so its simple 3^k = x its easier
#help-13
wraith daggerBOT
_basudev
lofty kernel
ok wait i got it
thin roost
simplify a bit
(x-1+2x)/2 = (3x-1)/2 now plug x
lofty kernel
from (3^k - 1)/2 + 3^k = (3^(k+1) - 1)/2
There are two liketerms of 3^k in the first term equation so if i combine them both it becomes
(3^(k+1)/2 = (3^(k+1)/2
the same thing
.close
cedar kilnBOT
thin roost
kul
cedar kilnBOT
Available help channel!
fiery valley
how do you factor ax^2 + bx + c, where the highest degree is 3, b = 0?
fiery valley
so i have here, x^3 - 1
humble karma
Well it's not quadratic then
But you can use the difference of cubes
$a^3-b^3=(a-b)(a^2+ab+b^2)$
wraith daggerBOT
Azyrashacorki
humble karma
This is easy to show using long division though.
If you have p(x) = x^3 - 1, you know instantly a root is 1, so you can factor out (x-1).
fiery valley
mhm
sudden anchor
so (x - 1)(x^2 - x + 1)?
x^3 - 1 = (x-1) ( x^2 + x + 1)
sudden anchor
(x - 1)(x^2 + x + 1)
yes
fiery valley
yesyes
humble karma
Yes.
sudden anchor
absolutely
safe edge
i am doing trigonometry for like 3 years now
i am also pretty good in solving "sums"
but all the time i feel like idk what is really going on there
i mean , i really think about very basic questions like why sin , cosec on 2nd quad is +ve , how trigno came in the world of graphs ? blah blah
i am really looking forward for the answers of these questions
is there any good resource where i can get answers of all these questions , who teaches trigno in deep?
cedar kilnBOT
i am doing trigonometry for like 3 years now
i am also pretty good in solving ...
@safe edge Has your question been resolved?
safe edge
i am doing trigonometry for like 3 years now
i am also pretty good in solving ...
<@&286206848099549185> plz?
dire geode
i am doing trigonometry for like 3 years now
i am also pretty good in solving ...
#book-recommendations for trig books
safe edge
<#716264872018706443> for trig books
noo i am not reallly looking for books
cedar kilnBOT
@safe edge Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
dusky peak
Hey
dusky peak
The topic is scalar products this time
I am looking at the scalar product (psi, O psi)
Here psi is a function and O is an operator that acts on the function
I want to flip their positions
But i know that i have to do some steps to do so
But i am not entirely sure if it was adjugating or conjugating
And also which parts are affected
crystal raptor
If you want to move it over you have to take the adjoint
dusky peak
$(a,b)=\bar{(b,a)}$
wraith daggerBOT
Martin
void pecan
Use over line for a long bar
dusky peak
Also til that adjungieren means adjoint in english
crystal raptor
Oh you want to flip the inner product itself not just move the operator over
Then yeah you can swap both argument at the cost of conjugating the whole thing
void pecan
Work from the definition of your inner product if you’re not sure why that’s the case it’s pretty immediate
wraith daggerBOT
dusky peak
At the bottom is what i would like to get somehow (with some factor or whatevrt)
Context is to show that hermitian operators have real and antihermitian operators have imaginary eigenvalues
But also to get used to it a bit more
Nvm got it
Definition of selfadjoint for O implies (f,Of)=(O*f,f) where * is adjoint
.close
eternal seal
How would one prove the theorem if there is one that there is no local maxima on end points of a differentiable function f defined on a closed interval.
eternal seal
Like there is no local maxima on a and b in [a, b]
cobalt storm
i would assume you would have to derive the function, and local maxima of a function can only appear when the derived function changes signs. If the derivation for those points is not 0, it cannot be a local maximum
unless i am wrong about the definition of a local maximum
ok there is another way that comes to mind
that is logically, if that local maximum exists, $\lim_{x\to\a} f(x)$ < f(a), and same with b
wraith daggerBOT
Matěj
that is logically, if that local maximum exists, $\lim_{x\to\a} f(x)$ < f(a), and same with b
```Compilation error:```! Argument of \a has an extra }.
<inserted text>
\par
l.52 ... that local maximum exists, $\lim_{x\to\a}
f(x)$ < f(a), and same wi...
I've run across a `}' that doesn't seem to match anything.
For example, `\def\a#1{...}' and `\a}' would produce
this error. If you simply proceed now, the `\par' that
I've just inserted will cause me to report a runaway
argument that might be the root of the problem. But if
your `}' was spurious, just type `2' and it will go away.```
crimson delta
the function f(x)=x on [0,1] has the local max at 1 and the min at 0
cobalt storm
that is true, pls ignore all i wrote
cedar kilnBOT
@eternal seal Has your question been resolved?
eternal seal
the function f(x)=x on [0,1] has the local max at 1 and the min at 0
That doesn't make sense, online it says that local maxima and min cannot be on endpoints
Isn't what you showed more like abs max min thing
eternal seal
that is true, pls ignore all i wrote
I think what you wrote is correct
cedar kilnBOT
cedar kilnBOT
Available help channel!
cedar kilnBOT
void pecan
The letter they use for any limit doesn’t matter
They’ve said that as x approaches c f(x) approaches b. Since g(x) is continuous at b you know it’s perfectly well defined there (and as you approach it in a limiting case) so you get the relation they start with
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
@crimson sedge Has your question been resolved?
dire geode
@crimson sedge Nope answered your question. What more did you want to ask?
dire geode
eps>0 is a requirement of the definition of continuous
delta needs to be > 0 yes. Where does it say otherwise?
x doesn't need to be equal to c is also a requirement from the definition
Look at the definition
Where does it say anything like that
Where does it say f(x) = b?
Right
x doesn't have to be c either
it doesn't mean it CAN'T be c
No
It's saying when x isn't equal to c
Doesn't mean x can't be c always
Just for the definition of continuous
continuous refers to the function, not the domain
The function doesn't care what happens at x=c
At least in your screenshot.
Yes
The continuity statement only cares about x not equal to c
Depends what you're trying to prove
For some statements and theorems you care about x=c, some you don't
Not really
- You care about x=c
2 you don't
3 you also don't
I don't know what you're saying
No
dire geode
All 3 must be satisfied
It depends on what you're proving
Or what requirement you're satisfying
dire geode
All 3 must be satisfied
.
dire geode
.
dire geode
1. You care about x=c
.
dire geode
2 you don't
.
dire geode
3 you also don't
.
Any limit
Find a limit problem
What about them
You can, but that isn't necessary to show the limit exists
Maybe!
Depends on the problem
dire geode
It depends on what you're proving
.
dire geode
Or what requirement you're satisfying
.
dense frigate
cedar kilnBOT
dense frigate
why is this incorrect?
at least the first one
partial derivative with respect to P is (V-nb) no?
and with respect to T is nR
so then you do dP/dT = -Ft/Fp and you get -(nR)/(V-nb)
cedar kilnBOT
@dense frigate Has your question been resolved?
dense frigate
.close
crimson sedge
cedar kilnBOT
green thorn
!xy
cedar kilnBOT
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.
green thorn
my brother in christ 💀
crimson sedge
you would leave if i show the original
timid pawn
My brother in christ, how are theta and alpha related, what's the relation between the sides?
Are they sides at all?
timid pawn
Nobody can help you without the original context.
crimson sedge
fine
their was a mistake in adding the fractions
but i fixed it
and when i made it BD^2=
tand alpha and theta cancled each other out
gtg
.close
pearl fog
cedar kilnBOT
wraith daggerBOT
lethal jackal
maybe I messed the equation up, but I didn't get the same answer as you did
lethal jackal
I actually have very little idea of what to fill into the table lmfao
pearl fog
It's just the rate and then the time
lethal jackal
my best guess would be:
500|t|500t
700|t-1|700(t-1)
but I don't see how that helps very much
pearl fog
Same I guess it's just to make answering it simpler or something
Idk why they're making us fill out some chart
Ok thanks I'll just try and figure this out
.close
steady plover
cedar kilnBOT
steady plover
I want to use the AM-GM inequality here
I reached this:
$\frac{(a+b)(b+c)(c+a)}{3} \ge \sqrt[3]{(a+b)(b+c)(c+a)}$
wraith daggerBOT
Shinutsi
steady plover
though I don't know if that's right
opal basin
This isn't right, because the the terms on the LHS have to be a sum
You can expand though and then use AM-GM
or use AM-GM on each factor individually
wheat ocean
Use AM-GM inequality for 2 numbers for each bracket
wraith daggerBOT
Shinutsi
wheat ocean
no
opal basin
$$\frac{a + b}{2} \geq \sqrt{ab}$$
wheat ocean
$$ x + y \ge 2\sqrt{xy}$$
opal basin
yeah, 2 on the other sides is more useful here
opal basin
yeah
fiery ermine
Would the answer be E?
cedar kilnBOT
Would the answer be E?
@fiery ermine Has your question been resolved?
Available help channel!
placid cloak
Hi
placid cloak
You forgot chain rule
Its Quotient rule
placid cloak
derivative of 5-x = ?
-1
placid cloak
Doesn't mean you ignore chain rule
Hm
dire geode
Use that to find dv
eternal sequoia
Is there any tool I can use to see how an operation is done step by step?
eternal sequoia
It'd help me relearn a lot of relatively basic math concepts that I've forgotten without having to watch a lot of videos or read a lot of documents
dire geode
Is there any tool I can use to see how an operation is done step by step?
Too vague
But probably not a tool. But definitely books or maybe videos
eternal sequoia
Can I embed links here?
I meant something like this (this is Symbolab)
only problem with this is that you have to pay to see all the steps
and if I'm not mistaken more often than not they will hide very important steps from the perspective of a high school student trying to deduce
dire geode
I meant something like this (this is Symbolab)
Any calculus book will cover this
Pick a popular one from #book-recommendations
cedar kilnBOT
@eternal sequoia Has your question been resolved?
modest dove
cedar kilnBOT
modest dove
Question iii) is when t = 3 and 7?
Does the direction change at the peaks of the graph?
nova glacier
no
dire thorn
Does the direction change at the peaks of the graph?
Peak means (local) max speed/min speed
modest dove
Right so, what is the change of direction at?
Is it when the graph intercepts the x axis?
alpine gulch
yes
modest dove
so at t=3, it is still moving in a rightward direction, just slowing down right?
until 7 until it speeds up again indefinitely?
alpine gulch
yeah, a little after t=3 the speed is getting closer to zero, hence it's slowing down but it's still positive, so it's the same direction
and after 7 it goes faster and faster
somber otter
where did T go in this rearrangement of variables?
cedar kilnBOT
where did T go in this rearrangement of variables?
somber otter
The question:
cedar kilnBOT
@somber otter Has your question been resolved?
cedar kilnBOT
@somber otter Has your question been resolved?
violet flume
where did T go in this rearrangement of variables?
it sure seems like its missing
somber otter
it sure seems like its missing
is it a typo?
violet flume
it seems like it
somber otter
how do you go from the original equation to the first one in the solution?
somber otter
if you take d/dx of the original eq, don't you get $$\frac{dx}{2\sqrt{x}} + \frac{y'}{2\sqrt{y}} $$
wraith daggerBOT
109105116
somber otter
and $$ y' = dy/dx \neq dy $$
wraith daggerBOT
109105116
white latch
so we have to express it in terms of x it seems.
I see.
Then rearrange
the initial equation and express y in terms of x and substitute
and boom.
somber otter
yeah but it seems like the solution writer got to the first equation directly?
your solution works
so ty
white latch
No worries please clarify your question one more time?
somber otter
im wondering if they performed some operation on the original equation to directly get it to $$\frac{dx}{2\sqrt{x}} + \frac{dy}{2\sqrt{y}} = 0$$
wraith daggerBOT
109105116
white latch
Well they differentiated both sides separately wrt to x via implicit differentiation.
somber otter
ok
wraith daggerBOT
109105116
white latch
Hold up dx and dy by itself is a bit ambiguous. Hmmmmmm.
somber otter
oops i accidentally typed that
white latch
uhhhhh why is there still a dx for the first term?
somber otter
Hold up dx and dy by itself is a bit ambiguous. Hmmmmmm.
oh yeah im also confused on whether or not you can reaarange dx and dy like variables
white latch
We differentiated that term fine.
somber otter
oh that's right, hmmmm
white latch
oh yeah im also confused on whether or not you can reaarange dx and dy like vari...
You mean multiply, etc. Isolate them right?
white latch
Mhmmm, so one way of conceptualizing this is that dy and dx represent nothing but differentials which means an infinitely small change in the slope. Picturize it as a fraction.
Ex. dy represents an infinitely small change in slope for y and dx represents an infinitely small change in slope for x.
somber otter
in $$\frac{dx}{2\sqrt{x}} + \frac{dy}{2\sqrt{y}} = 0$$ it seems like they expressed the first term as dy = ..., not dy/dx
wraith daggerBOT
109105116
white latch
Give me a second I'm going to try that out.
Mk, so here is what I came up with. Now for the first part, I simply manipulated dy/dx on one side and didn't solve for it but just ensured that if I did we would get the right answer.
Which it did give us thereby confirming this form they gave the solution is correct.
But its strange as that suddenly appeared as the first part of the solution.
So what we needa ask is if there was a simpler way as to how they get there first.
Hold up I got I think.
somber otter
where?
white latch
white latch
Mhmmm does it make intuitive sense for you as to why we can do that?
somber otter
yeah but it seems unnecessary
white latch
It is. In short, i guess they love to complicate life for no god damn reason.
However both methods r similar as to how long they would take, I guess it just simplifies the process a bit.
Alright man well assuming ur question is answered ima dip now, unless u got anything else u wanna clarify?
fervent pike
I don't want the answer, but want some guidance/hints for a proof by induction question
fervent pike
This is my work so far..
My understanding is that for proof by induction, you have to first find base case, then show how
a_n->a_(n+1)
I am confused as for the a_n portion, do I alter the given equation to have a(n-1)^2+2/3
or do I use 0<a_n<1
humble karma
The base case is n=2, so you check that 0 < a_2 = (a1^2+2)/3 < 1
For the induction step, you assume that 0<an<1 for some n.
Then, use the equation to show that 0<a_(n+1)<1.
fervent pike
oh ok
So if a question asks smth like "shows that this express..." you are basically using that for the induction step?
humble karma
Yes, that is what you want to show.
Induction is disguised through the definition of the set of natural numbers.
The primary definition of the set N of natural numbers is that :
- 0 is in it;
- if n is in it, n+1 is in it.
Sounds familiar?
fervent pike
ah ok
humble karma
For proof by induction, you essentially say : let S be the set of all natural numbers such that a given statement holds.
Then if you show that :
- 0 is in S
- if n is in S, then n+1 is in S,
It follows that N = S (i.e. the statement holds for all natural numbers)
(This can be adapted if your base case is n=2, but it conveys the same idea
So in general, if you have a statement P_n in terms of n that you want to show :
- Show that it works for some value (base case)
- Show that if it works for a value, then it works for the next (induction step)
In this case, the statement is : "0<a_n < 1"
cedar kilnBOT
@fervent pike Has your question been resolved?
fervent pike
Im working on the solution!
also, not sure what induction hypothesis means, just seen the word used often in solutions
I'm quite confident in my solution tho.. i think
actually I'm doing so bad w proofs i never trust my answers lol
humble karma
This is great! Maybe the only thing is that you don't really need to write a_n in terms of a_n-1, since you already know an<1.
But regardless it works, just a bit more clutter in this part.
broken parcel
Is my work correct so far?
cedar kilnBOT
Is my work correct so far?
ancient lodge
Is my work correct so far?
You found $\sin \left(\frac{\sin \alpha}{2} \right)$, not $\sin \frac{\alpha}{2}$
wraith daggerBOT
Civil Service Pigeon
ancient lodge
Instead, use the half angle formula
To deal with the sign, consider ||what quadrant alpha lies in||
broken parcel
okay gimme a sec to send it
@ancient lodge
My question is
what does sec (alpha) = -5/4 have to do with this problem?
ancient lodge
you dropped the square root
ancient lodge
what does sec (alpha) = -5/4 have to do with this problem?
I mean you used it
you use it to find $\cos \alpha$
wraith daggerBOT
Civil Service Pigeon
broken parcel
you use it to find $\cos \alpha$
And that is what I did, right?
broken parcel
you dropped the square root
thank you
ancient lodge
And that is what I did, right?
yes
ancient lodge
$\sqrt{\frac{9}{10}}$ is correct, which you can rewrite as $\frac{3}{\sqrt{10}}$ if you want to
wraith daggerBOT
Civil Service Pigeon
native shuttle
cedar kilnBOT
ancient lodge
I don’t think you have to
native shuttle
I don’t think you have to
i think so cause i dont see how u sub could work and im not really 100% abot integration by parts
but i know it invloves some trig
but now that i look at it i think i should plug in the values and try u sub
ancient lodge
What did you get so far
wraith daggerBOT
native shuttle
What did you get so far
here is what i have so far
native shuttle
i couldnt find a indentity for this on my formula sheet
but i found that
1-sin^2 = cos^2
googling ^
ill try plugging that in and update
ancient lodge
Yeah that’s just the Pythagorean identity rearranged
native shuttle
right so now i have tan^2*sin
i can use u sub on this i belive
a question i always have with trig integerals is that, how do you know what to chose as your u?
ancient lodge
right so now i have tan^2*sin
Don’t think this is right
ancient lodge
a question i always have with trig integerals is that, how do you know what to c...
Honestly idk a good answer for this
ancient lodge
also you can do it without trig sub
The question says to do so
native shuttle
you forgot the cos
oh i forgot to add it back i see
or multiply it more specifically
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
jade edge
What do you call the 0<theta<360 stuff
cedar kilnBOT
What do you call the 0<theta<360 stuff
crisp brook
a restriction?
cedar kilnBOT
@jade edge Has your question been resolved?
jade edge
Thanks I think its that
cedar kilnBOT
cedar kilnBOT
Available help channel!
last arrow
cedar kilnBOT
last arrow
pls help with this😭
vast pike
so P(2)=P(get two head in a row immediately)=(1/2)^2..are you able to go on ? ?
last arrow
can you explain why it is (1/2)^2?
vast pike
1/2*1/2=p(first head)p(second head)=p(two heads in a row)
vast pike
no ..if you do these we get probability of getting n-1 heads in a row
last arrow
oh ok ok, trying to comprehend
vast pike
just think about this deeply
raw gulch
Here it is important to recall the famous discrete distribution which describes such situations
if you realize that , then it is very easy
last arrow
i guesss im not able to
raw gulch
p*q^(x-1)
yes
exactly
so it needs from you only two things
p
and
q
and then fidn the formula fo rexpectaiotn value
last arrow
that is
raw gulch
the proff fo rthat is veyr nice fo rme, but i suppose yo do not need any proof
last arrow
1/p?
last arrow
the proff fo rthat is veyr nice fo rme, but i suppose yo do not need any proof
yes, proof is not required
raw gulch
yes, proof is not required
affirmatelively nods 🙂
last arrow
i guess im way too dumb here, dude
thanks for the help though
ill try connecting dots and see if i can solve this
cedar kilnBOT
@last arrow Has your question been resolved?
languid compass
Is this correct?
cedar kilnBOT
Is this correct?
languid compass
Method i mean
vast pike
Is this correct?
,rotate
wraith daggerBOT
vast pike
i think is n=4
languid compass
My answer is correct, they've asked for smallest n
vast pike
is your answer n=12?
languid compass
My answer is correct, they've asked for smallest n
Sirs method
vast pike
i didn t see the fraction sign ...
languid compass
Anyway is the method correct
vast pike
yes its correct to me
cedar kilnBOT
@languid compass Has your question been resolved?
digital bloom
Confused on why induced subspace topology is a topology
cedar kilnBOT
Confused on why induced subspace topology is a topology
digital bloom
The set Y n U for U open isn’t always open
crimson delta
well by definition it is called open inside the new topology
doesnt have to be open in the old one
cedar kilnBOT
@digital bloom Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
compact nest
Hello. I know the trick that the order of the truncation error is the next omitted term degree.
So like if it's e^x = 1 + x + (1/2!)x^2
then the next omitted term is x^3 so the order of the truncation error is going to be O(x^3)
but what about in such cases?, would it be O(x^7) or O(x^8) due to the power of 2 on the x?
compact nest
and if there's a better more proper way to calculate the degree, please lmk
now... I do believe it's O(x^8) cuz it's logically the next omitted term..
can anyone confirm?
tranquil crag
im having trouble with proving upper boundness for this type of sequences:
$b_n = \frac{1}{e + 1} + \frac{1}{e^2 + 2} + \dots + \frac{1}{e^n + n}$
wraith daggerBOT
Yanek
tranquil crag
so obviously: $b_{n+1} - b_n = \frac{1}{e^{n+1} + n}$
wraith daggerBOT
Yanek
tranquil crag
which proves that the sequence is ascending
so there is possibility that it has upper boundness
so here what i tried
tranquil crag
yeah but this is possitive
mighty drift
Indeed
tranquil crag
Which is less than e^-(n+1)
why does this matter?
mighty drift
Because that's an absolutely convergent series
mighty drift
In this case the term "absolute" is irrelevant
mighty drift
i haven't yet learned this stuff
Do you know the geometric sum formula?
tranquil crag
this is problem from intro to calc and all we covered were sequences and limits
yeah
i had the geometric sum
i didn't knew the name
in englis
my bad
mighty drift
Which is less than e^-(n+1)
Then you know this is a convergent series
tranquil crag
but this is not geometric series is it?
mighty drift
Which is less than e^-(n+1)
This is
tranquil crag
so i can do it like this:
$b_n \leq \frac{1}{e} + \frac{1}{e^2} \dots \frac{1}{e^n}$
wraith daggerBOT
Yanek
tranquil crag
and then
$\frac{1}{e} + \frac{1}{e^2} \dots \frac{1}{e^n} = \frac{1}{e} \cdot \frac{1 - (frac{1}{e})^n}{1 - frac{1}{e}}$
wraith daggerBOT
Yanek
mighty drift
Yes
mighty drift
The 2 last frac need their \ too
tranquil crag
is there some command to thank you on this server?
mighty drift
No need to
cedar kilnBOT
crimson sedge
geometrically
wraith daggerBOT
Joanna Angel
crimson sedge
what?
sweet willow
guys in this exercise, how am I supposed to know if I should differentiate with respect to x or y
runic garnet
Wrt x
subtle harbor
guys in this exercise, how am I supposed to know if I should differentiate with ...
use implict differentiation :)
runic garnet
Maybe if u were doing multivar and they were tryna trick u up then I could see that but this seems like just implicit
subtle harbor
yea
runic garnet
Actually, I recommend using df/dy / df/dx = dy/dx formula
rare adder
directly do differentiation to the equation,for example, $d(e^{xy})=xe^{xy}dy+ye^{xy}dx$
sweet willow
Thanks
wraith daggerBOT
pck
runic garnet
$\frac {dy}{dx} = \frac {\frac {df}{dy}}{\frac {df}{dx}}$
wraith daggerBOT
Stephen
wraith daggerBOT
Stephen
sly heart
Can anyone help me prove this?
cedar kilnBOT
Can anyone help me prove this?
sly heart
tried turning the cos(2x) to 2cos^2(x) but then stuck
hollow dawn
All good
sly heart
.close
wise verge
12- If A(3,1), B(5,7) and C(6,4) are three consecutive vertices of a parallelogram:
a) What is the fourth vertex?
b) What is the perimeter of the parallelogram?
c) What is the length of the two diagonals?
d) At what point do the two diagonals intersect?
wise verge
<@&286206848099549185>
sly heart
For a) questions you could try find the fourth vertex using
$(x_{2} - x_{1}, y_{2}-y_{1})=(x_{4} - x_{3}, y_{4}-y_{3})$
wraith daggerBOT
moghuu
sly heart
@wise verge
cedar kilnBOT
@wise verge Has your question been resolved?
sand osprey
Hi
cedar kilnBOT
@sand osprey Has your question been resolved?
crimson sedge
cedar kilnBOT
rare vault
is there a topic associated with this or is it a guessing game
crimson sedge
is there a topic associated with this or is it a guessing game
It's not a guessing game 💀
It just says four character passwords
I've been able to do the other ones but this one is different
Idk how to solve it
Also sorry for the late response I was helping someone with smth
fair geyser
show another one like this
fair geyser
show another one that's different
rare vault
You could arbitrarily justify any of the answers here
crimson sedge
Wait actually there are 2 of these questions
1 sec let me take a pic of the other one as well
rare vault
"it's A because the rule is any matching numbers in the first part have to correspond to matching letters in the second part"
crimson sedge
Well the answer is E I thought it might help a bit
Here is the second one@rare vault @fair geyser
They're the only ones like this
The other ones are different which I was able to solve
Let me show an example even
rare vault
that one looks like a direct char -> number mapping but I don't understand the order
crimson sedge
rare vault
that one looks like a direct char -> number mapping but I don't understand the o...
oh it's just reversed lmao
rare vault
Here is the second one<@153882568322711553> <@141791176540946432>
yeah this one is like super straightforward
reverse the input, then apply one to one mappings
K is 4, O is 3, T is 7, K is 1...
rare vault
¯_(ツ)_/¯
crimson sedge
¯\_(ツ)_/¯
I get how you found this but how do you find the answer
It's supposed to be c
But like I thought A was equal to 1
rare vault
make sure you reverse it
crimson sedge
I did?
Ooooh
Lol my bad
Wait even then
I get 5281
Not 2581
Aaaa forget it
Thanks for the help
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cedar kilnBOT
cedar kilnBOT
Available help channel!
gritty prairie
<..,..> and (..,..) are both used for describing vectors?
gritty prairie
Any difference between
gritty prairie
`<..,..>` and `(..,..)` are both used for describing vectors?
Please tell me if I’m wrong or correct
cosmic steppe
I've never seen () being used to describe vectods
I've seen the <> and the matrix form
But never ()
idle tusk
But never ()
bruh
idle tusk
Sounds European
possibly
cosmic steppe
Kinda an L
idle tusk
(1,2,3) is common here
cosmic steppe
European these nuts
cedar kilnBOT
@gritty prairie Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
marsh pond
cedar kilnBOT
royal loom
yes
compute the standard matrix like you just were doing
and then plug in (x,y) to it
the output vector, component-wise, is your answer to this
marsh pond
compute the standard matrix like you just were doing
should I use the top one?
RREF
royal loom
neither
marsh pond
but that's how I solved the prior question
royal loom
oh
marsh pond
royal loom
then do it like before
marsh pond
how would you recommend instead?
royal loom
I would've wrote the standard basis vectors, in terms of (-1,1) and (-2,1)
and then computed their transformation in respect to the transformations of the two vectors we know and how they're related using the linear combination we just found
likely there is more than one way to do this
marsh pond
likely there is more than one way to do this
I am following these instructions to get this final result
however, I'm not sure how to plug it into this
marsh pond
and then computed their transformation in respect to the transformations of the ...
like this?
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wicked badge
cedar kilnBOT
wicked badge
so we square root both sides, sec x less than or equal to 2, then 1/cos x is greater than or equal to 1/2
what do I do after that?
cedar kilnBOT
@wicked badge Has your question been resolved?
olive crescent
so we square root both sides, sec x less than or equal to 2, then 1/cos x is gre...
you can un-reciprocal both sides
loud estuary
olive crescent
doh yeah
olive crescent
I missed that you didn't recip both sides earlier
loud estuary
Wait is there plus minus for the sec x squared
loud estuary
Is there a plus minus
wicked badge
no
loud estuary
Why not??
wicked badge
uh idk lol
loud estuary
Wasn't it secant of x squared?
wicked badge
so I need to see where cos is less than 1/2
I'm gonna draw this
boom?
that's what, [pi/3, 5pi/3]
seem okay?
loud estuary
Yeah
wicked badge
wohoo!!!
loud estuary
I'm still wondering about that plus minus though
loud estuary
Hmmm
wicked badge
because we want the positive cos 1/2?
loud estuary
I'm trying the negative
loud estuary
Judging from the answer there is a plus minus I think
wicked badge
I think so too
loud estuary
Got same answer
wicked badge
loud estuary
@crimson sedge yup
loud estuary
olive crescent
sqrt(a/b) = sqrt(a)/;sqrt(b) yeah
wicked badge
casually throwing out complex identities
wicked badge
oh god my brain is melting
I think I get it
so it'll be 30 degrees
oh yeah my brain is dying
wicked badge
so x is less than 30 degrees
doesn't less than mean it'll go to the left
since cos gets smaller closer to the left or something
loud estuary
No I think that means there's a range
Just x needs to be smaller than 30
That's why there's interval notation and three unions
Because cos x is both positive and negative
So just need to apply the restriction that x is less than or equal to 30 degrees
loud estuary
Np
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lime seal
can anyone explain how this stem and leaf diagram work i rlly dont understand
cedar kilnBOT
can anyone explain how this stem and leaf diagram work i rlly dont understand
@lime seal Has your question been resolved?
hollow trail
each number on the left column is in the 10's place, each number in the right columns is in the 1's place. so the plot shows each individual data point, and you can find the value by combining the two digits.
for example, the third row contains all the numbers with 3 in the 10's place (in the 30's):
the datapoints are:
- 30+3 = 33
- 30 + 7 = 37
- 30 + 7 = 37
so 33, 37, and 37 are the three datapoints in the 30's.
mystic ferry
only allowed to use pigeohole principle and language closures
cedar kilnBOT
only allowed to use pigeohole principle and language closures
@mystic ferry Has your question been resolved?
cedar kilnBOT
cerulean sail
,rccw
wraith daggerBOT
modest dove
modest dove
I think I went wrong somewhere in the final lines?
Correct answer states in the brackets it is meant to be x - pi/6
modest dove
<@&286206848099549185>
ancient lodge
cedar kilnBOT
@modest dove Has your question been resolved?
ancient lodge
The transformation rules still apply
cedar kilnBOT
@modest dove Has your question been resolved?
cedar kilnBOT
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distant kite
Can I prove n^2 + 1 can be divisible by n + 1 by M.I.?
cedar kilnBOT
Can I prove n^2 + 1 can be divisible by n + 1 by M.I.?
alpine rune
Can I prove n^2 + 1 can be divisible by n + 1 by M.I.?
but it isn't
soft umbra
Oh it's fine
alpine rune
n^2 + 1 is not divisible by n+1
distant kite
HUH
alpine rune
what
distant kite
bruh
I looked wrong for the question
Find all positive integers n such that n^2+1 is divisible by n+1.
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cedar kilnBOT
cedar kilnBOT
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scenic oyster
2+2
scenic oyster
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cedar kilnBOT
cerulean sail
!occupied and this has already been closed by the owner
cedar kilnBOT
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).
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crimson sedge
cedar kilnBOT
crimson sedge
Isn't it when x=0??
livid hound
how are you getting that?
cedar kilnBOT
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crimson sedge
cedar kilnBOT
crimson sedge
I don't understand how to apply chain rule here
I am guessing I need to find the derivative of the lnx inside of ln
idle tusk
you have two functions
idle tusk
no need for x inside of ln
crimson sedge
no need for x inside of ln
i see
idle tusk
it would be 1/xlnx
close
crimson sedge
how would you go about it
idle tusk
i usually go inside out
crimson sedge
meaning
crimson sedge
1/x
idle tusk
and then the blue part
crimson sedge
1/lnx
crimson sedge
lmao
wraith daggerBOT
native heath
when solving depressed cubics
cedar kilnBOT
when solving depressed cubics
native heath
how do i simplify the last part?
the y=s-t
like how do I simplify something like this:
$\sqrt[3]{\frac{9-\sqrt{69}}{18}}-\sqrt[3]{\frac{-9-\sqrt{69}}{18}}$
wraith daggerBOT
Percy
native heath
yes
novel topaz
a^3+b^3 is 1
novel topaz
No
native heath
a^3+b^3 being 1
novel topaz
It's true here
native heath
mm
novel topaz
ab is 1/3
Which is something I got from calculations
It's not true for all a and b
So 1+t=t^3
cedar kilnBOT
@native heath Has your question been resolved?
native heath
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long fiber
what does as a function of x and z mean
cedar kilnBOT
what does as a function of x and z mean
livid hound
y = stuff with x,z (and constants (and no ys))
long fiber
huh
livid hound
depending on what you have: stuff like
y = x + z
y = x^2 - z
y =sin(x) + z + 42
pretty much write y in terms of x and z
long fiber
if y varies jointly as x2 and z and y=6 when x=4 write y as a function of x and z,THE value of constant AND C)THE VALUE OF Y WHEN X=8 and Z=12
my school doesn’t knows english
cedar kilnBOT
@long fiber Has your question been resolved?
blazing dune
$$\frac{d}{dx}[tan^{-1}(f(x))] = \frac{f'(x)}{f^2(x)+1}$$
wraith daggerBOT
Sherif Player
cedar kilnBOT
blazing dune
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cedar kilnBOT
✅
blazing dune
i don't think this solves it yet
the whole thing will output
$$\frac{1}{u^2+4}$$
wait
wraith daggerBOT
Sherif Player
blazing dune
yeah it is correct
,wolf derivative \frac12\times\arctan(\frac{x}{2})
yes as i said you get it wrong
wraith daggerBOT
