thats why we add the 1 to the exponents
#help-39
full frost
it is a problem from combinatorics more than number theory here
we chose the numbers
as for 24
leaden iris
so (exponent of 3+1)(exponent of 2 +1) would be (2+1)(4+1)??
full frost
3+1 but yeah
leaden iris
it is a problem from combinatorics more than number theory here
combinatorics?
full frost
language barrier might be a problem
for me here
but the thing is
we need to count the possible ways of choosing prime factors
from 2x2x2x3 which is equal 24
we can chose 2 in 0 ,1,2,3 times and 3 in 0,1 times
thats why we multiply 4x2 to get the number of divisors
full frost
because it is the number of simultanious choices from these groups
and going back to the 7056 thing
xd
leaden iris
mhmm
full frost
when you factor it
leaden iris
is there a reason they epressed the answers in powers of 84?
leaden iris
elaborate
leaden iris
if you prime factor 7056
ye
full frost
you see that it is 84^2
leaden iris
?
full frost
we can chose 2 in 0 ,1,2,3 times and 3 in 0,1 times
as here
we need the sum
so if we take the 24
and insted of the exponents we plug in numbers
as here
(2^0 + 2^1 +2^2+ 2^3)(3^0 + 3^1)
we would get the sum
because
we create every possible divisor
by multiplying one from each bracket
for ex 2^3 x 3^1 = 24
but 2^2 x 3^0 = 4 which also divides 24
and you would need to factor 19600 and do the same with it to score the anwser
the sum happens naturally by manually multiplying the brackets
full frost
nah not that much
leaden iris
do u mind if i ask a few other questions
full frost
could have been worse creating them manually
leaden iris
after i solve these two
leaden iris
could have been worse creating them manually
fr
full frost
after i solve these two
not at all but it might take me a while to respond cause in 10 mins i start a 2h class
not not lose it you might wanna send me pm
leaden iris
not not lose it you might wanna send me pm
pm?
full frost
private message
leaden iris
private message
uhmm i cant dm right noww but if i do get any quarries ill dm u later
can v continue our discussion here?
full frost
sure no problem
full frost
it would be the 84^45
leaden iris
im getting the prime factors as 2^4 x 21^2
full frost
happens
leaden iris
*cries
@full frost
another conceptual doubt T_T
you mentioned Product of all divisors of a number n-
Prime factorize n
Suppose n has prime factors 2^a x 3^b x 7^c
Then product of all it’s prime factors = (a+1)(b+1)(c+1)
1 is present for the possibility of d^0 where d is a divisor
so like-
wouldnt that mean product = 45
is there something i missed?
proper nova
wouldnt that mean product = 45
Wdym?
proper nova
product of all it's divisors
Where did you get the 45?
leaden iris
Where did you get the 45?
using the formula uhh
leaden iris
you mentioned Product of all divisors of a number n-
Prime factorize n
Suppose ...
look at ts
leaden iris
all of these options r wrong if im correct?
this one
proper nova
,w factorize 7056
jolly parrotBOT
proper nova
this one
Yeah the product of the exponents is 45, or in other words, 7056 has 45 factors
leaden iris
Yeah the product of the exponents is 45, or in other words, 7056 has 45 factors
mhm
well how to find product of factors
proper nova
Well
Someone told you to use $n^{\frac k2}$ where $k$ is the amount of factors right?
jolly parrotBOT
1 divided by 0 equals Infinity
proper nova
But since the amount of factors is odd, meaning this is a square number
proper nova
**1 divided by 0 equals Infinity**
So, we still apply the formula here, with $k$ being 44
jolly parrotBOT
1 divided by 0 equals Infinity
proper nova
And then times that with $\sqrt{7056}$
jolly parrotBOT
1 divided by 0 equals Infinity
proper nova
im a bit slow
You'll improve day by day
leaden iris
You'll improve day by day
yep
clear shore
n being the number 7056??
yeah
leaden iris
OKAY
naive sparrow
can i have help by $\int^{2}_{4} 4 + X = ?$
when x = 5?
pearl pondBOT
can i have help by $\int^{2}_{4} 4 + X = ?$
when x = 5?
jolly parrotBOT
Noah
pearl pondBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
naive sparrow
i cant im using an laptop
worldly jewel
what does using a laptop have to do with anything
tropic saddle
presumably no camera
naive sparrow
...
glacial bluff
if x is given a value, then the integrand becomes a constant, and that becomes a nothing-question, is it not?
naive sparrow
idk i aint good in integral activities
glacial bluff
presumably that is why everyone is asking for the original problem, OP.
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cedar marsh
.open
wet pecan
I have no idea what I'm doing wrong
Here's the goal as I understand it and what the letters mean
N=Number of turns
ℓ=Length
L=Something in H
A=Radius
𝜇0=Permability in air=4piE-7
Centi=E-2
Milli=E-3
I don't know what I'm doing wrong, I've been trying it the way of the third pic and at this point, just looking at it gives me a headache
wet pecan
I think the math part is right, it's just there's a crossed wire between the letters and numbers
toxic remnant
micro is 10^-6
pearl pondBOT
@wet pecan Has your question been resolved?
pearl pondBOT
@wet pecan Has your question been resolved?
fair creek
I have no idea what I'm doing wrong
Here's the goal as I understand it and what ...
what more help do you need with this?
wet pecan
what more help do you need with this?
It all makes sense but the answers I get are wrong
uncut vapor
I have no idea what I'm doing wrong
Here's the goal as I understand it and what ...
is your problem resolved?
@wet pecan i could help you
im Electrical Engineer
wet pecan
whats the correct answer?
I don't now but around 306 or so
uncut vapor
could you explain me the problem again
its smth about inductance of a solinoid
oh alr
i read the problem
gimme a sec
N=2584 Turns
@wet pecan
wet pecan
Thank you
uncut vapor
Welcome
potent sage
2 * 2 / 2. Fast
pearl pondBOT
2 * 2 / 2. Fast
grizzled matrix
I think its an question we need more information no?
like are there any () if not its an trick question i think
potent sage
I am not aware at the moment,
grizzled matrix
or from left to right then i think but im not sure
dire tapir
it's 2 
pearl pondBOT
@potent sage Has your question been resolved?
dense jasper
.close
junior anchor
Why is using law of excluded middle non constructive
pearl pondBOT
Why is using law of excluded middle non constructive
junior anchor
.close
pearl pondBOT
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ornate swan
how do i deal with the tan^-1
pearl pondBOT
how do i deal with the tan^-1
dense jasper
!xy
pearl pondBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
dense jasper
are you sure this isn't a calculator based question
because this is essentially the same as integrating arctan(x^2-x)
arctan(x^2-x+1) has a nice elementary antiderivative
,w integrate arctan(x^2-3x+2)
jolly parrotBOT
dense jasper
not so much for your f
ornate swan
are you sure this isn't a calculator based question
it is
dense jasper
Please show the original problem, **exactly as it was stated to you**, with the ...
can you show the actual question in full then
ornate swan
sorry let me put it all here
dense jasper
sorry let me put it all here
Recall that
$$\int^{b}_{a} f'(x) \dd{x}=f(b)-f(a).$$
This follows from the fundamental theorem of calculus.
ornate swan
yes
jolly parrotBOT
Civil Service Pigeon
dense jasper
yes
dense jasper
,w pi/2 + (integral of 3arctan(x^2-3x+2) dx from 1 to 3)
jolly parrotBOT
dense jasper
okay so c is the answer after putting it into the calc
good
ornate swan
how would u do this
pearl pondBOT
how would u do this
solar ember
Use your trig formula
cos(2u) = 2 cos^2(u)−1
rearranging gives cos^2(u) = 1/2 * (cos(2u) + 1)
dense jasper
cheat and interpolate since you have a calculator
ornate swan
~~cheat and interpolate since you have a calculator<:catgiggle:91245949795450065...
how would u do that?
dense jasper
fit g to a polynomial using rref and plug that in lol
this is mostly sarcasm unless you're down to punch 50+ buttons
ornate swan
cos(2u) = 2 cos^2(u)−1
i can't use this since my instructer never covered it 😭
i lose points when i use stuff she doesnt teach
feral apex
how would u do that?
u=2g(x)+1
du=2g'(x) dx
New limits are:
When x=0, u=2g(0)+1 = 11
When x=3, u=2g(3)+1 = -3
dx = du/(2g'(x))
Substitute in integral,
Integrate (1/2) cos²(u) du from 11 to -3
long steeple
i can't use this since my instructer never covered it 😭
but this is just pre calculus
It's just basic trigonometry
feral apex
Or integrate (-1/2) cos²(u) from -3 to 11
feral apex
rearranging gives cos^2(u) = 1/2 * (cos(2u) + 1)
Use this formula to simplify..
ornate swan
but this is just pre calculus
alright ill do that then
i think i got that one
for this one
after you use long divison to simplify
im left with integral from 0 to 1 ( 2x-1 + (4x+3)/(x^2 +1)
would i need to change my bounds?
feral apex
Or integrate (-1/2) cos²(u) from -3 to 11
This is much easier
pearl pondBOT
@ornate swan Has your question been resolved?
long nova
bro how i would differentiate this 
plush bramble
you really only need to check two cases of x. just find when |2x + 1| changes definition and find the derivative for the two cases
,tex .abs def
jolly parrotBOT
riemann
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keen beacon
pearl pondBOT
keen beacon
first instinct is integration by parts. e to the whatever wont reduce, so need to differentiate the x^2 but cant integrate the exponent part
plush sundial
U can use substitution method
keen beacon
with u = x^3?
pearl pondBOT
keen beacon
i checked by differentiation, put C in ln form and non-ln form
nothing seems to work
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Available help channel!
proven cosmos
Use your graphing calculator to obtain a simple random sample of size 4 from a population of size 50 by using the RandInt function and a seed of 6. List the 4 randomly generated numbers.
pearl pondBOT
Use your graphing calculator to obtain a simple random sample of size 4 from a p...
@proven cosmos Has your question been resolved?
pearl pondBOT
@proven cosmos Has your question been resolved?
tame plume
Hiii!!! I have a question about derivatives
pearl pondBOT
Hiii!!! I have a question about derivatives
tame plume
If i have a quantity Q which measures the energia that goes trought a surface in a period of time ( its called the radiant energy )
why is the quantity of energy that passes trough the surface per unit of time the derivative of Q with respect to time ?
The way i am thinking about this is the following
its written in portuguese
feral sedge
Is Q the amount of energy inside the volume bounded by the surface or the rate at which energy is passing through the surface?
tame plume
the amount of energy
in a period of time
inside the volume
my english is not the best, sorry if i am not being clear
but the way i am thinking about this is the following: Phi is the energy that passes trough the surface at time t, so if we want the energy that passes trough the surface from 0 to t we need to sum all values, so its the intregral of phi from 0 to t
so i understand that Q the energy that passes trough the surface in a period of time is the integral of phi, but i dont understand why is phi the derivative of Q, if that makes sense ?
I know that by definition if Q is the integral of phi then by the fundamental theorem of calculus phi is the derivative with respect to time
but what does dq/dt means geometrically
feral sedge
how quickly the energy is changing
tame plume
yeah thats what i thought it was, since its the derivative
should be how the energy passing trough the surface, lets call it S, is changing over time
but instead it is how much energy is passing by unit of time
forget it! i got it hahaha Thank you!!!
.close
pearl pondBOT
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ivory pumice
,tex
Given a circle with centre (0,0) and radius 2. Find the equation of the tangent line at $(\sqrt3 , 1)$
I can do this with implicit:
\begin{align*}
x^2+y^2=4 \
2x+2y\cdot\frac{dy}{dx} =0 \
\frac{dy}{dx}= -\frac{x}{y}\
(y-1)=-\sqrt{3}(x-\sqrt{3})\
y=-\sqrt{3}x+4\
\end{align*}
Now my lecturer suggested writing the circle in matrix form
$$f(x,y)=\begin{bmatrix}
x^2 & y^2
\end{bmatrix}$$
Then by our definition of matrix differentiation I have
$$f'(x,y)=\begin{bmatrix}
\frac{d x^2}{dx} & \frac{dy^2}{dy}
\end{bmatrix}$$
$$f'(x,y)=\begin{bmatrix}
2x & 2y
\end{bmatrix}$$
But I can't tell whats exactly useful about this result i.e. where to go from here.this is a multivar calc class
jolly parrotBOT
Athelar
summer imp
Did they explicitly give the form $f(x,y) = [x^2, y^2]$ to represent the circle?
jolly parrotBOT
Azyrashacorki
ivory pumice
yes
we dont normally write our matrices with , seperation though otherwise it looks like a set
summer imp
Yeah that's not the issue. I was more asking because I feel like if anything the more "classic" multivar setup would be to consider the circle as a level set of $$f(x,y) = x^2 + y^2.$$
jolly parrotBOT
Azyrashacorki
summer imp
Then the gradient vector will be normal to the level curve where you compute it.
And you can use that to get a tangent line
ivory pumice
Then the gradient vector will be **normal** to the level curve where you compute...
woah woah
can we stop here
[2x 2y] is my gradient vector
right?
but how do I know that this is normal to the curve
summer imp
Gradient vectors are always normal to level curves.
ivory pumice
why?
summer imp
It's somewhat by design.
Intuitively you might have learned that the gradient points in the direction of "steepest ascent" (zoomed way in), in which case it points perpendicularly to a direction of "no ascent at all", i.e. a level set.
worldly jewel
It is easy to see if you let γ: I → R^n be a curve so that fγ is constant (its image lies in the level set), then apply chain rule
ivory pumice
apologies, this makes no sense to me
perhaps I could be referred to something I could read about this kind of topic rather than waste everyone's time with it
worldly jewel
It's somewhat by design.
Intuitively you might have learned that the gradient p...
if you just want the intuition then this explanation is fine
the gradient points in the direction of steepest ascent, so naturally it is orthogonal to the level curve where there is no change at all
imagine you are hiking on a hill and you trace out a line on the surface on the mountain with constant height
ivory pumice
dot product of the function and its gradient should then be 0 and i can just expand it
ivory pumice
imagine you are hiking on a hill and you trace out a line on the surface on the ...
the concept of a level surface makes sense to me but not this "steepest ascent" part
worldly jewel
,tex $ abs{ nabla f(p) cdot v } leq norm{nabla f(p)} norm v = norm{nabla f(p)} $
jolly parrotBOT
worldly jewel
p is the point in the domain and v is the direction vector
the first inequality is by cauchy-schwarz and is attained (ie. the LHS is maximised) whenever v is pointing in the same direction as nabla f p
ivory pumice
because of cos(0)=1. v is just a direction vector so mag = 1 and mag nabla f
worldly jewel
yes
ivory pumice
how is this helpful?
worldly jewel
because the LHS is the directional derivative of f in the direction v
(assuming f differentiable)
this is telling you that the directional derivative in the direction v is maximised, precisely when v is pointing in the same direction as nabla f p
ivory pumice
lovely, but why do we need to maximize this derivative?
worldly jewel
maximising the directional derivative is what it means to be the "direction of steepest ascent"
in order to find the direction where it ascends the quickest, you look at the directional derivatives and find which one is the maximum
ivory pumice
sorry I'm ineffably lost
worldly jewel
ivory pumice
my apologies
worldly jewel
are you familar with what the directional derivative is
ivory pumice
no
worldly jewel
hmmm
this is a multivariable calculus class right
so you should learn about them sooner or later
honest spear
should I just leave this until I've gone through that?
worldly jewel
I thoguht I saw you post this a while ago
wary vault
LMAO he tricked himself
worldly jewel
Tbh, I think this is a rather bizarre suggestion for your lecturer to make if you haven't learned about directional derivative, gradient vector etc
ivory pumice
I think she wants us to try discover the concept intuitively
summer imp
He's got a good video about why the gradient is perpendicular to level curves (kinda same as what Plantianus explained)
First thing he discusses in fact, and I think he avoids directional derivatives for this one.
pearl pondBOT
dense jasper
**Athelar**
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Available help channel!
boreal flare
would it be A) because therye pointing bopposite ways
pearl pondBOT
would it be A) because therye pointing bopposite ways
warped violet
would it be A) because therye pointing bopposite ways
If, by they I assume vectors, are pointing opposite ways
Then isn't one just minus the other?
boreal flare
im confused
boreal flare
lioke going opposite direction
boreal flare
yes
jolly parrotBOT
USS-Enterprise
boreal flare
-a
boreal flare
oh theyre both going same direction
warped violet
no
boreal flare
what i meant is all the other ones are the same except that one
boreal flare
yes yes
warped violet
what i meant is all the other ones are the same except that one
what do you mean
boreal flare
like all pf the options excdept 1 are doing ther same thing
like all go towards same opoint with same lengtj
blazing plank
hi can any on prove -1*-1=1
warped violet
hi can any on prove -1*-1=1
<@&268886789983436800>
warped violet
like all go towards same opoint with same lengtj
uh, what?
blazing plank
??
spiral pivot
!help @blazing plank
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blazing plank
thx
warped violet
like all go towards same opoint with same lengtj
I don't understand what you are trying to say
You've got different vectors everywhere
Except in 3)*
warped violet
🤔
boreal flare
theyre parallel
warped violet
give me a second
to draw
oh
you mean
That the vectors are the same?
AB = 2AF?
boreal flare
yea
warped violet
Vector AB is the same as 2AF
Ah
Yes, that's correct
So 2) is correct
Then 3)
Is length of CB = length of CA?
boreal flare
yes
warped violet
Great
Now let's take a look at 4)
What is it saying
That vector AF is the same as vector BF
Is it?
warped violet
Yes
So as we said about opposite vectors before
They have the same magnitude (length)
and opposite direction
So the opposite of $\vec{a}$ is $-\vec{a}$
jolly parrotBOT
USS-Enterprise
warped violet
And here, we have learned that they have same length and opposite direction
So one is minus the other
But it says AF = BF
Not AF = -BF
boreal flare
You’re right
warped violet
I try to be
boreal flare
So it’s 4) because they’re going opposite direction unlike all other ones
warped violet
Not because of that
I suggest you revisit some material on vectors you have
The reason is AF and BF are opposite vectors
AF goes from left to right, BF goes from right to left
They have same length, opposite direction
That's why they are opposite vectors
That's why AF = -BF
And not AF = BF
Since that would mean both go left-right or right-left (in this case)
boreal flare
Yes I didn’t include they’re same length mb
warped violet
So I guess the correct reasoning for full marks would be: AF and BF are opposite vectors, since they have the same magnitude both opposing directions, therefore AF = -BF, yet 4) says AF = BF, therefore 4) is false.
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warped violet
I thought you didn't like triangles <:catthimc:732011802459635713>
this is just vectors placed on an ugly shape. I didn't have to deal with triangly-things here 
glass meadow
Never play Zelda either :
warped violet
Never play Zelda either :<:breadhehe:556700641427456020>
can I do anything without triangles 🙁
glass meadow
Idk Minecraft maybe
warped violet
Idk Minecraft maybe
I will go live in a hamster wheel forever and ever
there's no hamster triangle right
sleek sandal
hi
sleek sandal
i can answer part a and b those make sense, but i can't understand the
fyy or fxx and fxy (same as fyx)
so basically how would I imagine the derivatives being positve and negative for the second derivative?
what should i imagine with the inclines and stuff
sharp vigil
to find sign of f_xx, consider whether the partial derivative wrt x is increasing or decreasing as x gets larger; does it seem larger to the left or to the right
sharp vigil
for f_xx
the sign of f_xx tells you whether f_x is increasing or decreasing along the x-direction
sharp vigil
f_x is the slope or rate of change, so i'm asking whether the function appears to change faster to the left or to the right
sleek sandal
f_x chages faster on left
then how would i do f_xx
like f_x is negative I get that part
but how can i picture the second derivative
<@&286206848099549185>
manic oriole
Hey
brave sluice
i think so
sleek sandal
does the number on the countor lines not matter then?
like the fact that it;s 3 and 1
or does that only matter for the first partial derivative
brave sluice
it matters because you need to know if it's going up or down
sleek sandal
huh?
sleek sandal
ok
that makes sense for the first partial derivative
but what about the second one
are you tryna say the fact that the gap from the star to the z = 3 contour line is smaller than the gap from the start to the z = 1 contour line means it's increasing for the second derivative so it;s positve/?
sleek sandal
gotchu makes sense i guess
that is indeed the change of the change
but you said "I think so"
im kinda nervous now
i think ur judgement makes sense tho but i want someone to verify
wait
@brave sluice but i'd say the f_xx is positve no?
brave sluice
yeah looks positive to me
sleek sandal
yes f_x is negative, but since the countor lines are closer as you go right, it must be positve right
sleek sandal
if the numbers were reversed it would change the answer
then why'd u say this may i ask
brave sluice
the contour lines are spaced farther apart as you move to the right
brave sluice
the contour lines are spaced farther apart as you move to the right
don't look at the blue region, it's too distant. look at the green intervals
sleek sandal
ah
brave sluice
yeah idk how to do (e)
sleek sandal
you go diagonal?
im thinking let's say you go along the y path
the counter lines get further and further for the x as you go up
or is that wrong
brave sluice
is d^2 f / dx dy the change in df / dy as you change x?
(or is it the other way around?)
sleek sandal
it can be both right
if we're assuming a thorem is true
and in this class we assume it's true. caliraut's theorem i think
brave sluice
i see
plush bramble
We can’t understand f_xy
this isn't really a question. be more specific what you want answered
brave sluice
question (e) here
sharp vigil
is d^2 f / dx dy the change in df / dy as you change x?
strictly it is that, but for sufficiently smooth functions the other way around gives the same answer
for (e) you do sort of the same strategy you were doing but just looking at the change in gap distribution in one direction as you move in the other
sleek sandal
Oh
sleek sandal
Hm
brave sluice
but i think the answer is negative
sleek sandal
I’m just going up .5 units and drawing a line to the right
And noticing that it’s a further and further line. No idea if this right tho
The gaps get bigger so I guess the amount of time it takes to increase in height is more so it’s negative. Probably shouldn’t had added time but I hope it makes sense
@sharp vigil is this right? Sorry for pinging
brave sluice
around the origin, d/dx is zero, and higher on the y-axis d/dx is negative
sleek sandal
Ah nice catch
sleek sandal
How did u know it’s 0 at the origin?
Like I agree it’s probably 0
But how’d u think of it
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Available help channel!
formal fog
pearl pondBOT
formal fog
I am unsure how to start 3.
glacial bluff
there is one kind of basic function that has a domain of all reals but a max/min.
you've seen this kind of function before. one example is in the very image you sent.
once you've identified the kind of function, think about how a general graph for a function of that type looks like and try manipulating it to produce the desired range.
formal fog
.close
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lament eagle
How to solve 2d
pearl pondBOT
How to solve 2d
random ermine
lament eagle
Bro what 💀
worldly jewel
I mean, if you're allowed to use graphs then it becomes trivial right
just pick out the intersection points of y = |2x+3|/2 and y=3
lament eagle
I mean, if you're allowed to use graphs then it becomes trivial right
Yeah
lament eagle
I understand it now
lament eagle
just pick out the intersection points of y = |2x+3|/2 and y=3
y = |2x+3|/2 and y=3
Vertex
|2x+3|/2 = 0
2x + 3 = 0
x = -1.5
(-1.5, 0)
still hamlet
where i dicus my math question
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arctic tinsel
From the set
1,2,3,4,5,6,7,8,9
how many ways are there to choose 3 elements if order does not matter?
arctic tinsel
Ik the formula, it is n chose k = n!/k!(n-k)!
and value of n is 9
idk what k is tho
proper nova
well
$\binom{n}{k}$ is just how many ways can you choose $k$ elements from $n$ elements
jolly parrotBOT
1 divided by 0 equals Infinity
proper nova
yes
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restive bluff
I am basically just looking to confirm my work. I got an answer of ~151,509,259 babies in year 25
restive bluff
For part 5
The rest of the parts I am confident in if I got part 5 since I don't see how I could get that exact value without having done the prior steps correctly
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sweet tundra
It's a bit lame to ask to just check your numerical result lol
restive bluff
It's a bit lame to ask to just check your numerical result lol
I'll post work
Give me a second
It was messy though that's why I didn't post it originally
actually wait it will take me a bit to re-write it, it's incomprehensible as is
sweet tundra
You can just tell me the steps without the calculations to check if you got the idea globally
If yes then i believe you got thz right result
Ping me when you're done
restive bluff
@sweet tundra
I got a different answer this time with Bn, like ~35 million babies, which seems more reasonable but idk
sweet tundra
I got a different answer this time with Bn, like ~35 million babies, which seems...
From what i can see you got the global reasining right
restive bluff
The final equation is Bn = -900(-1)^n + 1400(1.5)^n
I think after simplifying maybe
sweet tundra
Even if you got wrong answer, if i was your teacher i would give you points
restive bluff
Dope
Thanks
Either way that's a big # of elephants
35 million?
pink elephants too, you would think they're more rare lol
sweet tundra
Yeah but those exercises ar enot meant to je realistic
chrome plank
after 3 generations, we should start getting fractional elephants
sweet tundra
Oh crap
chrome plank
35352535.61165929 to be (almost) exact
restive bluff
sucks to be the .61165929 elephant
sweet tundra
But that's intended
Because half the elephant die everytime and it's nit rounded up or down
restive bluff
yeah rounding would probably make more sense here
sweet tundra
But the problem would ge tway more complicated
chrome plank
that would break the matrix
sweet tundra
So yeah noninteger nulber of elephant doesn't mean you did anything wrong
chrome plank
anyway, all those fractions of elephants eventually produce a whole baby elephant
sweet tundra
Eventually
In 200 years maybe there will be quadrillions of elephants
Mad eout of fractional elephants
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hoary meadow
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autumn fossil
what was the point of finding t_0
"Find a formula for such point w"
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plush bramble
<@&268886789983436800> spam
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pastel umbra
It IS when the place you're trying to post it is specifically for people who want help on their maths problems.
There are some pretty good marksmen for moderators here, they'll shoot on sight if they see your spam here again
You might want to delete your other shitpost(s) before someone else sicks the mods on you. @rain hemlock
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sterile wigeon
Hey! So i have this question and i cannot seem to solve it, if somebody could show me how to solve it, it would be awsome!
flat hornet
can you convert them all into math equations? let the numerical value of A be a, B be b, and so on, where a, b, ... are variables
sterile wigeon
oh yea
flat hornet
or in other terms we want 4+H
flat hornet
T + A + S + T + E = 3
notice that S+T+E=2, so T+A=1. What can we say about h now?
versed mica
from taste
versed mica
T + A + S + T + E = 3
^
flat hornet
T+A+S+T+E=3 substitute S+T+E for 2, so T+A+2=3. Move the 2 over to get T+A=1
sterile wigeon
ah
flat hornet
get it?
sterile wigeon
OHHHH yea i get it
pastel umbra
because we can add an H to MAT to get MAT
^
pastel umbra
(btw @flat hornet that should say "to get MATH")
flat hornet
wait no we want to add H to MAT
flat hornet
(btw <@1185014113223589970> that should say "to get MATH")
mb lol
pastel umbra
no worries
sterile wigeon
so A+T = 1, H = 6, M = 3 so its 10?
sterile wigeon
Yayyyy
ima try a few more of those questions so i get it
fully
thanks so much!
flat hornet
but notice that we didnt need to get M because all he needed was to add H to MAT
works too tho
sterile wigeon
oh?
flat hornet
thanks so much!
Your welcome!
sterile wigeon
OHH yea i see that now lol yea
flat hornet
any more questions?
sterile wigeon
not at this moment
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prime bramble
any hints for this problem? 
pearl pondBOT
any hints for this problem? <:pikathink:879066872513970227>
prime bramble
I've not been able to come up with a single lead so far 
the errata says that the bounds of integration should be 0 and pi, not 0 and 2pi
and this exercise comes after a chapter on some big theorems for function spaces; namely, Arzela-Ascoli (which I doubt is useful here), and the Weierstrass approximation and Stone-Weierstrass theorems (which might be useful? idk)
warm swan
Fking Riemann is here wtf
plush bramble
indeed stone-weierstrass
prime bramble
how is it meant to be used here?
plush bramble
well if f(x) is continuous, then so is the product f(x) * sin(nx)
warm swan
any hints for this problem? <:pikathink:879066872513970227>
I was thinking Fourier series of Dirac delta functions
prime bramble
well if f(x) is continuous, then so is the product f(x) * sin(nx)
er, how does that help me?
rigid sphinx
any hints for this problem? <:pikathink:879066872513970227>
Wait, isn't cos a counterexample?
I thought sin(nx) and cos(nx) were orthonormal in L^2
plush bramble
yea on [0, 2pi]
sweet tundra
I thought sin(nx) and cos(nx) were orthonormal in L^2
wait i think you're right
rigid sphinx
yea on [0, 2pi]
Well, the bounds are 0 and 2pi too so
plush bramble
the errata says that the bounds of integration should be 0 and pi, not 0 and 2pi
did you see
rigid sphinx
Oh sob
sweet tundra
oh wait no i messed up in my mind
warm swan
Wait, isn't cos a counterexample?
I think it should be $[0, \pi]$ or $[0, \pi/2]$
jolly parrotBOT
《pasta》◇♡♤♧ 🍝🍕😋
warm swan
because cos(nx) depends on n
U can still expand lmao
Use f(x)=cosx
Expand cosx sinnx
sweet tundra
im not good with primitives
plush bramble
for another approach, did you learn about chebyshev polynomials
prime bramble
Wait, isn't cos a counterexample?
idt this works because f needs to be held fixed across all n
prime bramble
for another approach, did you learn about chebyshev polynomials
no
rigid sphinx
idt this works because f needs to be held fixed across all n
Yea, just f(x)=cos x
cos nx and sin mx are orthonormal for any n and for any m in L^([0, 2pi])
warm swan
That might even work in [0, pi] ig
prime bramble
ah ic, but we're on [0, pi]
prime bramble
That might even work in [0, pi] ig
it doesn't hold on [0, pi]
I'm honestly not sure how to use S-W here, as riemann suggested
warm swan
It doesn't ehh
warm swan
I'm honestly not sure how to use S-W here, as riemann suggested <:cat_happycry:6...
I was thinking sine series
prime bramble
a passing thought I had was to use the Weierstrass approx thm to "replace" f with a sequence of polynomials
prime bramble
I was thinking sine series
this isn't my PDEs class unfortunately
I can't do anything with Fourier analysis
prime bramble
a passing thought I had was to use the Weierstrass approx thm to "replace" f wit...
but I just didn't see what that'd do for me
warm swan
I can't do anything with Fourier analysis
F u cooked then
U can just use Fourier series of f(x) and prove all coefficients except a0 are zero
prime bramble
that would be nice, but not allowed here 
okay, I'm gonna go have dinner and keep this open till I return
if it automatically closes, then eh, such is life 
plush bramble
yea i think to use stone-weierstrass you to discover that $\sin(nx) = \sin(x) * U_{n-1}( \cos(x) ),$ where $U_n(x)$ are the Chebyshev polynomials. you don't really need to know the name, just that it's a polynomial for all $n$ which is easy to see with demoivre.
jolly parrotBOT
riemann
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quiet remnant
any hints for this problem? <:pikathink:879066872513970227>
wait i recognize this form
ugh i can't rack my brain 😭
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plucky carbon
Does this look correct ?
pearl pondBOT
Does this look correct ?
versed mica
are you just supposed to graph them?
quiet remnant
Does this look correct ?
wait if the period is 4π, then for the cosine graph, shouldn't the first minimum be at 2π, not π?
plucky carbon
wait if the period is 4π, then for the cosine graph, shouldn't the first minimum...
I still don't understand the difference between graphing csc and sec all I've heard it mark out the where x is 0
quiet remnant
I still don't understand the difference between graphing csc and sec all I've he...
do u know csc(π/2-x)=sec(x)
that tends to help
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tame plume
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tame plume
I have a question, my english is not the best sorry for that, but from my understanding here dphi / ds0 its a small quantity of flux that passes trough an infinitesimal area
is that it ?
I dont understand this formula, cause usually dphi / ds0 would be the derivative of E with respect to the Area but what does that mean ? i need to study this but i come from a math background i dont understand this
finite geode
I have a question, my english is not the best sorry for that, but from my unders...
yes i think
tame plume
But that is not a derivative would you agree ?
finite geode
E is defined as the area density, so its the ratio
finite geode
But that is not a derivative would you agree ?
it is
think of it like
velocity = displacement / time = s/t, but also v = ds/dt
tame plume
in a derivative dphi would be the variation of phi / variation of area
but that makes sense
finite geode
can you explain your question?
tame plume
Yeah i will try to draw a graph from your example, maybe with that i can explain it better
x(t) is the position
so the average velocity in an interval t, is the variation of x in that interval over the period of time
if we want the velocity at a point, instantaneous velocity we make the interval delta t go to 0
so we get v = dx / dt
dx is a variation, infinitesimal one, and dt also a variation infinitesimal one
so dphi / ds0 should be a variation in flux over a variation in area no ?
and not flux / area
that is my question idk if i made it clear sorry
pearl pondBOT
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finite geode
so dphi / ds0 should be a variation in flux over a variation in area no ?
yeah thats correct. but it means the same thign right
were just thinkign abt a small amt of flux through a small area
like dx is a small displacement, but we still say velocity is displacement per unit time
idk if that makes sense
like the flux is varying as you change the area
we just take a small portion of that
tame plume
but if you use the same reasoning with dx / dt , what would be small position / small time, that doesent make sense, you know what i mean ?
we need variation
tame plume
like the flux is varying as you change the area
i understand that
but mathematically it doesent make sense to me 😭
finite geode
sure, but think about it from the perspective of displacement
dx represents a small displacement
dt would be a small time
im not sure how to explain tbh
tame plume
dont worry!
tranquil bolt
but if you use the same reasoning with dx / dt , what would be small position / ...
S=v.t
tame plume
thank youu!! i will send an email to my professor
tranquil bolt
thank youu!! i will send an email to my professor
pearl pondBOT
@tame plume Has your question been resolved?
patent vessel
but if you use the same reasoning with dx / dt , what would be small position / ...
What doesn’t make sense to you about it?
You can think of derivatives in two different ways - one as literally a ratio of two infinitesimal quantities, and the other as an operator acting on a function
If the position of a particle at time t is vector r, and its position at time t+dt is r+dr, then the velocity dr/dt, which is both the time derivative of the position vector, and also the ratio of (if you want speed), the magnitude of the change in position vector to the small time interval
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rustic atlas
If a small increase in area leads to a big increase in flux, that means that the flux density is very high
patent acorn
I remember something called the Laplace Theorem of transforming n×n determinants to a sum of n n-1×n-1 determinants in highschool but I never knew how did this even happen
patent acorn
As in how did they discover that
tropic saddle
its not a very crazy formula
determinants have been around for a long time
sooner or later you'll stumble upon stuff like that
not sure what def of the determinant you know
coming from e.g. the leibniz formula, it makes sense to split S_n into different sets depending on e.g. sigma(1). and if you do that you pretty much immediately get the laplace expansion
patent acorn
sooner or later you'll stumble upon stuff like that
Well I did see it, but I never had to calculate a determinant of 4x4 or higher
patent acorn
not sure what def of the determinant you know
Since I did 3x3 and 2x2 I only knew the basic forms
With Saarus or triangle
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heavy wyvern
hey ive done a 22 question math exam but there is no worked solution
heavy wyvern
can anyone make a worked solution for these questions so i can mark my answers please?
(high-school level paper)
shell brook
eh
dense jasper
.close
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quick venture
pearl pondBOT
quick venture
Can someone help me with questions 11b onwards
I know it's the binomial distribution
quick venture
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@quick venture Has your question been resolved?
thorn shale
I can't see why my anser is wrong for question 19a
you want P(-1.6<Z<0.6) which is P(Z<0.6)-P(Z<-1.6)
because normal curve is symmetric, then P(Z<-1.6) = 1-P(Z<1.6)
so P(-1.6<Z<0.6) = P(Z<0.6) - (1-P(Z<16)) which is
P(Z<0.6)+P(Z<1.6)-1
and you have those values already
solar grove
I don't really know where to begin that would lead to a clean result
pearl pondBOT
I don't really know where to begin that would lead to a clean result
@solar grove Has your question been resolved?
midnight haven
help?
solar grove
help?
gng you can open a new help channel, this one is already occupied 🙏
refer to this
anywho idt im getting help ngl
.close
low matrix
Why is the yellow group an essential prime implicant
pearl pondBOT
Why is the yellow group an essential prime implicant
low matrix
I can do an alternate grouping of it by combining 14 with 12 and 30 with 31
pearl pondBOT
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@low matrix Has your question been resolved?
daring bay
hello i plugged 1/a into this function and why do i not have to consider the e^-1 here?
pearl pondBOT
@daring bay Has your question been resolved?
ripe vault
Are you trying to find the maxima and minima of the original function f(x) or the derivative f’(x)?
daring bay
Are you trying to find the maxima and minima of the original function f(x) or th...
original
i solved it i think
but im just wondering like
ripe vault
Ok, you shouldn’t need the second derivative then
daring bay
i can basically memorize the fact that i never include the e in any calculations?
daring bay
Ok, you shouldn’t need the second derivative then
yes but wouldnt it take more work checking the slope before and after the extreme point
actually no righr
yeah it doesnt
ripe vault
You just find where the first derivative equals 0, then either check the function values themselves to see if the point is a maximum or minimum, or check whether the derivative is positive or negative on each side of the point
daring bay
You just find where the first derivative equals 0, then either check the functio...
wdym by each side of the point
ripe vault
You know that the function is continuous, and you know that its derivative is continuous. That means that once you know where f’(x)=0, you know that the derivative can only be positive or negative between those two points
If the sign of the derivative is positive to the left of the point, and negative to the right, then the point is a maximum. The reverse means it’s a minimum. There might also be no sign change, such as the x^3 at x=0
daring bay
If the sign of the derivative is positive to the left of the point, and negative...
okay but in this case my value for f‘(x) = 0 is 1/a
so what would the point to the left be
ripe vault
It would probably change depending on the value of a
ripe vault
You already checked for a > 0 and a < 0
daring bay
e^4(5x+6x^2)
i never include the e^4 right
like
i can just work with the bracket without considering it
in any way?
ripe vault
i never include the e^4 right
Since it’s a constant multiplier not equal to 0, it will have no effect on where the function equals 0
ripe vault
Just to clarify, this is $e^4(5x+6x^2)?$
jolly parrotBOT
Mr. BananaHead
daring bay
**Mr. BananaHead**
yesh
ripe vault
Yeah, so it’s just an extension of the principal that if a•b = 0, then a = 0 or b = 0
daring bay
oh so in this case e^4
ripe vault
Yeah, but it also extends to functions. If you know a function is never equal to 0, such as f(x) = e^ax, then the function f(x)g(x) = 0 only when g(x) = 0
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green meteor
11b, how do i do WITHOUT integration by parts
pearl pondBOT
11b, how do i do WITHOUT integration by parts
green meteor
1
green meteor
Oh
prisma kernel
eh IG you might have to use IBP in the end, but it's be very straightforward
green meteor
What’s ibp
prisma kernel
integration by parts
prisma kernel
yup, I don't see a way to do it without IBP
you can wait for someone else, or we can proceed with the IBP method, your call
green meteor
The graoh is y= e^x so is lny=c useful
green meteor
This question is b4 ibp in the book so i wanna try avoid using ibp
lilac jackal
@prisma kernel @green meteor the sum of the integrals equals the area of the L shape on the graph
lilac jackal
np!