1 and 2 are in parallel
#help-27
quick dome
worn ivy
to get the equivalent resistance i need to remove the current source which makes the 4 ohm resistor in parallel with the two 6 ohm resistor(which are in series so i can just add then)
quick dome
Eq resistance is just (1/10 + 1/6)^-1
acoustic leaf
the equivalent resistance is between terminals a and b
quick dome
Which turns out to be 15/4
My apologies
For this one 3 ohms is correct
I misunderstood
acoustic leaf
Which turns out to be 15/4
that would be the correct equivalent resistance as seen by the current source, but for constructing the norton equivalent circuit we are interested in the equivalent resistance between terminals a and b
quick dome
I think it might just be a regional thing and you infer and approach things differently then I do
Like the in different places names for certain theorems are different and stuff
But I really don't know what you mean by Norton equivalent
So I really can't help you with that specific way of solving
acoustic leaf
well that is what the question was asking for in the first place
quick dome
I just know that for parallel resistor
Current will split in inverse ratio of resistance
And for series
In direct ratio of resistance
That's the only method I know
Can't help you with anything too specific
Sorry for the inconvenience caused
acoustic leaf
to return to this, this is called the "short circuit current" and if you can find it, it will be the same as the norton current (think about why that would be the case)
worn ivy
ive just realised i put Voltage down as 9V instead of 18V,
ive literally tried everything i can think so i might end up having to ask my professor for help
acoustic leaf
if you can correctly calculate the open circuit voltage then
(norton current) = (norton resistance)/(open circuit voltage)
devout snowBOT
@worn ivy Has your question been resolved?
worn ivy
if you can correctly calculate the open circuit voltage then
(norton current) = ...
would the open circuit voltage be 18V?
acoustic leaf
how do you get 18V?
worn ivy
how do you get 18V?
by using kirchhoff's current law, 6A = I1 + I2 -> 6A = V/6+V/6 -> 6A = V/3 -> V = 18
acoustic leaf
what happened to the 4 ohm resistor?
restive river
isn't this off topic?
worn ivy
what happened to the 4 ohm resistor?
Sorry, you right. I completely forgot about the 4 ohm resistor. Would this be correct?
Correct orientation
acoustic leaf
no, the 4 ohm resistor isn't directly connected to the current source
it might be simplest to take the 4 ohm and 6 ohm resistor in series, and use that to find the current going through them
devout snowBOT
@worn ivy Has your question been resolved?
static raft
Hi.
static raft
I am not stuying for a long time and I am stuck getting why this limit does not exist.
$\lim_{{(x, y) \to (-\infty, \infty)}} (x + y^2)$
woven radishBOT
Mary
stone fjord
you have $-\infty + \infty$ which is an undertimined form.
woven radishBOT
FluxusX2
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vast canyon
im trying to geaph the derivative of this and im struggling
devout snowBOT
im trying to geaph the derivative of this and im struggling
vast canyon
in wolframalpha
(Divide[8,Sqrt[Power[8,2]+Power[(40)(40)2π(40)580e-6(41)(40)x(41)(41)-(40)Divide[1,2π(40)56e-6(41)(40)x(41)](41)(41),2]]])
urban briar
Plot[f(x), x] ?
vast canyon
its not doing anything when I do that
supple knot
wolfram sometimes can't chain things
find the derivative first
then type it into the plot
urban briar
For those things I just switched to Mathematica
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abstract kiln
Anyone knows? I think the answer is 90, I'm not sure and I honestly don't know how to arrive at that answer either.
devout snowBOT
Anyone knows? I think the answer is 90, I'm not sure and I honestly don't know h...
abstract kiln
should I make a proportion between the two triangles?
abstract kiln
ooh, and for the calculation of the area of the quadrilateral having the numbers?
olive snow
Normally you will have thoses
abstract kiln
thank you very much, I think I have it
olive snow
You're welcome
abstract kiln
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oblique rover
how to find [\lim_{x\to\infty}ax+x\cos x=\lim_{x\to\infty}x(a+\cos x)] for $a\in\mathbb{R}$
devout snowBOT
how to find \[\lim_{x\to\infty}ax+x\cos x=\lim_{x\to\infty}x(a+\cos x)\] for $a\...
woven radishBOT
Slowaq
oblique rover
ive already found out that for a = 0 it doesnt have limit
what should be the other cases?
a≤0 and a≥0?
lucid oracle
I'm not sure if its enterily correct since its been a really long time since ive done limits and i was never the best at calculus but i think the limit doesnt exist for all a.
For one the limit of a sum is the sum of the limits so that the limit you wrote above is the same as lim(ax) + lim(xcosx) which are both divergent
sand dove
ive already found out that for a = 0 it doesnt have limit
why did a = 0 not yield a limit
iron sun
For one the limit of a sum is the sum of the limits so that the limit you wrote ...
Can’t apply that rule
lucid oracle
Can’t apply that rule
how come
oblique rover
why did a = 0 not yield a limit
because xcosx id unbounded function
sand dove
because xcosx id unbounded function
not lower bounded and not upper bounded
oblique rover
it oscilates between -infty and +infty
sand dove
to be precise
iron sun
how come
It’s when u know they’re convergent u can apply it
Unless u maybe have some other conditions
sand dove
it oscilates between -infty and +infty
not rigorously that but yes
so, find the other values of a that make you also "oscillate between - and + infinity"
lucid oracle
It’s when u know they’re convergent u can apply it
oh okey, i never knew
iron sun
It’s part of the hypothesis in the theorem
oblique rover
so, find the other values of a that make you also "oscillate between - and + inf...
hm from desmos im able to see that it also oscilates between -infty and infty for a\in(-1,1)
and for other values it oscilates in the same quadrant
sand dove
and for other values it oscilates in the same quadrant
by same quadrant you mean same half plane
sand dove
hm from desmos im able to see that it also oscilates between -infty and infty fo...
so yes for a in (-1,1) you will have oscillations between "- and + infinity"
sand dove
yes you mean for a = 1.4 it stays positive for x > 0
oblique rover
yes you mean for a = 1.4 it stays positive for x > 0
yea exactly
but since im evaluating x to infty i dont care about x<0
oblique rover
hm tbh im not sure but when a is not from that range both sqeeze functions tend to infinity
where as a\in(-1,1) they tend different ways
oblique rover
hm tbh im not sure but when a is not from that range both sqeeze functions tend ...
but i presume that this doesnt mean that limit is infinity
<@&286206848099549185>
sand dove
but i presume that this doesnt mean that limit is infinity
you are almost there
the last thing that would help you
is that for example when a > 0 and not in (-1,1)
is that the "range of oscillations" gets higher and higher lower-bounded
to the point where the lower bound becomes +infinity, and thus HAS to go to infinity
once again to remind you that -1 <= cos(x) <= 1 can help a lot
sand dove
is that the "range of oscillations" gets higher and higher lower-bounded
but you'll find that not every a outside of (-1,1) gets the range of oscillations higher and higher lower-bounded
even it the oscillations "stay in the same quadrant"
sand dove
for a = 1.4 as you can see no problem
the lower bound gets bigger and bigger
now to find if every a outside of (-1,1) is like that
oblique rover
now to find if every a outside of (-1,1) is like that
well it should be shouldnt it?
cuz the function is bounded by x(a-1) and x(a+1)
and these are monotonous functions and at some point they get to +-infinity
misty crest
the functions aren’t that boring
oblique rover
and these are monotonous functions and at some point they get to +-infinity
but there is a=+- 1
and this shouldnt have limit because it oscilates between 0 and +-infinity
random helm
and this shouldnt have limit because it oscilates between 0 and +-infinity
yes, there is no limit for a in [-1; 1].
sand dove
but there is a=+- 1
exactly
for a = 1, the function is bounded between x(1-1) and x(1+1)
so between 0 and 2x
so it has no limit because you can pick any non-negative finite value and the function will attain it forever
for a = -1 "reverse" the sign
and otherwise the oscillations on any fixed finite value will eventually end
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lament schooner
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versed jetty
where a should be
to a certain extent it's a free choice.
it's more what's pragmaatic than anything
but the i and j vectors are common
versed jetty
Mm?
versed jetty
not really
they're more like w1 and w2
and the diagonal vector is analogous to u in the first pic
lament schooner
cuz i needed to find orthogonal projection of e
this picture makes me believe that the diagonal line is a and w1?
or am i on crack
trail eagle
Aren't they talking about a = (cos θ, sin θ)?
lament schooner
yeah
trail eagle
That's a vector
So yeah, they are projecting e1 and e2, the basis vectors, onto the vector a
trail eagle
But this is a different image
trail eagle
This one is the projection of e1 and e2 on a.
lament schooner
This one is the projection of e1 and e2 on a.
so the line L or rather a
lament schooner
is like u here?
versed jetty
Aren't they talking about a = (cos θ, sin θ)?
but then why isnt it bolded
trail eagle
In this picture you are projecting e1 and e2 on the vector a, so a acts just like the a from the definition you had earlier.
trail eagle
In this one you are projecting a onto both basis vectors, so e1 and e2 act as w1 and w2.
lament schooner
In this one you are projecting a onto both basis vectors, so e1 and e2 act as w1...
oh ok ty
can i know what P_tetha
means
acoustic leaf
P for projection, theta being the angle of the line
trail eagle
can i know what P_tetha
If you have theta fixed, that defines a line in R^2.
Now imagine squishing points in R^2 onto that line by projecting all of their vectors onto the line.
When you multiply P_theta by a point (its position vector), it tells you where that point lands on the line after doing the transformation above. (Purple arrows show where the point at the back of the arrow ends up at after applying P_theta, not the actual vector that represents that point)
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trail eagle
This is what it would look like for the line y=x (or theta = pi/4)
native heart
why does Newton's method need the function f to be in C^2? Since the iterations only involve the first derivative
devout snowBOT
why does Newton's method need the function f to be in C^2? Since the iterations ...
native heart
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barren garden
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barren garden
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woven radishBOT
barren garden
A bit stuck with the bottom rhs integral
jaunty kernel
sorry <@764108874042703902> go ahead
no try
barren garden
tried to do the byparts shortcut by integrating sin(2x) or finding the derivative of sin(2x) and then doing the same with e^-sin(x) and nothing seems to be helping, so is it just not byparts then?
or am I messing it up somehow
timber pebble
tried to do the byparts shortcut by integrating sin(2x) or finding the derivativ...
maybe its nice to try uhh
$\sin 2x = \sin (x+x) = 2\sin x \cos x$
woven radishBOT
jan Niku
timber pebble
then we have $\int 2 \sin x \cos x e^{\sin x}\dd x$
woven radishBOT
jan Niku
timber pebble
this looks much more tractable
@barren garden do you have an idea of how to proceed with this hint?
jaunty kernel
not take sinx as a variable like z or something
and do by parts
@barren garden hey
jaunty kernel
its easier when u take sin(x) = z or any variable
u will get 2e^z z dz
@barren garden next u do 2 z d(e^z)
and by parts integration and ull get the answer
barren garden
and by parts integration and ull get the answer
Did I mess up somewhere?
Looks wrong
jaunty kernel
wait
jaunty kernel
when u take sinx = u why did u write sin (u)
u will get e^u not e^sin(u)
@barren garden
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sharp roost
guys what type of angle is this?
devout snowBOT
guys what type of angle is this?
lunar harbor
guys what type of angle is this?
(probably) a right angle?
you can't tell for sure b/c it's not given, but it looks like one
arctic ember
guys what type of angle is this?
right
lunar harbor
so it cant be right
If it's asking you to "identify the type of angle", then the idea is that you're just eyeballing it and going "good enough" (it's just to get a feel for the general definition, don't get too caught up on precision here)
gleaming socket
89° 😂
gleaming socket
Bro summoned the squad with the wrong question 😭
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lament schooner
the normals of the two parallel planes here
devout snowBOT
the normals of the two parallel planes here
acoustic leaf
yes, but in general we have that if we are given a plane equation
ax + by + cz = d
then (a,b,c) is a normal vector to that plane
any scalar multiple would also work, but those are the obvious normals
lament schooner
yes, but in general we have that if we are given a plane equation
ax + by + cz =...
what is a normal vector of a plane?
devout snowBOT
what is a normal vector of a plane?
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pastel bolt
how can i prove that if a probability density function has domain R then it has an asymptote at y = 0
devout snowBOT
how can i prove that if a probability density function has domain R then it has ...
solid hull
I mean I don't know a direct proof but given that for a PDF dom. R, f(x)>= 0 for all values of x, and the total area under the curve must add up to 1, I have a feeling you can make an equation to represent that the function must approach 0 as the ends of the PDF travel off to infinity
fiery marten
how can i prove that if a probability density function has domain R then it has ...
That's not true
pastel bolt
i had a sus feeling that it wasnt
fiery marten
You can construct a function such that it has infinitely many "spikes" as x increases
Each spike of height 1 and decreasing width
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pastel bolt
can i have some help here
devout snowBOT
can i have some help here
devout snowBOT
@pastel bolt Has your question been resolved?
fossil locust
im quite positive that A, B and C are all correct?
no A is not necessarily true
C is true by odd symmetry
pastel bolt
can you give an example when A is not true
fossil locust
can you give an example when A is not true
f(x) = |sin x| for x > 0 and -|sin x| for x < 0
pastel bolt
f(x) = |sin x| for x > 0 and -|sin x| for x < 0
but would this still be periodic?
fossil locust
fossil locust
but would this still be periodic?
oh wait shit
yeah that is interesting then, odd and periodic
pastel bolt
does periodic mean it has to be the same repetition for all x in R
wait but couldnt we use the example of |sin(x)| anyway
fossil locust
wait but couldnt we use the example of |sin(x)| anyway
wouldn't be odd then
fossil locust
can i have some help here
A, B, C all seem true but I don't have a reason
fossil locust
might just be a mistake
ah it's this
ah right they assumed the period was 2
so that doesn't directly relate to statement A
pastel bolt
ive been trying to find a function where only one of the options are true for like an hour
pastel bolt
can i have some help here
and wouldnt every term in options a,b and c be equal to 0 anyway
like all the individual integrals
wouldnt they all be 0
fossil locust
wouldnt they all be 0
nah, they cancel each other out
so sin x is a very good example of such an f(x)
ah that means that only A and C are true
fossil locust
ah it's this
forget about this, this is unrelated
fossil locust
A is k + (-k) = 0
C is also k + -1 * k = 0
pastel bolt
with period of n would be sin(2pi/n x)
fossil locust
B is like k - (-k), so not necessarily 0
pastel bolt
but k is equal to 0 is it not
if you take integral of kn to (k+1)n of sin(2pi/n x)
youll get 0
fossil locust
but k is equal to 0 is it not
no
fossil locust
with period of n would be sin(2pi/n x)
the period of any function is a number
the period of sin(x) is 2pi
pastel bolt
so n would be 2pi in that case
fossil locust
so n would be 2pi in that case
no, the period of sin(2pi x) is 2pi/2pi = 1
cause it's a horizontal compression of factor 2pi
so we're nearly there actually
pastel bolt
but you said sin(x)
fossil locust
yeah so the period of sin(2pi/n x) is n
pastel bolt
ye
fossil locust
but you said sin(x)
I was rushing ok
pastel bolt
allg
pastel bolt
if you take integral of kn to (k+1)n of sin(2pi/n x)
but then this
it doesnt matter what the period,n, is
or what value of k is
itll always equal 0
for sin(2pi/n x) atleast
fossil locust
jesus the question gets more insane the more I look at it
pastel bolt
ikr
i genuinely feel like its just a mistake
and all A,B and C are correct
but i just need confirmation ya know
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lament schooner
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olive snow
Cutting it in two equal part
lament schooner
Cutting it in two equal part
do you uh have an idea how to prove this
olive snow
Try paralelogram identity or smth like this
lament schooner
okok
lament schooner
devout snowBOT
lament schooner
what is u here?
delicate fossil
proj_b(u) is just b dot u right
static swallow
proj_b(u) is just b dot u right
no
it think it is the orthogonal projection of the vector
static swallow
on a
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@void knot Has your question been resolved?
void knot
why floor?
peak blade
devout snowBOT
peak blade
Can someone help me with 7?
hollow pulsar
do yk the exterior angle of a triangle rule?
peak blade
nooo
hollow pulsar
no?
peak blade
I don’t know
You mean the straight line ?
for example beta is 77
if we find the angle besides beta
is 180-77
hollow pulsar
How do I get angle acf
Sum of angles in a triangle is 180
peak blade
how
peak blade
Sum of angles in a triangle is 180
okok
peak blade
How do I find angle of DCF
peak blade
the angle is 35 degree
this was angle ACF
hollow pulsar
yes
peak blade
answer
hollow pulsar
now DCF
peak blade
I don’t know how to find DCF😭
peak blade
two angels are equal
hollow pulsar
thats for isoceles
peak blade
ohh yhhh
hollow pulsar
but for equilateral, theyre all equal to 60
hollow pulsar
its ok
peak blade
ACD = 18
Omgg yhhh
I’m so clumsy
I don’t know how to fix my clumsiness
😭😭
I always do small mistakes in exams
I got reduced points
visual maple
anyone know how i can make the green function connect both in its original form f(x) and derivative?
devout snowBOT
anyone know how i can make the green function connect both in its original form ...
visual maple
i want it to connect to the other points
north roost
what are the functions for blue and red
visual maple
oh ya sorry
forgot to provide
(ignore the one thats not activated g(x))
im happy to change the function completely btw
as long as it works
north roost
what the heck
north roost
im thinking of making derivative the same
polar chasm
just design some polynomial that does the job
visual maple
just design some polynomial that does the job
no thing is in my total sum of functions, i need minimum of two functions to be natural log, trig or exponential
its an annoying task
visual maple
im thinking of making derivative the same
wdym
polar chasm
no thing is in my total sum of functions, i need minimum of two functions to be ...
oh wait
visual maple
😔
polar chasm
damn
polar chasm
okay, log is probably the best bet here
polar chasm
a*ln(bx+c) + d
visual maple
ok look we CAN try to do trig but that means we'd need to change another function
polar chasm
a*ln(bx+c) + d
this will be your general form ig
north roost
oh lord
polar chasm
a*ln(bx_1 + c) + d = y_1
a*ln(bx_2 + c) + d = y_2
ab/(bx_1 + c) = y'_1
ab/(bx_2 + c) = y'_2
you need to solve this
unless im mistaken
polar chasm
second x coord
polar chasm
the points it will pass through are (x_1, y_1), (x_2, y_2)
and the derivatives will be y'_1 and y'_2
those are values you can get
and then you can solve the system
visual maple
$a \cdot ln(bx_1 + c) + d = y_1 \ a \cdot ln(bx_2 + c) + d = y_2 \ \frac{ab}{(bx_1 + c)} = y'_1 \ \frac{ab}{(bx_2 + c)} = y'_2$
woven radishBOT
pixel
visual maple
this is what u said right?
polar chasm
yeah, that's the system you'll need to solve
to find a,b,c,d
i dont think it will have nice sols
visual maple
thats fine but like
is there some sort of online calculator
😭 i dont wanna go through all that
polar chasm
wolfram alpha
visual maple
the points it will pass through are (x_1, y\_1), (x\_2, y\_2)
also for the coords, what coords do i choose
polar chasm
also for the coords, what coords do i choose
those you want it to pass through
visual maple
in the original function?
polar chasm
that'd mean end of the blue func and start of the red func
visual maple
or derived one
polar chasm
in the original function?
original
polar chasm
top ig
visual maple
oh
alr
(8, 36)
(13.5, 100)
original function ^
(7.98, 9.5)
(13.5, 5.29)
derived function
polar chasm
and y'_1 and y'_2 will be heights of the derivations
at x_1 and x_2
so blue'(x_1) and red'(x_2) respectiverly
visual maple
$a \cdot ln(8b + c) + d = 36 \ a \cdot ln(13.5b + c) + d = 100 \ \frac{ab}{(7.98b + c)} = 9.5 \ \frac{ab}{(13.5b + c)} = 5.29$
woven radishBOT
pixel
visual maple
smthn like that
polar chasm
,w aln(8b + c) + d = 36, aln(13.5b + c) + d = 100, ab/(8b + c) = 9.5, ab/(13.5b + c) = 5.29
woven radishBOT
polar chasm
Jesus fucking christ
visual maple
oh
polar chasm
Ahhhh
devout snowBOT
@visual maple Has your question been resolved?
thick schooner
why would you do that
it’s solutions have more probability of being right than just the answers
visual maple
why would you do that
well idk wolfram said no solution
visual maple
it’s solutions have more probability of being right than just the answers
well ok what should i do
thick schooner
idk
i just commented on the chatgpt thing
if WA said no solutions
then that’s probably right
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timber parcel
can anyone help me with these 2? i just need to get to the DE then i can solve them myself
devout snowBOT
can anyone help me with these 2? i just need to get to the DE then i can solve t...
dapper fable
for the second one, dW/dt = 0.05W
coarse egret
for the second one, dW/dt = 0.05W
You missed something 😅
dapper fable
huh
timber parcel
for the second one, dW/dt = 0.05W
wont it be dW/dt = 10 - 0.05W?
dapper fable
oh shoot
timber parcel
Well that was close 😅 thanks
im thinking about the first one now
its a bit harder
coarse egret
im thinking about the first one now
Are you familiar with the logistic growth model?
thorny herald
can anyone help me with these 2? i just need to get to the DE then i can solve t...
I think
dP/dT = k(P - C)
although that would mean that its negetive which is wierd
coarse egret
No bru..
devout snowBOT
@timber parcel Has your question been resolved?
timber parcel
Are you familiar with the logistic growth model?
Nope
timber parcel
Never came across anything like this?
Nope
is this thing in calculus ? like the subject itself
timber parcel
Wow ! tysm
coarse egret
ofc it is, it's rate of change
timber parcel
ofc it is, it's rate of change
i've studied related rates
but idk i wanted to make sure about the equation since if i made a mistake in making the equation i would waste alot of time solving something incorrect xD
Anyway thx everyone
.close
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proper tendon
I dont really understand this problem, Ive read through the AOPS solutions but still don't really understand, help will be appreaciated :D
devout snowBOT
I dont really understand this problem, Ive read through the AOPS solutions but s...
devout snowBOT
@proper tendon Has your question been resolved?
devout snowBOT
@proper tendon Has your question been resolved?
potent tusk
I dont really understand this problem, Ive read through the AOPS solutions but s...
I tried to figure this out
this triangle itself is impossible i think
$\textcolor{red}{\text{There is no triangle inscribed with the points of an equiangular hexagon that can be 70 percent of the area of the full hexagon }}$
woven radishBOT
Banana Steeler
devout snowBOT
@proper tendon Has your question been resolved?
devout snowBOT
@proper tendon Has your question been resolved?
left palm
@proper tendon a quick visual might help?
you can slide r around to verify there are two values which give an area ratio of 0.7
https://www.geogebra.org/classic/kpm5mn2y
i solved by getting the area of the hexagon and triangle in terms of r , setting their ratio to 0.7, then solving the quadratic; things should cancel out pretty nicely. was there anything in particular that was giving you trouble?
also i see it's been like eight hours since you posted lol. i'll assume you won't be responding immediately so im gonna make dinner and you can ping me 😄
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waxen schooner
I feel like I'm running in circles with this inequality for no reason.
Just taking the left side (the entire inequality makes sense to me, I'm only struggling with the inner parts).
Focusing on U <= inf.
We say that as we add more and more points to a partition, the upper sum gets smaller and smaller.
waxen schooner
We take the infimum of all of these upper sums, and that approaches the area under the graph. I'm cool with that.
So, any finite U_n > this inf.
So, why do we say U <= inf.
U can never be < inf.
velvet notch
I am sorry to bother you, but which course is this?
waxen schooner
It's a graduate analysis reading course, but this is something you'd typically see in Real Analysis.
restive river
I feel like I'm running in circles with this inequality for no reason.
Just tak...
damn
what unversitiy level is that??
fossil locust
what unversitiy level is that??
1st year or 2nd year depending on uni
waxen schooner
The book is Axler's Measure, Integration, and Analysis, which is a graduate level text. But this isn't graduate level work.
fossil locust
you're working with Riemann sums to prove the integral converges to a single value
velvet notch
The book is Axler's Measure, Integration, and Analysis, which is a graduate leve...
Gotcha
I never see this level of mathematics in my life lol
waxen schooner
If you pursue any math in university, you'll see it. Some schools have a rigorous calc sequence, in which you'd see it there. Otherwise, if you're a math major, you'd see it in an intro Analysis course.
It looks harder than it is. It's really just a matter of understanding notation and not forgetting how inequalities work because you've been out of school for 10 years.
You should be able to work through a real analysis book if you're sufficiently motivated 🙂
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tawdry wave
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tawdry wave
I can show my work idk if it is alright mathematically
Tell me if i am just brute forcing
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cyan scaffold
How can I prove that $3^n+1\geq (n+1)^2$ inductively
devout snowBOT
How can I prove that $3^n+1\geq (n+1)^2$ inductively
woven radishBOT
Popescu V2
cyan scaffold
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dreamy pelican
Hey i'm currently studying for my exam right now, is it alright if someone could take the time to explain how to do both of the questions in 1b?
devout snowBOT
Hey i'm currently studying for my exam right now, is it alright if someone could...
dreamy pelican
My only idea was to add up 40 + 60 + 30 + 35 but it's not right
Heres the answers from the answer key
winter patrol
start with drawing a NESW axis at the from point
dreamy pelican
Alright
winter patrol
and then use basic angle sums
dreamy pelican
What do u mean by basic angle sums??
winter patrol
angle sums on line, of triangles etc
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winter patrol
incorrect, watch what angles you want and are adding
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boreal pond
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errant hawk
ok so first think you think of is how can I cut this shape into parts that I actually can get the surface are of
so can you?
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atomic sparrow
You take y vs t data and you model it as
y=y_0 * e^(-μt) + δ
You know what y_0 is.
How can you fit the model onto the data such that it tells you what μ and δ are?
devout snowBOT
You take y vs t data and you model it as
y=y_0 * e^(-μt) + δ
You know what y_0 i...
atomic sparrow
<@&286206848099549185>
winter torrent
you need another data point
you'll get a system of equations
or if you have a lot of data you can do least-squares
atomic sparrow
Sys of eq? Like an infinite set of soln u mean?
Im guessing u mean i need to do nonlinear fitting models?
Im so eepy ah
fossil locust
You take y vs t data and you model it as
y=y_0 * e^(-μt) + δ
You know what y_0 i...
tbh, Desmos can do it for you
atomic sparrow
tbh, Desmos can do it for you
Oh im aware, i just wanted to know the logic behind it is all
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fossil locust
Oh im aware, i just wanted to know the logic behind it is all
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✅
fossil locust
Oh im aware, i just wanted to know the logic behind it is all
without getting too much into detail, you take the logarithm of both sides
$\ln(y - \delta) = \ln(y_0) - \mu t$
woven radishBOT
south's secret twin brother
fossil locust
this is pretty much in the form of a straight line
ln(y - delta) messes it up a little
but if you fix a value of delta, you can use least-squares linear regression to find the best value of mu that minimises the spread of the data away from the line
oh I think I know now
you always want your best-fit line to pass through the centre of the data
so you want the mean value of ln(y) and t over all your data points, then sub them into the equation
fossil locust
**south's secret twin brother**
then you have two equations in your unknowns, delta and mu
woven radishBOT
south's secret twin brother
fossil locust
you can solve for delta so you don't have to guess
yes it depends on which (y, t) you choose but all of them will give a good approixmation I feel
atomic sparrow
Ngl i am so fried that i was hearing the bbt theme while reading ur response
But ima screenshot ur response and try to analyze it another time cause im bouta pass out
fossil locust
hold on what you sub in isn't quite right
fossil locust
But ima screenshot ur response and try to analyze it another time cause im bouta...
cool so high school or below level for you right
atomic sparrow
cool so high school or below level for you right
Huh nah i graduated college
Im just poopie doopie
fossil locust
Huh nah i graduated college
what degree btw?
atomic sparrow
Physics
fossil locust
and you didn't study any linear regression for statistics?
I know it's not quite linear
atomic sparrow
grad?
Im taking a break rn, not in a hurry to earn less than minimum wage for another 4 years
twilit comet
ah
fossil locust
You take y vs t data and you model it as
y=y_0 * e^(-μt) + δ
You know what y_0 i...
basically the +delta is complicating things
atomic sparrow
and you didn't study any linear regression for statistics?
No i did, that was my first approach but the delta doesnt wana make it a simple line i can get all the info from
fossil locust
You take y vs t data and you model it as
y=y_0 * e^(-μt) + δ
You know what y_0 i...
computers are useful cause there's a unique exponential between any two pairs of (y, t)
so you could just calculate the least-squared distance for all possible two pairs
and find which point minimises it
atomic sparrow
And never took stats in college
fossil locust
And never took stats in college
right that's the thing
yeah cause it's super useful
surprised that they didn't make you take stats for experimental physics
fossil locust
yeah
atomic sparrow
I’m sure that a nonlinear fitting will do the trick. I just always feel icky using things I don’t understand
Taking it for granted type thing
Thx u for the help again south
Ur indubitably amazing
fossil locust
no worries!
fossil locust
Ur indubitably amazing
I've helped poor high school students try to do this
pretty much exactly like this cause they tend to take physics, chem etc
and thus when they have to do a maths investigation to graduate a lot of them think of modelling and so on
atomic sparrow
I've helped poor high school students try to do this
The fact that highschoolers do that is amazing
fossil locust
yeah it's exponential decay in one independent variable
two independent variables would be so much messier
atomic sparrow
I cant wait for the dopamine rush when all this clicks lmao
Getting the high
I shall now partake my leave and nap for ima pass out
Gn famerino
Or gm
Jeesus christ its already 9:27
Ahh
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fossil locust
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upper belfry
How do i prove the associativity?
devout snowBOT
How do i prove the associativity?
upper belfry
(x◦y)◦z = x◦(y◦z)
upper belfry
oh but x y and z are not functions
these are values and ◦ is just a placeholder for the operation
solar goblet
ahh
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@upper belfry Has your question been resolved?
near haven
How can the probability to win be 1/3?
devout snowBOT
How can the probability to win be 1/3?
@near haven Has your question been resolved?
supple knot
How can the probability to win be 1/3?
Did you find $P(X=1), P(X=2), P(X=3)$
woven radishBOT
riemann
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mighty quartz
this
@wide tendon come here lil bro
me and my friends are playing a Roblox ganme
and one of rthe qyuestions is this
we dont knwow heere to start
restive river
me and my friends are playing a Roblox ganme
:D
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shadow root
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shadow root
i put x=tan theta
but then I am clueless how to solve the contiinuity
can anyone pls help
<@&286206848099549185>
shadow root
i dont understand can you pls explain
white hazel
Do u know what an asymptote is
shadow root
ik what it is but tbh the concept is not that clear to me
white hazel
Both of these functions are one to one functions with horizontal asymptotes and the question is asking you to find the biggest and smallest value of k for where y=k has 2 solutions so therefore passes through both of these graphs once
So if u can find the horizontal asymptotes of each of these functions then it will help you find the values of k
Also finding where both of these graphs are at x=0
shadow root
i can understand what you are saying but might never be able to execute it
white hazel
Do u know how to find horizontal asymptotes?
I mean u should already know the horizontal asymptote for arctan(x)
white hazel
Ye but brcause arctan(x) is just for x>0 just pi/2
shadow root
yes
white hazel
Next the value of both graphs at x=0
shadow root
for arctan its 0
white hazel
Yep
shadow root
arccos its pi/2
white hazel
U get arccos(1/2)
shadow root
yep you just get pi/3
white hazel
Nice
Then you just gotta find the asymptote for the first function
If its more than pi/2 the m and n will be pi/2 and pi/3
shadow root
Then you just gotta find the asymptote for the first function
can you pls explain how to do this
white hazel
And of its less than it will be pi/3 and whatever the other asymptote is
Find the limit of the first function as it approaches -infinity
white hazel
Np
shadow root
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slow wedge
Can anyone help me with this, I got the second part wrong but the first part right even though I used the second answer to get the first
devout snowBOT
Can anyone help me with this, I got the second part wrong but the first part rig...
sand dove
Can anyone help me with this, I got the second part wrong but the first part rig...
can you show your exact computation?
sand dove
?
slow wedge
can you help
sand dove
I'm trying to look at it but I have to go unfortunately
slow wedge
ok
devout snowBOT
slow wedge
Thanks
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glacial ether
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glacial ether
@faint gorge
faint gorge
<@587715738484211754>
Guten Abend
glacial ether
Guten Abend
faint gorge
Guten Abend
Was ist das Problem?
faint gorge
ich verstehe nicht
Ist bei euch + direkte Summe?
glacial ether
ja. ich glaube
faint gorge
Ah ich bin blind da stehts doch
Ich denke man könnte zeigen für alle Elemente auf L(U u W) gilt dass sie auch in U + W sind
Und für alle Elemente in U + W gilt, dass sie in L(U u W) liegen
So als Idee
glacial ether
okay wie können wir sie zeigen.
faint gorge
Nehmen wir an ein Element $x \in \mathcal L (U \cup W)$.
woven radishBOT
bacc (unhelpful)
glacial ether
Dann existiert was?
ich weiss nicht
faint gorge
Was symbolisiert L
glacial ether
lineare Hülle
faint gorge
Genau
Sie besteht aus all möglichen Linearkombinationen sämtlicher Vektoren
Das heißt für ein Element aus der linearen Hülle existiert eine Linearkombination
woven radishBOT
bacc (unhelpful)
faint gorge
Das bedeutet x ist in U u W dann
faint gorge
Das ist doch die Definition?
glacial ether
ist x ein Element in der lineren Hülle?
faint gorge
Ja, das nehmen wir an
glacial ether
dann warum ist es jetzt die ganze lineare Hülle
faint gorge
hmm
Es ist nicht die ganze Hülle?
x ist nur ein Element
das als LK dargestellt werden kann der Vektoren v_1 bis v_n
glacial ether
aber sie sehen gleich aus
faint gorge
Jedes Element aus L(U u W) hat diese LK darstellung
nur die lamdas unterscheiden sich
Jedes Element hat eine einzigartige LK
glacial ether
ach so
ich verstehe. mach weiter
tut mir leid, ich habe lineare Hülle und lineare Kombination vermischt
faint gorge
tut mir leid, ich habe lineare Hülle und lineare Kombination vermischt
Da diese LK existiert für x, dann ist x in U u W
Hmm
Angenommen x ist tatsächlich echt in U
Dann kann man trotzdem sagen es ist in U+W, dann wäre w der Nullvektor
Also ob x eine LK aus nur Vektoren von U ist, oder nur W, oder beidem, dann könnte man es trotzdem runter reduzieren auf x = u+w und es wäre dann auch in U+W
🍒
glacial ether
ich verstehe nichts
faint gorge
Das tut mir Leid
glacial ether
warum ist w plötzlich der Nullvektor
faint gorge
vielleicht sollte ich mir einen Film anschauen
faint gorge
warum ist w plötzlich der Nullvektor
Also es kann sein
glacial ether
nein tut mir leid
faint gorge
Wenn x echt nur in U liegt
glacial ether
ich bin dumm
faint gorge
dann gibts keinen Vektor aus W außer dem Nullvektor
glacial ether
eigentlich habe ich die Lösung aber verstehe ich nichts davon
woven radishBOT
bacc (unhelpful)
faint gorge
Also das meine ich
Entweder ist x aus U, oder aus W oder aus U und W aber egal wie ich kann es so darstellen als u + w, sodass x dann auch in U + W ist
Ist vielleicht sogar kompliziert von mir aber ja
faint gorge
eigentlich habe ich die Lösung aber verstehe ich nichts davon
Du kannst alternativ die posten, und ich versuche es zu erklären, wenn es dir blöd wird
glacial ether
glacial ether
Du kannst alternativ die posten, und ich versuche es zu erklären, wenn es dir bl...
es ist mir sehr blöd. ich habe versucht selbst zu machen. aber es geht nicht
faint gorge
ups habe die blöden lambdas vergessen MAN
woven radishBOT
bacc (unhelpful)
faint gorge
Ah ok, die haben auch 3 Fälle behandelt
@glacial ether bitte nicht weinen
es ist alles gut
faint gorge
Hast du sohalbwegs meinee Erklärung verstanden
glacial ether
ja
faint gorge
Ok
Jetzt wollen wir die Umkehrung noch beweisen, dass jedes Element in U+W auch in L(U u W) ist
- Schritt Definition
Wir nehmen an ein Element x wieder, aber aus U + W
was gilt für x?
glacial ether
x= u + w?
faint gorge
genau super
woven radishBOT
bacc (unhelpful)
glacial ether
nein.
woven radishBOT
bacc (unhelpful)
faint gorge
Also wahr oder falsch?
glacial ether
wahr?
faint gorge
u und w sind natürlich in der Vereinigung von U, W
das sieht man auch auf dem Bild
Du vereinigst ja die Mengen, da kann es nicht sein, dass plötzlich ein Element fehlt
khishi
glacial ether
ja ich verstehe
faint gorge
Super
back
Wir waren stehen geblieben
Da $u \in U$, $w \in W$ gilt natürlich $u,w \in U \cup W.\$
Da $x = u+w$ eine Linearkombination ist folgt $x \in \mathcal L (U \cup W)$.
Moment ich muss kurz nachdenekn
glacial ether
ok
woven radishBOT
bacc (unhelpful)
faint gorge
Haarscharf, denn U u W ist nicht immer ein Teilraum
da sie manchmal nicht abgeschlossen sein kann
bzgl der Addition
Aber
Die Linearkombination ist natürlich im Spann von U u W
und somit auch x
glacial ether
da sie manchmal nicht abgeschlossen sein kann
warum
faint gorge
wie erwartet
Das einfachste Beispiel wieso, das so ist nehme an U = {(x,0) | x reell} und V = {(0,y) | y reell}
U u V = {(x,0) | x reell} u {(y,0) | y reell}
Angenommen du addierst (1,0) mit (0,1)
dann kriegst du (1,1)
was weder in U, noch in V ist
glacial ether
ach so
faint gorge
Also im Prinzip sinds die x-Achse und y-Achse
wenn du jetzt davon zwei nimmst und addierst bist du weder noch auf den Achsen
z.B (1,1)
Aber (1,1) ist eine Linearkombination aus u und v deswegen liegt der aber im Spann 😛
Weißst du die Leute sagen man spinnt, aber manchmal spannt man
glacial ether
was ist der nächste Schitt
faint gorge
Eig sind wir fertig
faint gorge
ja bitte kirschi
glacial ether
.solved
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opal heron
you decide to keep flipping a fail coin until you have an equal number of heads and tails. what is the expected number of flips you make
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you decide to keep flipping a fail coin until you have an equal number of heads ...
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