bro stop
#help-28
lunar veldt
sharp vine
Yes, if a point lies on a curve it means that its coordinates must satisfy the equation of the curve.
flint marsh
someones alr using this
Wdym?
lunar grove
Yh is it acceptable to do that or do I need to eliminate m
lunar grove
And then rearrange to form the equation
flint marsh
this room is occupied by <@584433588825620481>
So how to make my own channel?
hasty sail
So how to make my own channel?
sharp vine
You just have to show that this equality holds.
lunar grove
The markscheme derived the equation ig?
By eliminating m
Ig that's just a way to go about it eh?
sharp vine
Yes, it's possible, because we're supposed to prove it if m varies.
So it doesn't depend on m.
lunar grove
Also got a qucik question and ts kinda random and basic
But i want to ask
We got a locus
In parametric form
So like a circle
Simple example
X=costheta y=sin theta
And then dy/dx can be found by doing dy/dtheta x dtheta/dx
Ik the algebra works completely
What's like the concept tho like intuitively
Ofc doing it directly makes sense to me where u differintiate eq of a circle
And sub in those values
sharp vine
What's like the concept tho like intuitively
It's more useful dealing with implicit functions
I mean, when you can't directly solve for y in terms of x (or whatever the variable is)
And what you said is called chain rule
lunar grove
Yh yh ik it's chain rule haha but idk was kinda weird to think abt
But sure ig the algebra works fine
sharp vine
Yeah, notice that dy/dtheta x dtheta/dx is just dy/dx in fact
lunar grove
Yh yh ik ik
high cradle
Yh yh ik ik
There's a 3 blue one brown video explaining the intuition behind the chain rule
You could probably apply a modified version of that intuition to your specific case
The video is introductory level but I loved watching it personally anyway
9 minutes in is chain rule
full forumBOT
full forumBOT
Available help channel!
lucid cairn
is 61.5 correct
full forumBOT
is 61.5 correct
lucid cairn
im hvin doubts
robust slate
is 61.5 correct
Yeah
full forumBOT
full forumBOT
Available help channel!
shell dome
help 💔 🥀
shell dome
ping me when someone's here
full forumBOT
ping me when someone's here
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
shell dome
OHH okay thanks, lemme post it rq , it is a RLLY dumb problem btw so just don't judge 😔
√200y^4
lemme send my steps rq
glossy valveBOT
@ember solstice
ember solstice
<@751533372890677398>
Is that the question?
shell dome
√10^3 * y^4
√10^2 * 10 * y^2 * y^2
√10 * 10 * y * y
i finally got:
10y√10y
and ik its wrong since chatgpt said so but i CAN'T figure out what is wrong
ember solstice
√10^3 * y^4
√10^2 * 10 * y^2 * y^2
√10 * 10 * y * y
i finally got:
10y√10y
an...
How did you change $200 \to 10^3$?
glossy valveBOT
@ember solstice
ember solstice
√10^3 * y^4
√10^2 * 10 * y^2 * y^2
√10 * 10 * y * y
i finally got:
10y√10y
an...
Also, can you write your work on a paper? It's hard to understand it in text.
ember solstice
Also, your simplification of $\sqrt{y^2 \times y^2}$ seems off.
glossy valveBOT
@ember solstice
shell dome
Also, your simplification of $\sqrt{y^2 \times y^2}$ seems off.
ohh
what's wrong about it?
so that i can fix it
ember solstice
what's wrong about it?
You changed $\sqrt{y^2 \cdot y^2} \implies \sqrt{y} \cdot y$. \
But both $y$s should have come out of the square root.
glossy valveBOT
@ember solstice
shell dome
oh yeah, since square root of y^2 is y right?
ember solstice
100 * 2 * y * 2 * 2
This is not proper simplification of 200.
shell dome
chat gpt told me that i had to change anything squared to the base thing
so i started oding that w equations
ember solstice
chat gpt told me that i had to change anything squared to the base thing
That happens when take the base thing out of the square root. But you didn't do that here. Does that make sense?
shell dome
so if i take the y outside the square root, THEN i have to just remove the exponent?
wai but for previous problems i did, it were different
let me look for one of them really quick
shell dome
That happens when take the base thing out of the square root. But you didn't do ...
So far for this problem
It’s like that
And usually the numbers outside the square root are squared
Or cubed
Or quadrupled I think that’s what we call smth with ^4
ember solstice
So far for this problem
Here, some of the ys should have come out of the square root.
shell dome
That happens when take the base thing out of the square root. But you didn't do ...
so in here, wai wha do i do next
teh problem, so far it's √10 * 10 * 2
ember solstice
teh problem, so far it's √10 * 10 * 2
$$\sqrt{10 \times 10 \times 2}$$
Can you rewrite $10\times10$ to have an exponent?
glossy valveBOT
@ember solstice
glossy valveBOT
@ember solstice
shell dome
Smth like this 😭
shell dome
That happens when take the base thing out of the square root. But you didn't do ...
waitt, how do we know whether or not we're going to take something out of the square root or not
ember solstice
Smth like this 😭
You no longer need to factor this because you can directly use the exponent to help bring it out of the square root.
ember solstice
waitt, how do we know whether or not we're going to take something out of the sq...
It must have ...^2
shell dome
OHH OKAYY
So can't we bring the 10 square, and the two y squares out of hte square root?
that leaves two by itself then
is that the answer
ember solstice
Once you take the ...^2 out of the square root, you should drop the exponent.
ember solstice
You should only drop the ^2 exponents.
ember solstice
You should only drop the `^2` exponents.
In general, if you take something out of the square root, its exponent should be divided by 2.
shell dome
shell dome
In general, if you take something out of the square root, its exponent should be...
Ohh okay
echo marsh
yes
shell dome
okay so overall, from what i did in the whole question wai i'll write it all down in order
Accidentally added square to 10
At the end
is it right
echo marsh
what is this
echo marsh
$\sqrt{200y^4} \
\sqrt{2 \cdot 10^2 \cdot y^2 \cdot y^2} \
10 \cdot y \cdot y \sqrt{2} \
10y^2\sqrt{2}$
glossy valveBOT
Astar777
echo marsh
finally
shell dome
Damn
echo marsh
this is wrong
shell dome
lol
echo marsh
$\sqrt{y^2} = y$
glossy valveBOT
Astar777
echo marsh
you are taking y^2 out
echo marsh
**Astar777**
its done like this
echo marsh
wdym
shell dome
if i take the y outside the square root, THEN i have to just remove the exponent, right?
shell dome
yeah
shell dome
you are taking y^2 out
wai are u saying that's wrong or, the way i did it is wrong and that i should've done it a diff way?
glossy valveBOT
Astar777
echo marsh
wai are u saying that's wrong or, the way i did it is wrong and that i should've...
the way u did it is wrong
shell dome
ohh
shell dome
**Astar777**
what is the absoloute value signs for
echo marsh
what is the absoloute value signs for
beacuse y can be both positive and negative
$\sqrt{(-2)^2}$ and $\sqrt{2^2}$ both equal to 2
glossy valveBOT
Astar777
shell dome
ohh nvm that makes sense
echo marsh
**Astar777**
this is correct too for your case
echo marsh
**Astar777**
i just said this to be precise
echo marsh
full forumBOT
If you are done with this channel, please mark your problem as solved by typing .close
echo marsh
.close
minor swift
Don't know where to begin with. ( any hint_)
full forumBOT
Don't know where to begin with. ( any hint_)
green merlin
Don't know where to begin with. ( any hint_)
Convert all the log base 4,16 to log base 2
And the log base 9 to log base 3
minor swift
Convert all the log base 4,16 to log base 2
hey we met again
green merlin
Indeed
minor swift
And the log base 9 to log base 3
it was very long
green merlin
Okay
green merlin
<@1037315397143244860>
There is an error in your conversion
log_4(z) should be 2log_2(z)
green merlin
uh wait what
minor swift
$\log_{a^b} x = \frac{1}{b} \log_a$
glossy valveBOT
RUSTY_DUSTBIN
minor swift
Can you combine these?
let me try
green merlin
ok
minor swift
@green merlin
minor swift
oh
I took 4 as base in third equation because i do not think it will give 4root in any case
green merlin
Indeed
minor swift
@green merlin
green merlin
Hold up
minor swift
should i squre both side?
minor swift
oh how
green merlin
We can multiply the equations by a constant
The original equation
minor swift
i do not understand what u said
glossy valveBOT
Carbonite
minor swift
oh
green merlin
Multiply both sides by 4 might make it easier
unreal wren
Multiply both sides by 4, use log(a) +log(b) = log(ab), then change the 8 on RHS into log(?)
full forumBOT
@minor swift Has your question been resolved?
shadow tiger
Yo, I solved the problem, can I just send the uhh process or should I just give hints instead?
unreal wren
Helpers aren't allowed to give answers
full forumBOT
Yo, I solved the problem, can I just send the uhh process or should I just give ...
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.
shadow tiger
It's a system where u got 3 unknown values and 3 equations, what means you can solve it. You're almost there
minor swift
full forumBOT
full forumBOT
@minor swift Has your question been resolved?
minor swift
<@1088348536082550855> Has your question been resolved?
sorry but the electricity went off
well let me leave
leaden mica
Let there be $T:\mathbb{R}{3}[x] \to \mathbb{R}^{3}, and S:\mathbb{R}^{3} \to \mathbb{R}{3}[x]$ linear transformations.
prove that if dim(Im(TS)) = 2, then $1 \leq dim(Im(ST)) \leq 2$.
glossy valveBOT
Horsi135
onyx glen
full forumBOT
@leaden mica Has your question been resolved?
leaden mica
I didn't really found a way to approach it, The only thing i thought of was that 1. there isn't a difference between R^3 and R_3[x] they are the same just with a different writing, and i thought about converting to matrices but I don't think it would work.
waxen flax
Think about it
Could the rank of ST be 3?
Could it be 0?
leaden mica
if it is 0 then either dim(Im(S)) = 0 which is impossible because that would mean that dim(Im(TS)) = 0 or dim(T(Im(S)) = 0 and for that I'm not sure
nimble ridge
I have a question, isn't dim(R_3[x]) = 4?
leaden mica
I have a question, isn't dim(R_3[x]) = 4?
no, R_3[x] are all of the polynomials such that the highest degree of x is 2, p(x)=ax^2+bx+c
nimble ridge
no, R_3[x] are all of the polynomials such that the highest degree of x is 2, p(...
But a base of polynomials of degree 2 is {x^2; x ; 1} which means dim = 3
grand hatch
no, R_3[x] are all of the polynomials such that the highest degree of x is 2, p(...
ah okay
leaden mica
yes, dim=3
grand hatch
suppose dim Im ST = 0. since dim Im TS = 2, it means that dim im T ≥ 2 and dim Im S ≥ 2 which means dim ker S , dim ker T ≤ 1 by rank nullity theorem but from dim Im ST = 0, we have Im T ⊆ ker S which contradicts dim im T ≥ 2
nimble ridge
And a base of polynomials of degree 3 is {x^3; x^2; x; 1}, so dim(R_3[x]) = 4, no?
grand hatch
And a base of polynomials of degree 3 is {x^3; x^2; x; 1}, so dim(R_3[x]) = 4, n...
yes, but R_3[x] is polynomials of atmost degree 2 here
nimble ridge
Oh, I see!
leaden mica
but what about dim ST equals 3?
unreal wren
can somone explain the underlined and circled ones
full forumBOT
can somone explain the underlined and circled ones
@unreal wren Has your question been resolved?
rugged jay
Does TSTST stand for team selection test selection test lol
green merlin
Does TSTST stand for team selection test selection test lol
Yes
rugged jay
can somone explain the underlined and circled ones
You can get to the red one after submitting a=b=c=t^3
And the second one after submitting a=b=c=t
Well if I get to t^3 after applying the function t^9-t^3 times to t^9, and I get to t after applying the function t^3-t times to t^3; that would mean I get to t after applying the function t^9-t times to t^9
Because I just do those 2 things back to back
If this doesn’t make sense I can explain with a diagram
unreal wren
And the second one after submitting a=b=c=t
I know these alr
unreal wren
Because I just do those 2 things back to back
I don't get it sorry
rugged jay
You don’t see how those 2 equations gets us to the equation you underlined
rugged jay
I mean if I apply f to 5 a times and get to 10, and I apply f to 10 b times and get to 30 then applying f to 5 a+b times would make you get to 30 because you just do those 2 things back to back
unreal wren
I get it already
rugged jay
Oh okay
unreal wren
How about the circled paragraph?
rugged jay
Ill look when i have paper and pencil
full forumBOT
@unreal wren Has your question been resolved?
rugged jay
There is no problem in the proof of the lemma that says f^t^2-t(t^2)=t right
unreal wren
No, i just don't understand the proof
if t = abc, shouldnt it be f^(t-a) (t) instead of f^(t-a) (a)?
rugged jay
Yes first line in the circled part seems to be mistyped
rugged jay
unreal wren
how did they get from first line to second line??
rugged jay
I was like maybe it isn’t mistyped and somehow provable but it is just a wrong equation when you consider the function we are proving it is supposed to be (which clearly works)
rugged jay
how did they get from first line to second line??
Second line we will prove, i dont know why they just gave it and didnt bother like it is obvious
unreal wren
oh, so you mean there are a lot of steps between first and second line, but they didnt show it?
rugged jay
Yeah well prove the second line using some things we have so far
Consider the first term in the left side of the equation (in the second line)
unreal wren
yeah
rugged jay
So I used that
rugged jay
f^(t^2 - t) (t^2) = t, not t^2?
Yeah I know
rugged jay
Instead of applying the function to t^2 t^2-ab times im applying t^2-t times and then t-ab times, we get to t after the first step like you pointed out
unreal wren
yes it makes so much sense
rugged jay
yeah sorry
No need to be sorry lol
rugged jay
I mean proof isn’t done because they still dont turn into the exact things in the RHS
rugged jay
We will prove that the equation in the second line is correct, I don’t know how exactly they got to it tho there might be an easier way im not seeing
Maybe it is actually a simple observation
rugged jay
Oh wait the second line is so obvious actually
Forget about this well get to the second line equation in a way simpler way
unreal wren
Oh wait the second line is so obvious actually
yay
rugged jay
This is unnecessary apparently
It is just the equation that is given in the question
Just notice ab , t and c multiply to t^2
unreal wren
oh yeah
wait wait i will process
but why would it equal RHS?
i still dont see it
rugged jay
It is just the equation given in the question
rugged jay
I’ll look into it
unreal wren
ok
rugged jay
Second line we will prove, i dont know why they just gave it and didnt bother li...
I am taking this back it was obvious turns out
Okay third line is provable using first two lines but well do some arranging and stuff
The transformation I thought was necessary to prove the second line is actually useful here
unreal wren
i kind of see it
rugged jay
i kind of see it
Oh great
unreal wren
all we need to do is prove that f^(t^2 - ab) (t^2) + f^(t^2 - c) (t^2) = f^(t-ab) (t)
rugged jay
all we need to do is prove that f^(t^2 - ab) (t^2) + f^(t^2 - c) (t^2) = f^(t-ab...
How did we get to this
It is probably correct i just need it to be explained
unreal wren
It is probably correct i just need it to be explained
uh + f^(t-c) (c)
forgot to type that
oh i know
rugged jay
You’re saying we just need to prove this?
unreal wren
f^(t-c) (c) = f^(t^2-c) (t^2) so they cancel out
rugged jay
That is great because we will prove it with just one step
unreal wren
You’re saying we just need to prove this?
yeah
rugged jay
f^(t-c) (c) = f^(t^2-c) (t^2) so they cancel out
Yes they are equal but why are they equal?
rugged jay
Yeah
rugged jay
We are using the fact that applying f t^2-c times is the same thing as …
Fill the blank
Just making sure it is all understood before moving on
rugged jay
f^(t-c) (f^(t^2 - t) (t^2))
Wow great
Okay so after arranging and using this trick are we convinced third line is true?
unreal wren
yes
rugged jay
Nice
rugged jay
the g_t(a) + g_t(b) = g_t(ab)
This is equivalent to the third line we proved earlier
Just look at the definition of the function g_t()
unreal wren
wait
lemme process
oh yeah lol
didnt see that
that means only 1 underlined one leftt
rugged jay
Btw the reason they noted ab|t for that equation is because we are working with positive integers and the original equation given in the problem only works with abc being a multiple of a b and c
And they noted ab<t because they defined g_t() to work only with inputs smaller than t
rugged jay
Okay
I need to read the parts between the underlined we just went through and the next underlined and comprehend them too rn
I’m reading the solution for the first time
rugged jay
mightve seemed a little rude there sorry
No not at all dont worry
I don’t understand why the line right before the line you marked is correct
But I see how it is used to prove the line you underlined
unreal wren
I don’t understand why the line right before the line you marked is correct
which part of the line?
theres many equalities there i understand all of them
rugged jay
Why does pg_t(a)+qg_t(b)= g_t(a^p.b^q)
rugged jay
Ohh yeah
And getting to g_t(s) was useful because t is s^2 and we know how f^(k^2-k)(k^2) behaves
They made a typo in that line btw
rugged jay
It needs to be f^(s^2-s)(s^2)-s=0
They wrote f^(s^2-s)(s)-s=0
Look at definition of g_t it needs to have t in there which is s^2
rugged jay
And we know why it is correct when it is s^2 there, because of the first lemma we proved
rugged jay
well how did they get the last underlined one?
Oh okay here we go
The line you didn’t underline that you just explained to me says this right
unreal wren
yes
rugged jay
Well p divides 0, it also divides the first term on the left hand side (because there is a p in it)
What does this say
rugged jay
a+b=c , a b and c are all integers. If p divides a and c what does this say?
unreal wren
p divides q g_t(b)
rugged jay
Yeah
unreal wren
oooh
rugged jay
These are all integers so we can come to conclusions like this
unreal wren
yes
rugged jay
Well there are lots of numbers that are divisible by p, not just 0? How do we know g_t(b) is 0?
rugged jay
why does it have to be greater than -a tho
You’re looking at q|g_t(a) line we showed p|g_t(b)
unreal wren
oh sorry lol
unreal wren
Well there are lots of numbers that are divisible by p, not just 0? How do we kn...
what g_t(b) is 0?
rugged jay
g_t(b) > -b because just look at the definition of g_t() and remember that f gives positive outputs (N->N)
rugged jay
what g_t(b) is 0?
We will prove that yeah
unreal wren
g_t(b) > -b because just look at the definition of g_t() and remember that f giv...
wait let me process
oh yeah i see it
rugged jay
g_t(b) > -b because just look at the definition of g_t() and remember that f giv...
But I am not going to use the fact that g_t(b)>-b so forget that for a second
unreal wren
ok
rugged jay
We have shown p divides g_t(b). Well there are lots of numbers that are divisible by p, not just 0. How do we know g_t(b) is 0?
unreal wren
is it because g_t(a) is divisible by q?
rugged jay
No forget that too
rugged jay
Sure I’m waiting I’ll tell you how when you want
unreal wren
i dont have any idea
rugged jay
It is because it didnt matter which prime we choose as p. Like lets say q=37 a=5 b=3 and we chose 41 to be p. Well we could choose 43 to be p too couldn’t we? And p still would divide g_t(b)
So g_t(b) wouldn’t be only divisible by 41 but also by 43 and also by any of the infinite amount of primes we could choose p to be
unreal wren
oh wow
rugged jay
And I can only think of 1 integer that would satisfy that
unreal wren
wait wait
unreal wren
It is because it didnt matter which prime we choose as p. Like lets say q=37 a=5...
i need to process this
rugged jay
Sure
unreal wren
how about the restirction s = a^p x b^q?
rugged jay
Doesn’t really matter
unreal wren
why not?
rugged jay
If we chose p to be 59 s would be a^59.b^q (whatever we chose for those 3). If we chose p to be 61 s would be a^61.b^q
But we could always carry out the proof for p|g_t(a) the same way we just did
unreal wren
err let me think
rugged jay
p isnt infinitely many primes simultaneously, it is just that p can be any of them it wants and always divides g_t(a)
unreal wren
okk i think i get it
rugged jay
And I can only think of 1 integer that would satisfy that
Continue this thought
rugged jay
Only integer that is divisible by infinitely many primes is 0
For any positive integer you’d choose a prime bigger than it and for any negative integer you’d choose a prime bigger than its absolute value and they wouldn’t divide
full forumBOT
rugged jay
You’re welcome
full forumBOT
Available help channel!
full forumBOT
Available help channel!
thin lark
I am supposed to find the center mass of the space defined by y^2 = x and x^2=y but im finding some wrong i think integral of dE is wrong and is supposed to be 1/3 but idk why
glossy valveBOT
woeful pasture
not you, I meant him
i am blind srry 
full forumBOT
@thin lark Has your question been resolved?
vocal plume
How do i show that 214x215-214 is a square of something i know this must be easy but how
cinder gull
214 common
grand hatch
214x215 - 214 = 214(215 - 1) = 214^2
vocal plume
214x215 - 214 = 214(215 - 1) = 214^2
Damn thanks alot
green merlin
Any idea what is this general form of integral
!occupied
full forumBOT
Any idea what is this general form of integral
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
little field
Oh sorry
vocal plume
Np
onyx glen
How do i show that 214x215-214 is a square of something i know this must be easy...
consider: 214 * 215 - 214 * 1 = 214 * ?
oh ffs
onyx glen
214x215 - 214 = 214(215 - 1) = 214^2
i honestly wanna call !nosols on this
grand hatch
i can delete it, if you want (though its already too late), i guess i could have not included the last equality
thin lark
not you, I meant him
Ty
full forumBOT
@vocal plume Has your question been resolved?
full forumBOT
full forumBOT
Available help channel!
safe edge
Could someone please help me with the second shift? I know x moves to 0 but I can't get y
safe edge
yes
safe edge
I mean, my x shift is correct, yes?
safe edge
4 down vertically, and flip over x axis
woeful pasture
flip over first
then 4 down
otherwise that -4 becomes +4 after u multiply the entire thing by -1
now lets go about our thingy
we start from (0,1), now move right once we're at (1,1)
we got flipped so we're at (1,-1)
then we brought down 4 more units
so
(1, -5)
ya?
safe edge
Yes, that's a. Now b starts from 1, e. moves right so x value becomes 2, correct?
safe edge
yeah, then it goes to -e and down 4 more
woeful pasture
ya
full forumBOT
full forumBOT
Available help channel!
primal adder
So i have a question when should we use bounding to find a max and when u cannot use it ?
Cuz i was doing an exercise from MAT 2023 paper and in tge first questions i used like the y coordinate of the max by completing the sequare method but then i used it for the last question and it didnt work so im confused to when to use each method
full forumBOT
So i have a question when should we use bounding to find a max and when u cannot...
@primal adder Has your question been resolved?
full forumBOT
full forumBOT
Available help channel!
haughty ember
Build a 2nd degree equation with coefficients as whole numbers that have as roots:
torn path
my bad
haughty ember
Nah lol I’m joking
Gl with ur question
Build a 2nd degree equation with coefficients as whole numbers that have as roots:
full forumBOT
@haughty ember Has your question been resolved?
sharp vine
Build a 2nd degree equation with coefficients as whole numbers that have as root...
Use a(x-x1)(x-x2)
x1, x2 are roots
Then choose a so that all the coefficients are whole numbers
full forumBOT
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
cerulean ingot
Can someone help me with these graphing questions? Im not sure how they work
undone vector
You have a picture?
cerulean ingot
alright, so does that mean its going from increasing to decreasing?
void nova
No
void nova
They want you to find on the graph the intervals where the function is decreasing
cerulean ingot
i know
void nova
Alright
void nova
I don't know 😅
void nova
Because the answer i put in says wrong
Which answer did you find?
cerulean ingot
Which answer did you find?
(-inf, -4) U (0, inf) sorry i dont have an infinity key
void nova
Don't worry
void nova
(-inf, -4) U (0, inf) sorry i dont have an infinity key
Mmh this is correct though
void nova
I don't know 🤷♂️
cerulean ingot
Let me try something
void nova
Let's see if done other helpers have a different opinion
void nova
Oh weird
But okay lol
Tests with pen and paper still are the best in my opinion
Because you never know if the websites are bugged 😬
high cradle
Hey if you're trying to learn calculus
I am a shill for 3 blue 1 brown's intuitive explanations of the more entry-level concepts
high cradle
He visualises things such as these graphs and you can see exactly what a derivative looks like along a curve
It won't in anyway replace working on exercises and it's not without its faults, but it could help
obsidian ruin
How is cauchy schwarz used in this step? (what are alpha and beta?)
I don't understand how this can be true for all i..
obsidian ruin
for example I can write the rhs as
$$\norm{\Psi}\norm{\psi\otimes\phi}=1$$
but this upper bounds it with one, I cannot use that the two states are proportional
glossy valveBOT
schadowpop
obsidian ruin
o sorry maybe this provides more context and is clearer
full forumBOT
@obsidian ruin Has your question been resolved?
gritty rose
torn jolt
I need some practice materials and refernce materials for congruence
torn jolt
Like it should have lots of examples and some good theory
robust slate
Here have 10 random questions 
torn jolt
Thanks a lot now some theory?
distant vortex
I have these double integral volume questions and I have no clue how to set up the integrals, Im having a hard time what I need to set as my bounds, but other then that I can do partial differentiaion and integration pretty well I just need help understanding how to set the integrals up
distant vortex
.close
full forumBOT
full forumBOT
Available help channel!
hazy phoenix
can anyone help me with my math its really hard and i dont get it
runic galleon
just send the question
hazy phoenix
heres the thing
i dont understand how to do it
I dont want the awnser
i need help understanding it
runic galleon
any question in particular or the whole thing
onyx glen
the concept you're looking for is called collecting like terms
hazy phoenix
hazy phoenix
the concept you're looking for is called **collecting like terms**
terms?
onyx glen
yeah, terms. that's the word in algebra for things being added or subtracted
runic galleon
no, variables are individual letters. don't confuse.
oop mb
we were told terms and variables are the same
hazy phoenix
yay
onyx glen
what's 5 apples plus 3 apples?
hazy phoenix
*what's 5 apples plus 3 apples?*
8
onyx glen
8 what
hazy phoenix
8 apples
onyx glen
right
hazy phoenix
yay
onyx glen
5 apples + 3 apples = 8 apples
ok
let's try another one
what's 18 pencils minus 7 pencils
hazy phoenix
11 pencils
onyx glen
right
onyx glen
... im not taking any clients at the minute sorry
hazy phoenix
... im not taking any clients at the minute sorry
its ok i was kidding
onyx glen
anyway
onyx glen
well yeah it was a stand in for letters
like i literally replaced the variable a (scary) with apples (intuitive)
but the logic is still the same
i was then going to ask you for something like "6 billion + 15 billion" or something along these lines and then segue into things like "6x + 8x"
but it looks like you got it already
hazy phoenix
so 14x
onyx glen
just as
5 apples + 3 apples = 8 apples
so too
5a + 3a becomes 8a
onyx glen
ok so why don't you try doing the first six questions from here
don't worry about the rest just yet, we'll get to them
onyx glen
This is just algebra
you're technically but not morally right
undone radish
I can explain further
onyx glen
OP wants to learn how to do exactly this
onyx glen
I can explain further
no need, ive already gotten started
undone radish
Would you like me to draw a diagram
:D
I wanna become a math teacher some day ngl
onyx glen
calvin i appreciate your enthusiasm but i can handle this guy myself
onyx glen
on which one
undone radish
Okay
undone radish
I think he needs a diagram
onyx glen
I think he needs a diagram
i can handle it, thank you.
undone radish
D:
hazy phoenix
what's that give you
5
onyx glen
right
onyx glen
ok right well i did ask you to do the first six
so now you see how some of the terms contain the letter a while others contain c, right
hazy phoenix
yea
onyx glen
yeah so the idea is
ones with different letters don't interact so to speak
in the lingo, they're called unlike terms
hazy phoenix
in the lingo, they're called *unlike terms*
lingo?
onyx glen
math-speak
hazy phoenix
ok
onyx glen
but "lingo" generally means language or words specific to some discipline or subject
hazy phoenix
ok
onyx glen
so for example
hazy phoenix
so will it be ac
onyx glen
if you had a question that asked to simplify
15a + 8b
there would be nothing to do, as the two terms here are unlike and so don't interact with each other
onyx glen
on the other hand, with your question:
3a + 5c - a + 2c
you have two "a" terms:
- 3a
- -a
and two "c" terms: - 5c
- 2c
you collect these separately in the same way you've been doing thus far
you can think of this as:
3 apples, plus 5 carrots, minus an apple, plus another two carrots
you count the apples and carrots separately
hazy phoenix
idk
onyx glen
(with a for apples and c for carrots)
hazy phoenix
so 2a 6c
hazy phoenix
8
onyx glen
nope
hazy phoenix
8 ac?
onyx glen
2a+6c, that's your final answer
hazy phoenix
ok
onyx glen
anyway, this sort of logic should let you do up to and including q18
note also that raw numbers (ones without a variable) can only add/subtract with other raw numbers
hazy phoenix
wait
onyx glen
ok yeah you got me
5c+2c is 7c indeed
you said 6 carrots earlier and i didn't bother to double check
onyx glen
importantly though i hope you understood the logic
onyx glen
wdym stop
runic galleon
Probably means where he should do up to next
onyx glen
as i said earlier,
anyway, this sort of logic should let you do up to and including q18
so go until there
onyx glen
gonna repost the entire sheet for convenience
onyx glen
these are terms alright, they just don't have a letter
they are constants
or as i like to call them, raw numbers
note also that raw numbers (ones without a variable) can only add/subtract with other raw numbers
3-2 is 1. just 1. (and you should know what to do with 3x-x by this point)
hazy phoenix
ok
young tide
Im a bit confused on how the following trig identity is derived:
young tide
, , tan(a-b) = \frac{tan(a)-tan(b)}{1+tan(a)tan(b)}
glossy valveBOT
Rien
glossy valveBOT
Rien
young tide
, , tan(a-b) = \frac{sin(a)cos(b)-cos(a)sin(b)}{cos(a)cos(b)+sin(a)sin(b)}
glossy valveBOT
Rien
young tide
, , tan(a-b) = \frac{\frac{sin(a)}{cos(b)}-\frac{sin(b)}{cos(b)}}{1+sin(a)sin(b)}
glossy valveBOT
Rien
young tide
, , tan(a-b) = \frac{tan(a)-tan(b)}{1+tan(a)tan(b)}
glossy valveBOT
Rien
young tide
**Rien**
In this step you divide by Cos(a)Cos(b), but I don't quite understand how you can do that if cos(a)cos(b) could equal 0.
onyx glen
In this step you divide by Cos(a)Cos(b), but I don't quite understand how you ca...
if cos(a) = 0 then tan(a) is undefined anyway
ditto for b
inner hare
Assignment: Find the eigenvalues and eigenvectors of a given matrix
unique wagon
what part r u struggling with
inner hare
the getting the answer correct and finding where I did a mistake part
unique wagon
maybe some computation, have u tried doing it again slowly?
first lets see if u understand the concept, how did u find ur characterisitc polynomial?
inner hare
I semi understand it but the tasks are very similar so I dont care so much about the theory part currently, just want to pass the practical part of the exam so I'm focusing on that
inner hare
maybe some computation, have u tried doing it again slowly?
I'll try again
but I'm intrigued as to why this computation didnt work
twin wolf
have u tried using cofactor expansion along a row or column
inner hare
no, but still if I use this method that I used I should get the correct answer
twin wolf
idk what method ur using but if its correct then maybe ur algebra is messed up
inner hare
idk what method ur using but if its correct then maybe ur algebra is messed up
sarrus rule, and yea it probably is
urban jacinth
sarrus rule, and yea it probably is
That's for determinant though
Not for finding char poly
inner hare
whats a char poly?
urban jacinth
Characteristic polynomial
inner hare
yea but we find the characteristic polynomial by passing A-lambda*I through a determinant
inner hare
yea but we find the characteristic polynomial by passing A-lambda*I through a de...
polynomials* rather
inner hare
Assignment: Find the eigenvalues and eigenvectors of a given matrix
also I double checked and have every value correct
analog sand
It should be (3-lambda)[(4-lambda)(-1-lambda) +4]
analog sand
Hm idk what that is then
inner hare
Tried again buy same result...
prime harness
inner hare
Tried again buy same result...
<@&286206848099549185> anyone know where I messed up with the Sarrus rule? because if not, I've just proven Sarrus wrong
inner hare
Assignment: Find the eigenvalues and eigenvectors of a given matrix
did it two sepperate times and checked at least 4 times at this point but I still cant find the mistake
nevermind, it was actually correct lol
neon rivet
did i get this right?
my answer was f(2) = 4, therefore x = 2
vast fossil
Are you sure there are no other solutions?
neon rivet
oh we need to solve for two cases?
woeful pasture
yes
woeful pasture
wdym
woeful pasture
we're gonna get a negative value which does not = to 4
we should get negative x
woeful pasture
-x = 4
solve this eq
to solve f(x)
we consider which x s.t. f(x) = 4 for x < 0 and which x .s.t f(x) = 4 for x >= 0
u found that f(2) = 4 works for x >= 0
neon rivet
whats .s.t?
cinder gull
What is the question asking?
neon rivet
Two intersections
woeful pasture
Two intersections
so how many x should there be satisfying y=4?
neon rivet
so how many x should there be satisfying y=4?
two
neon rivet
Hmm
woeful pasture
consider -x = 4
what can x be
hint: multiply both sides by a number to get rid of the negative sign
cinder gull
💀
cinder gull
hint: multiply both sides by a number to get rid of the negative sign
Most realest hint ever
neon rivet
appreciate it
woeful pasture
are the solutions
full forumBOT
full forumBOT
Available help channel!
torn jolt
full forumBOT
covert flint
hi guys, I'm preparing calculus 1 and while I was doing the old exercises I got this limit that I don't understand. In the first part highlighted in red my teacher uses asymptoticity, and replaces e^x -1 with x, which is 0 for x->0. Then he replaces cot with cos/sen and I don't understand why it tends to 1/x. In the blue part, use the hierarchy of infinities to solve it. Can you explain to me why cos/sen is replaced with 1/x?
steel solar
hi guys, I'm preparing calculus 1 and while I was doing the old exercises I got ...
Well, $\cos(x)=1+O(x^2)$ as $x\to 0$ and $\sin(x)=x+O(x^3)$ as $x\to 0$, so (naturally?) $\cot(x)=\frac1x$ as $x\to 0$ (or I'm missing some use of $O$ notation, but you get the point)
glossy valveBOT
;(
steel solar
Really weird to not use $1-\frac12x^2$ though, for $\cos(x)$
glossy valveBOT
;(
covert flint
okay thanks i got it, it was pretty obvius my bad
fast peak
Really weird to not use $1-\frac12x^2$ though, for $\cos(x)$
well if 1 is enough...
hot kernel
full forumBOT
