@plush condor
#help-17
twin meteorBOT
paper depot
expand $(x-19)(x-12)$, use that to build a recurrence relation that the sequence $\alpha_n$ will satisfy. this is kind of newton's formula but going backwards conceptually.
twin meteorBOT
Ann
plush condor
<@946379454056386560>
Try using this
paper depot
Recurrence relation isn't taught yet
you solved a problem just 1 hour ago where you had a recurrence relation for T_n, the sum of nth powers of roots of a polynomial
but ok fine this isnt given to you in those terms whatever
vocal timber
I was only taught this concept please understand
dull elk
I never thought that I'm gonna stuck in this type of question but help me 😭
paper depot
I never thought that I'm gonna stuck in this type of question but help me 😭
!occupied
vocal sleetBOT
I never thought that I'm gonna stuck in this type of question but help me 😭
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).
paper depot
I was only taught this concept please understand
ok see this?
vocal timber
Yeah
paper depot
that is the kind of thing im calling a recurrence relation
it's an equation that gives a rule by which two or more nearby terms in a sequence are related to each other
paper depot
no, "recurrence relation" does not imply "has three terms".
i can try to give more examples but i can see you probably do not want to hear that
vocal timber
I am interested
paper depot
ok sure. have you heard of fibonacci sequence
vocal timber
Just heard of it never really seen what it is
vocal timber
No
paper depot
an AP with common difference $d$ is a sequence which obeys $a_{n+1} = a_n + d$
twin meteorBOT
Ann
paper depot
$a_{n+1} = a_n + d$ is a (particularly simple) recurrence relation
twin meteorBOT
Ann
vocal timber
Got it
paper depot
the "recurrence" part means it relates two or more terms
here the n'th and (n+1)st
but in principle you can think about relations between more terms
vocal timber
I'll be back in a while I'll read after
paper depot
k
vocal sleetBOT
@vocal timber Has your question been resolved?
vocal sleetBOT
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blissful sequoia
vocal sleetBOT
blissful sequoia
shouldnt the slope be b/a and -a/b cuz the slope of a line is the rise of the line over its run
ruby estuary
shouldnt the slope be b/a and -a/b cuz the slope of a line is the rise of the li...
b/a and -a/b to be precise
but yeah
ur right
blissful sequoia
b/a and -a/b to be precise
so the tb is wrong?
ruby estuary
wdym tb
blissful sequoia
textbook
vocal sleetBOT
vocal sleetBOT
Available help channel!
echo plaza
how do i do this i got no idea
vocal sleetBOT
how do i do this i got no idea
paper depot
do you know what phi(n) is in the first place
sleek saddle
Euler Totient I believe
rustic bloom
there has to be a function φ(x) above no
echo plaza
do you know what phi(n) is in the first place
yes
echo plaza
yes
sleek saddle
My guess is that if you write out the factorization of n, it can’t have a prime factor larger than 2023
And the power of the factor is also bounded
echo plaza
i was thinking about using the like "formula" for phi(n) to try and prove this but it didnt work so well
paper depot
,w factorize 2023
twin meteorBOT
paper depot
this ought to be a good starting pt
think about what prime factors p could divide n that would lead to either 7 or 17 or maybe 17^2 dividing p-1..
echo plaza
hm
echo plaza
yeah
paper depot
try playing around w that sorta thing
paper depot
if n = pq with p, q distinct primes, what is phi(n)
and let's also say they are distinct odd primes -- phi(2p) = p-1 is clearly even and so cannot be 2023
echo plaza
if n = pq with p, q distinct primes, what is phi(n)
(p-1)(q-1)
paper depot
ok and can that ever be equal to 2023
echo plaza
yeah
paper depot
for which odd primes p and q?
echo plaza
but we can have as many primes as we want
paper depot
... i think you're either dodging my question or trying to jump ahead
echo plaza
oh sorry
echo plaza
for which odd primes p and q?
any odd primes?
paper depot
give me a pair of odd primes p and q such that (p-1)(q-1)=2023
echo plaza
oh when i said yeah i though you said that they can never be equal
i misread
theres arent any such primes
echo plaza
generally if p divides n then p-1 will divide phi(n) yes?
yes
echo plaza
can you see a problem with that when it comes to phi(n)=2023
Yeah
Bc a product of bunch of even numbers can’t be 2023
paper depot
yup
echo plaza
But what about powers of prime factors
paper depot
wdym
you have just proven that if n has any odd prime divisor at all then phi(n) will be even.
echo plaza
Right
paper depot
and if n doesn't have any odd prime divisors?
echo plaza
and if n _doesn't_ have any odd prime divisors?
its a power of 2
echo plaza
right
paper depot
if k ≥ 2 you won't get any odd phi values
echo plaza
right
so basically
phi(n) can never be 2023
ig that means finite number of values?
echo plaza
ig so lmao
one last qestion though about like powers of primes
how do we know phi(p^n) is even
we cant use the multiplicative property
vocal sleetBOT
@echo plaza Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
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dapper flume
hey guys, Im tryna solve this question. I got the vertical component down but Im struggling on the horizontal part. aren't they supposed to be the same answer??
vocal sleetBOT
hey guys, Im tryna solve this question. I got the vertical component down but Im...
@dapper flume Has your question been resolved?
vast shale
vocal sleetBOT
@dapper flume Has your question been resolved?
dapper flume
Oh, oh my god
Wait it's late here I'll try doing that later morning
WAIT I GOT IT
235/6 + 18 = 343/6!!
TY
.close
vocal sleetBOT
vocal sleetBOT
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bitter pilot
Let $m \in \Z$. Compute the following $\oint_C (z-z_0)^m , dz$, if $C$ is the following:
[ \text{A \textbf{square} with sides parallel to the axes and center $z_0$ with counterclockwise orientation.} ]
My Ansatz was to divide $C$ into four curves (its sides) so that
[ C = C_1 \cup C_2 \cup C_3 \cup C_4. ]
Then for $m \ge 0$, I would argue that by Cauchy's Integral theorem we have
[ \oint_C (z-z_0)^m , dz = 0 ] since $(z-z_0)^m$ would be a polynomial, which are knowingly analytic on $\C$. Furthermore, $C$ is a closed curve and (the part that bothered me), we can construct $C$ in such way so that it is continuously differentiable (see picture).
Is this correct so far?
vocal sleetBOT
Let $m \in \Z$. Compute the following $\oint_C (z-z_0)^m \, dz$, if $C$ is the f...
bitter pilot
twin meteorBOT
modest onyx
Why do people care so much about figuring out the right formula to solving geometric area
Just get out a protractor and measuring stick or whatever and measure it
You can get a good enough estimation of it
bitter pilot
Why do people care so much about figuring out the right formula to solving geome...
too bad complex integrals cannot be interpreted as area
modest onyx
If they're too complex to exist in physical space then they're not worth thinking about
bitter pilot
It's not that simple, because in our lectures, we also said that the curve has to be continuously differentiable, so I was wondering if that was the case here since a square has cusps
regal bane
Fair. Note that this requirement is too strong, your class will likely drop it at some point
Could always just integrate all 4 sides
Say they're a distance r away or something
vocal sleetBOT
vocal sleetBOT
Available help channel!
glass galleon
im doing part B right now
vocal sleetBOT
im doing part B right now
glass galleon
this is what ive done so far
but my question is would -8 turn positive there
so 8rsinθ?
im following a similar question my teacher doing, and she changed the +10 to -10 when equaling
vocal sleetBOT
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.
glass galleon
<@&286206848099549185>
wet halo
im following a similar question my teacher doing, and she changed the +10 to -10...
Subtracted 10rsin(theta) from both sides of the equation
glass galleon
Subtracted 10rsin(theta) from both sides of the equation
ohh okay
so would i add 8
for mine
on both sides
wet halo
Yes 8rsin(theta)
glass galleon
Yes 8rsin(theta)
thats my answer i just got
wet halo
Also note that you can factor out an r^2 from the left side
glass galleon
And cos^2(theta) + sin^2(theta) = 1 always
yes i remembered that
glass galleon
And cos^2(theta) + sin^2(theta) = 1 always
thanks again
wet halo
Also
Do you know why it’s okay to divide r on both sides here?
In order to do that you need to specify something important
Because in general you would simply keep everything on one side and factor out an r to get the factored form of a quadratic
glass galleon
Because in general you would simply keep everything on one side and factor out a...
hmm okay i understand
i had the same idea
vocal sleetBOT
@glass galleon Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
rich sinew
i keep getting 72 rather than 144
i did 3 * 3 * 2 * 2 * 1 * 1 * 2
and also 2 * 3! * 3!
vocal sleetBOT
i keep getting 72 rather than 144
i did 3 * 3 * 2 * 2 * 1 * 1 * 2
and also 2 * 3...
paper depot
note that only girls are not allowed to be adjacent
rich sinew
the first method I figured there were 3 boys that could be seated first, then 3 girls, then 2 boys, then 2 girls etc., and multiplied it by 2 at the end to account for a boy being seated first or a girl being seated first
paper depot
but there's no such restriction for boys
BGBGBG
GBBGBG
GBGBBG
GBGBGB
there are 4 not 2 possible arrangements just looking at the genders
vocal sleetBOT
vocal sleetBOT
Available help channel!
bleak glade
can someone explain to me why the expression for "at least three-fifths of all flowers need to be roses" wouldn't be what i wrote in the image?
vocal sleetBOT
can someone explain to me why the expression for "at least three-fifths of all f...
thin jay
i mean
stuck junco
can someone explain to me why the expression for "at least three-fifths of all f...
What you wrote states that the number of roses, x, would be less than or equal to 3/5 of the total flowers, x+y+z
thin jay
it should be equal to
bleak glade
What you wrote states that the number of roses, x, would be less than or equal t...
oh
golden herald
It'd be fine if you just flipped the inequality
bleak glade
it should be equal to
no because it says "at least", it would be equal to if the wording was like the last bullet point in the question
bleak glade
It'd be fine if you just flipped the inequality
oh yea true true
golden herald
no because it says "at least", it would be equal to if the wording was like the ...
Think of working with
[
\4x{x+y+z}
]
I'd say
twin meteorBOT
bleak glade
Think of working with
\[
\4x{x+y+z}
\]
I'd say
ahh and then equating that fraction to three-fifths
okok thx i got it
.close
vocal sleetBOT
golden herald
noice
vocal sleetBOT
Available help channel!
pallid stream
why is the answer in part (c) perimeter ? isnt that top arc + base ? it doenst include sides... no ?
vocal sleetBOT
why is the answer in part (c) perimeter ? isnt that top arc + base ? it doenst i...
strong grove
why is the answer in part (c) perimeter ? isnt that top arc + base ? it doenst i...
the region is just bounded by the function (the curve) and the base
so there arent any sides or anything to add into the perimeter
strong grove
but how would i know that
kx^2 - x^3 = 0 gives the x intercepts (where the graph cuts the x axis)
solving just gives x = 0 which is the origin and another x=k , so u can just imagine a curve
or u could graph it if u have access to graphing calc
pallid stream
its x^2(k-x) so its js some curve that goes through 0 and k
strong grove
yeah cuts through those points on the x axis
vocal sleetBOT
strong grove
👍 np
vocal sleetBOT
Available help channel!
reef sapphire
Help
reef sapphire
I don't understand Chinese remainder theory
What does it do
How to intuitively understand it
Like for example I intuitively understand euler totient function
hard atlas
which version of crt have you seen
reef sapphire
Lmao there are versions
I seen the euclidean algorithm one
And the one with multiplicative inverse
Explain the one with multiplicative inverse
hard atlas
there are much more general versions
it would help if you showed the statement that you have
reef sapphire
Find the number
Equivalent to 2 mod 7
2 mod 3
1 mod 5
I just don't want to find out numbers
I want to know the real life application
I tried opening this book
But it kept saying
Groups fields
Isomorophic
Rings
Z/nZ
Don't understand any of that
reef sapphire
Like with primes euler totient function
hard atlas
and general modulo stuff?
reef sapphire
Yes xy mod n = 1
I know everything about multiplicative inverse primes euler function
reef sapphire
Fermat test
Yes
You can solve this using euclidean algorithm
But I want the best way
hard atlas
and presumably you have seen a proof which constructs some weird numbers and then constructs x with those, yes?
reef sapphire
Yeah
hard atlas
anyway
the key idea is that instead of solving for x, you first want to solve for some other variables
lets call them y1, y2, y3
what do they do?
reef sapphire
Ok
hard atlas
they have
y1 = 1 mod 7
y1 = 0 mod 3
y1 = 0 mod 5
reef sapphire
True
hard atlas
and
y2 = 0 mod 7
y2 = 1 mod 3
y2 = 0 mod 5
and
y3 = 0 mod 7
y3 = 0 mod 3
y3 = 1 mod 5
reef sapphire
Why are they 0
hard atlas
we'll get to that
hard atlas
can you at least intuitively see that maybe solving for y1,y2,y3 will be easier than solving for x?
reef sapphire
Yes absolutely
hard atlas
good
lets start with y1
like you said, its coprime with 7
but not coprime with 3 and 5
reef sapphire
True
hard atlas
so we know y1 = (some number)*3*5
reef sapphire
Facts
reef sapphire
Yes
hard atlas
so y1 = (some number) * 15 = (some number) * 1 mod 7
so (some number) = 1 in this case
yes?
hard atlas
yes
reef sapphire
True
hard atlas
that it will be the multiplicative inverse? yes
reef sapphire
Let me do it
Y2 = K*35
Y2 = k *35 = 1 mod 3
35 mod 3 = 2
2*k = 1 mod 3
K = 2
Y3
= k* 21 = 1 mod 5
Y3 = 1
K3 = 1
K2 = 2
hard atlas
k3 = 1, but y3=21
reef sapphire
K1 = 1
hard atlas
y2 = 70
reef sapphire
Ok
reef sapphire
Ok
hard atlas
so now we have y1, y2, y3
reef sapphire
Good one man
hard atlas
but we wanted to find x
hard atlas
so we want to solve
x = 2 mod 7
x = 2 mod 3
x = 1 mod 5
for this
now what happens if we take 2*y1 + 2*y2 + 1*y3
and take that mod 7, mod 3, mod 5
reef sapphire
30 + 70 + 21
30 + 70 + 21
121
Wait nah
My bad
191
Ok
191 - 105
86
86 mod 5 = 1
86 mod 3 = 2
86 mod 7
= 2
Ok this method is very sick
But what's the proof
hard atlas
yes lets try to see that without actually computing the number
lets look at 2y1 + 2y2 + y3 again
we know that y1 = 1 mod 7, y2 = 0 mod 7, y3 = 0 mod 7
so what happens if we just take this expression mod 7
reef sapphire
Exactly
hard atlas
next, we know y1 = 0 mod 3, y2 = 1 mod 3, y3 = 0 mod 3
so what happens if we take the expression mod 3?
reef sapphire
It would be 2
hard atlas
yes
which was the coefficient in front of the y2
and finally what happens if we take it mod 5?
reef sapphire
It would be 1
hard atlas
yes
reef sapphire
What if I want the number
Which is like
The least positive number
191
Wasn't the least positive number
Do I just do mod their products
hard atlas
you have to subtract 105 like you did
hard atlas
yes
reef sapphire
Ok thanks bro
hard atlas
yw
reef sapphire
You really showed me a much easier way
Than this bs I have been doing
Caveman fire momwnt
Btw
hard atlas
its the same formulas, isnt it?
reef sapphire
Are you still up for another question
Well the old one has more calculations
And multiplicative inverse bs
I like this one
hard atlas
well we skipped over all these
reef sapphire
Damn let me get another question
hard atlas
every number of those k's is a multiplicative inverse
reef sapphire
Yes
That's by design
Bro the other method had me get mi
For each equation
Then I would get a big M
For all 3
hard atlas
those m_i are just the 15, 35, 21 that we had
reef sapphire
Yeah true
hard atlas
if I had to guess
reef sapphire
And I assume
reef sapphire
I think we did the same method
But you explained it better
Cause the other method has multiplicative inverse
hard atlas
again, my method still needs that
reef sapphire
And we multiplied by the number on the rhs
hard atlas
it just was piss easy for these specific numbers
reef sapphire
Yeah exactly
It's the same method
You just explained it better
And the other method
Added modulo M
Which is the product of all 3
Now can you explain extended euclidean algorithm
reef sapphire
Yes
hard atlas
M=105
hard atlas
Now can you explain extended euclidean algorithm
I have to go, sry
reef sapphire
No problem thanks
vocal sleetBOT
Available help channel!
limpid mauve
Hey, does anyone know where the 2 in this formula comes from?
vocal sleetBOT
Hey, does anyone know where the 2 in this formula comes from?
cedar kernel
kinetic energy
limpid mauve
I was thinking that
cedar kernel
qed = kinetic energy ?
qe being the force on the electron
d the distance traveled
hence the work done by electric field to make a electrol travel d distance
pearl wadi
d the distance traveled
displacement i think you mean
limpid mauve
V²/d
cedar kernel
displacement i think you mean
yeah mb
pearl wadi
its supposed to be v^2/2d
limpid mauve
While keeping the E and V²
limpid mauve
its supposed to be v^2/2d
Really?
limpid mauve
Okay
Bro 😭
But I've never needed to do that when I derived anything else from F=ma
cedar kernel
ok so you can just write (v^2-u^2)/2d like yoda just showed using the motion equation
and to derive it from the energy method you can consider existing kinetic energy in the system
limpid mauve
Okay I found the one I was reffering to
• I did not add 2 here
• (Note that a_{c} is the acceleration and a_{cr} is the orbiting radius. I didn't notice that I called them the same thing when I did it)
• C_{oc} is the circumfrence of the orbit
• Did I just luck out? That the 2 would've been cancelled anyways?
• V_{J} = Volume of Jupiter
• v_{C} = Velocity of Callisto
cedar kernel
The F here is centripital
pardon my spelling
the velocity you mentioned is the tangential velocity
limpid mauve
the velocity you mentioned is the tangential velocity
Yeah
cedar kernel
The one your shared above(the orignal question)
however
reffers to a charger experiencing force due to an external electric field
limpid mauve
This one?
cedar kernel
and moving along the direction of the force
limpid mauve
reffers to a charger experiencing force due to an external electric field
Yeah yea
cedar kernel
yep
limpid mauve
and moving along the direction of the force
cedar kernel
so do you see the difference?
limpid mauve
The two questions are unrelated
limpid mauve
so do you see the difference?
For why one has the 2 and the other doesn't?
cedar kernel
i mean yeah
limpid mauve
Okay okay
limpid mauve
Yes
cedar kernel
different accelerations are causing force
the electric field one has linear acceleration
the other one has aceleration towards the normal ( planatory one )
limpid mauve
Is the normal the same a origin?
cedar kernel
normal just means perpendicular to tangent
limpid mauve
Oh right right
cedar kernel
so notice how the force is towards the centre ( for circles , nomal passes through the centre)
and the velocity is tangent to the force
here is the angular derivation
omega is v/r right?
here v is tangential velocity
limpid mauve
Yeah
cedar kernel
so wait i should set the scene first
im using a string of lenght r, which is attached to a ball and rotating it with omega angular velocity
the ball will be experiencing a centripetal force
towards me/direction of the string/ normal to its path of motion ( circular)
limpid mauve
Does the normal point outwards?
cedar kernel
here
no
generally can
normal just means perpendicular to tangent
force is along the yellow line
velocity is along the orange
limpid mauve
force is along the yellow line
Yeah, I was just unsure of which way the arrow was pointing
cedar kernel
ok i sence confusion still
lets consider
a non uniform cirular electric field , and the ball is positively charged
and the circular path is concentric with the
field
the ball will also feel a force tangentially now
yeah?
limpid mauve
Concentric is like multiple circles with the same origin, right?
cedar kernel
yep
limpid mauve
Alright
cedar kernel
i would preffer centre as the word but yeah it works too
limpid mauve
i would preffer centre as the word but yeah it works too
Alright alright
limpid mauve
Oh I'm so sorry
My flatmates needs help with making dinner
cedar kernel
tangential velocity is not affected by the centripetal acceleration
npnp
tyt
consult a organic chem tutor vid on introduction to centripetal acc
if you need help in furture
spiral linden
can someone plz help explain this to me, i dont think i conceptually understand it
vocal sleetBOT
can someone plz help explain this to me, i dont think i conceptually understand ...
spiral linden
like dumb it down plz
grave torrent
Could you be more specific of what part you don't understand? They used a unit circle but personally I would have sketched y = cos(x) and done it that way, maybe that's why you're confused?
spiral linden
im confused at the explanation, i think i sorta get the x/2 would be the x-intercept but i dont get the 2pim part or the n e Z part or the max/min
grave torrent
You mean x = π/2?
And n ∈ ℤ just means that n is an integer, so ...-3, -2, -1, 0, 1 ,2 ,3...
We also know that 2π is the number of radians in a circle. If I stand in one spot, and turn 2π (360°) around, I just face the same way I was already facing. So if I start facing any point from the centre of a circle, and turn 2π, I am facing the same point I started with.
This is also true if I turn 0π, 4π, 6π, 100π, -100π and so on. So any multiple of 2π that I turn, I end up where I started. we could describe this by saying that if I turn 2πn around, where n is the integers as shown previously, then I'll end up where I've started. So with trig functions, since they can be described by a unit circle, if I start at a solution and turn 2πn around, I'm still at a solution, but it's a different number than the solution, so it's also a solution.
So in this case π/2 is a solution, and so is π/2 + 2πn, for all n ∈ ℤ
spiral linden
ohh ok that makes sense thank you, i think i kinda get it now
and you're right a graph would have probably been easier to visualize imo
grave torrent
yeah I think in school they usually draw y=cos(x), but the circle does work too. Also the unit circle in the picture is more complicated than it needs to be for this question, which probably created unnecessary confusion. Do you now understand the min/max part or do you also want that explained?
grave torrent
Yeah the unit circle makes this more confusing, but don't worry. I'm going to stop explaining it with the unit circle because it's hard for me to do it on text well, but the cos value is actually the x value of any point on the circle, not the y. Sin(x) is the y. But I'm going to use the graph to explain it now (but I think it would be a good idea if you want to in your free time to watch a video on the unit circle, it isn't too hard I think you can get it), do you know how to draw y=cos(x)?
spiral linden
i think so its the x value over the radius drawn on a unit circle right?
grave torrent
yeah, but could you sketch it for me (on paint or anything it doesnt matter) just so I can see.
grave torrent
No I meant y=cos(x). Unless you want to keep using the unit circle and you want me to try and explain it that way?
grave torrent
yeah that's what i mean, sorry if that wasn't clear
spiral linden
nah its my bad
really bad drawing lol
i think the main difference b/w y=sin x and y= cos x is that sin x usually starts at the origin and cos x starts at (0,1) but depending on how its verically/horizontally shifted that could change. from my understanding
idk if thats completely right tho
grave torrent
yeah that's right, terrible drawing but ive never seen a math teacher who can draw so you're fine 😭
spiral linden
lmao
grave torrent
could you label where pi/2, pi, 3pi/2 and 2pi are?
grave torrent
okay good i'm sure this is what you meant but it's just the value of x so where you wrote pi would actually be (pi, -1) but it's fine. So can you tell me what values of x give you a maximum from this?
spiral linden
oh yeah i forgot to label that mb, thanks for correcting, the values of x would be 0 and 2pi b/c the maxes are (0,1) and (2pi, 1) i think
grave torrent
okay so since cos(x) has a periodicity of 2pi (the turning around by 2pi thing I explained above), and from the diagram, you can see that every mulitiple of 2pi you get a maximum, does that make sense?
spiral linden
yes that makes a lot more sense, i think i can actually figure out maxes, mins and x intercepts now. Thank you so much, literally a lifesaver
spiral linden
.close
bright lava
what are the equations for calculus,
what youtube channels or people would you recommend for me to watch and learn,
and how do i do this??
currently solving the second one
vocal sleetBOT
what are the equations for calculus,
what youtube channels or people would you r...
bright lava
plush condor
That looks correct
bright lava
im having doubts lowk idk tho
bright lava
oh damn?
plush condor
$f^{\prime} (x) = \exp(x)\sin(x) + \exp(x)\cos(x)$
tawny nacelle
you derivatives of e^x and sin(x) are correct, but you probably applied the product rule a bit incorrectly 
twin meteorBOT
@plush condor
tawny nacelle
you derivatives of e^x and sin(x) are correct, but you probably applied the prod...
,, (f(x)g(x))' = f'(x)g(x) + g'(x)f(x)
twin meteorBOT
higher!
vocal sleetBOT
Available help channel!
distant perch
AFGE = GEBH = EDHC = 1cm^2
vocal sleetBOT
AFGE = GEBH = EDHC = 1cm^2
distant perch
How do I prove that GJI's height = GIB's height
vocal sleetBOT
@distant perch Has your question been resolved?
distant perch
<@&286206848099549185>
vocal sleetBOT
vocal sleetBOT
Available help channel!
open vessel
I'm trying to mathematically explain to my logic professor that if he keeps conducting his class as strictly as he is - where students explaining topics to each other is punished the same as copying answers - it's statistically better to outright cheat than to risk learning. But I'm having a bit of trouble with the proof.
Right now I have:
P(L) := "percentage of material understood on your own"
P(C) := "probability of being caught cheating"
P(T) := "percentage taught by other student", P(T) <= P(L)'
Average Result of Cheating = 1 - P(C)
Average Result of Learning = P(L) + P(C)*P(T)
But I'm having trouble relating the two to each other. I don't think you can solve it like an equality, since they aren't strictly equal. I also don't really know how to denote cheating as a strict binary outcome, like (C == 1) => 100%.
Obviously the end result is "if P(C) < P(L) (which it almost always is, your class is online ffs), cheating is the statistically better path, which means no one's learning jack shit, which defeats the whole point of the course, you fucking asshat", but I really need to drill it into his head.
vocal sleetBOT
I'm trying to mathematically explain to my logic professor that if he keeps cond...
bright crypt
what do you mean by "cheating is the statistically better path"?
once you have that well-defined, the rest should be algebra
open vessel
Statistically results in a better grade
bright crypt
so you want to show 1 - P(C) > P(L) + P(C) * P(T)?
open vessel
I don't condone cheating btw, it just annoys me to hell and back because I want to teach people without getting punished for cheating
bright crypt
you solved it?
open vessel
no it just made me realize that I was going about it wrong
yeah it's just algebra
of course you'd assert ">" and then prove that it's the case. hypothesis then proof
thanks!
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
lean iris
$\forall x \in ]-\infty; -1[U]0; +\infty[$
vocal sleetBOT
$\forall x \in ]-\infty; -1[U]0; +\infty[$
twin meteorBOT
SELVATOR
lean iris
$\ln(\frac{x}{x+1})$
twin meteorBOT
SELVATOR
lean iris
Let's say we are working at ]-infty:-1[
bright crypt
$$[-\infty, -1]$$?
twin meteorBOT
vhj
lean iris
If we want to divide ln in this way: ln(a/b) = ln(a) - ln(b)
Do we have to multiply inside both of them by the minus?
As: $\ln(-x) - \ln(-x - 1)$
twin meteorBOT
SELVATOR
lean iris
$$[-\infty, -1]$$?
U cant close brackets on infinity side
bright crypt
$$(-\infty, -1]$$
twin meteorBOT
vhj
lean iris
**SELVATOR**
.
lean iris
**SELVATOR**
.
lean iris
**SELVATOR**
Is this correct?
bright crypt
don't multiply the minus into the ln, that'll make it undefined
ln(negative number) is undefined
magic quarry
What kinda math is this😭🙏🏿
bright crypt
$$\frac{x}{x+1} = \frac{-x}{-x-1}$$
twin meteorBOT
vhj
bright crypt
but only the left version can be usefully split for ln
bright crypt
nvm you're right
left side is what you split for positive x, right side for negative x
twin meteorBOT
SELVATOR
lean iris
$$\frac{x}{x+1} = \frac{-x}{-x-1}$$
We can use both of them to calcul (ln(x/(x+1)))'
Ty.
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
novel vector
how do you tell if a function has a bouncing zero
vocal sleetBOT
how do you tell if a function has a bouncing zero
bright crypt
as in x^2 instead of x^2 - 1?
raven owl
Check if the zero is a min/max
vocal sleetBOT
vocal sleetBOT
Available help channel!
digital crag
vocal sleetBOT
crimson sleet
isn't it just +360 -360
digital crag
i tried that but its not working
ill show u the correct answes
like i dony get the 750 one
crimson sleet
yea it is +- 360
digital crag
no but for 750 its wrong
digital crag
oh
crimson sleet
750-720=30
digital crag
thanks!!
crimson sleet
np
hollow pendant
It’s good to know that y = r sin(theta) and x = r cos(theta).
digital crag
huh
hollow pendant
@crimson sleet
Will you be helping with this?
crimson sleet
u got it 👍
digital crag
i dont get it
hollow pendant
$$y = \sin(\theta)$$
$$x = \cos(\theta)$$
twin meteorBOT
@hollow pendant
hollow pendant
<@751533372890677398>
@digital crag
Do you understand how I got this after my original definitions of x and y?
hollow pendant
First, can you identify x and y from the given point?
hollow pendant
now what
Now, given these definitions, can you show what sin(theta) and cos(theta) are?
digital crag
thank you!
hollow pendant
thank you!
So you understand it now?
digital crag
yeah
vocal sleetBOT
yeah
If you are done with this channel, please mark your problem as solved by typing .close
digital crag
need helo
hollow pendant
From this, you essentially want x to be positive.
hollow pendant
i dont get it
In which of these quadrants is x positive?
hollow pendant
is this correct or wrong
hollow pendant
subtract 360
That would not get you in between 0 and 360.
hollow pendant
That would not get you in between 0 and 360.
Do you need help on what to do?
hollow pendant
why was 230 wrong
It's just a completely different angle.
digital crag
so it has to be the exact same angle
hollow pendant
why was subtracting wrong
-130 was wrong because it is not within 0 and 360.
Subtracting 360 only makes that worse; it gets you do -130 - 360 = -490.
hollow pendant
why was 230 wrong
Who told you that 230 is wrong? It is correct.
digital crag
new problem
HELP
ME
bro come n
HURRT UP
nvm i got it
Find the reference angle of -240°.
vocal sleetBOT
@digital crag Has your question been resolved?
digital crag
NO
vocal sleetBOT
@digital crag Has your question been resolved?
twin meteorBOT
hello
novel vector
and then adding 360˚ makes it still the same angle
digital crag
List the greatest negative angles that would have a reference angle of 30\degree in each quadrant.
crimson sleet
**hello**
yea ref angle is between 0 and 90
ref angle means which angle is equivalent to the angle in quad 1
digital crag
List the greatest negative angles that would have a reference angle of `30\degre...
no but
for quadrant 1 here
the ref angle is not the same
crimson sleet
angle is theta,
if Quad 1: Ref angle = theta
if Quad 2: Ref angle = 180- theta.
if Quad 3: Ref angle = theta - 180
if Quad 4: ref angle = 360- theta
one way to think of it is that the ref angle gives you the location of where the absolute value of sin and cos ( y and x) are the same in quadrant 1
vocal sleetBOT
digital crag
.reopen
vocal sleetBOT
✅
digital crag
do i round
raven owl
No your answer should be something like $\frac{\sqrt{\cdot}}{\cdot}$
twin meteorBOT
purururuuriuruin
digital crag
whattttttttt
novel vector
I suggest to rewrite -315˚ as 45˚. They are the same angle
digital crag
what will that do
novel vector
-315˚ + 360˚ = 45˚
novel vector
but then do you know the special triangle?
digital crag
i think its just a coding error
novel vector
digital crag
im so confusedx
novel vector
ok so -315˚ is the same angle as 45˚
flat whale
i think its just a coding error
Yea or formatting
digital crag
ok so -315˚ is the same angle as 45˚
yes
flat whale
,calc cos(-315 deg)
twin meteorBOT
Result:
0.70710678118655
thats the answer
digital crag
but its marking me wrong
flat whale
thats the answer
No
digital crag
okay
flat whale
The answer is an irrational number that can't be expressed as a finite decimal
digital crag
it wants you to put sqrt(2)
what do you mean
novel vector
raven owl
it wants you to put sqrt(2)
That is not in the range of the cosine function
raven owl
Also don't give the exact answer
digital crag
what the heck
flat whale
Use sohcahtoa
digital crag
im confused
flat whale
,tex .sohcahtoa
twin meteorBOT
riemann
flat whale
https://cdn.discordapp.com/attachments/903463353417072641/1373873009961734174/2d...
And this
digital crag
whats the answer
novel vector
So -315˚ is the same thing as 45˚
cos(45˚) = ?
Use this special triangle:https://cdn.discordapp.com/attachments/903463353417072641/1373873009961734174/2d_2.png?ex=682bfe72&is=682aacf2&hm=9ef36e829edb3be32f6fbefa643830871ae0d23726e121c8d5dad895f0e966d2&
digital crag
and then explain
flat whale
whats the answer
Use
flat whale
**riemann**
This
novel vector
$\cos\left(45\ degrees\right)=\frac{1}{\sqrt{2}}$
novel vector
do you know how to simplify: $\frac{1}{\sqrt{2}}$
twin meteorBOT
hello
novel vector
without any radical in the denominator?
novel vector
are you still on this one?
digital crag
yes
novel vector
and then using this triangle: https://cdn.discordapp.com/attachments/903463353417072641/1373873009961734174/2d_2.png?ex=682bfe72&is=682aacf2&hm=9ef36e829edb3be32f6fbefa643830871ae0d23726e121c8d5dad895f0e966d2&
cos(45˚) = adjacent ÷ hypotenuse
digital crag
yes bc soh cah toh
novel vector
what is the value of the side adjacent to 45˚ from the image?
and the value for the hypotenuse?
novel vector
yes, so $\cos\left(45\ degrees\right)=\frac{1}{\sqrt{2}}$
twin meteorBOT
hello
novel vector
and then proper form is to never have a radical (square root sign) in the denominator,
so:
try doing this: \frac{1}{\sqrt{2}}\cdot\frac{\sqrt{2}}{\sqrt{2}}
$\frac{1}{\sqrt{2}}\cdot\frac{\sqrt{2}}{\sqrt{2}}$
twin meteorBOT
hello
digital crag
wait ur a genius
novel vector
so then what do you get?
digital crag
sqroot 2 divided by 2
digital crag
lets do another problem
ima atempt it on my own first
thats the problem
okay so
sin of -240
is the same as
sin of 120
but the problem is
sin of 120 is
not a special case
so we cant like do the soh cah toa here
novel vector
so we should first find the reference angle that is equivalent to -240˚
novel vector
and remember that reference angles are $0\le\theta\le90$
twin meteorBOT
hello
digital crag
oh its more than 90
digital crag
it does
novel vector
so the reference angle, which is the same as -240˚, is -60˚
novel vector
wait so
digital crag
so the reference angle, which is the same as -240˚, is -60˚
no its the same as 60
novel vector
but it's different from -60˚, im pulling up an image
digital crag
not neg 60
digital crag
that would be the initial side
novel vector
so using this triangle:
you can find sin(60˚)
imagine the triangle on the right put on this image:
digital crag
im confused
novel vector
so -240˚'s reference angle is 60˚
60˚ is the angle between the line and the x-axis
there's 60˚ between the blue? line and the x-axis here
novel vector
yes, using this special triangle that u should memorize:
the triangle on the right
so then get sin(60˚) from it which is sqrt(3)/2
digital crag
so u made a equal to 1
novel vector
made what = 1
well the a just cancels out
you can ignore "a" because it cancels out when you do it: $\frac{a\sqrt{3}}{2a}=\frac{a}{a}\cdot\frac{\sqrt{3}}{2}=1\cdot\frac{\sqrt{3}}{2}=\frac{\sqrt{3}}{2}$
twin meteorBOT
hello
novel vector
so first you know this: