so, since our angle is in quad2, this is outside of that
#help-17
thin vale
so think about what answer is is giving us
it must be giving us the answer from imagining the other triangle
the one that would be in quad ||4||
so how to rotate from quad ||4|| into quad ||2|| ?
iron crown
I wanna say we would just adjust our angle by 180 deg
thin vale
I'd want to agree
iron crown
So if this is correct, my angle would be arctan(-2) + 180 deg
iron crown
yes
thin vale
so +pi
iron crown
gotcha tysm
thin vale
np
iron crown
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bright fog
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tropic tiger
Hello, i need to explore this numerical series(sorry i dont know how this called in english) for convergence. I dont even know how to make up a normal equation.
vocal sleetBOT
Hello, i need to explore this numerical series(sorry i dont know how this called...
tropic tiger
like this whole line is just one number of numerical series, so it goes like 5/7+(5*8)/(7*13)+(5*8*11)/(7*13*19) and etc
vocal sleetBOT
@tropic tiger Has your question been resolved?
tropic tiger
<@&286206848099549185>
vocal sleetBOT
@tropic tiger Has your question been resolved?
flat whale
Use the limit test
vocal sleetBOT
@tropic tiger Has your question been resolved?
runic arrow
Hello, i need to explore this numerical series(sorry i dont know how this called...
let's say the n'th item of the sum is a_n . Notice how a_n = a_n-1 * (3n+2)/(6n+1)
vocal sleetBOT
@tropic tiger Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
low lake
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devout urchin
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devout urchin
can anyone explain why the integration range changes?
from 0 to 1
becomes
from 1 to 82
full kiln
you integrate in w.r.t to u
devout urchin
whats wrt?
full kiln
with respect to
hasty pulsar
Yeag
devout urchin
but it's not necessary isnt' it?
full kiln
and integrate from the range originally
but if u are still in terms of u then u have to change the integrating interval
devout urchin
so all u substitution works this way?
vast shale
how do i find a sequence with $\map f x = e^{x^3}$ as its exponential generating function
vocal sleetBOT
how do i find a sequence with $\map f x = e^{x^3}$ as its exponential generating...
twin meteorBOT
vast shale
Product to sum idenity.
Why does the order of multiplication matter in this?
vast shale
It says it does in the image 
vast shale
sin(a)cos(b)
cos(a)sin(b)
vast shale
glossy maple
They are just written "differently" to help students
Like
sin(a)cos(b) can be written as cos(b)sin(a)
which is the same as
cos(a)sin(b) but with the a and b flipped
vast shale
Not understanding
glossy maple
This is the same as saying
Ok actually
I thought I had a good example but nvm
Lol
vast shale
Product to sum idenity.
Why does the order of multiplication matter in this?
the first two look kinda simliar to the double angle formula 
How are these formulas derived
glossy maple
From the sum of angles formulas I'm pretty sure
vocal sleetBOT
@vast shale Has your question been resolved?
eternal glacier
vocal sleetBOT
eternal glacier
should I use this theorem ^ to solve this?
"Write the vector V as a linear combination"
paper depot
no you don't need to know what a dot product even is for your problem.
eternal glacier
OK
eternal glacier
this is Ax = b
am I on the right track here?
paper depot
yes but two notation issues exist
- the original linear combination should be written as $V = x_1U_1 + x_2U_2 + x_3U_3$ (you can use names other than $x_i$ but you CANNOT name the coefficients $U_i$ again and you CANNOT put the $U_i$, themselves vectors, into a column vector)
- your seven is uncrossed.
twin meteorBOT
Ann (glomed)
eternal glacier
your seven is uncrossed.
0 marks
eternal glacier
1. the original linear combination should be written as $V = x_1U_1 + x_2U_2 + x...
hmmm, lemme ignore 2, but lemme think about 1 for a sec
oh OK
eternal glacier
yes but two notation issues exist
so it would be better to use [x y z] for the x column vector in Ax = b?
glossy maple
`your seven is uncrossed.`
0 marks
I agree
paper depot
sure as long as you understand what's what
i.e. you're able to write "V is a linear combo of the U_i with yet unknown coefficients, but im giving the coefficients names to write equations with"
vast shale
how to find x?
vocal sleetBOT
how to find x?
vast shale
wait does x + 20 + 40 = 180?
glossy maple
No
Try drawing a line, parallel to the existing lines, and going through where the angle x is
quaint oriole
Yeah draw a line that is perpendicular to the two original parallel lines and that also passes through the angle x, such that two right angle triangles are created
vast shale
do we know for sure they are right though?
quaint oriole
quaint oriole
do we know for sure they are right though?
Because the line will be perpendicular to the two parallel, the angle between them must be 90 degrees
leading to the two right triangles
now, here you can see that z + x + y = 180
and you can also see that z = 180 -90 -20
y = 180 -90 -40
so z = 70
y = 50
so 180 - 70-50 = 60
so x = 60
hope that helped @vast shale
quaint oriole
np!!
solid dawn
An automobile manufacturer is concerned about a fault in the braking mechanism of a particular model. The fault can, on rare occasions, cause a catastrophe at high speed. The distribution of the number of cars per year that will experience the catastrophe is a Poisson random variable with λt =3 What is the probability that at most 3 cars per year will experience a catastrophe?
vocal sleetBOT
An automobile manufacturer is concerned about a fault in the braking mechanism o...
@solid dawn Has your question been resolved?
serene parrot
is this correct
vocal sleetBOT
is this correct
serene parrot
, rotate
twin meteorBOT
serene parrot
solid dawn
.reopen
prisma meadow
How would this be solved?
vocal sleetBOT
How would this be solved?
vast shale
How would this be solved?
hint: ||acceleration, deceleration, uniform motion||
prisma meadow
huhhhhh
is there a specific law to describe whats happening
i think ik what the motio nis but i can't describe why it is
lusty sphinx
hint: ||acceleration, deceleration, uniform motion||
the train is accelerating yes?
as the train constantly changes its velocity the object will resist this change according to the law of intertia?
prisma meadow
hint: ||acceleration, deceleration, uniform motion||
is it the training is moving to the left or it was moving right and came to a sudden halt?
vast shale
the train's acceleration is to the left
doesnt matter which way its moving or its velocity
prisma meadow
oh
lusty sphinx
doesnt matter which way its moving or its velocity
ok
prisma meadow
how would that be done
lusty sphinx
what would happen to the ball if the string were to suddenly break?
my colleague has just posted this question above
vast shale
how would that be done
the question is incomplete since we do not know the frame of reference
prisma meadow
what is frame of reference
vast shale
just say the mass doesnt move since the choice of frame of reference can be the ball itself
tho if u consider it as the train itll go to the right
if u consider it as the earth itll go to the left
vast shale
say u drop a ball inside a train what is its path
lusty sphinx
say u drop a ball inside a train what is its *path*
yes?
prisma meadow
wdym yes
lusty sphinx
idk bro we're only yr10
prisma meadow
lmao
lusty sphinx
😦
prisma meadow
🤣
prisma meadow
say u drop a ball inside a train what is its *path*
wouldnt it just go to the back of the train
lusty sphinx
I appreciate your help Jester, however you will need to explain this concept to us a little more eloquently as we do not possess the fundamental knowledge to fluently follow your explanation.
prisma meadow
I appreciate your help Jester, however you will need to explain this concept to ...
bro its fine :ksul
vast shale
so basicly, if u are standing inside the train, and the train is constantly accelerating to the left
prisma meadow
💀
vast shale
then from ur perspective the ball will move like this
lusty sphinx
then from ur perspective the ball will move like this
Ahhhh I understand
prisma meadow
thats what the answers said but why
wouldnt it just drop to the floor
and roll
cos gravity
vast shale
u mean like this?
lusty sphinx
u mean like this?
that wouldn't make sense though
because the train is accelerating left
vast shale
yeah its accelerating to the left
vast shale
but if u are standing outside the train itll look like this
prisma meadow
what why
vast shale
u are outside the train
prisma meadow
wouldnt it appear the same
vast shale
look at this peppa pig animationhttps://www.youtube.com/watch?v=V8YteuxWDwo
prisma meadow
look at this peppa pig animationhttps://www.youtube.com/watch?v=V8YteuxWDwo
at tjhe start the trains moving so why does it just go up and down
vast shale
tho u dont need to think outside the train, the answer is fine if ur inside the train
prisma meadow
if there is no acceleration and the velocity is constant
vast shale
at tjhe start the trains moving so why does it just go up and down
because the train is moving constantly
prisma meadow
does that mean the bal ljust goes up and down?
but if say the train was moving at like 50km/h
vast shale
does that mean the bal ljust goes up and down?
yeah
prisma meadow
constantly
wouldnt the balls inertia cause it to be
going toward the back of the train
lusty sphinx
wouldnt the balls inertia cause it to be
inertia only occurs when there is a change in motion
when it's constant the ball is moving with the train in the constant velocity
prisma meadow
oh
prisma meadow
doesnt matter its 50km/h or 67,000 mph
do i need to use the parabola from the ball in the future?
lusty sphinx
Jester could you please explain this question to us?
prisma meadow
and that
tough kraken
Can someone help me with this arithmetic problem?
vocal sleetBOT
Can someone help me with this arithmetic problem?
ember ledge
Can someone help me with this arithmetic problem?
u can simplify the 6 and the 2
thorn current
is there a reason why 2 is used a divisor? can you use any prime divisor of 10 in this example?
vocal sleetBOT
is there a reason why 2 is used a divisor? can you use any prime divisor of 10 i...
vast shale
yes
thorn current
ty
For the last part of the solution, This means any multiple of 10 has 2 as a divisor and is therefore composite idk why, but this statement confuses. is it basically because 2 is a prime and any multiple of a prime number (prime number * x where x > 1) is composite?
rough barn
a number that is a multiple of something is never prime
after all, the definition of a prime number p is a number that satisfies n |\ p for all 1 < n < p
outer warren
2 happens to be a prime but that's not really the main point here
thorn current
yeah i want to make sure i understand this correctly
like i know even numbers are composite except 2, but i want to understand this properly
rough barn
"this means any multiple of 10 has 2 as a divisor and is therefore composite" basically means 10n = 2 times something
which is not the definition of a prime
thorn current
ok
thorn current
a number that is a multiple of something is never prime
can't you multiple a number by 1 and it would be a multiple? isn't 2 a multiple of 2?
eternal glacier
vocal sleetBOT
eternal glacier
how would I solve for these?
dot product is involved somehow?
and with this column vector am I allowed to move v1 to the top?
brittle minnow
you need to know how elemantry row transformations behave with determinants
eternal glacier
you need to know how elemantry row transformations behave with determinants
elementary means one operation away from identity matrix, yeah?
brittle minnow
umm... noo.. (as in not a good working definition)
I mean in a sense yes
But not very helpful here
eternal glacier
But not very helpful here
Oh, how would you define it in this context?
brittle minnow
well, there are 3 types of elementary row operations
eternal glacier
so if the determinant of the 4x4 matrix is -5
I need to do some reverse engineering to get back to the 4x4 matrix somehow
and then I believe they are just asking for the first column of the original 4x4 matrix, with scalar of 3 on the first entry, if I understand correctly
eternal glacier
I need to do some reverse engineering to get back to the 4x4 matrix somehow
so if my understanding is correct here, I would be stuck on this part, and knowing how to proceed
brittle minnow
swap
scalar
add
you need to know how determinant interacts with these
vocal sleetBOT
@eternal glacier Has your question been resolved?
sleek flame
can someone help to explain what each option means? I need help with understanding
vocal sleetBOT
can someone help to explain what each option means? I need help with understandi...
sleek flame
vocal sleetBOT
@sleek flame Has your question been resolved?
vocal sleetBOT
@sleek flame Has your question been resolved?
vocal sleetBOT
@sleek flame Has your question been resolved?
vocal sleetBOT
@sleek flame Has your question been resolved?
fringe prairie
@sleek flame Do you understand what multiplying a matrix by a vector represents?
So I know what sort of explanation you might find more intuitive.
You've selected the correct answer but perhaps it might not be useful to say something along the lines of "This can only happen when A is non-invertible or singular or has liearly-dependent columns, or has a null space that isn't only 0, and A's shape tell us none of that."
If you understand what a linear transformation does then it's a bit more intuitive. Otherwise it just sounds like a bunch of jargon.
sleek flame
can we go through the options one by one
I got my answer, cause it sounds right to me, but I don't exactly understand the other options
fringe prairie
Well, let's start at the beginning. Do you know aht it means for there to be non-trivial solutions?
I suppose not? If x is the zero vector, then Ax = 0 is always true. The question is whether or not there are vectors x that are not the zero vector that satisfy out equation.
But I have to go back to the original question of whether or not you understand what a linear transformation or what it looks like. Cause if we go through what each of those "means" I'm not sure you will gain much understanding.
sleek flame
I know that linear dependent is non trivial solutions, linear independent is trivial solutions and they are both consistent
not consistent means no solution
if the matrix can be transformed then its consistent
vocal sleetBOT
@sleek flame Has your question been resolved?
sleek flame
.close
vocal sleetBOT
stiff pumice
crimson pumice
vocal sleetBOT
crimson pumice
how do you exactly take out the x's from the trig
I can really only think of making sinx/cosx = sqrt3
and since that makes tanx = sqrt3
does tan move to the other side as tan^-1?
sudden compass
Wdym?
sudden compass
does tan move to the other side as tan^-1?
When u do tan^-1 on both sides u cancel out the LHS one
sudden compass
do I multiply tan by tan^-1 to cancel them out
Not multiply, apply the function
crimson pumice
yea I know you cancel them out but I am so used to "carrying it"
sudden compass
yea I know you cancel them out but I am so used to "carrying it"
I don't think I have done thst
crimson pumice
yea because were taught differently
sudden compass
And tan^-1(sqrt3) is easy
crimson pumice
yea but I need 2 points still
sudden compass
I can really only think of making sinx/cosx = sqrt3
I guess for the 2nd one u set sqrt3 cos x = -sin x
crimson pumice
-sinx?
sudden compass
Yeah
crimson pumice
:V
sudden compass
Hmm..Well idk but perhaps u can 2npi
crimson pumice
it is symmetrical :))))
ehhh plus minus
rose flower
¯_(ツ)_/¯
sudden compass
it is symmetrical :))))
Aren't almost all trig functions symmetrical
crimson pumice
sqrt3 kinda doesn't make it symetrical anymore
rose flower
...
wind frost
can someone help me with dilations geometry #1115514300598067271
crimson pumice
anyways were not trying to find those points
sudden compass
sqrt3 just moves amplitude
Yes
crimson pumice
can someone help me with dilations geometry <#1115514300598067271>
you can't do this you know
sudden compass
can someone help me with dilations geometry <#1115514300598067271>
U can't advertise bruh
sudden compass
oh no shot
Do an <@&286206848099549185> ping
wind frost
okay
crimson pumice
why did you ping them
were getting off point
so folow your guys guide
would the answer be pi/3 and 4pi/3?
sudden compass
would the answer be pi/3 and 4pi/3?
Yeah ig
crimson pumice
whats n in this senario
crimson pumice
but theres no n in there?
actually nvm
I'll just work with these numbers for now
sudden compass
Sorry I am not very good at trig...still improving yk
sudden compass
I'll just work with these numbers for now
Are there more questions?
vast shale
vocal sleetBOT
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Available help channel!
royal grove
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royal grove
can i say that this is not possible as 1295 multiplied by some number will always result in a number with ending digits 0 or 5
where as (2^l -2^k)(2^l + 2^k) will always result in numbers with ending digits as 2, 4 or 6
hence it is not possible for (36a + b)(a + 36b) to be a power of 2
sorry for the bad handwriting.
vocal sleetBOT
@royal grove Has your question been resolved?
royal grove
<@&286206848099549185>
royal grove
<@&286206848099549185>
vocal sleetBOT
@royal grove Has your question been resolved?
patent nymph
can i say that this is not possible as 1295 multiplied by some number will alway...
must they be integers?
royal grove
must they be integers?
yes
patent nymph
where as (2^l -2^k)(2^l + 2^k) will always result in numbers with ending digits ...
What about (2^5 - 2^3)(2^5 + 2^3)
royal grove
What about (2^5 - 2^3)(2^5 + 2^3)
but k and l must be greater than 5
as minimum value of (a, b) can be (1, 1)
so 2^k = 37 = 2^l
patent nymph
How about (2^25 - 2^23)(2^25 + 2^23)
royal grove
yuppp makes sense
patent nymph
does that answer your question?
royal grove
it doesn't
royal grove
want to prove this
patent nymph
what happened between the second and fourth lines of the notebook
royal grove
what happened between the second and fourth lines of the notebook
i replaced value of 72ab
72ab = 4^l - 1296b^2 - a^2
patent nymph
I see
patent nymph
When I saw the question, I thought about trying to prove some things about a and b
because every factor of a power of 2 is a power of 2
royal grove
When I saw the question, I thought about trying to prove some things about a and...
a and b must be even right
patent nymph
How did you get from the first step to the second
royal grove
I used the value of 2^k + 2^l from this (line number 9 of notebook)
I am just complicating things sorry
patent nymph
i got 2 more relations
The way I found that a and b were even was like this: for the sake of contradiction, assume a(or b, without loss of generality) is odd. Then a + 36b is odd and more than 1 since b is positive so 36b is even and at least 36. So a + 36b is odd and larger than 1, so isn’t a power of 2. Contradiction, so a and b are even
And using a similar line of reasoning another stronger property about a and b can be derived
But then I didn’t know how to go on from there, so maybe this combined with your method could work
royal grove
The way I found that a and b were even was like this: for the sake of contradict...
i did it using b = 2^k - 36a. This shows that b is even as an (even - even = even)
patent nymph
i did it using b = 2^k - 36a. This shows that b is even as an (even - even = eve...
You can reduce that modulo another number to get something else
royal grove
You can reduce that modulo another number to get something else
i got
(-1)^l ≡ a (mod 3)
(-1)^k ≡ b (mod 3)
oh since a and b are even
a and be must be of the form (3m + 1) and (3n + 1)
l and k must be even
patent nymph
You can reduce that modulo another number to get something else
I meant for you to notice that 36 is divisible by 4 and 2^k = 36a + b is larger than 37
royal grove
you mean to say that b should be of form 4m
royal grove
4n
patent nymph
Could you try putting these expressions for a and b into the formulas you got
royal grove
in this one right?
patent nymph
You could also try in this one
See if you can find any parity things you couldn’t do the first time
twin meteorBOT
royal grove
i got this
and lets say i keep on repeating this process
so the RHS will reach 2^0 at some point
and at LHS we will have some 36x + y
so 36x + y = 1. This is not possible
as the minimum value of 36x + y = 37
royal grove
yes i can but this would be my first time writing a proof clearly
so please correct if there would be any mistakes in it
patent nymph
Looks ok to me
royal grove
Looks ok to me
Thanks for you help ^^
royal grove
.close
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Available help channel!
dusty phoenix
vocal sleetBOT
dusty phoenix
Quick question, for part c, why is Y south? Isn’t south where I put “w”
I thought y would be considered west of the lighthouse
quiet valve
L is the lighthouse and you’re traveling to B. Which is south compared to L.
The green diagram at the start of the example shows dotted lines pointing to north. @dusty phoenix
dusty phoenix
Oh
But I’m still confused, even if I’m trvalleinf to B, wouldn’t y be west of L
OHHHH I got it
.close
reef scarab
I'm kinda lost. When doing this basic DE, I got a different result from that in the answer sheet, and I'm unsure as to whether I made a mistake. My answer began to differ from the answer sheet's when I integrated -cos(2x)/2, which I evaluated as -cos(x)sin(x)/2, instead of -sin(2x)/4. I was thinking that they're equivalent (or are they?), but they led to a difference in answers...
vocal sleetBOT
I'm kinda lost. When doing this basic DE, I got a different result from that in ...
reef scarab
what did I overlook?
reef scarab
after getting -sin(x)cos(x)/2, when integrating again, I got cos^2(x)/4
reef scarab
I’m still learning the basics of trigo
basic differential equations
olive veldt
I’m still in 10th
solid sage
Na that’s the same thing
reef scarab
Na that’s the same thing
thought so too, but I got a different constant for the last term, which made me go "ok wtf"
(constant I got was 3/4)
viral copper
Assuming you made no mistake they're the same
But if you're getting different final answers then you messed up somewhere
There's only one solution to the DE with those parameters
reef scarab
yeah, probably messed up somewhere in the computations ig...
hm.
gonna have to type everything out 💀 here I go
viral copper
$y = \iiint 2 + \sin 2x \dd x^3$
twin meteorBOT
NEONPerseus
viral copper
solid sage
I see no error
reef scarab
$y' = x^2 - \frac{\cos x \sin x}{2} +2.5x$, so c = -6 (same as answer aside from the trig)
then
solid sage
Wait lol I just looked at the solutions and said it had no error thinking they were you’re answers
twin meteorBOT
Kiameimon | Welt Rene (glomed)
chrome tundra
sin2x = 2sinxcosx
solid sage
I mean you prolly just went wrong somewhere in calculations
chrome tundra
,calc 7/2
twin meteorBOT
Result:
3.5
how'd you get 2.5x
reef scarab
.........................
solid sage
What you get when you integrated -cossin/2
reef scarab
What you get when you integrated -cossin/2
cos^2 x/4
chrome tundra
also missing the constant
reef scarab
when we set it = 0
so it isn't the cause
$y = \int x^2 - \frac{\cos x \sin x}{2} +3.5x - 6$
twin meteorBOT
Kiameimon | Welt Rene (glomed)
solid sage
I mean it would help to see your solution if possible
reef scarab
I mean it would help to see your solution if possible
gimme a moment to typeset everything out 
solid sage
chrome tundra
**Kiameimon \| Welt Rene (glomed)**
this is fine, you're practically done at this point, just use sin2x = 2sinxcosx before integrating
reef scarab
$y'' = \int 2 + \sin 2x dx = 2x - \frac{\cos 2x}{2} + c$, evaluate to get c = 3.5
twin meteorBOT
Kiameimon | Welt Rene (glomed)
reef scarab
this is fine, you're practically done at this point, just use sin2x = 2sinxcosx ...
but why isn't it the same?
like, they're both equal, yet integrating them gives different results?
chrome tundra
wdym?
reef scarab
like why wasn
chrome tundra
**Kiameimon \| Welt Rene (glomed)**
complete this integration first
reef scarab
why wasn't the integral of sinx cos x /2 = sin(2x)/4
chrome tundra
what?
reef scarab
**Kiameimon \| Welt Rene (glomed)**
integrating again gives this $x^2 - \frac{\cos x \sin x}{2} +3.5x$, which constant evaluates to -6
twin meteorBOT
Kiameimon | Welt Rene (glomed)
chrome tundra
**Kiameimon \| Welt Rene (glomed)**
integrate this
i mean complete that integration
x^2 integrates to x^3 / 3
reef scarab
**Kiameimon \| Welt Rene (glomed)**
and then integrating this gives me $\frac{x^3}{3} + \frac{cos^2 x}{4} + \frac{7x^2}{4} -6x$
twin meteorBOT
Kiameimon | Welt Rene (glomed)
chrome tundra
write -sinxcosx/2 as -sin2x/4 integrating that gives +cos2x/8
you don't get a cos^2
you get a cos(2x)
/8
reef scarab
you get a cos(2x)
but it's the same as cos^2 x/4 I thought... what I did was factorise out -1/2 and then integrate cos(x)sin(x) as u usually would
chrome tundra
cos(2x) is the same as cos^2x / 4?? what are you smoking
reef scarab
as in
chrome tundra
cos(2x) = cos^2x - sin^2 x isn't it
reef scarab
I'm saying that
since -cos(x)sin(x)/2 = -sin(2x)/4, their integrals should be the same
or so I thought
well
solid sage
Cos no
chrome tundra
yea so integrate -sin(2x)/4
what does that integrate to?
$\int sin(ax)dx = -\cfrac{cosax}{a}+c$
reef scarab
I know that it integrates to cos(2x)/8
chrome tundra
is that the formula?
solid sage
They do equal the same thing
twin meteorBOT
pikachupikachu
reef scarab
cos^2(x)/4
chrome tundra
yea so show how you integrated it
cobalt crypt
,w expand cos^2(x)/4 - cos(2x)/8
twin meteorBOT
cobalt crypt
its almost as if ... theyre the same up to a constant
reef scarab
GAH SNOW
chrome tundra
using sub for cosxsinx is wild
reef scarab
Your manners of talking like this makes me feel so... 
not in a negative way tho
it's unique to say the least
geez, so it IS the same...
solid sage
Yea
reef scarab
💀
cobalt crypt
anyway
solid sage
But how did you get your final answer wrong
reef scarab
But how did you get your final answer wrong
the thing is I didn't
it just differed by a constant
which is 1/8
and when my constant is 3/4
it adds up to give the answer
cobalt crypt
you should see all the forms of the secant integral
reef scarab
7.8
reef scarab
you should see all the forms of the secant integral
NO
NO
NO
JUST
NO
Ima stop you RIGHT THERE
chrome tundra
close
reef scarab
.close
vocal sleetBOT
solid sage
Lol
vocal sleetBOT
Available help channel!
lyric sluice
The red is a function
Which out of the blue and green is the correct derivative of that function?
vocal sleetBOT
The red is a function
Which out of the blue and green is the correct derivative ...
solid sage
Blue
floral seal
i would say blue and green are the same line
rugged vortex
Why is one of your graphs different
Domain
solid sage
Ah
rugged vortex
The red is a function
Which out of the blue and green is the correct derivative ...
They're both fine as long as you restrict the domain
So the blue curve would be for all x > 0
floral seal
ah
rugged vortex
The green one needs no domain restriction, but it's also a pain in the ass looking equation
It's like how the derivative of ln(x) is 1/x for all x > 0, but the derivative of ln|x| is 1/x for all x in its domain
rugged vortex
The green one, if you simplify it fully, becomes the blue curve
rugged vortex
the right answer should be green one then
Both are fine as long as you communicate domain
wary mantle
For the proof of the first law of Kepler, the geometric way uses the following: \begin{align*} a &\sim \frac{1}{r^2} \ a &= \frac{k}{r^2} \ \frac{v}{t} &= \frac{k}{r^2} \ v &\approx k \cdot \frac{\Delta t}{area \ swept \ out \ in \ \Delta t}\end{align*}
vocal sleetBOT
For the proof of the first law of Kepler, the geometric way uses the following: ...
wary mantle
Apparently, they arrive at v by eliminating r^2.
How can they get that expression from t/r^2 though?
viral copper
The first law is proving that the paths of the planets are elliptical with the sun at one of the focii right
wary mantle
The first law is proving that the paths of the planets are elliptical with the s...
Yes
wary mantle
The first law is proving that the paths of the planets are elliptical with the s...
This is just one part of the proof, it shouldn't have to do with the actual law yet though
It uses the second and third laws of Kepler
wary mantle
That planets have constant areal velocity?
No, I've proven the second and third laws, I'm proving the first now.
wary mantle
That planets have constant areal velocity?
The proof in the StackExchange post I sent uses
\begin{align*} a &\sim \frac{1}{r^2} \ a &= \frac{k}{r^2} \ \frac{v}{t} &= \frac{k}{r^2} \ v &\approx k \cdot \frac{\Delta t}{area \ swept \ out \ in \ \Delta t}\end{align*}
but how did they arrive at the last expression?
viral copper
I don't know how valid what they did is
It seems to be that they determined the areal velocity depends on v by virtue of dimensions
You can arrive at that expression yourself with the second law I think
$\dv{A}{t} = \frac{L}{2m}$
twin meteorBOT
NEONPerseus
wary mantle
**NEONPerseus**
Yep
wary mantle
$\dv{A}{t} = \frac{L}{2m}$
the distance planets traverse in an infinitesimal of time is constant, thus they travel traverse same distances in same times
But if they got their last expression from this, then isn't what they've done before unnecessary? Starting with the inverse square law, breaking a into v/t, ...
wary mantle
Hm, they have that $v = k \cdot \frac{t}{r^2}$, the third law of Kepler says that $T^2 \sim r^3$
If they used the third law of Kepler, they would arrive at v \approx k, but they arrived at k * dt/dA
vocal sleetBOT
@spring solstice Has your question been resolved?
viscid ore
You might try #groups-rings-fields
vocal sleetBOT
@spring solstice Has your question been resolved?
vocal sleetBOT
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Available help channel!
eager hearth
How do I know if a matrix has an orthonormal set. (Eigenvalues, eigenvectors and characteristic polynomial)
vocal sleetBOT
How do I know if a matrix has an orthonormal set. (Eigenvalues, eigenvectors and...
eager hearth
I know if the matrix is real and symmetrix you have a solution
But for example this matrix also has an orthonormal set:
0 j
j 0
the set for eigenvaleu j is {1/sqrt(2), 1/sqrt(2)}
vocal sleetBOT
@eager hearth Has your question been resolved?
eager hearth
<@&286206848099549185>
vocal sleetBOT
@eager hearth Has your question been resolved?
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prisma imp
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grizzled bear
20/2=10
Or half of the triangle BAD using this length
If the cente of the base is F, draw triangle FAD
Might be easier than BAD
grizzled bear
Seems correct
prisma imp
what doi do after
grizzled bear
What angle did you find
prisma imp
=45.6
prisma imp
ohk
grizzled bear
(the pyramid is symmetrical)
prisma imp
its the same
grizzled bear
Ye
Just multiple the angle you got by 2
You can approximate to 90 degrees if approximation is required
91*
prisma imp
so thats the ans
grizzled bear
Approximately, yes
fiery elbow
In how many different ways can 20 squares of the puzzle grid of 100 unit squares be colored so that only 2 squares are colored in each row and column?
vocal sleetBOT
In how many different ways can 20 squares of the puzzle grid of 100 unit squares...
fiery elbow
this is probably the hardest permutation problem i've ever encountered
i don't even have a clue on how to begin solving this
vocal sleetBOT
@fiery elbow Has your question been resolved?
dark kiln
i know how to begin, there's 10! ways to pick 10 squares, so each row and column has 1 sqaure
but I can't continue
in the example they made 5 rectangles
i don't know if that's necessary though
nah that can't be important
vocal sleetBOT
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Available help channel!
prisma imp
vocal sleetBOT
desert hornet
didn't someone already help you?
prisma imp
no
desert hornet
yes they did
prisma imp
i was stuck
desert hornet
you just didnt listen to what they said
desert hornet
what have you tried
prisma imp
i was tryinh to re arrangle the formula
desert hornet
what formula
prisma imp
yh but
52.7=1/2(xy) x 8.426
?
how should i do the next one?
@winged fossil
?
ok
i am confused
@winged fossil
?
oh
so
u dont put b to get 4.213
thxxx
.close
river kettle
What is question A asking? I don’t understand it
vocal sleetBOT
What is question A asking? I don’t understand it
@river kettle Has your question been resolved?
fringe prairie
What the heck is the second number of degrees listed there?
39 degrees 53 degrees? Is it supposed to be 39.53 or what?
rugged orchid
I suspect that’s in minutes
fringe prairie
Yes, probably a typo.
lyric fossil
are you asking what $\frac{17}{8} \div 3$ is?
twin meteorBOT
maximo
rose raft
i think its (1 7/8 )/3
lyric fossil
it is
vocal sleetBOT
@vast shale Has your question been resolved?
pliant coyote
I derivate with L'Hopital and I got -e^x/1-e^x
vocal sleetBOT
I derivate with L'Hopital and I got -e^x/1-e^x
hidden kelp
if you just plug in $\infty$ you get a $\frac{\infty}{\infty}$ case, so have you tried using L'Hopital?
twin meteorBOT
imTyp0
hidden kelp
actually nvm, e^x would just repeat forever
pliant coyote
I derivate with L'Hopital and I got -e^x/1-e^x
pliant coyote
but you can do this without lhopital
Oh, can I?
hidden kelp
well you get e^x/e^x = 1
oh fair
lyric fossil
Oh, can I?
yes
lyric fossil
I derivate with L'Hopital and I got -e^x/1-e^x
first and formost this also has an indeterminate form
so you could apply lhopital again
pliant coyote
oooh
lyric fossil
as for the non lhopital way, you can factor e^x from the top and bottom
pliant coyote
-e^x/-e^x = e^x/e^x, I see
lyric fossil
you'll get $\frac{1+e^{-x}}{xe^{-x} - 1}$
twin meteorBOT
maximo
lyric fossil
the limit of this as x goes to infinity should (hopefulyl) be clear
river kettle
What is part A exactly asking?
vocal sleetBOT
What is part A exactly asking?
river kettle
I don’t understand it
lusty sphinx
What is part A exactly asking?
you can use trigonometry to find the length of AC
river kettle
But what does it mean when I have to find the expression?
lusty sphinx
But what does it mean when I have to find the expression?
it means that you leave it as a fraction in simple terms
vocal sleetBOT
@river kettle Has your question been resolved?
dark field
But what does it mean when I have to find the expression?
I think it means your answer should be formed by a messy combination of sin cos tan, but not in form of decimal number returned by your calculator.
vocal sleetBOT
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Available help channel!
undone aurora
is my answer correct?
paper depot
how do we know 1 ∈ P? have you proved that this must hold in any ordered field?
lyric fossil
they have earlier
vocal sleetBOT
@undone aurora Has your question been resolved?
undone aurora
how do we know 1 ∈ P? have you proved that this must hold in any ordered field?
oh sorry for not including that
but i proved that earlier
because someone in my class with a similiar solution asked the prof if his answer was correct for this question and the prof replied with "if you think something is wrong then something IS wrong". So idk if my proof is correct
this was my classmates solution
paper depot
so you have proved that 1 is positive in any ordered field
ok
yeah idk i cant see a way to like, improve that in any way
i personally would see this as a specific case of a more general phenomenon, namely that fields of positive characteristic (i.e. ones where you can add some finite number of copies of 1 and get 0) are never ordered
by an argument similar to what you did
in an ordered field 1 must be positive, thus so must be 1+1, and 1+1+1, and so on, but then you hit zero and the order breaks down.
sonic wyvern
an airplane is flying at an airspeed of 345km/h on a heading of 040 degrees. The wind is blown at 18km at a bearing 087 degrees. Determine the ground velocity of the airplane and include a diagram in your solution.
vocal sleetBOT
an airplane is flying at an airspeed of 345km/h on a heading of 040 degrees. The...
@sonic wyvern Has your question been resolved?
vocal sleetBOT
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Available help channel!
lapis ruin
need help to do this activity on desmos
vocal sleetBOT
need help to do this activity on desmos
sudden compass
need help to do this activity on desmos
What is question 3?
Also I don't really understand what u wanna do on desmos
sudden compass
Bruh
prisma imp
Pls
prisma imp
K
sudden compass
Wait for someone
sudden compass
Oh this one
sudden compass
Q4 is a calculation question. Just use trig + herons formula
sudden compass
Huh? U haven't been taught that?
lapis ruin
nope
vast shale
$A = \sqrt{s(s-a)(s-b)(s-c)}$
twin meteorBOT
Feynmann
lapis ruin
i think the angle can be taken out by the desmos
sudden compass
i think the angle can be taken out by the desmos
It should show u when u click on the angle
lapis ruin
so in the 4a i need to find the angle of abc and cda
sudden compass
As for area draw a perpendicular from opposite vertices to the disgonals
sudden compass
so in the 4a i need to find the angle of abc and cda
Yeah
lapis ruin
ok so i get it how to do 4a now
for the 4a i got the angle is this the correct way?
oh we need to do the quadrilateral area and angle on geobra not desmos my mistake sorry
sudden compass
It's okay
lapis ruin
is this correct for 4a)
sudden compass
Pretty sure yeah
fathom hedge
vocal sleetBOT
fathom hedge
the zero vector is present, so that axiom works
scalar multiplication also works
so its gotta be the addition axiom
but im not sure how to show that
or how to come up with a set of values that disprove it
fathom hedge
<2,0,1> & <-4,2,2>
resultant of addition gives <-2,2,3>
which does not comply
so i guess thats it?
I just chose random vectors that i noticed fit though
paper depot
yeah sure
paper depot
what is the "natural" defn of scaling on R^n with complex scalars tho
fathom hedge
<:thonk:406575732563902485> what is the "natural" defn of scaling on R^n with co...
umm
Idk 💀
paper depot
exactly me neither
fathom hedge
well
ima ignore that one
im tryna prove all these mfs now
1 was aight but a reliased
well i went from v = v to
v + 0 = v + 0v
and i was like ooh 0 = 0v
but what like axiom allows me to infer like
v + a = v + b implies a = b
and 2 i got no idea
worthy citrus
The axiom that says vector spaces are groups under addition
Or one of the specific axioms that falls under that
worthy citrus
Yeah ofc
fathom hedge
wait waht
r u sure
like if im proving shit i mean
cus theres no axiom that seems to imply
fathom hedge
but what like axiom allows me to infer like
stuck on number 2
i tried to like seperate
ill call lambda n cus easier to type
n0 = n0 + 0
but that does nothing
fathom hedge
n0 + (-0)
fathom hedge
λ0 = λv - λv
how so?
paper depot
allow yourself to multiply both sides by λ
paper depot
allow yourself to recognize that subtracting a vector from itself gives 0
paper depot
do you have a list of axioms handy
fathom hedge
paper depot
ok so then have you already proved that -u = (-1)u and (-λ)u = -(λu)
fathom hedge
hm yueah
fathom hedge
agree
fathom hedge
agree
fathom hedge
uhh
-v is just (-1)v
so yeah disagree
wait
i meant to type agree
yes
agree
paper depot
-v is just (-1)v
formally these are different things
paper depot
despite them being provably equal
paper depot
im using the theorem that -u = (-1)u and axiom #9 and commutativity of field multiplication and that same theorem again
vocal sleetBOT
@fathom hedge Has your question been resolved?
vocal sleetBOT
@fathom hedge Has your question been resolved?
vocal sleetBOT
@fathom hedge Has your question been resolved?
vocal sleetBOT
@fathom hedge Has your question been resolved?
vocal sleetBOT
@fathom hedge Has your question been resolved?
west mortar
Related rates question. Answer to a is 0.833rot/s. Please help I don’t understand this at all, how do you solve this?
vocal sleetBOT
Related rates question. Answer to a is 0.833rot/s. Please help I don’t understan...
@west mortar Has your question been resolved?
west mortar
<@&286206848099549185>
hushed pewter
,calc 90*(1000/3600)/(2pi30)
twin meteorBOT
Result:
0.13262911924325
Hmm.. I get something different
vocal sleetBOT
@west mortar Has your question been resolved?