@vapid vortex Has your question been resolved?
#help-23
safe radishBOT
lean birch
The number of people in a house, t minutes after john arrives, is modelled by the differential equation dn/dt = -k(n - 20) where k is a constant.
The house has 80 people originally. Using k = 0.1 use two iterations of the approximate formula (dy/dx)0 = (y1 - y0)/h to estimate the number of people in the house 3 minutes after john arrives.
safe radishBOT
The number of people in a house, t minutes after john arrives, is modelled by th...
lean birch
The number of people in a house, t minutes after john arrives, is modelled by th...
So is n = 80?
Also the 0 next to “(dy/dx)0” is a subscript
lean birch
The number of people in a house, t minutes after john arrives, is modelled by th...
Is this even possible
safe radishBOT
@lean birch Has your question been resolved?
lean birch
<@&286206848099549185>
plucky elk
So is n = 80?
n is a function of time. The initial value of n(t=0)=80
plucky elk
What step size is h?
lean birch
What step size is h?
uuh what do you mean step size?
Like h is a very small number (that isnt zero)
lean birch
n is a function of time. The initial value of n(t=0)=80
So we are trying to find n(3) for this problem(i think)
safe radishBOT
@lean birch Has your question been resolved?
plucky elk
Like h is a very small number (that isnt zero)
You're told to use two iterations. The iterations are in terms of (y1-y0)/h. You need to know h so you know how to evaluate each iteration
safe radishBOT
@lean birch Has your question been resolved?
lean otter
Assuming that all the derivatives exist and the function $f(x,y)$ is continuous and satisfies the Laplacian equation;
\bigskip
how do I prove that
[
\ointccw_{C}\pdv{f}{y}\dd{x} - \pdv{f}{x} \dd{y} = 0
]
Is true for all closed curves C for which Green's function applies?
safe radishBOT
Assuming that all the derivatives exist and the function $f(x,y)$ is continuous ...
flat frigateBOT
♡LexQa♡
lean otter
Had a small case of sleeping so my channel closed 
safe radishBOT
@lean otter Has your question been resolved?
prime cobalt
**♡LexQa♡**
is this University?
lean otter
Yeah first year
prime cobalt
ohh interesting
winter pivot
isnt this a direct conseqeuence of mv chain rule
lean otter
Wot?
winter pivot
or the total derivative, rather
lean otter
What?
You are just saying words, can you elaborate more instead of saying one-liners?
safe radishBOT
@lean otter Has your question been resolved?
toxic stratus
hey look it's even more complex analysis 
solar hazel
OMG
toxic stratus
lean otter
hey look it's even more complex analysis <:KEK:889278761235808276>
Also no no no
solar hazel
analysis that is complicated, or complex analysis?
lean otter
Oh so the complex complex analysis
lean otter
i need to get something i can type on
Pls keep it simple for poor lil lex's tiny brain 🥲
toxic stratus
okay so
toxic stratus
oop typo
lean otter
Also
flat frigateBOT
lean otter
\tuple to make the large brackets instead of the \left and \right bs?
toxic stratus
$\tuple a$ $\parens a$
flat frigateBOT
toxic stratus
theyre the same macro just different names
lean otter
Okay okay we learn latex as we go 
toxic stratus
so wtf is the curl of this thing lets see
flat frigateBOT
lean otter
Okay im with u so far, I have done this
toxic stratus
the other one that you didnt ask about is uh
lean otter
Oh right, yes
flat frigateBOT
toxic stratus
so what happens
lean otter
Okay sounds good sounds good
flat frigateBOT
toxic stratus
which makes this zero
and also lets just assume f is smooth enough that you can interchange partial derivatives
flat frigateBOT
lean otter
Oh so it is basically just that? I did half of that but I thought i was going off the rails 
lean otter
Wow okay, really surprised nobody was like "dude lol just expand this" For the past 24 hours this question was open but here we are
lean otter
untold sky
what institution teaches this in first year
complex analysis here is 3rd year with i think 5 prereqs
lean otter
It is not complex analysis it is calc 3 lol
Well
Idk differences never took analysis sooo
lean otter
If layla says so
toxic stratus
basically you have something like uh
untold sky
that doesn't make it much better
calc 3 here is the hardest 2nd year subject by a very long shot
goddamn my uni sucks
lean otter
Oh what, we have calculus 2 and 3 in the same course in the second semester of first year
I kinda just Speedran through it all though
flat frigateBOT
toxic stratus
and then the other one is just like
lean otter
If layla says so x2
flat frigateBOT
lean otter
Cauchy what 
toxic stratus
cauchy's integral theorem
lean otter
Oh okay never heard time to... Look it up
lean otter
Why does this Cauchy fella have the most obscure stuff with him I swear
toxic stratus
its your FTLI or whatever but for complex analysis
toxic stratus
solar hazel
there are like 100 cauchy’s theorems
lean otter
Pain
toxic stratus
cauchy condensation
untold sky
cauchy is obscure.. if you don't study maths ig 😔
solar hazel
literally multiple different things called “cauchy’s theorem”
untold sky
man's actually in like every field
lean otter
Anyways thank you snow and laylaa (yes layla, you just have to continue being pretty dw)
.close
stable current
what is infinite sum
safe radishBOT
what is infinite sum
stable current
so not neverending sum?
lapis shadow
no?
stable current
Anyways thank you snow and laylaa (yes layla, you just have to continue being pr...
you and @solar hazel dating?
i scrolled up and saw that lmao
solar hazel
@toxic stratus
stable current
when will i find my snow
toxic stratus
solar hazel
hands off
toxic stratus
lean otter
you and <@984319941417250907> dating?
No lmao 😵💫
stable current
No lmao 😵💫
lmaoio
safe radishBOT
@stable current Has your question been resolved?
slow fern
safe radishBOT
untold sky
relate the problem statement to a function
slow fern
untold sky
basically it's trying to use a load of garbage to confuse you about something that's intrinsically not very complicated
hint: even though you're talking about sequences, you can instead think about continuous functions
slow fern
I don't understand
zinc token
expand out the definition lol
deltaA 1 = a2-a1
deltaA 2 = a3-a2
delta (delta A) 1 = (a3-a2)-(a2-a1)
untold sky
am i way overcomplicating this
i mean i got the right answer but it felt like it took a little more effort than i should
slow fern
$a_n+a_{n-2}-2a_{n-1}=1$
flat frigateBOT
zinc token
hint: even though you're talking about sequences, you can instead think about co...
I feel like a continuous function would make this a bigger pain in the arse
untold sky
i mean it took like 5 lines
but the computation is a little more annoying than you'd usually expect
untold sky
these are integer points on a quadratic
and you can just bash the quadartic
but using finite difference is probably not very rigorous and now that i've gotten the answer the stupid way i can't figure out the simplification trick from recurrence relations 
toxic stratus
shitty bash
flat frigateBOT
untold sky
oh, just do that
better than me going "ok second order finite difference =1 lets bash x²/2+bx+c"
toxic stratus
its basically the same tho
slow fern
I found one more solution
toxic stratus
you bash a quadratic
toxic stratus
,w a + (19 - 1)d + (19 - 1)(19 - 2)/2 = 0, a + (92 - 1)d + (92 - 1)(92 - 2)/2 = 0
flat frigateBOT
untold sky
second order finite difference looks like second derivative if you squint your eyes hard enough
toxic stratus
theyre roots
untold sky
oh yeah why did i go back to bash for coefficients after knowing a=1/2 
untold sky
consider arbitrary quadratic
slow fern
Ok
untold sky
second derivative = 2ax
slow fern
Yeah
untold sky
setting 2ax=1 yields a=1/2
slow fern
Right
flat frigateBOT
untold sky
so your original quadratic is of the form x²/2+bx+c
slow fern
Got it
flat frigateBOT
karmic vine
link?
slow fern
There are 6 different solutions for the same problem
This is a question from AIME 1992
untold sky
this is the kinda stuff you'll see only in competition maths
"yeah bro this looks like its right and so it's the answer"
so snow's is the only rigorous solution
flat frigateBOT
toxic stratus
its probably just 2022
lean otter
lol
untold sky
so f(x)=x but you have to show it
toxic stratus
lean otter
what
untold sky
i mean obviously i) gives the upper bound
so i guess you have to deduce f(x) >= x from ii)
cosmic grove
so f(x) <= f(x) kinda
untold sky
ye but that's just a tautology 
cosmic grove
ye I know but I have no idea how to tackle this
slow fern
@toxic stratus 
lean otter
f(x+0) <= f(x) + f(0)
this should imply f(0) => 0
cosmic grove
this should imply f(0) => 0
why
lean otter
yes
toxic stratus
suppose there exists a such that f(a) < a
then f(0) = f(a - a) <= f(a) + f(-a) < a - a = 0
contradiction
untold sky
pain
untold sky
guessing ||(1,1,1), (2,3,4)|| and show impossibility for the rest?
toxic stratus
natural
slow fern
Set x <= y <= z
untold sky
oh, assume x>=y>=z, then 2+xyz<=xy+yz+zx<=3xy, so z < 3
slow fern
untold sky
ok then you just check cases
oak basin
A plot with a 15 m frontage is in two buildings, one that is 24 m high and the other
7m high too. You must represent the situation in a drawing and calculate the distance
between the two highest points of the neighboring buildings on the site.
safe radishBOT
A plot with a 15 m frontage is in two buildings, one that is 24 m high and the o...
oak basin
With this one, I've absolute o idea what to look for, or even begin with.
oak basin
How I find it?
The onlñy think that goes trough my skull rn
Is that the highest point has to be at the center of that 15m
right?
Like 7.5m
But I don't know what to do there
foggy salmon
um
lapis shadow
Draw a line from the top of the orange line all the way upto the blue one
whole acorn
That doesn't seems right
it looks fine to me.
oak basin
22.67?
whole acorn
it should be correct
whole acorn
yes
dreamy harbor
The equation of a curve is y = (3x+1)+1.
(1)
Find the gradient of the curve at the point where x = 1.
(ii) Find f((3x+1)+ 1) dx
(iii)
Solution:
Hence find the area of the region enclosed by the curve, the x-axis and the lines x-0 and x-1.
Entire question I am stuck
safe radishBOT
The equation of a curve is y = (3x+1)+1.
(1)
Find the gradient of the curve at t...
final bay
The equation of a curve is y = (3x+1)+1.
(1)
Find the gradient of the curve at t...
is there meant to be a power?
flat frigateBOT
ed
misty coral
safe radishBOT
@dreamy harbor Has your question been resolved?
wintry mantle
A homogeneous wheel (solid cylinder) with mass M = 1 kg and radius
r = 10 cm is set in rotation around its axis of symmetry via a cord. There is a mass m = 1 kg on the cord in the earth's gravitational field (see figure). After the mass has dropped the distance h = 1 m, the weight hits the
floor up. The wheel initially rotates without friction.
a) (3 points) Using conservation of energy, show that the
mass goes down with an acceleration of
a = 2/3g. Hint: d v^2/dt = 2 va
What is the maximum angular velocity, with
rotating the wheel?
safe radishBOT
A homogeneous wheel (solid cylinder) with mass M = 1 kg and radius
r = 10 cm is ...
wintry mantle
I don't know how I'm supposed to find an acceleration of 2/3 g here when I use the conservation of energy. does anyone have an idea?
cosmic grove
did you use conservation of energy tho ?
wintry mantle
I tried but I never got a correct answer😢
cosmic grove
show what you tried
wintry mantle
I thought: potential energy = rotational energy + kinetic energy?
cosmic grove
conservation law states that the sum of the initials potential energy and kinetic energy is equal to the sum of the final potential energy and kinetic energy of the system
And I dont understand the question a
send the image where you took this
wintry mantle
the original task is not in english
cosmic grove
perfect, now we know now that the system is the mass m = 1 kg
using the energy conservation law, we have :
$\frac{1}{2} m(v_{initial})^2 + mgh_{initial} = \frac{1}{2} m(v_{final})^2 + mgh_{final}$
flat frigateBOT
Ｈｅｒｅｌｓ
cosmic grove
I suppose the mass goes down without an initial velocity (?)
wintry mantle
i think so and h_initial should be 1
cosmic grove
ok, so we should have this :
$$mg = \frac{1}{2} mv^2$$
flat frigateBOT
Ｈｅｒｅｌｓ
wintry mantle
yes
cosmic grove
and $g = \frac{1}{2} v^2$
flat frigateBOT
Ｈｅｒｅｌｓ
cosmic grove
$\frac{dv^2}{dt} = 2v \frac{dv}{dt} = 2va$
flat frigateBOT
Ｈｅｒｅｌｓ
cosmic grove
$\frac{1}{2} \frac{dv^2}{dt} = va$
flat frigateBOT
Ｈｅｒｅｌｓ
cosmic grove
welp I dont know how they want u to get a = 2/3 g
or should have consider friction ?
wintry mantle
no it says the rotation is frictionless.
I thought the 2/3 would somehow come from rotational energy, but idk
cosmic grove
we dont have the formula for angular velocity tho
wintry mantle
for angular velocity we always did w = v/r i think
cosmic grove
yea thats the formula, i forgot that
but you need velocity of the wheel
but anyway, lets retry
wintry mantle
I think the wheel starts to rotate when the mass is dropped so its accelerated by the mass
cosmic grove
using the energy conservation law, we have :
$\frac{1}{2} m(v_{initial})^2 + \frac{1}{2} J \frac{v_{initial}^2}{r^2}+ mgh_{initial} = \frac{1}{2} m(v_{final})^2 + \frac{1}{2} J \frac{v_{final}^2}{r^2} + mgh_{final}$
flat frigateBOT
Ｈｅｒｅｌｓ
cosmic grove
$mg = \frac{1}{2} \left( mv^2 + J\frac{v^2}{r^2} \right)$
what is the moment of inertia of a cylinder
wintry mantle
1/2mr^2
cosmic grove
$mg = \frac{m}{2} \left(v + \frac{1}{2}v^2 \right)$
flat frigateBOT
Ｈｅｒｅｌｓ
wintry mantle
the v should be v^2 ?
cosmic grove
where ?
wintry mantle
kinetic energy is 1/2 m v^2
cosmic grove
ah u right
flat frigateBOT
Ｈｅｒｅｌｓ
cosmic grove
$mg = \frac{v^2}{2} \left( m + \frac{m}{2} \right)$
flat frigateBOT
Ｈｅｒｅｌｓ
cosmic grove
$g = \frac{v^2}{2} \frac{3}{2}$
flat frigateBOT
Ｈｅｒｅｌｓ
cosmic grove
$g = \frac{3v^2}{4}$
flat frigateBOT
Ｈｅｒｅｌｓ
flat frigateBOT
Ｈｅｒｅｌｓ
cosmic grove
$= \frac{3}{2} va$
flat frigateBOT
Ｈｅｒｅｌｓ
cosmic grove
but $v^2 = \frac{4}{3} g$
flat frigateBOT
Ｈｅｒｅｌｓ
cosmic grove
$v = \frac{2}{\sqrt{3}} g$
flat frigateBOT
Ｈｅｒｅｌｓ
cosmic grove
yes nah, that wont work
safe radishBOT
@wintry mantle Has your question been resolved?
wintry mantle
@cosmic grove ok thank you, i hate this task lol
the 2/3 is actually correct and one can show it using forces, so I guess im just going to ignore that the task is telling me to use energy conversion lol
edgy rover
can someone give me a hint, how do i start this (part b) ?
safe radishBOT
can someone give me a hint, how do i start this (part b) ?
edgy rover
arctic locust
Use question a to rewrite the integral
safe radishBOT
safe radishBOT
Available help channel!
stable current
sup
tall bough
split it into two integrals
stable current
how
tall bough
(a+b)/c = a/c + b /c
stable current
x^3/ + sinx/?
lapis shadow
yes
stable current
but after that?
timid pasture
integrate them separately
tall bough
first one long division, second one ibp
junior smelt
first one long division, second one ibp
Or $x^3 = x^3 + 2x - 2x$ (first one)
flat frigateBOT
chartbit
junior smelt
Though same thing in the end haha
stable current
how will that help
tall bough
shouldnt numerator be derivative of denominator for that to work
junior smelt
how will that help
The first bit factorises into $x(x^2 + 2)$, allowing you to cancel immediately
flat frigateBOT
chartbit
stable current
how do i deal with the sin
tall bough
ibp
tall bough
idk just integral by parts
timid pasture
yes, tabular
tall bough
LIATE, take derivative of the lagbneraic expression and integral of trigonometric
young scroll
tf isnt it ILATE?
tall bough
L and I can be changd
young scroll
oo
flat frigateBOT
stable current
?????????
young scroll
dude
flat frigateBOT
tall bough
,w integral of sin(x)/(x^2+2)
flat frigateBOT
young scroll
it goes into complex numbers?
tall bough
pretty sure the question isnt to integrate it
young scroll
this is the answer
tall bough
he needs to send full question
safe radishBOT
safe radishBOT
✅
timid pasture
how did u close it
Yeah, helpers can close any help channel
tall bough
he isnt a helper
young scroll
i am
stable current
guys
tall bough
why is helpers role white
stable current
help
young scroll
idk
tall bough
#BringBackGreenHelpersRole
stable current
young scroll
i sent the answer above its way too long
timid pasture
Maybe, you don't actually need to evaluate the integral, there might be another way
young scroll
yeah
stable current
whats the way
young scroll
are u sure the questions correct tho?
stable current
ye
timid pasture
Where is this question from?
stable current
school
young scroll
which grade
stable current
grade?
stable current
math
timid pasture
Judging from the options, this might be a numerical method question where you aren't expected to find a closed form solution but an approximation
stable current
1
timid pasture
Is this from calc 1?
tall bough
did u see taylor series?
timid pasture
I am bad at numerical approximations so I am out
stable current
taylor here?
tall bough
yeah u can taylor the integrandum then integrate it
young scroll
tf
stable current
integrandum?
tall bough
thing inside integral
young scroll
integrand
tall bough
,w taylor series of 1/(x²+2)
flat frigateBOT
tall bough
,w taylor series of sin(x)
flat frigateBOT
young scroll
btw your question does not have any elementary antiderivative
young scroll
so yeah maybe its going in complex or somthing idk
tall bough
,w integral of (x^3 + x -x^3)/(1/2 - x^2/4 + x^4/8)
test time
,w (1/8)((5^6)/6 - (5^4)/2 + 25^2)
flat frigateBOT
flat frigateBOT
tall bough
,w integral of (x^3 + x -x^3/6)*(1/2 - x^2/4 + x^4/8)
flat frigateBOT
tall bough
,w (1/48)((55^8)/8 - (25^6)/3 + 2 * 5^4 + 125^2)
flat frigateBOT
stable current
thats not in options tho
flat frigateBOT
tall bough
10% error
tall bough
thats not in options tho
did u solve similar question
tall bough
let me see what answer is by taylort
flat frigateBOT
safe radishBOT
@stable current Has your question been resolved?
lean otter
looks fine
marsh sphinx
.close
safe radishBOT
safe radishBOT
Available help channel!
safe radishBOT
Available help channel!
gentle zodiac
how 2 prove this false mhm?
safe radishBOT
how 2 prove this false mhm?
stoic dune
Is it false?
gentle zodiac
yea
stoic dune
Well, all we need is a counter-example.
That's the perfect proof for things that are false
gentle zodiac
Well, all we need is a counter-example.
mhm do you think this could be a counter example?
cause we can set a to 0
mhm
stoic dune
Then f(a) is undefined, and [f(x) - f(a)] / (x - a) is undefined
We need a statement where [f(x) - f(a)] / (x - a) tends to infinity for x approaching a
gentle zodiac
We need a statement where [f(x) - f(a)] / (x - a) tends to infinity for x approa...
i thought of like f(x) = x. But if a can't be "set" to infinity then it fails
stoic dune
Indeed, a is a real number
gentle zodiac
Indeed, a is a real number
then would this work
right
cus
derivative at 0 is inf
and lim x->0 f'(x) is undefined?
stoic dune
You've got that backwards haha. Derivative at 0 is undefined, but the limit does go to inf
stoic dune
I honestly have no clue with this question, haha. It seems true to me, but this kind of thing sometimes has really weird counter examples. Maybe someone smarter than I knows one
gentle zodiac
thanks for the help tho
gentle zodiac
I honestly have no clue with this question, haha. It seems true to me, but this ...
how bout this mhm
o wait no
nvm
.close
real mountain
How do I simplify this? (The division problem)
safe radishBOT
How do I simplify this? (The division problem)
zinc token
you can extract c^3d from the numerator first
I'm assuming the second term is 36c^6 d^2 and not 3bc^6 d^2
real mountain
Yes sorry for the late reply ^^ extract c^3d ok
actually I’m gonna go- God bless! Jesus loves you! Merry Christmas!
.close
safe radishBOT
safe radishBOT
Available help channel!
lilac trout
I need to prove that ABC ~ ACD
safe radishBOT
I need to prove that ABC ~ ACD
zinc token
what have you tried
safe radishBOT
@lilac trout Has your question been resolved?
lilac trout
<@&286206848099549185>
safe radishBOT
@lilac trout Has your question been resolved?
winged flare
hmm
winged flare
I need to prove that ABC ~ ACD
the marked lengths in the diagram are already given in the question?
lilac trout
yes
winged flare
hm ok
lilac trout
so how do i do it i am stuck it in for like 1.5 hours
winged flare
im trying
safe radishBOT
@lilac trout Has your question been resolved?
lilac trout
i have asked for help since 3 hours ago and nobody helped me <@&286206848099549185>
hasty coyote
I need to prove that ABC ~ ACD
what are the measurements again? I can’t tell if that’s 12 or 72 and i also can’t tell if that’s 2.5 or 3.5.
lilac trout
12 ans 2.5
hasty coyote
thanks give me a second
this is definitely complicated and i’ll need my note pad. i’ll check in shortly.
lilac trout
ok
low pasture
I need to prove that ABC ~ ACD
I presume
AD=12
AB=3
BE=2.5
DE=10
Right?
lilac trout
yup
low pasture
So, AE can be computed using Stewart's Theorem.
lilac trout
whats that?
low pasture
low pasture
It gives a way to compute the length of a cevian.
It's not a thing you learn in any course.
lilac trout
yea but we are only supoosed to use things we learned
low pasture
Only through math competitions or reading Wikipedia.
Still trying to figure out how to even tackle this problem though.
lilac trout
i dont i think i need to use that given i am only 14
low pasture
What theorems do you have to tell if two triangles are similar?
lilac trout
triangle similarity
low pasture
I said that <BCA = <ADC
How did you prove this might I ask?
lilac trout
Angle between tangent and chord
low pasture
triangle similarity
There are a few triangle similarity theorems. (2 equal angles, proportional sides, etc...)
Which one did you have access to?
lilac trout
i think all of them
low pasture
Angle between tangent and chord
Looked this up. Quite a neat theorem. So now we hopefully have to find one more pair of angles
low pasture
I noticed the segments are proportional to themselves. 12/3=10/2.5.
Still haven't found a way to use this.
lilac trout
another one
f(x)=[(x^2-a)e^x]/(x+b)^2
f(x)<0 when - √12<x<-2
find a , b
and idk how to do it
low pasture
(x+b)^2>0 and e^x>0. So this is asking then x^2<a on the interval.
lilac trout
ok but how do i find a and b
low pasture
a>=12 and b can be anything.
lilac trout
ok but i need to find their values
low pasture
Those are the possible values. There isn't enough information about a, and ther is no information about b.
lilac trout
yea do you think the graph may help???
1 is the derevative
2 is the function
wait so it is impossible to find a and b?
literally all i gotta do to finish this question is find a and b cuz i did all of the other sub qestions
low pasture
Hmm, you can bound b if you need the function to be defined on the interval.
But you don't have enough information to pinpoint a and b. Inequalities generally are like that.
The only time you can get an exact value from inequalities are when you know the answer must be an integer. (There is only one integer between 2.2 and 3.2)
Is there any other information? And is this an online assignment?
low pasture
Can you simply choose any value of a and b that works?
lilac trout
it says find a and b
so no
so do i just say its impossible to pinoint their values?
low pasture
Can you post a screenshot of the whole problem?
lilac trout
its not in english
low pasture
i think there is an asymptote in y=9
Knowing where the asymptote is let's you determine b.
low pasture
Is it a vertical asymptotic or horizontal asymptote?
lilac trout
horizontal
low pasture
The horizontal asymptote comes from e^x. Knowing where the vertical asymptote is would help.
Moreover, knowing the value of f at two points would help too.
lilac trout
no thats all there is
low pasture
Can you tell me what the a and 2 kn the right side of the graph represent?
And what does the dotted graph represent? Is that for s different problem?
lilac trout
dotted is the derivative
low pasture
So the derivative is 0 at 2. That can help somewhat.
lilac trout
and also 0 at 0
low pasture
That should be enough to pinpoint a and b.
lilac trout
yup i will tell you if i get mixed up with the algebra
low pasture
If f(0)=0, then -a/b^2=0. What can you infer?
lilac trout
no f'(0)=0
lilac trout
so i will take the derivative and do x=0 y=0 and also x=0 y=2
low pasture
Alright. Then all you have to do is take the derivative and plug in x=0 and x=2 and set it to zero.
Recall, if a fraction is equal to zero, then the numerator is zero.
lilac trout
bro when i take the derivative to desmos and put b<0 (cuz there as an asymtote somewhere there) it never looks like the derivative from the picture
low pasture
I plugged in the derivative with the correct values of a and b and it does resemble the graph. Albeit stretched since the graph isn't truly to scale.
low pasture
so i will take the derivative and do x=0 y=0 and also x=0 y=2
Try computing the derivative algebraicly.
low pasture
Looks about right.
lilac trout
did u get a and b?
cuz i got a=0 (doesnt make sence) and b=2(also doesnt make sence because b<0)
waint
no
b=2
makes sence
idk about a tho
low pasture
b=2 is correct.
lilac trout
yea what about a is it 0?
low pasture
Now, plug in x=2 for the derivative.
low pasture
I seem to have gotten a=12.
lilac trout
when b=2
and a = -12
low pasture
I got a=12.
lilac trout
thats a=12
low pasture
Well, a=-12 seems correct. Not sure where I am making a mistake
lilac trout
ok then thanks so much for your help!
low pasture
Well. No problem!
low pasture
another one
f(x)=[(x^2-a)e^x]/(x+b)^2
f(x)<0 when - √12<x<-2
find a , b
Ah. I found the discrepency.
Here you have (x^2-a).
The answer requires (x^2-12).
low pasture
when b=2
and a = -12
So I think you are plotting (x^2***+***a)e^x/(x+b)^2.
safe radishBOT
@lilac trout Has your question been resolved?
safe radishBOT
safe radishBOT
Available help channel!
fiery elbow
Can someone explain how it makes sense to be able to multiply one of the functions by two?
safe radishBOT
Can someone explain how it makes sense to be able to multiply one of the functio...
fiery elbow
I understand its so the y's cancel out
but how can you multiply only one function but not the other?
idle sage
we multiply one bec it doesn’t change the eqn
we js do it so that it cancels one variable
here we multiplied y=3x+14 throughout by 2 yesh
fiery elbow
yea
idle sage
so we get 2y -6x=28
but if u simplify this
basically dividing by 2 throughout
it’s the same eqn again
fiery elbow
But then wouldnt we have to divide by 2 at the end to make it the same?
for the final answer
thin bridge
1 = 1
multiplying both sides by 2 to get
2 = 2
the equation is still valid
fiery elbow
Thanks guys, much clearer
idle sage
✨
fiery elbow
.close
lean otter
Is there any online tool for Taylor polynomials of functions of two variables?
safe radishBOT
Is there any online tool for Taylor polynomials of functions of two variables?
@lean otter Has your question been resolved?
compact ferry
there is an extension to taylor polynomials for multivariable calculus
with partial derivatives and the such
this should work
lean otter
Thamls
spare storm
Number 11
stable hearth
I’m confused on how they got to the final answer
safe radishBOT
I’m confused on how they got to the final answer
final halo
You don't understand the green step?
final halo
Yes
wicked birch
wicked birch
in red: my opinion.
since we keep "d(n+1-k)" and not d(n), why should we have (nCk) instead of (n+1)Ck ?
why noone answer me ?
wicked birch
@wheat cave you should say that to my teacher 🥲
not me
maybe my question has no sense because i've been lost for hours on a big math problem that brings this problem.
i just want to know if the 1st line is true or if the 2nd line is true or if they're both false c:
shut inlet
first of all :
$$\sum_{k=0}^{n+1} \binom{n+1}{k} d_{n+1-k} = d_{n+1} + \sum_{k=1}^{n} \binom{n+1}{k} d_{n+1-k}+ d_0$$
$d_{n+1}$ and not $d_n$
d_n+1 and not d_n
flat frigateBOT
Mehdi_Moulati
safe radishBOT
flat frigateBOT
Mushfiqur
gloomy scaffold
I get 0 for the left expression and ∞ for the right expression
safe radishBOT
gloomy scaffold
.open
obtuse plover
gloomy scaffold
Oh
safe radishBOT
Available help channel!
lean otter
Can someone please explain this answer to me?
safe radishBOT
Can someone please explain this answer to me?
lean otter
wheat cave
Can someone please explain this answer to me?
its the ways to place 5 objects into 3 different boxes divided by the permutation of the 5 objects (5!) and the 3 boxes (2!) since their order doesn't exist (the boxes and the balls are the same for us) but I have no glue how they got this so fast without any prior calculations or thinking
lean otter
Yes, that's the problem here 😦
wheat cave
actually nevermind, I don't get the r-1
drowsy moss
It’s called stars and bars.
Basically, you have 3 categories (boxes) so you need 3-1 dividers to break them into those categories
As for placement, since there’s 5 balls and 2 dividers you have to have 5 + 2 (= n + r -1)places to place the balls and dividers
So you get 7 choose 2 because you choose the two places to put your dividers, and the balls fill in the rest of the spots, and you that gives you how many balls are in each box
So, for example, if it’s BBB|BB|
You have 3 balls in the first box, 2 in the second and none in the third
lean otter
Gotcha!
You are awesome!
Thank you @wheat cave and @drowsy moss for your help today 🙂
wheat cave
nice
lean otter
.close
safe radishBOT
lean otter
.reopen
safe radishBOT
✅
drowsy moss
My gut instinct says you do stars and bars for the box placement and then multiply by the permutation of the balls
But I’m not sure
That might miscount somehow
drowsy moss
Correct.
In the case of your problem I think it’d be (5!) * (7C2)
Because you permute the order of the balls, then choose the placement of the bars
barren raptor
how much is x?
safe radishBOT
how much is x?
stiff inlet
Use the quadratic formula
barren raptor
oh how does it work
plucky elk
oh how does it work
stiff inlet
sharp lynx
safe radishBOT
sharp lynx
Stuck on this.
it should be the original term multiplied by root 20 over root 20
so I did that
Numerator came out to be root 20
lean otter
do you know how to simplify roots
sharp lynx
the denominator was 400root20
yea
hm
if i simplified the numerator
that'd be 2root5
sharp lynx
and if i simplified the denominator
thin bridge
the denominator was 400root20
how are you getting that
sharp lynx
@thin bridge20root20 x 20
lean otter
shouldn't be 400root20
thin bridge
20sqrt(20) * sqrt(20) isn't 400sqrt(20)
thin bridge
yes
sharp lynx
root 20 x root20 is 20 right?
thin bridge
yes
thin bridge
yes
sharp lynx
forgot you only multiply roots by roots and indices by indices
so 2 root 5 / 400
would n be 200?
i was right
thanks guys didnt see that error
.close
sharp lynx
safe radishBOT
sharp lynx
Back again with another silly question
I made the side length to be
2 + root6 / root10
so to simplify id need to rationalise
when i did that I got a denominator of 10
but my numerator is wrong
i did 2 + root6 x root 10
and got 2root10 + root60
whered i go wrong?
junior smelt
,calc 60/4
flat frigateBOT
Result:
15
sharp lynx
eh
Idk what you mean by that sorry
alright
got a new question
(The website i use gives you the same question but with different numbers)
step by step this time
so would
junior smelt
but my numerator is wrong
I agree that your numerator is “factually correct” with this one, but…
junior smelt
Result:
```
15
```
…there is a way to simplify what you had further
junior smelt
This one will have a similar issue as per the last
sharp lynx
numerator is 3root6 +root90
i have to fully simplify
i can simplify root 90 as 3root10
so itd be 3 root 6 + 3 root10
over 6
that can be simplified to root6+root10 over 2
or root 16 over 2
i know
root 16 is 4
so 4/2
so 2?
idk man tbh i was just freestyling
junior smelt
that can be simplified to root6+root10 over 2
Here is all good, and probably what they wanted
,calc sqrt(6) + sqrt(10)
flat frigateBOT
Result:
5.6117674029516
would my other simplifcations be wrong?
junior smelt
Result:
```
5.6117674029516
```
Yeah, the ones I reacted to accordingly
sharp lynx
why, isn't root16 correct or nah
flat frigateBOT
chartbit
sharp lynx
ah
junior smelt
why, isn't root16 correct or nah
No - sqrt(16) is 4, and check the calc I did
safe radishBOT
safe radishBOT
Available help channel!
keen mural
Is it correct to assume that, for any given vector, a linear function can be created in which any vector inside of it will be orthogonal to the first one? For instance, in the vector (1;4) that function would be f(x)=-x/4 and any vector that inhabits that line, such as (1;-1/4) or (-2;1) will be orthogonal.
safe radishBOT
Is it correct to assume that, for any given vector, a linear function can be cre...
paper idol
Is it correct to assume that, for any given vector, a linear function can be cre...
yeah, what you're looking for is called an orthogonal projection. Take your arbitrary vector, then the second arbitrary vector, compute the projection of the second one onto the first and subtract it from the second vector. The resulting vector will be orthogonal to the first vector, and you can easily prove that this function is linear and you can find a corresponding projection matrix for any given non-zero vector.
And in case of (0, 0, 0), it's already orthogonal to any given vector by definition.
keen mural
ohh, that's what it's called
it's fun to rediscover math
even if it's something simple like this
thank you
I'll write this down so I don't forget it
.close
narrow spindle
Rather confused. I’ve tried using the information they’ve given, but I’m still stuck
safe radishBOT
Rather confused. I’ve tried using the information they’ve given, but I’m still s...
@narrow spindle Has your question been resolved?
plucky elk
Show your work
safe radishBOT
@narrow spindle Has your question been resolved?
tawny coral
P(AnB|C) = P(A|C)P(B|C) means conditional indeoendence. I didn't work through them (Maybe using Bayes theoreom) to see if one happens to be true. But I'd say a. Or do you know the answer is not a?
unique valley
Could someone hint me with the second question
safe radishBOT
Could someone hint me with the second question
dusty raven
Small hint: This sequence goes through all rational numbers <1. Try to think of how to get close to an arbitrary number using rational numbers
Big Hint: ||Perhaps think about decimal expansions for l||
safe radishBOT
@unique valley Has your question been resolved?
lean otter
safe radishBOT
plucky elk
Fyi this channel will close soon
safe radishBOT
Available help channel!
unreal kindle
safe radishBOT
unreal kindle
I want to know how do i prove that these matrices are similar or not
i know the formule A=PB P-1
but i dont really understand the method when we don't have P
safe radishBOT
@unreal kindle Has your question been resolved?
junior smelt
Hey @unreal kindle! 🙋♀️
One thing I wanted to also mention in the previous one is that if matrices are similar, then they have the same determinant (was a quicker way to show the last ones weren't similar)
So if you have that the determinants of two matrices aren't the exact same, then they can't be similar
junior smelt
One thing I wanted to also mention in the previous one is that if matrices are s...
(Proving this is pretty easy using determinant properties)
lean otter
safe radishBOT
lean otter
i messed up somewhere idk wehre
wide hamlet
yo
queen parcel
lean otter
yes