That value calculates the profit per book when x books were produced, so yes.
#help-13
austere zealot
austere zealot
No problem!
crimson sedge
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
tacit ermine
what does f[] (x) = mean ? (its meant to be like f ^box (x) )
tacit ermine
tropic oxide
can you show a screenshot/picture of the question
wraith daggerBOT
tacit ermine
.close
near rapids
near rapids
.close
gilded gate
Hello, I am stuck on a problem involving points on a 3D sphere.
gilded gate
Hello, I am stuck on a problem involving points on a 3D sphere.
For a school project I need to gather information on how gps works, and I nee dhelp on proving why we need a minimum of atleast 21 satellites. For gps to work there need to be atleast 4 satellites able to reach you, so there should always be 4 satellites above your head. I have found a way to find the minimum amount of satelites needed on a 2D circle, here is how
p1 is your position
a is the distance between the satellites
n*s is the minimum required satellites
r1 is the radius of the earth
r2 is the radius of the satellites to the center of the erath
note that on a 2D circle you need atleast 3 satelliets above your head
gilded elm
do you know whats the area covered by each satellite?
cedar kilnBOT
@gilded gate Has your question been resolved?
gilded gate
do you know whats the area covered by each satellite?
i do not
tho i could fgure out a way
i think
gilded elm
well you first can figure out whats the area covered by each satellite
woven crater
well you first can figure out whats the area covered by each satellite
he meant that a satellite can reach you if there’s no earth between you and the satellite
gilded elm
wdym no earth
woven crater
if the satellite can draw a line between you and itself without going through the earth first, it can reach you, otherwise it can not
gilded gate
yeah and the circumference the satellite can be on is O wich i have shown how to calculate
woven crater
this question has not been asnwered yet^
cedar kilnBOT
@gilded gate Has your question been resolved?
quiet plover
umm this reminds me of some concept involving location and i cant remember what it is 
i saw it in a coding question
got it!
not sure if this is the correct reference needed tho
i saw 'gps' and 'three satellites' so looks like it
cedar kilnBOT
@gilded gate Has your question been resolved?
cedar kilnBOT
@gilded gate Has your question been resolved?
mild valve
note that on a 2D circle you need atleast 3 satelliets above your head
if 4 satellites were needed would the answer have been 8?
cedar kilnBOT
@gilded gate Has your question been resolved?
crimson sedge
cedar kilnBOT
lusty grotto
u again?
bold vine
This problem is currently being discussed
obsidian coral
Are you asking someone else's question?
crimson sedge
Are you asking someone else's question?
yeah
bold vine
They got it lmao
lusty grotto
oh
obsidian coral
See <#903463354654404658>
.
cedar kilnBOT
cedar kilnBOT
Available help channel!
grizzled stone
yo
grizzled stone
second line howd they get lnx + 1+..
<@&286206848099549185>
the question
part b
mighty drift
It's just the induction hypothesis
mighty drift
d^k / dx^k x^k = k!
If you don't know it it's a trivial induction
Then the other one is just (k+1) d^k / dx^k (x^k ln x) which is given by the induction hypothesis
mighty drift
You mean the intuition?
grizzled stone
yea
mighty drift
idk it's just a derivative
grizzled stone
idk it's just a derivative
hm is there of explaining the logic behind it though
mighty drift
If I tried to give meaning to each term here's what I'd say:
Since d^n/dx^n x^n = n!, it makes sense to see it here along with a small correcting factor to account for the ln x
Since ln x is somewhat constant compared to x^n, it makes sense it can kind of just be considered as a constant, and therefore give n! ln x.
Then Hn appears to correct that approximation because ln x isn't really constant, and neither are its higher derivatives, which, interestingly enough, are (-1)^n (n-1)! when evaluated at 1
grizzled stone
If I tried to give meaning to each term here's what I'd say:
Since d^n/dx^n x^n ...
whats Hn?
mighty drift
The nth harmonic number 1 + 1/2 + ... + 1/n
grizzled stone
ah
mighty drift
Which is close to ln n + 0.577 when n gets big
grizzled stone
thx man
cedar kilnBOT
@grizzled stone Has your question been resolved?
crimson sedge
Does anyone know how to determine the value of this potency series?
crimson sedge
crimson delta
is the question asking for the value or asking whether it converges
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
.close
cedar kilnBOT
sacred grail
.reopen
cedar kilnBOT
✅
sacred grail
is the question asking for the value or asking whether it converges
answer denascite's question
crimson delta
if they aren't here to answer the bot's question then they arent here for that question either
cerulean sail
Maybe they have the read channels hidden or something 🤔
sacred grail
cerulean sail
Quite a few people end up making new channels cause of that
violet night
skill issue
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
is the question asking for the value or asking whether it converges
it is specifically asking for the value so we know it converges
but idk how to do that
crimson sedge
does someone know how to find the value of it?
für alle = for all
?
no one willing to help
?
?
cedar kilnBOT
@crimson sedge Has your question been resolved?
cerulean sail
Wild thought would be to express $cos(n \phi)$ in exponential form and use that...
wraith daggerBOT
chartbit
cerulean sail
Ah fucc forgot whatever that symbol's called atm 
gusty forum
Ah fucc forgot whatever that symbol's called atm <:broke:586078546984697856>
$\varphi$
wraith daggerBOT
IV
gusty forum
close 
cerulean sail
close <:KEK:586240877358350341>
LMAO of course it's almost that, those var's always get to me 
Honestly I hate the normal $\epsilon$ and always go for the $\varepsilon$
wraith daggerBOT
chartbit
lusty grotto
$\varomega$
wraith daggerBOT
SilverSoldier
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
lusty grotto
i hate $\omega$
wraith daggerBOT
SilverSoldier
cerulean sail
i hate $\omega$
Looks way too close to a normal w imo, arghhh 😷
lusty grotto
$w$ vs $\omega$
wraith daggerBOT
SilverSoldier
lusty grotto
yeah
cerulean sail
Like if you're glance reading and not paying attention, and someone used both...
...actually, there's an idea 😈
crimson delta
View it as the real part of a certain complex number
crimson sedge
Could you give me some more hints?
cerulean sail
**chartbit**
If you take what I said here, you should notice the sums split up into two things that should be easy to work with...
crystal raptor
Could you give me some more hints?
what famous formulas do you know involving trig functions and exponentials
crimson sedge
what famous formulas do you know involving trig functions and exponentials
nvm just z = r * exp(i * phi)
for z = a + bi
or what exactly do you mean otherwise)
?*
crimson delta
There is a very famous formula linking exp(i phi) to trig functions
gilded elm
It's named after a very famous mathematician
cedar kilnBOT
@crimson sedge Has your question been resolved?
latent bloom
Very famous in fact
He appears in almost all Math problems
Also
What does $e^{i\varphi}$ draw out?
wraith daggerBOT
VulcanOne
crimson sedge
cedar kilnBOT
crimson sedge
what’s the answer
dire geode
• Show your work, and if possible, explain where you are stuck.
cedar kilnBOT
@crimson sedge Has your question been resolved?
dire geode
i don’t understand anything
h is the height and is a function of time meaning at time t, h(t) tells you the height
so you can plug in any time for t and use the formula for h(t) to calculate the height at that time
for example, 1 second later
$h(1) = -16 (1)^2 + 69 (1) + 4$
wraith daggerBOT
riemann
dire geode
,calc -16 (1)^2 + 69 (1) + 4
wraith daggerBOT
Result:
57
now you check all times in a-d and see which one gives the correct height in the problem
crimson sedge
,calc -16 (1.35)^2 + 69 (1.35) + 4
wraith daggerBOT
Result:
67.99
,calc -16 (3.31)^2 + 69 (3.31) + 4
wraith daggerBOT
Result:
57.0924
,calc -16 (1.35)^2 + 69 (3.31) + 4
wraith daggerBOT
Result:
203.23
,calc -16 (2.96)^2 + 69 (2.96) + 4
wraith daggerBOT
Result:
68.0544
,calc -16 (3.31)^2 + 69 (3.31) + 4
wraith daggerBOT
Result:
57.0924
,calc -16 (0.69)^2 + 69 (0.69) + 4
wraith daggerBOT
Result:
43.9924
.close
tranquil lotus
could somebody check if my proof is correct?
cedar kilnBOT
could somebody check if my proof is correct?
tranquil lotus
,rotate
wraith daggerBOT
wraith daggerBOT
riemann
tranquil lotus
aaah true
sacred grail
wait what
you're trying to prove that if P(A) + P(B) + P(C) = 1 then A, B, C are mutually exclusive?
tranquil lotus
yeah
sacred grail
that sounds very wrong
tranquil lotus
my proof or the statement
sacred grail
the statement
what if you just have 3 random events which each are P(A) = P(B) = P(C) = 1/3
sacred grail
like uniform distribution on {1, 2, ..., 12}
and you choose like
A = {1, 2, 3, 4}, B = {2, 3, 4, 5}, C = {3, 4, 5, 6}
tranquil lotus
yeah the statement does sound sketchy
and the exercise did ask for me to show a counterexample if it was false
dire geode
yeah the statement does sound sketchy
can you screenshot the original question
sacred grail
well there you go
tranquil lotus
dire geode
and the exercise did ask for me to show a counterexample if it was false
this is important to tell us
sacred grail
by extension that also means your proof is wrong
because you hopefully shouldnt be able to prove an incorrect result
save that for proofs by contradiction
sacred grail
and when you're making the examples
dont just try to construct the ones that satisfy the statement
try to break it too and see if its possible
plucky holly
plucky holly
<@&286206848099549185>
cedar kilnBOT
@plucky holly Has your question been resolved?
elfin hemlock
What have you tried?
plucky holly
i'm leaning towards the 4th option
elfin hemlock
Try thinking about how you calculate that again
How many options for 1st digit? How many for 2nd?
elfin hemlock
Can you list the even digits?
plucky holly
wait no
4 for the first
2,4,6,8
4 for the second
0,___
then 3 for the third
is that correct then?
the fourth option?
coarse lance
Very quick question:
When integrating sin(4x+2) I can use u-substitution (I know its not necessary here, just taking a simple example) to get the correct result 1/4*-cos(4x+2)+C
But when integrating sin(4x^2+2) the result is something completely different. Why am I not allowed to use u-substitution here? When can u-substitution be used and when not? Only when the to-be substituted term is linear?
zenith sail
If you have
integral sin(4x^2+2) dx
and you do u = 4x^2 + 2
then du = 8x dx
The 8 is easy, you can create that from thin air, but there's not much you can do to produce that x
coarse lance
I can see how the x is a problem but what exactly do you mean with "produce"?
zenith sail
Well, that's what I mean, there's not really anything to do
coarse lance
are you simply saying that in the first example, we end up with dx=du * 1/4 which is a constant and thus can be taken out of the integral
whereas in the second example we end up with dx = du * 1/8x which is NOT a constant and thus cant be removed from the integral?
zenith sail
are you simply saying that in the first example, we end up with dx=du * 1/4 whic...
more or less
if the x was already there, then u-substitution is appropriate
∫ x sin(4x^2+2) dx
coarse lance
more or less
at first I thought that when my integral has du at the end I can put any terms with x in front of the integral just like if it were a constant, but I assume I cant do that because u refers to x, right?
zenith sail
right, if you have something like u = 8x, then u and x depend on each other
so x is not a constant in terms of u
x = 1/8 u, it depends on u
coarse lance
okay okay, that certainly makes sense
just trying to understand the method a bit more before blindly applying it
thanks for the explanation
.close
cedar kilnBOT
dire geode
!15m
cedar kilnBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
why does inverse sine in radians not give the original domain value of any sine input
crimson sedge
it only works with degrees for some reason
brisk dirge
Maybe because of the value of pi
modest storm
how do you compute the error vector from an orthogonalized matrix
modest storm
my orthagonalized matrix is
[5 -10 5]
[0 1 2]
and my x is
[5]
[2]
original equations were 3x-6y=-1, 4x-8y=7, y=2
gilded elm
$$
\begin{bmatrix}
5 &-10 &5\
0 &1 &2
\end{bmatrix}
$$
wraith daggerBOT
DerpZ
gilded elm
ok so M^T = M^-1
modest storm
yes
modest storm
e=b-p
gilded elm
oh this is a linear estimator
gilded elm
original equations were 3x-6y=-1, 4x-8y=7, y=2
can you quickly express this in matrix form
wraith daggerBOT
Kingvt
gilded elm
alright nice
modest storm
the pain of latex 😭
gilded elm
oh is the error here an MSE?
modest storm
modest storm
ah so that what its called
cedar kilnBOT
@modest storm Has your question been resolved?
crimson sedge
Sorry for the badly worded question ahead but;
\bigskip
What exactly is the "projection" that the dot product describes? The formula of the dot product is given by $||\vec{A}|| \cdot ||\vec{B}|| \cdot \cos(\theta)$ for some two vectors $\vec{A}$ and $\vec{B}$ and the angle between them $\theta$
\bigskip
Now, from what I know, that formula describes the projection of $\vec{A}$ into $\vec{B}$ as a scalar. "How much of A is in the direction of B", if you will. But also $\vec{A} \cdot \cos(\theta)$ is another way to describe the same statement above, so why do we have to multiply by the magnitude of $\vec{B}$?
wraith daggerBOT
♡LexQa♡
crimson sedge
The argument I heard is that this helps with the dot product being commutative, as $||\vec{A}|| \cdot ||\vec{B}|| \cdot \cos(\theta) = ||\vec{B}|| \cdot ||\vec{A}|| \cdot \cos(\theta)$ and that scaling that projection with $||\vec{B}||$ does not matter all in all since the the "projection" We are talking about is "relative"
wraith daggerBOT
♡LexQa♡
crimson sedge
But that doesn't make much sense in my mind, since I know there is some sort of more abstract explanation to the dot product than that
crimson sedge
Sorry for the badly worded question ahead but;
\bigskip
What exactly is the "pr...
||A|| for the A*cos one oops
copper crest
Noobs be like:Shadow
violet flume
But that doesn't make much sense in my mind, since I know there is some sort of ...
dot product is an inner product, so idk
im not a math knower
but inner product provides a notion of angle between vectors
which i think in turn gives you an idea of one going in the direction or not in the direction of another
by some amount
thats really the component thats giving you projection
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
thats really the component thats giving you projection
Yes but so does |A|cos(theta)
Does it not
But anyways I will give that video a watch
violet flume
i mean the important part is that the dot product is giving you a notion of angle is what i mean
not that it is defined in terms of theta or not
there are inner product spaces without any geometric notion of angle at all
where you can still do projections
violet flume
idk im just trying to intuit what your question might be
so i might be misanswering
it seemed like you were asking why the dot product specifically provides a sense of "projection"
crimson sedge
My question is more of why is that projection given as something that is unique?
violet flume
ah
crimson sedge
Because it is not unique right?
violet flume
it is
crimson sedge
How so
violet flume
crimson sedge
Isn't ||A||cos(theta) another description of that projection for example?
violet flume
theres a lot of analysis in this proof
violet flume
Isn't \||A\||cos(theta) another description of that projection for example?
youre just talking about the dot product for one, thats not the projection
crimson sedge
Hm I see so there is something more rigourous about it
violet flume
i think
violet flume
Hm I see so there is something more rigourous about it
yea but there doesnt have to be
i mean im more just uhh
im linking you something that says clearly that it's unique
manic acorn
Yes but so does |A|cos(theta)
Projection of vector a on vector b is dot product of a and unit vector b, so for dot product to give projection of a on b, wouldn't magnitude of b have to be 1?
violet flume
its probably not the most immediate way to understand it
crimson sedge
Projection of vector a on vector b is dot product of a and unit vector b, so for...
Yes but take a step back from the formula of "projection" and just think of what the dot product describes by itself
Like I can just say it is that by what you said but that doesn't intuitively explain anything to me, I'm just regurgitating the same formulas in that case
violet flume
dot product just describes how much of a vector lies in the direction of another
or how much of one is shared with another
thats the most helpful way to think about it imo
if you think about like uhh
orthogonality, or like primary colors, that sort of thing
it makes sense that a brighter color is going to have more 'red' in it than a darker color
so it makes sense to scale by the combination of colors
idk im just trying to think of ways to explain it 
crimson sedge
Hmm I see I think it is just one of those questions where I have to explore by myself to fully understand it ig
crimson sedge
I will look over this conversation and read over the links shared
violet flume
but
understanding inner product is high level IMHO
like, you should be comfortable just thinking of it as saying something meaningful about how much two vectors point similarly
at least for now
crimson sedge
Alright I already understand that part, but I guess I will suck it up until I slowly climb down that abstractness ladder lol
Thanks!
.close
cedar kilnBOT
crimson sedge
Yeah it is very not satisfying
violet flume
i mean
crimson sedge
But I guess understanding has its limitations
violet flume
abstractness removes all immediacy of interpretation lol
because you have to understand something completely agnostic of normal intuitive approaches
it just takes time
cedar kilnBOT
Available help channel!
violet flume
you will see it in more contexts
cedar kilnBOT
you will see it in more contexts
violet flume
inner products never stop coming up
crimson sedge
I think I have yet to acclimate to the concept of abstractness, since at some point you just have to admit to yourself that it is impossible to explain something that is very abstract intuitively anymore
violet flume
no i mean it is
there are people that understand stuff that you cant have a picture for or talk about IDK how but
violet flume
intuitive is relative
crimson sedge
True
violet flume
depends on how you have constructed the math language in your head
crimson sedge
Yeah
violet flume
I think I have yet to acclimate to the concept of abstractness, since at some po...
explaining, understanding, and like
demonstrating proving
coral imp
Damn
violet flume
all different stuff
crimson sedge
Sometimes breaking down the whole structure and building it up again is the way to go
violet flume
i feel like if you understand something you should be able to explain it
coral imp
Lexqa send me ur screen time imma see how long ya use discord daily fr
cedar kilnBOT
violet flume
gl
crimson sedge
Lexqa send me ur screen time imma see how long ya use discord daily fr
I'm kinda curious as well lemme see
About 6 hours yesterday 
But thank you jan
Appreciate it
lusty grotto
so the problem is something like why does c somehow lie "more" in the direction of a than b
?
crimson sedge
so the problem is something like why does c somehow lie "more" in the direction ...
Hmm not really it
lusty grotto
but is this not a problem u have
cedar kilnBOT
✅
crimson sedge
but is this not a problem u have
Yeah
I will say it is something I can't answer to well
cedar kilnBOT
@violet flume Has your question been resolved?
stone crystal
Hey guys!
Ive been trying to freshen up on my math, and more currently linnear functions.
And i understand the first 3 questions. However i run in to the same problem everytime a question is stated like this!
if its f(-4), then i understand you place that instead of the x.
But when it says (f) = 30, i dont quite understand what that 30 represents. Or where to put it, or how to deal with it when we have a given equation already?
I understand that if we have no given equation it would basically be that (f) = 30 means its 30 on the Y coordinates. But in this case, im completely lost and i cant seem to find an answer when i try to google it :S
violet night
f(x) = 30
crimson sedge
am i dumb too or does this look right
violet night
represets the function equalling that value for a corresponding value of x
so 30 = f(x)
30 = 3(4x-2)
solve for x
stone crystal
You mean on the top the red dot?
stone crystal
Yes because i initially didnt know the answer. So i pressed reveal answer and therfor it gave me a red dot
😛
crimson sedge
ah, makes sense
violet night
@stone crystal what i've wrote out should be sufficent to understand
stone crystal
ahaaa
No i understand! You solve it as an equation
And remove the F
Thats what confused me as the other one you just replace X and not the entire f 😮
Ive been sitting for hours trying to see if i can understand this shit but couldnt see where the 30 went xD
Really appreciate your help a lot bro ❤️
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
unborn sonnet
cedar kilnBOT
unborn sonnet
can someone help me with this
tropic oxide
have you made progress so far?
crimson sedge
A hint: ||try to transform the 4 in 2^2, 8 in 2^3 and simplify the numerator by denominator in the expoent||
coral imp
Ig ya can rewrite that as
$2^1/4.2^1/8.2^1/16..
unborn sonnet
like this
crimson sedge
Ig ya can rewrite that as
$2^1/4.2^1/8.2^1/16..
Yep, and now just aply the sum of expoent
unborn sonnet
crimson sedge
But to do this u will need the ||infinite geometric series||
unborn sonnet
okk
crimson sedge
a1/(1-r), a1 is the first term
unborn sonnet
s=a/1-r
crimson sedge
Yep
unborn sonnet
unborn sonnet
can someone help me with this
upper garnet
Where ur stuck at
wild barn
calculate A and B separately
unborn sonnet
i lose my that channel
unborn sonnet
calculate A and B separately
how
wild barn
what did you try
upper garnet
He can just do A/B directly coz things will cancel
wild barn
He can just do A/B directly coz things will cancel
how, A and B are sums
my idea was to separate each sum into odd and even tersm
the series of odd terms + the series of even terms
foggy merlin
He can just do A/B directly coz things will cancel
:/
wild barn
I really thought he was serious
unborn sonnet
ok
foggy merlin
^
wild barn
K
foggy merlin
since we cant deal properly with (-1)^n
its better to separate into sum of odd and even terms
unborn sonnet
how can we separate
wild barn
n ranges from 1 to infinity
wild barn
so it ranges through all odd numbers and all even numbers
wild barn
1 ,3, 5 .... and 2,4,6 ...
wild barn
rewrite A for odd numbers
foggy merlin
a change of variable, n= 2p (for even) and n=2p+1 for odd
copper crest
Is this mains
unborn sonnet
Is this mains
yes
unborn sonnet
<@987071591169011762> what is (-1)^n for odd terms ?
if i put odd numbers in n
foggy merlin
$A = \sum_{p=1}^{\infty} \frac{1}{(3 + (-1)^{2p})^{2p}} + \sum_{p=1}^{\infty} \frac{1}{(3 + (-1)^{2p+1})^{2p+1}}$
unborn sonnet
i will get alternate - sign
wraith daggerBOT
Ｈｅｒｅｌｓ
wild barn
i will get alternate - sign
nope
unborn sonnet
**Ｈｅｒｅｌｓ**
what is this?
foggy merlin
what is this?
what we are asking you to do
wild barn
what we are asking you to do
he probably doesn't get what 2p means
or how it got there
foggy merlin
like I said, you do a change of variable for n=2p (which means for even term) and the other sum n=2p+1 (for odd terms)
foggy merlin
$A = \sum_{p=1}^{\infty} \frac{1}{16^p} + \sum_{p=1}^{\infty} \frac{1}{4^p \times 2}$
wraith daggerBOT
Ｈｅｒｅｌｓ
foggy merlin
good looking geometric series
wild barn
yep
unborn sonnet
srry i dont get it
wild barn
he has to be careful with p starting from 1 though
foggy merlin
<:blobcry:971797574916907028> srry i dont get it
did you read our explanation ?
unborn sonnet
yes
foggy merlin
and what didnt you understand
unborn sonnet
**Ｈｅｒｅｌｓ**
why you converted that series into this
foggy merlin
again, I said that we cant deal with (-1)^n properly so we need to separate the sum into a sum where n is even and a sum where n is odd
unborn sonnet
ok
foggy merlin
by a change of variable :
the first sum with n even : n=2p
the second sum with n odd : n =2p+1
foggy merlin
and yadayada, easy algebra
foggy merlin
**Ｈｅｒｅｌｓ**
now I got this
thats something we can now calculate
since its two geometric series
I wont do it, Im lazy
you do the same method for B, and you do A/B, youll have your result
unborn sonnet
help me plss
foggy merlin
Im on a travel rn
unborn sonnet
.close
manic acorn
cedar kilnBOT
manic acorn
I know
manic acorn
QP cross QR gives 2(a cross b), however QR cross QP gives 2(b cross a)
The direction of the area vector just gets reversed
manic acorn
do you know this
Yea
manic acorn
🗿
unborn sonnet
lol
cedar kilnBOT
@manic acorn Has your question been resolved?
honest rune
Well, this is just a convention we follow, the area vector is taken vertically upwards from the surface we are measuring the area of. Your question is logically correct but it is what it is.
So take (QR x QP) as your answer.
meager glade
Can someone explain what the y=y equation is used for?
cedar kilnBOT
Can someone explain what the y=y equation is used for?
meager glade
Im doing revision and i know that my question requires simultaneous equations to find x and y of a equation, but when would i use y=y?
buoyant latch
when you have y = 3x + 4 and y = -x - 1
y = y will mean equate the 2 equations
so 3x + 4 = -x - 1
2nd example, if you have 2y = 6x + 8 and 3y = 6x + 9
then y = y means to turn them into y = 3x + 4 and y = 2x + 3 then equate them
so 3x + 4 = 2x + 3
(all the numbers are nice and divisble because i chose them so, didn't want any fractions in my explanation)
buoyant latch
👍
meager glade
.close
marsh pond
cedar kilnBOT
marsh pond
How do you memorize the square root values?
quiet plover
it just sticks to you the more you do trig problems? 
marsh pond
Is there an easy way for you to remember them all? I see they alternate 1-2-3 on numerator, or 3-2-1 on numerator and 2 on denominator, but wondering if there is a special tactic to remember them all
latent bloom
Hyp(2), shortleg(1), longleg(sqrt(3)) for the 30, 60, 90 triangle
unborn sonnet
thanks for the wallpaper
quiet plover
what?
latent bloom
And hyp(sqrt(2)), shortleg(1), longleg(1) for the 45, 45, 90 triangle
That's all you need to memorize
latent bloom
it just sticks to you the more you do trig problems? <:catshrug:5638187350859448...
True
marsh pond
Ah OK I haven’t learned this yet but how exactly would you solve for 46 degrees? You need to draw a right angle triangle and calculate?
latent bloom
Yeah
marsh pond
Interesting, after finding calculations via the unit circle (1 unit) it can be blown up in size or shrink down in size it doesn’t matter the angle is going to be exactly the same
Pretty fascinating how far back thus unit circle was invented, BCE
And I’m still having trouble memorizing the fraction values for it lol
latent bloom
Lol
When a 30-60 triangle is involved, keep in mind that it has a root 3 and a half
Like 30° is like 60° in the unit circle
But they are flipped
cedar kilnBOT
@marsh pond Has your question been resolved?
obsidian coral
And I’m still having trouble memorizing the fraction values for it lol
Just memorize the first quadrant, and the rest are reflections over the axes. Like quad 2 is a reflection over y axis so the x coords flip signs
Quad 4 is a reflection over x axis, so y coords flip signs
quartz salmon
can i get help with c)?
cedar kilnBOT
can i get help with c)?
quartz salmon
<@1008715274574377040>
could you tell me how you arrived at this formula please
quartz salmon
It means the volume of a circle multiplied by the height.
quartz salmon
so the integral is used to calculate the area
long swan
A cylinder is infinitely many, infinitely thin circles, stacked on top of each other
quartz salmon
and the 2π is from the circumference of a circle
long swan
Yeah
quartz salmon
so 2π * r where r is?
long swan
Your r here is the function
Your h here is the entire positive real line (0,inf)
Wait my bad I wrote that down wrong
$\pi \int_0^\infty (\exp(-kx)\sin(x))^2 dx$
wraith daggerBOT
Mr. Gamer
long swan
That should be your integral
quartz salmon
where do you get the exp(-kx) from?
long swan
where do you get the exp(-kx) from?
This was given
long swan
The radius is the entire function y(x)
Yeah
This might explain
$\pi \int_0^\infty y^2 dx$
wraith daggerBOT
Mr. Gamer
quartz salmon
what was this formula called now again
is it this one?
how do i "find the total volume of all the beads as a function of k>0"
cedar kilnBOT
@quartz salmon Has your question been resolved?
unborn sonnet
HELP
livid hound
how are you getting 11 for a
livid hound
are you just asserting that a is 11 out of thin air?
unborn sonnet
means
livid hound
the first image didn't load
i don't know how you got 11 (which is wrong) for the value of a
wild barn
i don't know how you got 11 (which is wrong) for the value of **a**
he wrote a-d + a + a+d = 33
in the first image
unborn sonnet
why is a wrong
crimson sedge
i don't know how you got 11 (which is wrong) for the value of **a**
i need help
Bro
livid hound
if you're using
a-d + a + a+d = 33
the a in that is different from the a in the general term of the sequence
unborn sonnet
livid hound
note that in
a-d + a + a+d = 33
the a represents the second term
while in
a_11 = a + 10d
that a represents the first term
unborn sonnet
help
velvet mortar
Use the knowledge you know about AP
unborn sonnet
how
inland ocean
What have you tried
inland ocean
the term summation of AP
Can you show your work
unborn sonnet
ok
livid hound
hint: do not make any attempt to determine a_1 and d
obsidian coral
Don't do the work for people or give out answers
cedar kilnBOT
inland ocean
I have solution to the last one too
inland ocean
Alr
inland ocean
Don't do the work for people or give out answers
I thought they will understand better just looking at the solution since its only calculation here.
unborn sonnet
nice you can
obsidian coral
I thought they will understand better just looking at the solution since its onl...
Not exactly, it's more beneficial to see their work and see what they messed up on instead of doing it for them.
cedar kilnBOT
Available help channel!
obsidian coral
.You pretty much gave them the opportunity to take the work and run instead of having them do it on their own
unborn sonnet
cedar kilnBOT
inland ocean
.You pretty much gave them the opportunity to take the work and run instead of h...
I understand, im sorry😭
unborn sonnet
with this one
obsidian coral
<@548061006170161163>
Don't ping specific people
obsidian coral
• Show your work, and if possible, explain where you are stuck.```Did you try anything?
scarlet garnet
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
unborn sonnet
yes lemme show
obsidian coral
`1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an...
7. I hate math and don't wanna do it anymore
unborn sonnet
unborn sonnet
~~7. I hate math and don't wanna do it anymore~~
7.i love maths i wanna do it all life .❤️
i need help
ok bye
guys
its time to sleep
.close
cedar kilnBOT
cedar kilnBOT
✅
tropic oxide
what
tropic oxide
i was going to say something but then decided against it.
unborn sonnet
help me with this
tropic oxide
well, i guess i'm being ordered around now.
unborn sonnet
i was going to say something but then decided against it.
whta is meant by against it?
ok
should i go
??
or you will tell
something
tropic oxide
whta is meant by against it?
when you decide against something, it means you decide not to do it or not to choose it
anyway, you asked for help, so now i have reason to say that your handwriting is kind of bad.
upper garnet
go sleep u did a lot today
tropic oxide
so you now know that $f(x) = \frac12(3^x + 3^{-x} + 2^{1+x} + 2^{1-x})$
wraith daggerBOT
Ann
tropic oxide
do you know how to find the minimum value of this function?
tropic oxide
ok, great. then why not do that?
unborn sonnet
arithmetic mean is >= geometric mean
its kinda tough to apply
i already check
but i dont know
how to solve it
tropic oxide
why not apply it to 1/2 (3^x + 3^(-x)) and then separately to 1/2 (2^(1+x) + 2^(1-x))?
unborn sonnet
ok
tropic oxide
if you find that these things reach their minimum values at the same x, you will find that their shared minimum point is also the minimum point of their sum.
tropic oxide
good night.
cedar kilnBOT
static yarrow
cedar kilnBOT
Available help channel!
limpid tree
13 and 14
cedar kilnBOT
@limpid tree Has your question been resolved?
limpid tree
<@&286206848099549185>
soft owl
is it $\int^0_{-1} f '(X) dX ?$
wraith daggerBOT
Mehdi_Moulati
soft owl
I think the main function is -x²+1
i don't think so
soft owl
$\int^0_{-1} f '(X) dX = [f(x)]^0_{-1}$
wraith daggerBOT
Mehdi_Moulati
soft owl
isn't ?
limpid tree
We want it in 2nd and 4th quad
It cuts y axis at 0,1 and x axis at 1 , 0
If u can use those
,w graph x³
wraith daggerBOT
wraith daggerBOT
soft owl
,w -x3 + 1 ,x from -3 to 3,y from -3 to 3
wraith daggerBOT
limpid tree
Answer is -1
soft owl
yeah of course since from the graph f(0) = 1 and f(-1) = 2
so f(0) - f(-1) = -1
soft owl
you need to find the two points where the two curve are intersect
limpid tree
Ok so
0 and 0
Wait
I can't have a 0
It's impossible
One of the curves have 4/x
I must end up with a number
soft owl
you need to solve the equation:
4/x = 5-x
limpid tree
1,4 and 4,1
soft owl
so know we just calculate the integral between 1 and 4
limpid tree
Those are intersection points?
soft owl
Those are intersection points?
Yes, but we only care about the value of x
to integrate in that range