rule
green shoal
cuz I'm watching 3b1b, and I don't understand why he keeps taking the derivative of higher order
green shoal
as far as *why* that's the formula, that's maybe beyond the scope of help channe...
I see, thank you
I'll try and find one at a library somewhere
naive valley
I'll try and find one at a library somewhere
i bet it's covered somewhere on khan academy too, if you just want a free resource
they're usually pretty good on most subjects
green shoal
what calculus level is this?
naive valley
in the usa it's typically calculus 2, but that probably varies around the world
green shoal
is this something covered in highschool at some point
naive valley
possibly, depending on the calculus class
green shoal
Alright thanks! Well I'll go ask the older teachers and I'll refer to this khan academy you speak of
I think what I don't understand is why it's the formula
naive valley
this seems like a promising start: https://www.khanacademy.org/math/ap-calculus-bc/bc-series-new/bc-10-11/v/maclaurin-and-taylor-series-intuition
green shoal
thank you very much!
well I think I'm good to go with this then, as you mentioned this is beyond help channel topics so I'll close it. Have a good day
.close
lament basalt
About converting vertex equation to quadratic equation and back to the vertex
lament basalt
I wanted to convert this into quadratic equation first, so that I can also revert it back to vertex through steps bcs I wanted to learn the process
So this is what I did (the crossed out steps are also included as well sry I crossed them out too early)
The arrow line is the continuation to 2nd image
lament basalt
At the very first or above part of this image, it's
y = 3(x^2 - 2x +1) + 3
lament basalt
Can someone help me find my mistake here? Thanks bcs it's not leading to this equation
left isle
what is $\frac{-6}{2(3)}$ ?
ocean sealBOT
Wumbo
left isle
this is where the mistake is
lament basalt
what is $\frac{-6}{2(3)}$ ?
From a (b/2a)^2 where a is cut out along with ax^2 + bx
Which then becomes
a[x^2 + bx/a + (b/2a)^2]
Then outside of that, there's
- c - a(b/2a)^2
terse raptor
did you check the values
lament basalt
did you check the values
Yeah
lament basalt
did you check the values
Oh shit no nvm yeah I didn't see it
lament basalt
**Wumbo**
I got this part with an exponent wrong
Cuz they're both 6,and when exponentiated, they become 36, then 1
Damn hahaha
left isle
yeah the value of the whole thing is just -1, then you square it
lament basalt
Yeah I see thanks
lament basalt
yeah the value of the whole thing is just -1, then you square it
May I also ask one thing?
left isle
of course
lament basalt
How did you become better at math?
left isle
lots of practice
lots and lots and lots of practice
it's hard to see our own mistakes though. sometimes another set of eyes if really helpful
lament basalt
it's hard to see our own mistakes though. sometimes another set of eyes if reall...
Yeah
left isle
especially when it's something as simple as a missing negative sign or incorrect arithmetic
lament basalt
Yeah it's like hidden
left isle
our brains are really good at looking over our own mistakes
mhhm
it's tough
best advice i could give would be to just start the problem from scratch on a new piece of paper
go through it again, and sometimes in the middle of the problem you'll realize your mistake
sometimes
lament basalt
best advice i could give would be to just start the problem from scratch on a ne...
I see
Bcs I'm trying to master algebra, log, and trig or at least learn them before college
In which I only have prolly more than half a month before college basically I want to learn them before taking calculus and it's rly tough
Idk if I'll make it but I'm just keeping reviewing stuff
left isle
i used youtube a ton when i was getting my degree. watching other people do and explain math really helps me
lament basalt
I don't want to suffer in college like they say you need good foundation in math
left isle
sometimes they just have a really good way of explaining certain properties that really just click
lament basalt
i used youtube a ton when i was getting my degree. watching other people do and ...
Same but sometimes I tend to deeply think why this happens or why this becomes a(x^2 + bx vertex eq. earlier
lament basalt
sometimes they just have a really good way of explaining certain properties that...
Yeah
I'm pretty scared on college honestly
left isle
Same but sometimes I tend to deeply think why this happens or why this becomes a...
you saying this makes me think that you will do just fine in math.
asking "why?" is essential for truly understanding the math you're doing
and you always have this discord to fall back on
i wish i had had this when i was going through school
lament basalt
Yeah and I just kind of doing problems so that that logic will be remembered in my head
lament basalt
i wish i had had this when i was going through school
But you had ppl irl explaining it to you, right?
Your colleagues
lament basalt
asking "why?" is essential for truly understanding the math you're doing
I rly hope I'll be able to learn or even master them before college hahahaha damn but yeah I want to
Ig I'm not the only one that makes mistakes over and over XD
left isle
i mean....yes and no. half of my college was online and it was the latter half, so the complicated stuff i had to learn on my own, it was the basic stuff that was taught to me in person
i don't think anyone expects you to master certain math topics before college, the learning process is about making mistakes so that you can learn from them
left isle
Ig I'm not the only one that makes mistakes over and over XD
literally this.
i still make silly mistakes all the time, but it's the conceptualization that's really important. understanding why certain things the way they are is more important than getting the right answer. as long as you understand the process, you'll do just fine.
like, oh duh, -6/2(3) is -1, but you fully understand that you can convert vertex form to quadratic and back, and you know how to do it and you know what both forms are useful for
that's the important part
lament basalt
i don't think anyone expects you to master certain math topics before college, t...
The professors don't expect that?
left isle
i mean they're gonna dock you for getting a question wrong
but if you understand a topic, you won't be getting every question wrong
that and the more often you do the same types of arithmetic, the better you'll be at catching your own mistakes
sure i make mistakes all the time, but i'm MUCH better at catching them then I was in high school.
lament basalt
sure i make mistakes all the time, but i'm MUCH better at catching them then I w...
I see, I appreciate your tips and advices bro
left isle
wheat isle
- Find an equation for the tangent line to x^2/3 + y^2/3 = a^2/3 at a point (x1, y1) on the curve,
with x1 cannot equal 0 and y1 cannot equal 0. (This curve is an astroid.)
lone heartBOT
@wheat isle Has your question been resolved?
wheat isle
.close
rancid hatch
can someone explain this to me
lone heartBOT
can someone explain this to me
umbral star
this is just the seperation of variables method, is there some specific part you don't understand?
rancid hatch
this is just the seperation of variables method, is there some specific part you...
im not sure how they get to the xe^x - ex and where does the 1/2 come from
im not sure why there is a minus sign there
rancid hatch
and the 1/2 is from a u substitution
what method do u use for this substitution
umbral star
try u=2t
umbral star
so first $du=2dt$, which means that $dt=\frac{1}{2}du$
ocean sealBOT
qianqian07
umbral star
so from here, we have that $\int e^{2t},dt=\int \frac{e^u}{2},du$
ocean sealBOT
qianqian07
umbral star
👍
rancid hatch
.close
daring totem
lone heartBOT
daring totem
!status
lone heartBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
1
umbral star
do you know the standard form of the equation of a circle?
daring totem
Yes
umbral star
can you write it out?
daring totem
(x-h)^2 + (y-k)^2 = r^2
i dont know how to write the latex
( (x - h)^2 + (y - k)^2 = r^2 )
ocean sealBOT
renato
umbral star
so if the point A is on the circle, then (x, y) = (-1, 1) must satisfy that equation
so $(-1-h)^2+(1-k)^2=r^2$
ocean sealBOT
qianqian07
umbral star
and we can do something similar with the other two points
then, we have a system with 3 equations and 3 variables, which is possible to solve
umbral star
in the first equation of the expanded form, it should be +2h, not -2h
lone heartBOT
@daring totem Has your question been resolved?
umbral star
check the last line
umbral star
I think here you also changed the -5h to -6h in the last line
and also we want to have a single solution to the system
not just write one variable in terms of another
since it is a system of two linear equations, we can find an explicit solution
daring totem
wait a second please
lone heartBOT
@daring totem Has your question been resolved?
spare forum
lone heartBOT
spare forum
Question 7
ocean sealBOT
lone heartBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
Show your work, and if possible, explain where you are stuck.
@spare forum Has your question been resolved?
Available help channel!
warped topaz
To get the velocity at a point on a parametric I use √(x'(t)^2 + y'(t)^2) right?
warped topaz
Like I get the derivatives of x(t) and y(t), then sub in the values of t
warped topaz
I dont want it in the form of a vector though, I just want a number
A is at (0, 4)
warped topaz
To get the velocity at a point on a parametric I use √(x'(t)^2 + y'(t)^2) right?
I did this question already and I think I did this ^^ to get the answer, but I dont remember why
vale wigeon
on whose authority do you have it that the answer to part a is supposed to be a number and not a vector?
tardy stag
i would be upsetti spaghetti if they asked for a velocity and wanted speed instead
warped topaz
This is an exam paper hahaha so rest in peace the people who took this exam I guess
vale wigeon
ok so then the problem is full of tricks and lies
and is written in an intentionally confusing manner to deceive you and other test-takers and bring down the average and median scores
dense dove
lone heartBOT
dense dove
My working out:
But my answer is wrong
I've done the workings multiple times over and I can't see why I am wrong
If anyone could let me know what I've done wrong that would be much appriciated
near apex
Because you haven't considered all the terms that'll form terms of x.
For example, terms of x from first, and constant from second would still form terms of x.
near apex
BTW, YOU ARE UNNECESSARILY COMPLICATING IT. TRY TO EQUATE WITH THE CONSTANT TERM.
Shit. Sorry about caps lock.
dense dove
Nah you're good LMAO
near apex
yeah I did that and worked it through and it led me to 0 = 0 💀
Shouldn't have. Show me the working.
near apex
oh like (nx)^1?
Yes, and constant from other one.
dense dove
Shouldn't have. Show me the working.
Give me a second I have to write it up from my book onto MS Whiteboard
Sorry not 0 = 0, but n = 0:
Hey @near apex, just letting you know this is here.
near apex
Hey <@1116326425088241714>, just letting you know this is here.
Good thinking. I forget. LOl
No. You aren't supposed to take either of them alone. Consider both cases and their sum should be 100x.
Think about it.
There are two ways you can get terms of x.
dense dove
No. You aren't supposed to take either of them alone. Consider both cases and th...
Sorry, could you clarify what you mean by "both cases" I'm not exactly sure what you're referring too.
near apex
You take the constant term from (5+nx)^2. Let's say it's b.
You take the x term from (1+3x/5)^n. Let's say it's cx.
You get bcx.
Now, You take the constant term from (1+3x/5)^n. Let's say it's e.
You take the x term from (5+nx)^2. Let's say it's fx.
you get efx here.
Totally, bcx + efx = 100x
Because, terms of x will be added after all. Right?
So, you should be considering total coefficient of x.
Does that make sense, yet?
dense dove
I'm trying to make sense of it give me a moment 😂
What do you mean by taking the constant term from (5+nx)^2.
As in, if I were to find the sum of (5+nx)^2 it would give me b?
near apex
What do you mean by taking the constant term from (5+nx)^2.
As in, if I were to...
Constant term from (5+nx)^2 refers to the term which won't have any x when you expand (5+nx)^2.
near apex
For example, $(5+nx)^2 = (5)^{2} + (nx)^{2} + 2\cdot (5)\cdot (nx)$
ocean sealBOT
Enemagneto
dense dove
How so? Surely if n was, lets say 5, you would get 125 as the constant?
Or am i thinking about this wrong
I mean I know we are told in the question that the constant term from the binomial expansion is 25 and the x^1 term has a coefficient of 100
near apex
How so? Surely if n was, lets say 5, you would get 125 as the constant?
How would you get 125?
try expanding (5 + 5x)^2
dense dove
Oh I see becuase the n is always connected to the x term so you can't multiply non-like terms
near apex
Can't multiply? What do you mean?
In (a+bx)^2: you'll only get the constant term a^2. All other terms will have x or x^2.
near apex
**Enemagneto**
Like here.
dense dove
Yeah that's what I was trying to say 😭😭 I understand that part now, thanks
dense dove
You take the constant term from (5+nx)^2. Let's say it's b.
You take the x term...
Wouldn't bcx + efx be = [constant term], + 100x?
near apex
Wouldn't bcx + efx be = [constant term], + 100x?
No.
You are adding two terms of x. How can you get constant in the sum ?
Can (5x + 6x) be anything extra than 11x ?
dense dove
yeah idk what just went through my head I need to go back to year 1 algebra 💀💀
I'm confused as to how I solve for n though
dense dove
Just write terms and it'll just be a linear equation in n.
So just fully expand (5 + nx)^2 and (1 + 3/5x)^n?
And collect like terms
near apex
Umm... No.
near apex
Try to think. You need to figure out how the term of x in LHS and equate that with the term of x in RHS.
near apex
I mean I have this mark scheme but I don't really understand what it has done:
They are doing exactly what i told you.
See. You have these two expressions being multiplied.
$(5 + nx)^{2}$ and $\left(1 + \frac{3x}{5}\right)^{n}$.