but with that don't know what to do
#help-23
supple shore
safe radishBOT
@supple shore Has your question been resolved?
safe radishBOT
@supple shore Has your question been resolved?
proper crypt
try to prove it's a decreasing sequence by induction
strictly decreasing
@supple shore
safe radishBOT
@supple shore Has your question been resolved?
supple shore
it's not stricly decreasing, it's more like decreasing in a certain rank, or am I wrong ?
safe radishBOT
@supple shore Has your question been resolved?
safe radishBOT
@supple shore Has your question been resolved?
proper crypt
try it
wait you're right
im not sure then. you need to show its decreasing from a certain point
supple shore
yes I know, i tried but don't know how to do, i will try again but i can't solve this
mortal sandal
does this really converge?
you don't have l=sqrt(l)
l = "sqrt(nl)"
It should just shoot off to infinity
supple shore
yes it converges to 1 and we have our $l = \sqrt(l)$
flat frigateBOT
phoestaclies
placid kelp
yes it converges to 1 and we have our $l = \sqrt(l)$
so it's $\sqrt{u_n}$ not $\sqrt{u\cdot n}$? i think that's the confusion
flat frigateBOT
nilpotent nix
placid kelp
it's not stricly decreasing, it's more like decreasing in a certain rank, or am ...
they're effectively the same thing. if you just lob off the terms where it is not strictly decreasing, then you still get a sequence which has the same behavior as n goes to infinity. if you show that it's strictly decreasing after some index, then you can use the fact that it is bounded below to prove it converges.
if something is constantly getting smaller, but is always greater than 1, then it must be getting closer and closer to 1. you can't necessarily say it converges to 1 from just that. technically it's also getting closer and closer to 0, -2, and -100000. but it has nowhere to go but to converge to some value. greater than or equal to 1. imagine you can only walk forward towards a wall. eventually you have to stop at some point, at or in front of the wall.
this is called the monotone convergence theorem
supple shore
Yes i konw That but with this proof I know that it converge to 1 or diverge and just need to prove after that it can't diverge so it converges to 1 and decreasing by a certain rank
Or maybe i'm getting this wrong but it was here to say that the sequence has 2 possibilities and after eliminate one of them
placid kelp
wdym by "decreasing by a certain rank"
supple shore
what is wdym sorry I'm not english maybe an abreviation that I didn't know
placid kelp
what is wdym sorry I'm not english maybe an abreviation that I didn't know
my bad. it's "what do you mean"
placid kelp
Yes i konw That but with this proof I know that it converge to 1 or diverge and ...
if you prove it's convergent, then it is automatically not divergent. so you can use the monotone convergence theorem for that.
supple shore
Yes np it's me, so like the sequence is decreasing but from a certain rank and not strictly decreasing at the start
Yes but we need to study also if it stricly decreasing or increasing or whatever
placid kelp
and the monotone convergence theorem does work even if the sequence isn't initially monotone, because you can always delete finitely many of the first terms and get a sequence with the same convergence.
supple shore
Yes but how do we know that the sequence is strictly decreasing or increasing, or decreasing by a certain rank or increasing at a certain rank ?
We don't know that with this theorem
It just says when it converges or not
And it's for that I tried to calculate the difference between $u_{n+1} - u_{n}$
flat frigateBOT
phoestaclies
supple shore
But I get nothing
fair dagger
Steps how to proof that is converfes to 1:
-
Show for any threshold $L > 1$ you have that any $a \geq L$ satisfies $\sqrt{a} - a < \sqrt{L} - L < 0$.
-
Let $T_{\varepsilon} := \lceil-\frac{2}{\sqrt{1 + \varepsilon} - 1 - \varepsilon} - 1\rceil$ and $M_{\varepsilon} := -\frac{\sqrt{1 + \varepsilon} - 1 - \varepsilon}{2}$.
-
Show that for any $\varepsilon > 0$ and $n \geq T_{\varepsilon}$ either
\ - if $u_n \geq 1 + \varepsilon$ then $u_{n+1} \leq u_n - M_{\varepsilon}$ due to the first point.
\ - or otherwise then still $u_{n+1} \leq u_n + \frac{1}{n+1} \leq u_n + M_{\varepsilon}$.
-
Conclude with an $\varepsilon$-proof of convergence: For any $\varepsilon > 0$ look at $n \geq T_{\varepsilon} + \max \left( 0, \frac{u_{T_{\varepsilon}} - 1 - \varepsilon}{M_{\varepsilon}} \right)$ and it will be $u_n \leq 1 + \varepsilon + M_{\varepsilon}$. This is because because while during the first $T_{\varepsilon}$ steps anything can happen, afterwards the value is going to be decreasing to $1 + \varepsilon$ due to the third point. And afterwards while it may go up again if it went below $1 + \varepsilon$, it will not increase by more than $M_{\varepsilon}$ and decrease below $1 + \varepsilon$ in the next step.
-
because $1 + \varepsilon + M_{\varepsilon}$ converges to $1$ for small $\varepsilon$ this proofs the convergence.
flat frigateBOT
M8732
fair dagger
Let me know if you find typos or need further clarification
supple shore
Yes please I read that but it's not of my level if you can clarify it @fair dagger
fair dagger
Yes please I read that but it's not of my level if you can clarify it <@29565493...
You need to ask specific questions
because I don't really know what to clartfify
fair dagger
that is just an arbitary definition that turns out to work
like your u_n
it is just set like this
supple shore
Yes ok
fair dagger
and then you work with it
supple shore
How do you come with this formula
fair dagger
That is difficult to explain lo
it has something to do with wanting to make the u_n decrease
supple shore
yes sorry it's not really my level
fair dagger
as the third point expaions it determins some cinditions when u_n will be handable
because after T_espilon it will no increase anymore
fair dagger
yes sorry it's not really my level
To understand the proof though you do not really need to understand how I came about these specific ones
it suffices to see that they do as I say they should
supple shore
I need to understand because it can be solve with my knowledge and it's less high
and need to understand how it works, like where the formula comes up
fair dagger
you learn how to do this stuff by studying preexisting proofs and understanding howe the value matters
safe radishBOT
@supple shore Has your question been resolved?
safe sparrow
How is this related to the derivative of exponentials and how can I solve for the value of kt/time of death answer
safe radishBOT
How is this related to the derivative of exponentials and how can I solve for th...
wise venture
safe radishBOT
wise venture
How did the underlined information led us to conclude that the equation would be x-cos^-1(7cosx) instead of cos^-1(7cosx)-x?
Here x ∈ (0,pi/2)
safe radishBOT
@wise venture Has your question been resolved?
safe radishBOT
@wise venture Has your question been resolved?
safe radishBOT
@wise venture Has your question been resolved?
safe radishBOT
@wise venture Has your question been resolved?
wise venture
Dmitri 😠
lean otter
How did the underlined information led us to conclude that the equation would b...
Which step exactly do you not understand?
Which line to which?
Oh my bad I must be blind
I don't see what the underlined information has to do with the conclusion
cos^-1(cos(x))-cos^-1(7cos(x)) = x-cos^-1(7cos(x)) regardless
wise venture
The formula which has been applied is cos^-1 a - cos^-1 b. How did we decide that cosx was a while 7cosx was b instead of it being the other way around?
lean otter
The formula which has been applied is cos^-1 a - cos^-1 b. How did we decide tha...
What formula are you talking about? Don't you mean cos^-1 a - cos^-1 b = ...?
wise venture
lean otter
-+ symbol 
lean otter
Yeah, the right-hand side of this formula doesn't care about the order of x and y
wise venture
-+ symbol <:thonk:406575732563902485>
Its representing two formulas.
lean otter
Its representing two formulas.
Yeah I know
I just thought it looked funny seeing that for the first time
wise venture
Yeah, the right-hand side of this formula doesn't care about the order of x and ...
I do see it now; thank you for your time and assistance.
.close
safe radishBOT
safe radishBOT
Available help channel!
fickle trail
safe radishBOT
fickle trail
Do these both mean exactly the same thing?
If so, which way do you prefer to write it?
thin bridge
they'd usually be interpreted the same way,
the latter is in no way ambiguous
fickle trail
they'd usually be interpreted the same way,
the latter is in no way ambiguous
So the first is the preferred way to write it?
thin bridge
ideally you'd use the latter imo
fickle trail
Not sure what you mean by “ambiguous”
thin bridge
especially if you have stuff like
$$\dv{x} \big[f(x)g(x) \big]$$
compared to
$$\dv{x} f(x)g(x)$$
where it might not be entirely clear whether whether the operator is intended to apply to just the $f(x)$ or the entire product
flat frigateBOT
ℝamonov
lean otter
Although the ambiguity could start with you trying to differentiate between[
\parens{\dv{x}\bracks{3x^2 -4}}^{100} \textss{and} \dv{x}\bracks{\parens{3x^2 -4}^{100}}
]
fickle trail
Oh OK
flat frigateBOT
lean otter
Although I think the first case is never going to appear
fickle trail
I’ve only seen cos(pi)^2 and cos^2(pi) where the exponent has that commutative property without brackets
thin bridge
well its not that different to
$$\dv{x} x^2$$
and there doesn't really seem to be a need for explicit parentheses:
$$\dv{x} (x^2)$$
flat frigateBOT
ℝamonov
thin bridge
reasonable parentheses use to avoid ambiguity doesn't hurt
make an effort to ensure there's no miscommunication
fickle trail
I’ve only seen cos(pi)^2 and cos^2(pi) where the exponent has that commutative p...
So would you recommend extra brackets for this? Or trig functions with exponents are an obvious norm now, so no need
thin bridge
$\cos^2(\pi)$ is fine \
if you want the power on the outside, aim for $(\cos(\pi))^2$
flat frigateBOT
ℝamonov
fickle trail
**ℝamonov**
Both mean exactly the same thing right?
thin bridge
yes
thin bridge
but NEVER under any circumstances write stuff like
$$\cos \pi^2$$
flat frigateBOT
ℝamonov
fickle trail
Yeah
thin bridge
unless to make that point of not doing it
fickle trail
**ℝamonov**
It’s weird because other algebra can do just that
Only trig it’s kinda different
thin bridge
not just limited to trig
fickle trail
But I guess it’s because it’s the input
thin bridge
applies to predefined functions like logs as well
thin bridge
ensure the arguments/inputs are unambiguous
fickle trail
I kinda wish arguments used a different style of brackets
Just to be crystal clear.. about what is inside of the brackets.. but maybe it wouldn’t solve anything
thin bridge
it would not, already different grouping symbols for different things
fickle trail
Yeah and when you get into coding it’s the same thing there too
fickle trail
{} are needed for objects. I do find it kinda interesting the “norm” with syntax, we all just accept it’s the standard and have to live with it until death do us part… Like for logs maybe if someone other than John Napier invented their syntax, they could be a bit better
Oh well… “finders keepers” I guess
Just gotta be the first, or invent a better way that gets traction
thin bridge
like {} was the next best option after square []
so if you want a new grouping symbol
its gotta be worse than {}
and also distinguishable from it
if it aint broke, dont fix it
function( input )
already clearly indicates the argument
no need to invent new symbols
fickle trail
VSCode has so many extensions to help with this. Quality of life has improved ten fold for developers. And typescript is an example of strict formatting for JavaScript to ensure no breakage before deployment
fickle trail
no need to invent new symbols
Yeah I think extensions and AI are kinda the new thing now instead of inventing symbols
.close
novel cargo
Can someone explain. My questions are in red
safe radishBOT
Can someone explain. My questions are in red
peak estuary
yes your first part is wrong
matrix multiplication is not commutative so (AB)^2 is not the same as A^2B^2
(AB)^2 = (AB)*(AB)
for your second question, they just changed the brackets
safe radishBOT
@novel cargo Has your question been resolved?
safe radishBOT
novel cargo
.reopen
safe radishBOT
✅
novel cargo
for your second question, they just changed the brackets
Oooh
Lol
How would I do the (P^-1AP)^2
Like what does that look like
safe radishBOT
@novel cargo Has your question been resolved?
novel cargo
(P^-1 A P)(P^-1 A P)
Yeah but how? Like expanding brackets?
safe radishBOT
@novel cargo Has your question been resolved?
novel cargo
P^-1 A (P P ^-1) A P
Yeah I get that
Is that the only way to do it
Like can we not do like expand it out like we do in algebra
peak estuary
what do you want to expand
it's only a product
there is no + or anything else here
graceful yoke
in calculus, is it logical to say f obtain a local minimum or local maximum at a point named c and not interval?
safe radishBOT
in calculus, is it logical to say f obtain a local minimum or local maximum at a...
split ether
Yes, you can do that
graceful yoke
but c is a point, if it has a local maximum then for every x in a point c f(c) >= f(x)?
hoe you could take a point from a point ?
split ether
" x = c is an extremum point of f " -> " f'(c) = 0 "
Are you familiar with derivatives yet?
graceful yoke
yep
split ether
" x = c is an extremum point of f " -> " f'(c) = 0 "
Then that means this
Or
You can consider the point c to be the point where the function stops increasing and starts decreasing or vice versa
vast obsidian
" x = c is an extremum point of f " -> " f'(c) = 0 "
That both sided implication is not 100% correct. The endpoints of a closed intervall can also be local minimums/maximums
split ether
Ah, right, saddle points too
vast obsidian
Just wanted to mention it for completeness
manic wing
safe radishBOT
manic wing
i have been able to get 1/2 as one of the roots using rational root theorem but im not sure how to factor it any further
how do i factor 5x^4+41x^2+42
:')
white hollow
let u = x^2
manic wing
do you just use quadratic formula from there?
white hollow
do you just use quadratic formula from there?
yes
and then once you get your values you plug back in x^2
and then take the square root
white hollow
you should get a quadratic equation with the coefficients that will give you solutions for u
manic wing
i got -6/5 and -7
white hollow
yeah, those follow from what you got
x^2 = -7
x = + sqrt(-7) or - sqrt(-7)
= i sqrt(7), -i sqrt(7)
white hollow
np
novel magnet
safe radishBOT
novel magnet
how do i do this?
compact ferry
brute force
safe radishBOT
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novel magnet
brute force
how do i brute force this?
safe radishBOT
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patent vault
i just need a hint
safe radishBOT
i just need a hint
patent vault
maybe similar triangles?
safe radishBOT
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tardy mango
maybe similar triangles?
Don't see similar triangles rn, I'd consider $\angle CAB$ and $\angle DAB$
flat frigateBOT
Civil Service Pigeon
patent vault
Don't see similar triangles rn, I'd consider $\angle CAB$ and $\angle DAB$
whjats to consider about them?
tardy mango
||their sizes relative to each other||
patent vault
||their sizes relative to each other||
how would i know that tho
tardy mango
D is in the interior of $\triangle ABC$
flat frigateBOT
Civil Service Pigeon
safe radishBOT
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crude quiver
i just need a hint
What matwrial is this, vector? I forgot 🥺
patent vault
geometry
safe radishBOT
patent vault
.reopen
safe radishBOT
✅
lean otter
@patent vault Instead of pinging helpers multiple times, I recommend closing this channel again and reopening it with the same question. Then, once 15 minutes have passed in that channel without an answer, ping helpers. If yet still no one comes, pretty much all you can do is look for help elsewhere
I personally tried my hands at your question and couldn't solve it myself
gilded fiber
safe radishBOT
gilded fiber
Any help tips on this algebra
I need to find (x^2 + y^2)
given X^3 + y^3 = 2
And x+y=5
trim swan
Hm, your factoring and expanding is a bit off
You used the sum of cubes formula on (x+y)^3, but that's not a sum of cubes
(also one of the terms in that formula is negative)
gilded fiber
Which formula?
gilded fiber
You used the sum of cubes formula on (x+y)^3, but that's not a sum of cubes
what do you mean?
gilded fiber
(x^3 + y^3) = (x+y)(x^2-xy+y^2)
i'm confusd how you get a negative
I just did
(x+y)(x+y)(x+y)
gilded fiber
(x^3 + y^3) = (x+y)(x^2-xy+y^2)
oh are you talking about (x+y)^3 or (x^3 + y^3) ?
trim swan
I'm talking about this part
gilded fiber
oh ok
trim swan
but
actually
I think the way to solve this is to just do a substitution
x + y = 5
x^3 + y^3 = 2
Like the same way you might solve a system of linear equations
gilded fiber
ohh just isolate x
trim swan
yeah x = 5-y
and substitute that in the other equation
cubic terms should disappear and then you jus have to solve a quadratic
gilded fiber
oh i got th answer another way
3(x+y)(xy)=123
x+y=5 so xy = 123/15
but x^2 + 2xy + y^2 = 25 from expanding (x+y)^3
so substituting in x^2 + y^2 = 25 - (246/15) = 43/5
trim swan
but x^2 + 2xy + y^2 = 25 from expanding (x+y)^3
no this was not correct, thats what I was talking about earlier
gilded fiber
wait how
i see ur saying we get a negativ sign
instead of positive
but idk how we get that if its (x+y)^3
trim swan
Where did (x+y)(x^2+xy+y^2) = 125 come from?
gilded fiber
(x+y)(x+y)(x+y) = (x+y)^3
(x+y)(x+y) = (x^2+xy+y^2)
(x^2+xy+y^2)(x+y) = (x+y)^3 = 125
trim swan
(x+y)(x+y) = (x^2+xy+y^2)
x^2 + 2xy + y^2
Sorry, I thought you made a different mistake
gilded fiber
x+y=5 so (x+y)(x^2+xy+y^2) = 125 = 5(x^2+xy+y^2) = 125
so x^2 + 2xy + y^2
oh yeah lmao
thanks
trim swan
np I thought you were trying to use the sum of cubes formula on the wrong thing and forgot a negative sign
safe radishBOT
Available help channel!
bold perch
safe radishBOT
https://research-repository.griffith.edu.au/bitstream/handle/10072/58722/88799_1...
bold perch
would someone be able to explain what happens in section 3.2?
safe radishBOT
@bold perch Has your question been resolved?
safe radishBOT
@bold perch Has your question been resolved?
plucky elk
would someone be able to explain what happens in section 3.2?
it's like a page long. ask a more specific question and screenshot relevant parts
sick yoke
riemann 
plucky elk
what's i and h?
bold perch
what's i and h?
h is thickness of toilet paper, i is the 'i' th layer of toilet paper
i think theres also an algebraic mistake this paper makes (i-h)h is not distributed properly
but regardless, i don't really get how original equation is derived
plucky elk
$R'_i = R + (i-1)h + h/2$?
flat frigateBOT
riemann
bold perch
yes
bold perch
also question thats a bit unrelated: was everyone laughing when you guys got introduced to the riemann sum?
flat frigateBOT
riemann
bold perch
ah R1 radius is R1+h/2, R2 radius is R1+3/2, ...
so the equation represents the average radius between two concnetric circles
why would that be the case?
plucky elk
it's just an assumption / estimation
bold perch
whats the basis of the assumption
why not just look at radius of the concentric circles?
plucky elk
idk ask the authors
prisma latch
safe radishBOT
prisma latch
I did parts A and B and fully understand them, but I don't understand how to do part C
safe radishBOT
@prisma latch Has your question been resolved?
prisma latch
<@&286206848099549185>
safe radishBOT
@prisma latch Has your question been resolved?
prisma latch
<@&286206848099549185>
rancid hill
<@&286206848099549185>
yes
prisma latch
hi, can you lead me through part C? I know how to do parts A and B but C has me stuck
rancid hill
hi, can you lead me through part C? I know how to do parts A and B but C has me ...
sure what is the qustion
prisma latch
Basically, event A is saying that it takes an odd number of tries to roll a 10 with two 6 sided dice
what is P(A)
rancid hill
p is how many part there are to the equsion and a is your answer
prisma latch
lol thats the question being asked
im having trouble finding the probability of event A occuring
rancid hill
so u are tring to figher oit what a means ok
prisma latch
im trying to figure out the chance of A happening
safe radishBOT
@prisma latch Has your question been resolved?
prisma latch
<@&286206848099549185>
safe radishBOT
@prisma latch Has your question been resolved?
safe radishBOT
@prisma latch Has your question been resolved?
toxic raft
I did parts A and B and fully understand them, but I don't understand how to do ...
Let the probability of rolling a 10 be x. What is the probability of it taking 3 tries in terms of x?
We'll go from there
prisma latch
Let the probability of rolling a 10 be x. What is the probability of it taking 3...
3/x
prisma latch
@toxic raft
safe radishBOT
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Available help channel!
oak fiber
safe radishBOT
oak fiber
where do i start with this
faint seal
what is the formula of linear approximation?
oak fiber
L(x) = f(a) + f'(a)(x-a)
oak fiber
but what is f(x)?
oak fiber
so L(4) = N(t) + (0.06N(t))(x-4)?
oak fiber
then the eqaution would be L(t) = N(4) + 0.06N(t)(x-4)
and then you plug in 4.1 for t to find the answer?
faint seal
yes
faint seal
then the eqaution would be L(t) = N(4) + 0.06N(t)(x-4)
the x would change to t
as well
safe radishBOT
safe radishBOT
Available help channel!
simple gazelle
hello
tiny mirage
You wanna hop on vc and we talk and I’ll help solve its a tad hard to explain on messages
safe radishBOT
@simple gazelle Has your question been resolved?
barren crest
Does anyone know how to do vedic math? please add me and train/tutor me
plucky elk
Does anyone know how to do vedic math? please add me and train/tutor me
don't ask for services here
.close
barren crest
what?
wind osprey
Hello, i have a probably question
safe radishBOT
Hello, i have a probably question
wind osprey
The question is : how many different ways are there to make a 4 digit PIN code ( all numbers ranging from 0 to 9 ) containing exactly one double ?
This is my answer but you apparently need to /2 and i don’t understand why ?
safe radishBOT
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fickle jungle
this is physics-math
safe radishBOT
this is physics-math
fickle jungle
why is the blue side not accounted for on either vertical or horizontal values
noticed now, the second horizontal value is wrong too
or I'm not getting it
because shouldn't it be 60sin60
since 90-30 is 60
safe radishBOT
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safe radishBOT
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Available help channel!
white apex
Help pls idk where to start
safe radishBOT
Help pls idk where to start
white apex
do i do 106.8 - 63.8/104-68
lean otter
yea
white apex
and miles per min right
lean otter
i mean those are the units you were given so
flat frigateBOT
Result:
1.2
lean otter
how did u get 38.187
lean otter
lmaoo
safe radishBOT
@white apex Has your question been resolved?
sullen vapor
safe radishBOT
sullen vapor
I've tried going about this a number of ways but cant get the right answer
im not sure if i know the process of solving this fully
stoic dune
You'd take an implicit derivative in terms of t first
Remember to use the product rule in doing so
safe radishBOT
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stiff stump
safe radishBOT
stiff stump
derivative of (5x^6 + 2x^3)^4
I checked the answer and it’s 24x^11, I’m not sure where I’m missing 6 x’s
is there a rule about adding exponents that I’m misunderstanding here?
zinc token
,w derivative of (5x^6 + 2x^3)^4
flat frigateBOT
lean otter
the 2nd line seems right, after that I kinda got confused as to what u were doing
stiff stump
sorry my work can be messy
I tried factoring the two terms, I took a 6x^2 out of the first one and a 4x^3 out of the second
just a x^3 actually sorry
those two with the 4 got me 24^5
stiff stump
the answer might be wrong
is what I have right then?
zinc token
check against wolframalpha lol
stiff stump
I checked my textbook and a different derivative calculator and they agreed
I just don’t know where all those x’s are coming from
stiff stump
?
lean otter
$4(5x^6+2x^3)^3 * (30x^5 + 6x^2)$
flat frigateBOT
hibyehibye
lean otter
thats line 2 right?
stiff stump
yes
lean otter
and the original function is $(5x^6 + 2x^3)^4$
flat frigateBOT
hibyehibye
stiff stump
yea
flat frigateBOT
hibyehibye
lean otter
right?
stiff stump
I factored 6x^2 out of the second one
flat frigateBOT
hibyehibye
stiff stump
yea that looks right
lean otter
ok
stiff stump
and then x^3 out of the first one
lean otter
thats ur issue
you cant extract x^3 from first one
because its a cubic term
like its
(ac+bc)^3
$(ac+bc)^3 \not = c(a+b)^3$
flat frigateBOT
hibyehibye
lean otter
**hibyehibye**
you can factor out a 6 here giving the same as the wolfram answer
safe radishBOT
@stiff stump Has your question been resolved?
velvet hearth
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viscid folio
hi, this is about curve discussion!
So the gist is that the second derivation must be 0 to prove it's turning point/show where it is.
Now my question is: how does e^-x get eliminated by multiplying the term with e^x ?
shouldn't ''e^-x times e^x'' result in a number other than 0?
scarlet talon
rigid inlet
you believe correctly
viscid folio
ooh, and multiplying by e^x is the same as dividing by e^-x due to the inversion of the exponent?
bold ferry
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bold ferry
why is the answer -2/3 < p < 0?
I only get p < 0
because I converted it to 1 / n^(2 - 3p - 1)
2 - 3p - 1 > 1
p < 0
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@bold ferry Has your question been resolved?
bold ferry
okay i think the key is wrong
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tame oxide
wouldnt you literally get the same equation for both f and g?
safe radishBOT
wouldnt you literally get the same equation for both f and g?
lean otter
how do i ask for help
tame oxide
:P
lean otter
wouldnt you literally get the same equation for both f and g?
Well try and see if you indeed find there is only one possible quadratic that fits all the criteria
rigid inlet
wouldnt you literally get the same equation for both f and g?
You need 3 points to uniquely identify a quadratic, however only 2 are given
lean otter
You need 3 points to uniquely identify a quadratic, however only 2 are given
and both have a maximum value of 18
Do you know whether this and 2 points is sufficient to uniquely identify a quadratic?
hexed dune
You need 3 points to uniquely identify a quadratic, however only 2 are given
the x coordinate of the maximum is -b/a
shouldnt that count as a point
rigid inlet
It's half a point
hexed dune
if its subsituted into ax^2 + bx + c it should yield a valid equation
that isnt derived from the other 2
lean otter
"You can't say it's only a half"
- Some old reference I hope someone else knows about
rigid inlet
Not me
hexed dune
so that we have a system of linear equations
rigid inlet
I love half points
lean otter
wouldnt you literally get the same equation for both f and g?
Since they both have a maximum value in the first place we know that their second derivative is negative
Or in other words, if it is represented as ax^2+bx+c, a is negative
tame oxide
I love half points
i love bing chilling
im going to read this
and i have no clue what any of you mean
lean otter
and i have no clue what any of you mean
Bruh
cinder ivy
why hasnt a channel opened for me
grave flint
wouldnt you literally get the same equation for both f and g?
yep, you have 3 points, done deal
lean otter
why hasnt a channel opened for me
tame oxide
👍
grave flint
yep, you have 3 points, done deal
hold on i thought both points provided were x intercepts
you should use the vertex form of a quadratic
y = a(x-h) ^2+ k
vertex: (h, k)
grave flint
heres the two points and y = 18
@tame oxide
the third point can be anywhere on that line (to the left of the red point)
do you think there are more than one quadratic
grave flint
but how do i get the actual formula
formula for what
tame oxide
like how do i actually find a function that fits the parameters
grave flint
like how do i actually find a function that fits the parameters
you gotta pick a point
for the max
pickety pickety
lean otter
Oh shi-
grave flint
Best I got was a cubic
do better 
lean otter
Yeah you can just do that
lean otter
do better <:angrymoth:966541988566536273>
Shut the up the fuck
grave flint
damn you got me there
tame oxide
Best I got was a cubic
quadratic 💀
how does a cubic have a max value
massive confuzzlement
lean otter
how does a cubic have a max value
I'm saying I got a cubic equation
lean otter
And that solving it would've gotten me the values for the quadratic I needed
lean otter
theres probs some restrictions on the point
Are there though? Any 3 points can make a quadratic as far as I know
grave flint
Are there though? Any 3 points can make a quadratic as far as I know
yeah but whos to say that the point u pick makes a max
tame oxide
💀
tame oxide
why do you think im here ;-;-;-;
grave flint
🙂
lean otter
yeah but whos to say that the point u pick makes a max
Ah, right
grave flint
why do you think im here ;-;-;-;
why are you here
grave flint
charge it
tame oxide
can you tell me how to solve it
grave flint
fixed
tame oxide
but like all i get would be
tame oxide
y = a(x-h) ^2+ k
like if i did itwould become
y=a(x-h)^2+18
0=a(1-h)^2+18
10=a(0-h)^2+18
would that be correct
lean otter
Alright so I've found a technique that works and can find you 2 functions but it's pretty ugly
Basically I'm just taking y=-x^2+18 and shifting and rescaling it in a way that'll get a function that works
Which is like probably the dumbest way of solving this
Yeah I'm not gonna continue this
grave flint
epic
grave flint
nope i dont think that works 💀
make it work
tame oxide
Which is like probably the dumbest way of solving this
any way is fine as long as it works 💀
tame oxide
i found a piece of paper :)
grave flint
and thers two graph yeha
tame oxide
lol
grave flint
like if i did itwould become
y=a(x-h)^2+18
0=a(1-h)^2+18
10=a(0-h)^2+18
would t...
i just did this
tame oxide
but ihad not brain
tame oxide
where coulkd i go to buy
tame oxide
hot
grave flint
where coulkd i go to buy
second hand shop is afforable
tame oxide
if u cant get the algebra just dm me
im sure i would have gotten it but i just happen to be stupido brain moment because very late
or early
whichever one you like
thank s
native nebula
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hexed dune
@native nebula no it shouldnt
things inside the bracket only effects the x
and things outside the bracket only effects the y
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@native nebula Has your question been resolved?
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Available help channel!
lean otter
hx - h90 +1
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hx - h90 +1
lean otter
hx - h90 +1
ig
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@lean otter Has your question been resolved?
lean otter
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@lean otter Has your question been resolved?
safe radishBOT
@lean otter Has your question been resolved?
lean otter
.close
split ether
It's clearly already closed
fickle trail
I closed both and they are still showing
I deleted the original image, Discord auto-closed
so I made a new one
but original post won't close, and now second post won't close either
ancient escarp
they’re closed. just takes a second
grizzled shoal
anyway, what is the problem? y depends on x therefore we use the chain rule
fickle trail
anyway, what is the problem? y depends on x therefore we use the chain rule
Wondering if someone can help me “see the light”.. I’m struggling to understand why we use chain rule on y
grizzled shoal
we have to take the derivative of y with respect to x
however y is not x
therefore we cant just do it normally
ancient escarp
this channel is gonna close soon. whether or not it’s sent to the shadow realm or is able to be opened back up is the bot’s choice
grizzled shoal
y could be anything, for example (2x+1)^2, where we would also have to use the chain rule
no matter what y is, the chain rule will work like it did in the image
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fickle trail
nooooooo
fickle trail
lol OK I'm back
fickle trail
we have to take the derivative of y with respect to x
so we treat y as f(x)?
grizzled shoal
yes
fickle trail
and that's the reason 'y' is considered a composite function?
whereas x is just a function
y is "f of x"
like saying f(g(x))
I've never seen y written like this for x, with the of "o" notation.. can it be done?
pseudo scroll
fogx
fickle trail
what is g?
pseudo scroll
Another function
fickle trail
but I want just y and x
pseudo scroll
$\circ$ indicates composition
flat frigateBOT
NEONPerseus
pseudo scroll
I don't think so but wait for someone else
As far as I know that's only for composition
fickle trail
As far as I know that's only for composition
but y is a composition
quasi bison
is this about implicit differentiation
fickle trail
yes
quasi bison
it's not that y is itself viewed as a composition of two functions,
it's that it is one of the functions in a composition
e.g. y^2 is the squaring function composed with y.
quasi bison
...yes?
fickle trail
hmmm
when we say "function".. that means one input, one output, yeah?
has to pass the vertical line test
x is part of the function, but it's only the input of the function
i thought that y is part of the function, but it's only the output of the function
and together with x and y, they make up a function
so does this boil down to how y= can also be written as f(x)=? f() is the "function" and x is the input within the argument of the function
y = f() is technically not correct, as it requires an input... but y = f(x) is correct
therefor y = f(x) meaning that y is a function with an input of x within the argument of the function
does that mean y is always treated as a composite function? similar to f(g(x))
or are there cases where y is just the variable? such as inverse functions, where you swap x with y.. then x becomes the composite function and y becomes the variable within the function argument... x = f(y)
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@fickle trail Has your question been resolved?
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bronze hound
can someone help me prove or disprove this: A is a square matrix with columns c1, c2 ,...,cn. If A is not invertible, there are some non-zero real numbers b1 , b2, . . . , bn such that b1c+ b2c + · · · + bnc = ⃗0
safe radishBOT
can someone help me prove or disprove this: A is a square matrix with columns c1...
wheat cave
can someone help me prove or disprove this: A is a square matrix with columns c1...
can you assume that the rules for 'a matrix is invertible when ...' are given?
bronze hound
can you assume that the rules for 'a matrix is invertible when ...' are given?
we know that it means the matrix will have rank < n in its rref
wheat cave
mhm?
bronze hound
so the homogeneous system would have non trivial solutions
wheat cave
a matrix is invertible exactly when its rank is full
bronze hound
and this isn’t invertible
wheat cave
yes, so I guess you can use the counterstatement
you know a matrix multiplied by some linear combination can only result in 0 if all the constants are 0
alas, b1c+ b2c + · · · + bnc = ⃗0 with b_n != 0 only works when the rank isn't full
wheat cave
can someone help me prove or disprove this: A is a square matrix with columns c1...
therefore
invertible matrix A in dimension C^n => rank(A) < n => there are non-zero real numbers that solve to 0 in linear combination
bronze hound
we were told to use this fact: the system of equations C⃗x = ⃗b has a solution
if and only if ⃗b is equal to a linear combination of ⃗c1, ⃗c2, ⃗c3
so I get the part where we say that it has non trivial solutions
but this linear combination thing is confusing me
wheat cave
but this linear combination thing is confusing me
this would be one for a 3x3 matrix
A are row vectors
a are the constants, or the b's in your thingy
there is a rule that says a matrix with full rank cannot result in the zero vector as a result of such combination except for when all constants a are 0
I assume you have to prove that latter part
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@bronze hound Has your question been resolved?
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lean otter
Why is the log of 1 always zero, no matter what the base is?
safe radishBOT
Why is the log of 1 always zero, no matter what the base is?
rich stratus
Log of 1 base 5=x means "5 to the power of x equals 1"
And 0 is the only power that satisfies
And it is the same thing for any positive base you can find (except 1)
misty bay
another way to see it is that log_b a = log a / log b
where the logs on the right side can be of any base
plugging in 1 for a
you see that log_b 1 = log 1 / log b
so if log 1 is 0 for any particular base, then it's 0 for all bases
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tawny summit
How does this make any sense at all
safe radishBOT
How does this make any sense at all
tawny summit
All i know about logistics models is that they follow an equation and you can manipulate them to follow the equation if they dont so you can parse information from them
This is wizardry
stray socket
Eh not really
It tells you the initial population is 40, so they let (t, P(t)) = (0, 40) to isolate k
tawny summit
why does the 200 go there
stray socket
$\limit{\frac{A}{1+ke^{-rt}}}{t}{\infty} = A$
flat frigateBOT
Umbraleviathan
stray socket
i dont know what to ask it doesnt make any sense
https://www.desmos.com/calculator/oslr5kdtv0 play around with this
Oh shit lemme
Update it
tawny summit
is k never negative
stray socket
tawny summit
i want to punch a hole in my wall
stray socket
Yeah don't let k be negative
It'll create an asymptote
And then it's no longer a sinusoid
tawny summit
i see that it worjks
is it worthless to understand or too convoluted
i dont understand why i dont understand or why i dont know this
stray socket
No it's important to understand for the course's sake
If you know limits it'll make more sense
stray socket
Limits will explain why A is the carrying capacity
tawny summit
i mean i see graphically why
i can see that that is how it works
and that that is a limit
because its a limit
i dont
i dont know what im supposed to extract
i am worried that when i see this in a different scenario on the exam that i will not understand anything and i will fail
or that it will be even further removed from my already rudimentary understanding of logistic models and i will not understand
misty bay
initial population 40 means that P(0) = 40 (convince yourself that's what the English means)
carrying capacity means that the population will approach that value over a long time and stay there
convince yourself that means that lim t->infinity P(t) = 200
tawny summit
yeah i get all of that
misty bay
so knowing these two facts, you can actually solve for the value of the constant k
without relying on anything that people have told you about logistic models before
misty bay
$\limit{\frac{A}{1+ke^{-rt}}}{t}{\infty} = A$
that's this fact right here
misty bay
you don't know that beforehand
but you can figure it out
you know that
$\lim\limits_{t\to\infty} P(t) = 200$
flat frigateBOT
Saccharine
misty bay
but you also know $\lim\limits_{t\to \infty} P(t) = \lim\limits_{t\to \infty} {\frac{A}{1+ke^{-rt}}} = A$
flat frigateBOT
Saccharine
misty bay
so therefore A = 200
tawny summit
ive given up ill just accept it
everything i look at doesnt make sense and i cant do by myself
misty bay
what doesn't make sense about what I said
misty bay
**Saccharine**
this thing comes from the commonsense definition of "carrying capacity"
misty bay
**Saccharine**
this thing comes from what some random person told you on the internet,, but you could figure it out by taking limits
tawny summit
i guess i dont understand limits then
misty bay
so you don't understand where the second thing comes from?
tawny summit
i think?
the function is the function?
because P(t) is the function and that is what the equation looks like
misty bay
right
so the reason why this limit is equal to A
is because as t gets really large
e^(-rt) gets really small, goes to zero
and therefore ke^(-rt) also goes to zero
so it becomes very much like A/1
which is just A
tawny summit
if the 1 wasnt there it would be very much opposite
misty bay
if the 1+ weren't there