i'd maybe also try to add a bit of flourish to the bottom of the two (whether a loop or a thingy at the end) to make it more distinct from a z, but you did well enough scaling the z down to size that it'll be an extra improvement rather than a necessity
#help-19
wooden python
brittle plinth
wooden python
can also suggest copying this thing a bunch of times to help cement letter sizing
brittle plinth
this is my f, g and y
wooden python
that's your f?
brittle plinth
yes
brittle plinth
pretty much all my teachers do that f like that
shrewd trellis
i'd maybe also try to add a bit of flourish to the bottom of the two (whether a loop or a thingy at the end) to make it more distinct from a z,
bitter lodge
why is it arranged like this ?
shrewd trellis
I dont understand what u mean
brittle plinth
shows how i write f
doing the downstroke from the right then a stroke from left to right in 2 motions is uncomfortable to me
wooden python
why is it arranged like this ?
short letters -> ascender letters -> descender letters -> f, which has both
bitter lodge
ahh
brittle plinth
wooden python
I dont understand what u mean
brittle plinth
guess what letter it is
wooden python
cyrillic я
brittle plinth
it's the r lol
wooden python
your r is bad and you should feel bad [meme reference]
wooden python
blechhhh
i mean this may be ok for text but it sucks ass for math notation
@shrewd trellis i want to reiterate by the way that you're already doing pretty damn well with your handwriting
shrewd trellis
1000x improvement
shrewd trellis
<@1098469645347995748> i want to reiterate by the way that you're already doing ...
thank u but not at the same level of many people
brittle plinth
the 7:
shrewd trellis
damn i forgot
brittle plinth
god the 7 is killing me
shrewd trellis
i need to get used to it thats my next step
wooden python
,rcw
clever fjordBOT
wooden python
ok your four is much better
i will second a recommendation that someone said here earlier (idr who) to make your x's with two intersecting lines rather than two back-to-back curves like you got rn
and uhh yeah the 7.
shrewd trellis
"to make your x's with two intersecting lines rather " u wnt me to change x?
wooden python
yes
shrewd trellis
also write it in paper, im not sure what u are referring to about my x
wooden python
yeah sorta
but the key difference is that x is aligned to the baseline while × floats above it
shrewd trellis
somethinng like this?
wooden python
wooden python
somethinng like this?
that could work but who's that person you drew over a picture of
wooden python
from that wiki page
since you're handwriting it's OK to make ascender height = cap height
shrewd trellis
im conf, what is this?
wooden python
a diagram summarizing some terms used in typography for vertical spacing/alignment
just to explain what i meant with
but the key difference is that x is aligned to the baseline while × floats above it
shrewd trellis
makes sense
wooden python
oh yeah btw if you ever want specific advice or feedback about your handwriting in the future feel free to ping me in like #discussion or whatever
wooden python
oh you got the studying role 
shrewd trellis
,iamnotstudying
clever fjordBOT
Removed the studying! role from you.
shrewd trellis
oh yeah btw if you ever want specific advice or feedback about your handwriting ...
thanks, ill let u know
.close
odd edgeBOT
ocean bramble
.dont use 3-digit separators. Use half a space if needed
odd edgeBOT
Available help channel!
soft wharf
odd edgeBOT
bitter folio
!xy
odd edgeBOT
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.
bitter folio
I assume we are finding all 3 digit numbers (top bar) abc such that it is equal to product of digits
odd edgeBOT
@soft wharf Has your question been resolved?
soft wharf
fill in the box
<@&286206848099549185>
How
this sht math investigation subject is killing me
open cove
Check the convergence of this series.
[
\sum_{n=1}^{\infty} (-1)^n \frac{2n + \sqrt{n}}{n^2 + 1}
]
clever fjordBOT
Koren
open cove
can't figure where to even start
wooden python
do you need to distinguish absolute vs conditional convergence
open cove
i need to check if it's absouletly conv conditionally conv or div
wooden python
in other words yes
wooden python
in this case you should check for absolute convergence first
wooden python
i think Leibniz
what
oh leibniz
yeah why not
i would also check convergence of the same series without (-1)^n though
wooden python
for absolute convergence, squinting at the series gives 2n/n^2, which is 2/n => harmonic => ...
open cove
comparison?
wooden python
sure
or limit comparison
this at least gives you an idea of what to compare against
open cove
in absoulute values it conv
wooden python
does it???
open cove
if you do limit compar it gives 1
i think
0<1<inf
oh so that's enough to say it's absoulotly conv?
open cove
[
\lim_{n \to \infty} \frac{\dfrac{2n + \sqrt{n}}{n^2 + 1}}{\dfrac{2}{n}}
= \lim_{n \to \infty} \frac{n^2 + \frac{n\sqrt{n}}{2}}{n^2 + 1}
= 1
]
clever fjordBOT
Koren
open cove
oh wait
2/n div
🤦♂️
ok, anyway now i need to check without an absoulute value to check if it's conditional conv
wooden python
yes
open cove
so how do i prove it decreases monotonically
wooden python
i guess look at either the difference or the ratio of adjacent terms
whichever is easier to work with
see if you can prove difference < 0 or ratio < 1
open cove
but the lim of an is 0 and an is positive so from a certain point it gotta decreas monotonically
right?
odd edgeBOT
@open cove Has your question been resolved?
odd edgeBOT
@open cove Has your question been resolved?
wooden python
but the lim of an is 0 and an is positive so from a certain point it gotta decre...
no, it may fail to be monotone in general.
just saying it's >0 and approaches 0 is not enough
open cove
So how can we say it decreases montonically?
odd edgeBOT
@open cove Has your question been resolved?
somber lily
**Koren**
\lim_{n \to \infty} \frac{\frac{2n + \sqrt{n}}{(n^2 + 1)/2}}{n}
= \lim_{n \to \infty} \frac{2(2n + \sqrt{n})}{n(n^2 + 1)}
= \lim_{n \to \infty} \frac{4n + 2\sqrt{n}}{n^3 + n}
= \lim_{n \to \infty} \frac{n(4 + \frac{2}{\sqrt{n}})}{n(n^2 + 1)}
= \lim_{n \to \infty} \frac{4 + \frac{2}{\sqrt{n}}}{n^2 + 1}
= \lim_{n \to \infty} \frac{4 + 0}{\infty}
= \frac{4}{\infty} = 0
north sparrow
So how can we say it decreases montonically?
you could check the derivative of (2x+sqrt(x))/(x^2+1) is negative for x >= 1 or try to prove more explicitely that a_{n+1} <= a_n for n >= 1 with a_n not including the (-1)^n
odd edgeBOT
@open cove Has your question been resolved?
mild stream
multiple choice , help me its just practice
odd edgeBOT
multiple choice , help me its just practice
sand horizon
What is -20+5 ?
mild stream
What is -20+5 ?
-15
sand horizon
times 3 ?
sand horizon
!nogpt
odd edgeBOT
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
sand horizon
Its clueless
mild stream
thx may I add you
sand horizon
Nah i keep math here
hasty dome
how do we close it
Say .close
mild stream
.close
young stone
Hello,
Could someone please help me understand geometric sequences? I’m preparing for an exam and would be grateful for any assistance. Thank you!
quasi sparrow
Hello,
Could someone please help me understand geometric sequences? I’m preparin...
Just do problems and place them here when you get stuck
young stone
Got it, I’ll ask when I need help!
odd edgeBOT
@young stone Has your question been resolved?
stoic viper
hello i am not sure if i did 61 1 a correctly
odd edgeBOT
hello i am not sure if i did 61 1 a correctly
stoic viper
im pretty new to these proofs
amber veldt
a right inverse of f is a function g such that f o g = id
stoic viper
yea
amber veldt
not bothering to write the domain or the codomain because theyre the same here, but in general it matters
amber veldt
well f o g = id has to hold for all values in the domain of g, all values in the image of g, all values of the domain of f, all values in the iamge of f
but i think i misunderstood your question
g will have to be piecewise defined, is that your question
gilded needle
hello
stoic viper
g will have to be piecewise defined, is that your question
yes
sorry idk why i said composition
thank you bro
amber veldt
sorry idk why i said composition
that's what o is
gilded needle
I have a question about the logarithmic function
The question asks to graph this set of functions on the same axis
amber veldt
I have a question about the logarithmic function
!inuse
amber veldt
or whatever the command is for inuse
rich socket
hello i have a simple question about exponantial et logarithm
stoic viper
yo guys
stoic viper
sorry
rich socket
why we say that exponantial its the opposite of the logarithm
amber veldt
2a is fine, I would instead just write sqrt(x^2)=x because we are only considering x>=0 I think that's more clear than introducing +- and then erasing the minus. But that's purely a matter of opinion, what you said is not wrong
amber veldt
why we say that exponantial its the opposite of the logarithm
.inuse
stoic viper
alright thakns
amber veldt
wtf what is the command
stoic viper
i kinda suck at them
@rich socket its just like you gotta create your own help thread in from math avaliable catholgery
amber veldt
!occupied
odd edgeBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
amber veldt
there we go
amber veldt
i cant lie inverses got me trippin
youve basically found the inverse when you did part a of both
gilded needle
The question asks to graph this set of functions on the same axis
but when I look for the points for the graph it gets a bit complex because I end up having 3 points the value of x, the point of the first function which would be Euler raised to x and in the second the logarithm of the value of x in the base of Euler
amber veldt
but when I look for the points for the graph it gets a bit complex because I end...
!occupied
odd edgeBOT
but when I look for the points for the graph it gets a bit complex because I end...
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
amber veldt
@stoic viper btw
the contrapositive of a statement is of course equivalent in general to all implications but
amber veldt
the contrapositive of injectivity is in particular often states in the contrapositive
because it's often easier to prove the contrapositive, and it's almost never harder to prove the contrapositive, for injectivity
so it's kind of standard to use the contrapositive: if f(x)!=f(y), then x!=y
not mandatory at all, just something you'll see
weary pelican
so it's kind of standard to use the contrapositive: if f(x)!=f(y), then x!=y
this isn't the contrapositive of injectivity xd
if x!=y, then f(x)!=f(y)
odd edgeBOT
@stoic viper Has your question been resolved?
stoic viper
youve basically found the inverse when you did part a of both
Oh sick. What’s the inverse for 2 tho
stoic viper
the contrapositive of a statement is of course equivalent in general to all impl...
Yes
amber veldt
you found it already!
tepid orbit
Could someone post an image of a step-by-step solution of an example of the problem that Hooke posed to Newton involving determining the trajectory of a body under an inverse-square central force? I don’t have an example simply because I couldn’t find one.
Make sure to label each step.
Thank you in advance!
odd edgeBOT
@tepid orbit Has your question been resolved?
amber veldt
Could someone post an image of a step-by-step solution of an example of the prob...
is this the catenary problem
odd edgeBOT
odd edgeBOT
Available help channel!
tepid orbit
<@1274029008056750217> Has your question been resolved?
Not yet
zinc glacier
why are you prompting us like chatgpt
tepid orbit
is this the catenary problem
It is not. Here are the differences that I have found:
“Hooke challenged Newton with the hypothesis that the elliptical orbits of planets were caused by an inverse-square force exerted by the Sun. He suggested that the force of attraction decreases with the square of the distance from the Sun. This was a significant idea, as it linked the inverse square law, already proposed by some thinkers, to the observed elliptical orbits described by Kepler's laws.
The catenary curve, on the other hand, describes the shape that a flexible cable or chain takes when hanging under its own weight.”
tepid orbit
why are you prompting us like chatgpt
Mainly because I want to make sure that my question is understood properly
odd edgeBOT
@tepid orbit Has your question been resolved?
odd edgeBOT
tepid orbit
.reopen
odd edgeBOT
✅
quasi sparrow
It is not. Here are the differences that I have found:
“Hooke challenged Newton ...
what is your MATH question man
ivory grove
Could someone post an image of a step-by-step solution of an example of the prob...
!1c
odd edgeBOT
Could someone post an image of a step-by-step solution of an example of the prob...
Please stick to your channel.
tepid orbit
what is your MATH question man
That is my math question
Math is more than just numbers
ivory grove
@tepid orbit No, we do not mean that. We mean, what is the problem that Hooke posed to Newton? We don't know what it is, so you have to tell us.
and then we can give you an example
tepid orbit
<@1274029008056750217> No, we do not mean that. We mean, what is **the problem**...
How do I determine the trajectory of a body under an inverse-square central force?
digital pike
<@1274029008056750217> No, we do not mean that. We mean, what is **the problem**...
Hey Marianne
pallid epoch
Set up a differential equation for the motion
dapper canyon
$\ddot{x} = \frac{c (x-a) }{|x-a|^3}$
pallid epoch
What is x here?
dapper canyon
x(t) is the position of the particle at time t
tepid orbit
Newton’s law of universal gravitation?
quasi sparrow
can you ask questions using complete sentences
clever fjordBOT
unc
tepid orbit
can you ask questions using complete sentences
Are you talking to me?
Don’t be condescending
quasi sparrow
https://en.wikipedia.org/wiki/Classical_central-force_problem
this should answer most of your questions
odd edgeBOT
odd edgeBOT
Available help channel!
stuck fulcrum
hello. I have a question. A piece-wise function can be continuous at the point where two pieces of functions look like meeting?
like for example, let's say two pieces are f(x) = x where x<0.
And another one is f(x)=x^2 where x>=0
IS it continuous at x=0?
vague plaza
stuck fulcrum
so why not in this case?
pastel orbit
hello. I have a question. A piece-wise function can be continuous at the point w...
yes
this is continuity
not differentiability
a function $f(x)$ is continuous at a point $a$ if $\lim_{x \to a} f(x) = f(a)$
clever fjordBOT
higher!
pastel orbit
this can equivalently be stated as $\lim_{x \to a^+} f(x) = f(a) = \lim_{x \to a^-} f(x)$
clever fjordBOT
higher!
pastel orbit
in your example of f(x) = x when x < 0 and f(x) = x^2 when x >= 0, the left handed and right handed limits both evaluate to 0, which is equal to f(0) = 0^2
so your function is continuous at 0
manic sleet
**higher!**
(provided the limit and function exist at x=a)
stuck fulcrum
in your example of f(x) = x when x < 0 and f(x) = x^2 when x >= 0, the left hand...
thank you!
.close
odd edgeBOT
odd edgeBOT
Available help channel!
hallow lark
odd edgeBOT
hallow lark
I’m not certain with the a and e and g and h
night bone
your g and h are correct
j is not correct
and that should also tell you something about e
hallow lark
It doesn’t exist for both
night bone
that's correct but why do you think that is?
hallow lark
Because for the left to right none correspond with 4x
night bone
wdym
hallow lark
None reach 4 on the x
hallow lark
Left to right tho
night bone
are you saying that the right-hand limit does not equal the left-hand limit?
or am I misunderstanding u idk
hallow lark
Yes
hallow lark
I think I understand now
night bone
and it's the same for (e) since the left-hand limit does not equal the right-hand limit
and then (a) is incorrect still
hallow lark
Right
night bone
whenever there is an open circle, the function is undefined at that point although the limit may be defined
hallow lark
I got undefined for a
night bone
that's correct
hallow lark
Thanks I think I get it now
night bone
np
odd edgeBOT
odd edgeBOT
Available help channel!
slow wharf
hello, i kinda need help on this question
odd edgeBOT
hello, i kinda need help on this question
amber schooner
slow wharf
ik we can derivate it and f'(1) must equal to 10
is it..?
amber schooner
lim x -> 1 f’(x) = 10
narrow crypt
condition for l'hopital to apply?
narrow crypt
can it be inf/inf?
oak crown
Yeah
sand horizon
must be 8
can see it as ( f(x) - f(a) )/(x-a) where a = 1 and you have your answer
Aswell
copper quarry
yakuuuuuuuuuuuuuuu
slow wharf
what if 10 value changes
does it matter?
oak crown
does it matter?
No
sand horizon
It just has to exist
oak crown
Because you know that if lim x->1 f(x) != 8 you will get undefined
slow wharf
kk
narrow crypt
By l'hopital, $\lim_{x \to 1}$ \text{that} = 10. Therefore,
[ 10 = \lim_{x \to 1} f'(x) = \lim_{x \to 1} \frac{f(x) - f(1)}{x-1} = \lim_{x \to 1} \frac{f(x) - 8}{x-1}]
clever fjordBOT
k
slow wharf
can see it as ( f(x) - f(a) )/(x-a) where a = 1 and you have your answer
are this gonna work in the 2nd one?
sand horizon
What is it
narrow crypt
[ \frac{f(x)}{x^2} = \frac{\frac{f(x)}{x}}{x}]
clever fjordBOT
k
amber schooner
lim x->0 f''(x) = 10?
this isn’t useful
it’s the same principle as before
since the limit exists and is some finite number but the denominator approaches 0 then what must be true of the limit of the numerator
amber schooner
yep
amber schooner
sure
slow wharf
a bit different from the highschool 🥀
Thanks @amber schooner @narrow crypt @oak crown @sand horizon
.close
odd edgeBOT
odd edgeBOT
Available help channel!
unborn tiger
Can anyone tell me what the mistake is here?
odd edgeBOT
Can anyone tell me what the mistake is here?
wooden python
step 2, complex square roots dont quite work that way
like specifically writing 1/sqrt(-1) as sqrt(1/-1)
unborn tiger
But when I do like this it works fine
√16 × √-4 = √(16 × -4) = √-64 = 8i
@wooden python
north kraken
Can anyone tell me what the mistake is here?
The whole √-1 is i, not √1/-1
unborn tiger
The whole √-1 is i, not √1/-1
Aren't -1 and 1/-1 the same thing?
north kraken
same but you cant distribute sqrt in this case
fast kraken
Can anyone tell me what the mistake is here?
you should keep i as it is
and not replace it with -1
otherwise you'd see terrible results
just multiply by i and devide by it
,, \frac{1}{i}= \frac{1}{i}\cdot \frac{i}{i}
clever fjordBOT
<rajel />
unborn tiger
I know that but I want to know what exactly the mistake is in my case
low locust
thinking that sqrt laws that hold for positive real numbers also hold for other numbers
sqrts of numbers that arent positive real numbers are wacky
north kraken
thinking that sqrt laws that hold for positive real numbers also hold for other ...
Perfect
unborn tiger
So, for negative numbers, there's no guarantee it'll work right?
low locust
ultimately this boils down to the fact that x^2=-1 has two solutions, -i and i. you have -i on the left and i on the right
north kraken
No for imaginary numbers
low locust
and along the way you switched from one solution to the other
by trying to use a sqrt law which just doesnt hold
odd edgeBOT
@unborn tiger Has your question been resolved?
autumn bolt
the problem is that it gets kind of tricky when we try to define square root for imaginary numbers
proper maple
odd edgeBOT
steel quarry
It's just seperable
odd edgeBOT
proper maple
thanks
odd edgeBOT
Available help channel!
hoary marsh
Hello
hoary marsh
I'm not sure how to set up my equation
quasi sparrow
You substitute rho=1 into (x, y) = ...
steel quarry
you can then eliminate psi
hoary marsh
You substitute rho=1 into (x, y) = ...
As in like x = rhocos(theta) and y = rhosin(theta)?
steel quarry
You're meant to replace rho with 1
hoary marsh
Ohhh
steel quarry
you've replaced a and b with 1
quasi sparrow
As in like x = rhocos(theta) and y = rhosin(theta)?
You're still using rho
hoary marsh
you can then eliminate psi
How does that eliminate psi?
quasi sparrow
And missing a and b
hoary marsh
So acos(psi), bsin(psi)?
steel quarry
How does that eliminate psi?
you need to do work to eliminate psi
use the fact that $\cos^2 (\psi) + \sin^2 (\psi) = 1$
clever fjordBOT
jewels!
hoary marsh
Ohh and then I apply this to the ellipse equation?
steel quarry
"apply"?
hoary marsh
Sub?
clever fjordBOT
jewels!
hoary marsh
Ellispe is x^2/a^2 + y^2/b^2 = 1 right?
steel quarry
yes
hoary marsh
you need to sub x/a and y/b
Sub this where?
steel quarry
**jewels!**
here
hoary marsh
**jewels!**
That would make this x = x?
hoary marsh
you need to sub x/a and y/b
And y = y
steel quarry
uh no
steel quarry
**jewels!**
from this you have cos psi being x/a and sin psi being y/b
hoary marsh
Ohh ic
steel quarry
Ellispe is x^2/a^2 + y^2/b^2 = 1 right?
which is this
hoary marsh
which is this
What do I do next?
hoary marsh
you've done it
What can I do for b)? 🥲
wanton bison
Can you draw the region?
hoary marsh
Can you draw the region?
wanton bison
Yes, specifically:
Given the boundaries, I would say dydx or dxdy you'd still need two integrals to evaluate the area.
You can split the region into a triangular piece, and an elliptical part.
You can also use a polar coordinate transformation, are you familiar with that?
hoary marsh
Do I just use change of variates to set up my integration?
Yes
Oh wait
Yeah
This is polar
clever fjordBOT
wanton bison
You would just have to figure out the bounds for theta.
They are determined by the lines y=x and y=-x.
wanton bison
Yes, we actually use elliptical coordinates (see the scale factors a and b are being considered).
hoary marsh
And radius be 1 to 0?
wanton bison
I guess the bounds are π/4 to -π/4
Not necessarily, for circles, yes.
You have to derive the bounds from the equations.
hoary marsh
From this eq?
wanton bison
And radius be 1 to 0?
That yes, because if you plug in the parametric equations into the elliptical equation you get r = 1.
wanton bison
For the bounds of theta you need to plug in the parametric equation into y=x and y=-x, and solve for theta.
clever fjordBOT
hoary marsh
What's E?
clever fjordBOT
hoary marsh
Ohhh
hoary marsh
For the bounds of theta you need to plug in the parametric equation into y=x and...
theta = arccos(y/rho)?
hoary marsh
Is this right?
$\int _{\theta _2=arccos\left(\frac{y}{x}\right)}^{\theta _1=arccos\left(\frac{x}{y}\right)}:\int _0^1:x^2+\frac{y^2}{3}\left|\rho \right|d\rho d\theta$
wanton bison
**Chaewon**
not quiet
x and y are functions of theta
so you didn't really solve for theta, did you?
past mango
Area of ellipse is pi a*b
past mango
Are you asking me by the way?
wanton bison
Nobody is talking to you, so no.
past mango
OK
hoary marsh
I'm so confused 😭
wanton bison
What's the part that confuses you?
hoary marsh
The a and b part
wanton bison
Can you bring it into the form as shown above?
hoary marsh
What do u mean?
clever fjordBOT
wanton bison
This
hoary marsh
a = 1 and b = √3?
wanton bison
Yes, exactly!
wanton bison
Now use these for that.
hoary marsh
tan theta = ±1/√3
hoary marsh
π/6 to -π/6?
wanton bison
Because it's not a perfect circle.
hoary marsh
That makes sense
wanton bison
π/6 to -π/6?
Yes!
clever fjordBOT
wanton bison
The integrand is actually just 1.
hoary marsh
Ohh
wanton bison
Because you are computing the area of the region, not a volume that is between an integrand function and your region.
If you want the area itself it's just a volume with height 1 basically.
hoary marsh
I understand now! Thank u so much guys 🙂
wanton bison
For example: A cuboid's volume is V = width x height x length, but if height = 1 then it just reduces to width x length which is the area of a rectangle basically.
clever fjordBOT
odd edgeBOT
@hoary marsh Has your question been resolved?
brittle adder
Is the distributive property of multiplication for fields the only thing that makes multiplication unique from addition
brittle adder
And would that make multiplication considered the same as addition plus the distributive property
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vital sentinel
hi, im trying to calculate something weird. So, lets say i have villagers that collect resource at 20 per minute. Each villager costs 50 res. I can either spawn new villagers every 30 seconds, or i can save up resources, which i need 500 of. How do i find the optimal rate at which to stop spawning new villagers and wait for resources to pile, rather than spawn more.
Can you help me get an optimal formula, where i dont have to numerically solve it?
I tried cgpt but it suckes
odd edgeBOT
hi, im trying to calculate something weird. So, lets say i have villagers that c...
@vital sentinel Has your question been resolved?
sharp oak
AOE fan?
vital sentinel
yes
like return on vil is 2.5 min (i just made the nrs up btw, so might not make sense)
basically 50/20
sharp oak
I do remember that vils return very, very fast
vital sentinel
im on my phone and id like to calc real rates later
but my example above will do
i would need to know n, which is nr of villagers to stop product more
or optimal t
sharp oak
I did solve this a long while back, I'll see if I can remember the method I used.
Worth saying that having more vils is more valuable than aging up. Still, the question is interesting
vital sentinel
i just wanna find the optimal
or know how to
and ideally w/o any numerical formulas
odd edgeBOT
@vital sentinel Has your question been resolved?
steep mantle
500/20x+sum^(x)_(0) (50/(20x))
oop wait every 30 seconds, that complicates things
youll get your minimum at buying 6 villagers
*assuming you alr start with 1 villager
ehhwait
waitt
its 50/20n but its still at 6
vital sentinel
issue is, your vils make resources, while you wait
so at 3, you make 60/m, and you also get it while were waiting for new one
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@vital sentinel Has your question been resolved?
proud fog
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atomic void
i thinmk you should draw probability tree
@proud fog do you know how to draw a probability tree?
proud fog
as in a tree diagraam?
atomic void
yep
proud fog
yh, i got 8/9
atomic void
wait lemmme check
proud fog
because the prob of no cheese is 1/3 X 1/3=1/9, so the prob of cheese is 8/9
odd edgeBOT
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proud fog
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woeful rivet
copper quarry
bum chicekn
woeful rivet
hi water ebam
wooden python
this manipulation was incorrect
you would have had $10(\log_{10}(P) + 16)$ there and not $10 \log_{10}(P) + 16$ as you wrote.
clever fjordBOT
Ann
wooden python
also would have been better to just divide by 10 right off the bat and thus avoid this error-opportunity entirely
odd edgeBOT
@woeful rivet Has your question been resolved?
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slow cradle
tropic copper
,, \int_a ^b [f(x) \pm g(x)] \dd x = \int_a ^b f(x)\dd x \pm \int_a ^b g(x)\dd x
clever fjordBOT
Bettim
broken schooner
alright this is just transformation
fleet tapir
And substitute x=u+2 in the original integral
broken schooner
f(x+2) moves it left by 2, thus to match, the integral must be from 0->2
+1 moves it up by 1, thus adding 1*(2-0)=2
fleet tapir
And substitute x=u+2 in the original integral
Substituting gives $\int_{0}^{2}f(u+2)\mathrm{d}u$ = A
broken schooner
therefore it is B
clever fjordBOT
Herzog
odd edgeBOT
@slow cradle Has your question been resolved?
kindred osprey
I need to calculate the level curves of a function but none of my results fit
kindred osprey
domain of the function are all (x,y) that comply to these three rules
wooden python
this looks suspiciously like a current test
kindred osprey
but it is not, im sitting at the class and working on the solutions
wooden python
does dziedzina mean domain?
kindred osprey
we give our phones away at the real tests
kindred osprey
does dziedzina mean domain?
yes
wooden python
ok in that case you should double-check that
bc your answer to it looks suspicious
it's only the denominator here that affects the domain at all and the denominator just needs to be ≠ 0
(so accordingly you should put brak in the other two boxes there)
kindred osprey
okay, thanks, will work with that
wooden python
for the level curves presumably you want to start with the equation f(x,y) = C
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shrewd trellis
,rotate
clever fjordBOT
shrewd trellis
where did I go wrong
odd edgeBOT
@shrewd trellis Has your question been resolved?
sturdy cape
I've seen crop circles that are more convincing of alien life /s
idk where I was going with that lol
wooden python
@shrewd trellis are you still here or are you going to keep dropping offline every 10 minutes due to your bad internet
shrewd trellis
you gotta redo the whole thing from scratch
I was redoing the question but I keep messing up
,rotate
clever fjordBOT
shrewd trellis
@wooden python
wooden python
yes correct now
shrewd trellis
yes correct now
but if i sub 0 into x to get the derivative of 0, its not giving me a value of 0
because i need to prove it that it is a stationary point
its giving me 10
wooden python
how are you getting 10? show your work.
also derivative at 0 not "of" 0
derivative of a function but at a point
shrewd trellis
how are you getting 10? show your work.
u can see on the last line
wooden python
i do not see the last line
shrewd trellis
if i sub in 0 into x, it will just be 0
wooden python
you worked out the correct derivative and then began to calculate f'(0) but scratched it out
f'(x) = (10-x)(-4x^2+20x) is correct but i do not see where you calculated f'(0)
wooden python
tbh if you had factored out x (as you could've) it would have saved you some effort.
shrewd trellis
tbh if you had factored out _x_ (as you could've) it would have saved you some e...
On the fourth line?
wooden python
it could've happened at basically any stage in your working
also for comparison this is how i would have written down the working for this derivative
(though i could still have broken it down further i suppose)
shrewd trellis
also for comparison this is how i would have written down the working for this ...
How is your hand writing really consistent
wooden python
years of practice i guess
shrewd trellis
years of practice i guess
damnnn
wooden python
there was never any secret trick to it
like, i developed my own semi-cursive handwriting style back in grade 5 but that's it
shrewd trellis
yeah that’s fair
wooden python
idk what exactly you mean by "good in english"
shrewd trellis
alright thanks for the help up there
shrewd trellis
idk what exactly you mean by "good in english"
english as a subject
wooden python
i sat an English exam offered by Cambridge and got a certificate that says my proficiency in it is C2 (which is the highest possible)
does that count as "good at english"?
brittle plinth
if that doesnt count as "good at English" then idk what to say
shrewd trellis
does _that_ count as "good at english"?
well, I was going to ask you how do I get better at English as a subject
That’s my weak subject
wooden python
(C2 on the CEFR scale, for the record)
late sinew
flex
wooden python
well, I was going to ask you how do I get better at English as a subject
yeah im the wrong person to ask
im not even a native speaker
pulsar tiger
Is this proof of contradiction induced by 0 not being the greatest lower bound here?
odd edgeBOT
Is this proof of contradiction induced by 0 not being the greatest lower bound ...
@pulsar tiger Has your question been resolved?
clever fjordBOT
Triaengle
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
turbid comet
So we can always find n larger than 1/t in the set
pulsar tiger
Yeah, makes sense
turbid comet
By the way I assume t is from 0 to 1
woeful vine
The argument here is this:
- we know inf{1/n} = 0, which means 0 is the greatest lower bound of {1/n}
- any other lower bound will have to be smaller than 0
- if we take t > 0, then t is not smaller than 0, so it can't be a lower bound
- by definition this means we can find an element in {1/n} which is smaller than t, which is the conclusion
pulsar tiger
The argument here is this:
- we know inf{1/n} = 0, which means 0 is the greatest...
A smaller t that we can find would be 1/n - t for example that could be smaller than t.
Hence, why it can't be ethe loewr bound, right?
woeful vine
the reason t cannot be a lower bound is that we know what the greatest lower bound is already
inf = greatest lower bound
so when they write inf = 0 this means that the number 0 is the greatest lower bound,
No lower bound can be greater than the greatest lower bound, do you agree?
pulsar tiger
Yeah, agreed
woeful vine
so if 0 is the greatest lower bound, can a number greater than 0 be a lower bound?
odd edgeBOT
@pulsar tiger Has your question been resolved?
glossy crown
Done with PDNF now how to convert to PCNF?
odd edgeBOT
Done with PDNF now how to convert to PCNF?
glossy crown
yep
glossy crown
Should apply negation to PDNF expression will it work?
tepid pelican
that wouldnt be PDNF anymore
can you write the truth table as intermediate step?
Or is that forbidden
glossy crown
without truth table
tepid pelican
can you at least use it somewhat implicitly
without explicitly writing it otu
if you have sth like this
(A ^ B ^ C) v (A ^ B ^ -C) v (-A ^ -B ^ C) v (-A ^ -B ^ -C)
When is it not true?
can you write the PDFN of the negation of it?
glossy crown
This is PDNF A = (p∧q∧r) ∨ (p∧q∧¬r) ∨ (¬p∧q∧r) ∨ (¬p∧q∧¬r)
glossy crown
ok
tepid pelican
- means ¬
glossy crown
ok got it
glossy crown
Should apply negation to PDNF expression will it work?
!
tepid pelican
if you can write PDFN of -A, you can then simply demorgan it
demorganing it flips ^ and v and adds one negation
so youll end up with PCDNF of --A
which is just PCFNF A
tepid pelican
Should apply negation to PDNF expression will it work?
Applying negation to it flips it too early
If you just applied negation, youd have to use demorgan and youd get PCNF of -A
but we need PDNF of -A
glossy crown
ohhh ok
¬A = (¬p ∨ ¬q ∨ ¬r) ∧ (¬p ∨ ¬q ∨ r) ∧ (p ∨ ¬q ∨ ¬r) ∧ (p ∨ ¬q ∨ r)
thats it?
tepid pelican
¬A = (¬p ∨ ¬q ∨ ¬r) ∧ (¬p ∨ ¬q ∨ r) ∧ (p ∨ ¬q ∨ ¬r) ∧ (p ∨ ¬q ∨ r)
this is PCNF
we need PDNF of -A
ill show you how to get it
PDNF A = (p∧q∧r) ∨ (p∧q∧¬r) ∨ (¬p∧q∧r) ∨ (¬p∧q∧¬r)
note that the PDNF consists of stuff like this: (p∧q∧r), (p∧q∧¬r)...
you can make total of 2^3 of those for 3 variables
because for each variable, you can either have it negated or not negated
tepid pelican
PDNF A = (p∧q∧r) ∨ (p∧q∧¬r) ∨ (¬p∧q∧r) ∨ (¬p∧q∧¬r)
here we have 4 of them
which of the 8 are missing?
tepid pelican
(p∧q∧r), (p∧q∧-r), (p∧-q∧r), (p∧-q∧-r), (-p∧q∧r), ...
those
4 of them are in PDNF of A and 4 of them are missing
which are the missing ones
you can imagine the truth table (total of 8 rows, 4 are covered by the terms in PDNF, 4 are missing)
glossy crown
yes
tepid pelican
so can you list out all the terms which are missing in PDNF of A?
glossy crown
(p∧¬q∧r), (p∧¬q∧r) ,(¬p∧¬q∧r) ,(¬p∧¬q∧¬r)
tepid pelican
(p∧¬q∧r) is contained in PDNF of A
its not missing
,(¬p∧¬q∧r) isnt missing either
oh wait i was looking at the wrong one
sorry
PDNF of A = (p∧q∧r) ∨ (p∧q∧¬r) ∨ (¬p∧q∧r) ∨ (¬p∧q∧¬r)
glossy crown
PDNF A = (p∧q∧r) ∨ (p∧q∧¬r) ∨ (¬p∧q∧r) ∨ (¬p∧q∧¬r)
tepid pelican
Yeah, it looks right, good
glossy crown
ok now what i should do with missing terms
tepid pelican
(p∧¬q∧r), (p∧¬q∧r) ,(¬p∧¬q∧r) ,(¬p∧¬q∧¬r)
so now the cool thing is that
PDNF -A = (p∧¬q∧r) ∨ (p∧¬q∧r) ∨ (¬p∧¬q∧r) ∨ (¬p∧¬q∧¬r)
if you think about it, it makes sense
tepid pelican
(p∧¬q∧r) is only true if p is true, q is false and r is true
glossy crown
yes
tepid pelican
and since it doesnt appear in PDNF of A, A must be false when that's the case
so we include it in PDNF of -A to make it true
glossy crown
ok
tepid pelican
we are basically making PDNF of -A to be true whenever PDNF of A is false
tepid pelican
--A = -((p∧¬q∧r) ∨ (p∧¬q∧r) ∨ (¬p∧¬q∧r) ∨ (¬p∧¬q∧¬r))
okay and now we can negate both sides
--A turns to plain A
and the right hand side turns to PCNF once you apply demorgan
tepid pelican
np
glossy crown
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odd edgeBOT
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sudden charm
Hii, I need a hint for this problem, I dont know how to begin
odd edgeBOT
Hii, I need a hint for this problem, I dont know how to begin
@sudden charm Has your question been resolved?
low locust
think about the first columns of B and D
they have to be linear combinations of the columns of A and C
sudden charm
oh yeah right for it to have rank n
$\begin{bmatrix}
B\
D
\end{bmatrix}
= \begin{bmatrix}
A \
C
\end{bmatrix}
\cdot X
$
clever fjordBOT
Γ
sudden charm
for some matrix X
low locust
X doesnt have to be invertible
low locust
yes
patent parcel
Hello
patent parcel
In Question 12 the relationship between sets A_a is they r same sets
I mean there is only one set
Is it correct
Question 14 is wrong right?
patent parcel
Like if j is subset of I then it is possible that in all set there's is no common element but few of them (for example within j) have common element/elements
latent scaffold
It's not necessarily wrong, just wondering
patent parcel
Its one possibility
That is enough
Oh wait
Might they have some other elements as a common
latent scaffold
Like if j is subset of I then it is possible that in all set there's is no commo...
That wouldn't be a counter example though, because it still follows that the whole intersection (with I) would be empty, and the empty set is a subset of the intersection with J.
patent parcel
That wouldn't be a counter example though, because it still follows that the who...
That's why I said that whole intersection might have other elements as a common
And within j others
latent scaffold
I think this question is more easily thought about if you write down what it means for a given element to be in the left intersection, and what it means for it to be in the right intersection.
latent scaffold
Say you pick some $x \in \bigcap_{\alpha \in I} A_\alpha$. Then can you show that $x \in \bigcap_{\alpha \in J} A_\alpha$?
clever fjordBOT
Azyrashacorki
patent parcel
Some x is common element in whole intersection of sets A_a then it must be in every set of A
Thanks @latent scaffold
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twin vigil
Why there is x_0 in the Eq2-36 generally we write x = ut +1/2(at²)
placid wolf
$x_0$ is the initial position. it acts as $+C$ here
clever fjordBOT
Rose
twin vigil
Here what do u mean by +C
placid wolf
the constant of integration
twin vigil
There is no constant of integration
placid wolf
if you are not familiar with integration, don’t worry about that
twin vigil
I am familiar
placid wolf
$x_0$ is just a part of the derived equation for kinematics. the rest of the expression represents the displácement from $x_0$
clever fjordBOT
Rose
twin vigil
Got it got it
placid wolf
i mean that if you took the antiderivative of $v_{0x}+a_xt$, the constant of integration would be $x_0$
clever fjordBOT
Rose
waxen adder
Hello, i am really stuck on this problem. I know all the terms but i honestly have very little insight on where i should even start.
vale vortex
cant u just plug in values
x=1 y=0 first vector is just 1 0 -1
for starters u need 2 linearly indepedent ones
waxen adder
x=1 y=0 first vector is just 1 0 -1
ehhh i'l try
waxen adder
for starters u need 2 linearly indepedent ones
how do we know that??
vale vortex
to get more than 2 vectors
waxen adder
ohh right
vale vortex
you need 2 vectors that arent parallel
if they were you wouldnt be able to
once you have your first 2 you can literally just add and subtract them
and thats all 4 I believe
unless im missing something
waxen adder
they probably wouldn't write 4 vectors then
cuz if 1 of them can be expressed as a linear combination of others then we can remove it and keep the span the same by the linear dependence lemma
so the whole list probably has to be linearly independent
waxen adder
If a list of vectors is linearly dependent then one of them can be expressed as a linear combination of the vectors before it, furthermore, if it is removed from the list the span of the list stays the same
waxen adder
also it's not hard to prove that if one of the elements is a linear combination of the previous ones then the whole list is linearly dependent
vale vortex
so its actually impossible for their to be 4 linear independent vectors in it
Im p sure im right but you can be skeptickle im not positive
but im like 95% sure thats true
waxen adder
so its actually impossible for their to be 4 linear independent vectors in it
ahhh you're right
it's either 3 or less
vale vortex
Yea you get it
waxen adder
since the list that spans F^3 is 3 elements long
i'm still very confused on how to find the vectors tho...
vale vortex
what part
for the second one u can just swap the values
x= 0
y=1
than you have 2 vectors
than you add those and subtract them and thats all 4
waxen adder
ohhh right
how did i not see that.. thank you for the help!!
vale vortex
its no worries glad you understand now
vale vortex
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low lily
what are the types of probability functions and where are they applicable
vale vortex
im ngl thats very googable but they are discrete and continuous
and u can prob figure out application on ur own
bitter folio
odd edgeBOT
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mystic saffron
i shouldn't need to ask this, but how do you convert this RREF to this parametirc form, my brain is dead 💀
mystic saffron
so I know
x1 + 0x2 -2x3 + 0x_4 = 0
0x1 +x^2 + 2x_3 - x_4 = 0
x_3 =x_3
x_4 = x_4
(i am stupid, never mind)
i just figured it out 🤦♂️
.close
magic notch
a projectile of unit mass is launched vertically upwards from a horizontal plane with an initial speed v0 ms-1, the resistive accelleration is 0.01v^2ms-2, where v is the velocity. take g = 10, and find the value for v0 such that the projectile lands at 1/7 th of the initial speed
rich quarry
a projectile of unit mass is launched vertically upwards from a horizontal plane...
theres no gravity involved right?
OH IY IS
fk
i misread it
mb
im so sorry
late sinew
a projectile of unit mass is launched vertically upwards from a horizontal plane...
!status
odd edgeBOT
a projectile of unit mass is launched vertically upwards from a horizontal plane...
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
@magic notch Has your question been resolved?