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#help-26
topaz sinewBOT
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vocal rock
Hello!
vocal rock
An area in the xy-plane is bounded by the x-axis, the line x = 1 and the curve y = sqrt(ax-a^2) where a is a constant such that 0 < ɑ < 1. Let the area rotate around the x-axis and determine a so that the volume of the body of rotation is maximum
(Google translate) also this task should be solved without a calculator
I don’t know how to begin but the x values should go from 0 to 1 in the axis
Or maybe it can be negative too :/
topaz sinewBOT
@vocal rock Has your question been resolved?
vocal rock
<@&286206848099549185>
Trying to find when the function crosses the x axis
sqrt(ax - a^2) = 0
a can’t be 0
a can’t be 1
vocal rock
sqrt(ax - a^2) = 0
For this to be true a = x
Then the area must be within the positive axis of x and y
The values for the integration should then range from 0 < x < 1
No I don’t understand this problem
<@&286206848099549185> please help
brazen bough
Can you draw this out and upload a photo?
brazen bough
Are you given a picture?
vocal rock
Nop
And then the area that I’m given is spinning around the x axis
or I should find the number of a that gives me the biggest volume
brazen bough
are you trying to find where the curved line meets the x axis?
vocal rock
The curved line is to connect the function to the question mark, to show that I don’t know how the graph looks like
But yes looking for when the function meets the x axis is what I’m looking for
To start a solution
But y is the sqrt of ax-a^2
brazen bough
give me a few
vocal rock
Okok
brazen bough
I'm sorry I can't help you, but I did find this resource that may help you: https://www.youtube.com/watch?v=btGaOTXxXs8
vocal rock
I'm sorry I can't help you, but I did find this resource that may help you: http...
Thanks anyway bro 👍
<@&286206848099549185> still stuck 
topaz sinewBOT
@vocal rock Has your question been resolved?
topaz sinewBOT
@vocal rock Has your question been resolved?
vocal rock
<@&286206848099549185>
topaz sinewBOT
@vocal rock Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
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zealous berry
How would I do this question?, the equation i wrote is as I far as I could go, I’ve never seen a problem worded like this so I’m honestly just lost
topaz sinewBOT
How would I do this question?, the equation i wrote is as I far as I could go, I...
neon iron
Is it related to mclaurin series?
zealous berry
I’ve never heard of that
If this helps this is question 6
I also only have like 2 months of ap calc ab knowledge, so any advance series or theorems I won’t really know
neon iron
Yea well I never really saw this type of questions
zealous berry
Yeah this question is worded pretty weirdly 😅
topaz sinewBOT
@zealous berry Has your question been resolved?
zealous berry
.close
vital fog
.close
neon iron
topaz sinewBOT
sturdy oracle
What have you tried
neon iron
@sturdy oracle This is the right answer
but i dont know how to express it like this
Because I have to express it in one of those ways
and I dont know how to convert the first form to the second
sturdy oracle
Remember that $3 = \log_5{125}$
thorny flameBOT
Umbraleviathan
sturdy oracle
Then use the property that log(a) - log(b) = log(a/b)
sturdy oracle
Then that $\log_a(b) = \frac{\ln(b)}{\ln(a)}$
thorny flameBOT
Umbraleviathan
sturdy oracle
<@349354952961032192>
Painting the ceiling red
neon iron
right
sturdy oracle
ln, log
neon iron
yeah sorry
noble laurel
@sturdy oracle
sturdy oracle
Holy shit Austin why are you fuckin insufferable today
sturdy oracle
well you can express log(5/441) as a sum and difference of series of logs
so obviously log(5/441) = log(5) - log(441)
Then log(441) must equal to something
neon iron
dont understand
topaz sinewBOT
@neon iron Has your question been resolved?
terse sable
topaz sinewBOT
terse sable
how do you do questions like this
i dont udnerstand how they got the -2pi -pi and 2pi
what is the process to solving such questions
topaz sinewBOT
@terse sable Has your question been resolved?
knotty tusk
4pi/3 = pi/3 * 4
they most likely are using reference values and logic
so you can tell what quadrant the vaue will land on based on a couple things, this will help you
if you do it my way which sucks
but you probably should use arithmatic formulas for whichever thing you are using
sin(2pi + pi/6) = sin(2pi)cos(pi/6) + cos(2pi)sini(pi/6)
2pi is simple calculatin
sin 2pi = 0, cos 2pi =1
0* cos(pi/6) + 1*sin(pi/6)
we can ignore left
because 0 cancels out cos
terse sable
So my teacher uses this identity but doesnt show?
knotty tusk
from memory i think sin pi/6 = 1/2
terse sable
Also what if its not 2pi
knotty tusk
So my teacher uses this identity but doesnt show?
You can use it, but IDK if your teach wants you to
terse sable
Like in q b
knotty tusk
a and B?
terse sable
I feel like there is an easier method that my teacher is using
terse sable
No special way?
knotty tusk
you can tell which quadrant it is because each quadrant has bounds
terse sable
Cause i thought (at least for degrees) you subtract by 90 180 270 or 360
Get raa
Then done
knotty tusk
pi/2 = 1, pi =2, 3pi/2 = 3, any thing bigger than 3pi/2 is quad 4
terse sable
But this is something else
knotty tusk
Cause i thought (at least for degrees) you subtract by 90 180 270 or 360
something like that. I'm more of a "logic" user at math, so the way i do things is different. I don't really stick to some algorithm
knotty tusk
Then done
those angle's radian counterparts = this
woops sorry responded to wrong one
knotty tusk
pi/2 = 1, pi =2, 3pi/2 = 3, any thing bigger than 3pi/2 is quad 4
this is angle radian counter parts
0 -> pi/2 = quad 1, pi/2 -> pi = quad 2, pi -> 3pi/2 =3, 3pi/2 -> 0 = quad 4
topaz sinewBOT
terse sable
Tf
terse sable
.reopen
topaz sinewBOT
✅
knotty tusk
4pi/3 = pi/3, sin doesn't flip values between 0->pi
terse sable
Im just unsure how this teacher managed to get that 1st step
knotty tusk
4pi/3 = pi/3, sin doesn't flip values between 0->pi
this logic
topaz sinewBOT
knotty tusk
Ok i think i get it
actually 4p/3 is > pi
because 4/3 = > 1, and (4/3)* pi is equevelent to 4pi/3
topaz sinewBOT
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long plaza
Can you show me an example of this y=6x-4
topaz sinewBOT
Can you show me an example of this y=6x-4
long plaza
In order pairs
neon iron
Can you show me an example of this y=6x-4
what
sweet shard
In order pairs
you just pick a few different, convenient x values, and plug them in
if x=0, y = ?
(0, ?) is one ordered pair
long plaza
you just pick a few different, convenient x values, and plug them in
Yea I don't know how tho I need someone to do it an example
Pleaseeeeee 🥺
sweet shard
Yea I don't know how tho I need someone to do it an example
,calc 6 * 0 - 4
thorny flameBOT
Result:
-4
sounds like you just input a vaue you want to the function
long plaza
I need the answer to be a order pair tho
long plaza
you see how i plugged in x= 0?
Yea
sweet shard
(0, ?) is one ordered pair
.
knotty tusk
hes telling you how to get the values
what you need to do here is
evaluate the first part as the input for func
than check if the right part = f(x), where x = left part of the set
long plaza
Oh alright
knotty tusk
which ever ones are correct you include
by correct i mean if result of func matches right part
where input = left part of the set
long plaza
Yea thx for the help but I think I'ma pass out I feel dizzy cuz I can't focus I don't know my head hurt I can't even type
knotty tusk
take a break prob help
long plaza
Bro it's 12:06 haven't sleep since before yesterday I feel like I'ma throw up and I didn't eat anything
topaz sinewBOT
@long plaza Has your question been resolved?
topaz sinewBOT
@long plaza Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
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unique thunder
topaz sinewBOT
unique thunder
why change the signs?
lucid junco
why are you on an alt lol
uncut crow
It's just an algebra step. Why is it confusing?
unique thunder
It's just an algebra step. Why is it confusing?
can you explain it
uncut crow
You multiply both sides by -1
unique thunder
oh
frank granite
https://cdn.discordapp.com/attachments/903486479064522752/1170340985662865508/Sc...
Multiplied everything by (-1)
uncut crow
The equation is still true
sharp dew
Given equation:x^2+ax+(x+3)=0 has two solutions alpha and beta and them both are positive numbers.
topaz sinewBOT
Given equation:x^2+ax+(x+3)=0 has two solutions alpha and beta and them both are...
sharp dew
what's the range of a.
hold on
I'm not asking about how to solve the question
Yet im seeking for someone to check my approche
tawny spade
Sure
sharp dew
So
that blue-arrow pointed system is the circumstance of alpha and beta are both positive
tawny spade
-B/A should be -a if you have x²+ax+(a+3)
drifting swift
alpha+beta is -a not a, yeah
tawny spade
But yeah if your approach is that AB should be >0 and A+B should be >0
Id say thats valid
drifting swift
do we not also want the discriminant to be >0 btw
sharp dew
and I suppose it could lead me to the correct answer
tawny spade
Oh yeah
sharp dew
do we not also want the discriminant to be >0 btw
why
drifting swift
so that there are two real roots
drifting swift
otherwise you could make a complex conjugate pair whose sum and product are both positive
sharp dew
You could have complex number solutions that fit this i guess?
yes i could
sharp dew
Complex numbers arent "positive" thi
So b^2-4ac >=0 for these solutions to not be some complex numbers
tawny spade
Yeah
ruby tree
Monotonically increasing just means it always "goes up", that doesn't mean it's convex
Kinda
Convex means if you draw a line segment between two points of the graph, that line is above the graph (on that interval)
Wrong
It's just another way to think about it
Take the log function
It's concave, yet always increasing
e^-x is convex, yet always decreasing
"Convex function" I guess
Not really, Lagrange has a few things named after him
It means "much greater than"
In some contexts it might mean "grows asymptotically more quickly than"
I think it mostly means that the right side is negligible
I don't think it has any rigorous definition
I don't really study anymore haha
I just had some basic undergrad maths education
And a bit of curiosity
I'll take that as a compliment 
The internet is a great place for finding stuff you're curious about, especially related to the sciences
topaz tulip
topaz sinewBOT
topaz tulip
how is vb substituted?
where does the second part come from? after the addition sign?
i dont know how it is simplified
topaz sinewBOT
@topaz tulip Has your question been resolved?
topaz tulip
.close
topaz sinewBOT
@neon oak Has your question been resolved?
topaz sinewBOT
@neon oak Has your question been resolved?
topaz sinewBOT
@neon oak Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
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wintry raft
I’m trying to show that x^4 -5x^3 + 10x + 7 is irreducible in Z[X]. Can someone help me out
topaz sinewBOT
I’m trying to show that x^4 -5x^3 + 10x + 7 is irreducible in Z[X]. Can someone ...
wintry raft
Eisensteins criterion does not work here
acoustic tangle
Try using rational root theorem
wintry raft
A hint I got was try find a prime number p such that f is irreducible modulo p. A necessary but not necessarily sufficient condition is that f has no roots mod p. Try some small primes
acoustic tangle
That works too with p = 2
wintry raft
In that case the polynomial becomes x^4 + x^3 +1 right?
And then in that case do we have to show that it has no linear/quadratic roots?
acoustic tangle
It's easier than that
Factor x^4 + x^3 and show that it's always congruent to 0 via considering cases
wintry raft
Does this sufficiently show that the polynomial is irreducible or just that it has no linear roots?
acoustic tangle
I just realised showing absence of roots only shows we can't reduce it into linear factors
We still need to show it can't be reduced into quadratics yeah
wintry raft
Do you know how to approach that
acoustic tangle
Eh I think I would do it by contradiction but that will take a lot of work, let me think if there's anything else
wintry raft
Thank you! Currently thinking about it too!
acoustic tangle
Well we just shows that the polynomial is equal to 1 in Z_2, which is irreducible, meaning it should be also irreducible in Z I think
wintry raft
Okay so yeah if we just show there’s no quadratic factors, then we’re essentially done
marble skiff
unless i'm mistaken, eisenstein criterion also works if you can show that the criterion is valid for any other polynomial Q(x) with Q(x) := P(x+a) where a is a whole number
otherwise if there was some way that P(x) = P1(x)P2(x) then there would be a factorization for Q(x) = Q1(x)Q2(x) = P1(x+a)P2(x+a) which would be a contradiction to the criterion being fulfilled (sorry for just coming in here while you were going through another way of solving this but just wanted to show another idea)
topaz sinewBOT
@wintry raft Has your question been resolved?
sleek needle
what does it mean by 'non-trivial periodic solution'?
sleek needle
so when i work out the eigenvalues of the ode system
i get real and complex
so will the complex be the periodic one
since itll contain sine and cosine
im kinda guessing
brittle canopy
that's probably it
topaz sinewBOT
@sleek needle Has your question been resolved?
sleek needle
.close
plucky talon
I have 2 questions. First, by (s,t) do they mean gdc(s,t)? Second, I don't understand how looking at the prime factorization of p on both sides shows us that p divides t.
topaz sinewBOT
I have 2 questions. First, by (s,t) do they mean gdc(s,t)? Second, I don't under...
plucky talon
Like, what equation am I supposed to look at?
topaz sinewBOT
@plucky talon Has your question been resolved?
plucky talon
<@&286206848099549185>
topaz sinewBOT
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topaz sinewBOT
Available help channel!
gritty matrix
how would I do this probala?
y = x^2
topaz sinewBOT
how would I do this probala?
y = x^2
gritty matrix
is this correct? the vertext is 1,1 and the axis of symmetry is 1, and optimal value is minimum, and lastly the step pattern is 1, 3, 5
vertex*
modern bloom
is this correct? the vertext is 1,1 and the axis of symmetry is 1, and optimal v...
Hello. Use the vertex form equation of a parabola. Why would the vertex be (1,1)? 🤔
topaz sinewBOT
@gritty matrix Has your question been resolved?
gritty matrix
Hello. Use the vertex form equation of a parabola. Why would the vertex be (1,1)...
because like it's y=x^2 and there's no values for h and k
so it would be 1
modern bloom
so then the vertex is 0,0?
yes
gritty matrix
aos is 0, and step pattern is 0,0,0
but how do I figure optimal value
if it's maximum or minimum
modern bloom
I don't know what step pattern is 😵💫
you can get any parabola in this form: a(x-h)^2+k
so you can compare the parabola with this form
x^2 and a(x-h)^2+k
If a>0, the parabola has a minimum
the vertex is point (h,k)
notice you can write x^2 as
x^2 = 1(x-0)^2 + 0
gritty matrix
If a>0, the parabola has a minimum
so if it's in the negatives it's minimum?
topaz sinewBOT
@gritty matrix Has your question been resolved?
thick oyster
topaz sinewBOT
thick oyster
idk what i did wrong
scenic flare
absolute max in [0,8] is 7
only the local max is 6
the absolute max is the highest value within that interval
regardless of whether it sits on an extreme point.
thick oyster
local max is asking for x value
thick oyster
it says incorrect
scenic flare
with x=3?
surreal quiver
try deleting the space
thick oyster
where
surreal quiver
grave latch
Just checking in, why is absolute max 7?
grave latch
There... shouldn't be a maximum
thick oyster
there is
grave latch
Okay, which value of x gives y=7?
thick oyster
3
surreal quiver
that gives 6
surreal quiver
try writing none in 3.
thick oyster
but theres a maximum
surreal quiver
there isnt
grave latch
but theres a maximum
7 isnt the maximum
surreal quiver
Okay, which value of x gives y=7?
answer this question then
grave latch
there is literally no absolute maximum
thick oyster
at y = 6
surreal quiver
thats not an absolute maximum
surreal quiver
there are points with higher y value
proven narwhal
proven narwhal
they cancel each other out
cinder imp
are you sure
proven narwhal
I was also thinking its A too but yeah its not
acoustic pecan
say x was 3pi/2 cos(3pi/2) is 0,
arccos(0) will generally just return pi/2, which is 2pi-x
since arccos tends to give the solution between 0 and pi
where as x is between pi and 2pi
the result is 2pi-x
topaz sinewBOT
@proven narwhal Has your question been resolved?
proven narwhal
say x was 3pi/2 cos(3pi/2) is 0,
arccos(0) will generally just return pi/2, ...
I still don't get it
vernal matrix
Note that $\cos^{-1}(\cos(u)) = u$ only when you have $0 \leq u \leq \pi$
topaz sinewBOT
@proven narwhal Has your question been resolved?
proven narwhal
Note that $\cos^{-1}(\cos(u)) = u$ only when you have $0 \leq u \leq \pi$
still don't understand where the 2pi - x comes from
vernal matrix
<@788085606483361802>
Have you seen this before?
cinder imp
is it just something I have to memorize?
yes thats a formula i didnt see the question correctly
my bad
proven narwhal
is it also the same for sinx ?
acoustic pecan
no
cos is symmetrical about pi which is why it works (even)
sin is skew symmetric about pi (odd)
proven narwhal
.close
twilit robin
topaz sinewBOT
twilit robin
I need to find the local max and local min of the function (which I just labeled as (f(x))
So I found the critical points at x=3 and x=10
and then made the domains with 0, 3 and 10
and then ran some f'(x)'s
but got - - + +
So I'm wondering where I went wrong or maybe I'm right but I'm thinking about the rest of the problem wrong or something
from my understanding I only have one local min with the calculations I've made
Here's a pic of the question tho
ah nvmd
wasnt supposed to bring in the 0
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
cursive thistle
can anyone help me with simplifying this?
topaz sinewBOT
can anyone help me with simplifying this?
surreal quiver
which part do you not understand?
drifting swift
ough t h e sp a c i n g on the first line
drifting swift
this is just adding all the fractions together with the lowest common denom
surreal quiver
see what theyre doing is changing all the fractions to have the same denominator
drifting swift
$\frac{2}{3(2x-1)} - \frac{1}{x} - \frac{3}{3x+1}$
thorny flameBOT
Ann
cursive thistle
nah wait i'm still confused lol how do you get the lcd from that equation? i've forgotten a lot of algebra and i'm having lots of troubles with fractions
surreal quiver
$\frac{1}{3} * \frac{2}{2x-1} - \frac{1}{x} - \frac{3}{3x+1}\ = \frac{2}{(3)(2x-1)} - \frac{(1)(3x+1)}{(x)(3x+1)} - \frac{(3)(x)}{(3x+1)(x)}\ = \frac{2}{3(2x-1)} - \frac{3x+1 +3x}{x(3x+1)}\ = \frac{(2)[x(3x+1)]}{[3(2x-1)][x(3x+1)]} - \frac{(6x+1)[3(2x-1)]}{[x(3x+1)][3(2x-1)]}$
bitter hemlock
nah wait i'm still confused lol how do you get the lcd from that equation? i've ...
to find lcd you would just multiply all the different (ideally prime) factors together
so a simple example:
$\frac{1}{2}+\frac{1}{3} = \frac{1}{2}\times\frac{3}{3}+\frac{1}{3}\times\frac{2}{2}$
surreal quiver
this is less daunting
surreal quiver
and after expanding, youll get
$\frac{2x(3x+1) - (6x+1)(6x-3)}{3x(2x-1)(3x+1)}\ = \frac{6x^{2}+2x-(36x^{2}-18x+6x-3)}{3x(2x-1)(3x+1)}\ = \frac{6x^{2} + 2x - 36x^{2} + 18x - 6x + 3}{3x(2x-1)(3x+1)}\ = \frac{-30x^{2} + 14x + 3}{3x(2x-1)(3x+1)}$
thorny flameBOT
Tangerine
cursive thistle
damn that's a lot to sink in. i appreciate it a lot though and it's definitely a lot clearer now. although i can't say i fully understand it yet. do you perhaps have any resources/videos i could reference to so i could grasp this better?
surreal quiver
damn that's a lot to sink in. i appreciate it a lot though and it's definitely a...
cursive thistle
thanks man u're the best! i'll watch that video then go back to your explanation to see if i could understand it perfectly
surreal quiver
thanks man u're the best! i'll watch that video then go back to your explanation...
npnp
topaz sinewBOT
@cursive thistle Has your question been resolved?
chilly fable
I tried to do another example, with the R-vs of differentiable functions (let's call it $S$). Let $W = {f \in S : f (0) = f(1) = f'(0) = f'(1) = 0}$ and $\mathbb{R}_3$, the space of polynomial functions of degree 3. I want to show that they are complementary in $S$.
topaz sinewBOT
I tried to do another example, with the R-vs of differentiable functions (let's ...
thorny flameBOT
mechap
chilly fable
I set $f(x) = ax^3 + bx^2 + cx + d + g(x)$ with $g \in W$
thorny flameBOT
mechap
chilly fable
so that we get $g(x) = f(x) - ax^3 - bx^2 - cx - d$, for $x = 0$, I get $d = f(0)$. for $x = 1$, I get $a + b + c = f(1) - f(0)$
thorny flameBOT
mechap
chilly fable
$g'(x) = f'(x) - 3ax^2 - 2bx - c$, for $x = 0$, I have $c = f'(0)$ and for $x = 1$, I have $3a' + 2b' = f'(1) - f'(0)$
thorny flameBOT
mechap
chilly fable
for example $d = f(0)$ so $d' = f'(0)$
thorny flameBOT
mechap
chilly fable
because I have constraints on differentiation for x=0 and x=1
strange whale
ok yes this I get
but how do you get 3a'+2b' = .... ?
shouldn't it just be 3a+2b= .... ?
chilly fable
but a' may not be equal to a
strange whale
I don't even get why you have a' in the first place is my question
chilly fable
I am not differentiating a with respect to x, a is the value of some composition of functions at some point, and I define a' to be the derivative at that point
strange whale
"I am not differentiating a with respect to x" "I define a' to be the derivative at that point" what are you differentiating with respect to, if not x ?
a is just a constant, so I don't even see why you'd even try to differentiate it wrt anything in the first place
strange whale
like if you plug in $x=1$ in the equation $g'(x) = f'(x) - 3ax^2 - 2bx - c$, you get directly that $-3a-2b-c = 0$
thorny flameBOT
aPlatypus
strange whale
no need to differentiate constants or whatnot
strange whale
yeah I read it backwards yes
chilly fable
so I have
\begin{cases}
a+b = f(1) - 2f(0) \
3a + 2b = f'(1) - f'(0)
\end{cases}
thorny flameBOT
mechap
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
neon iron
How can i find the red part
topaz sinewBOT
How can i find the red part
bitter hemlock
,rotate
thorny flameBOT
bitter hemlock
so what's going on there, you have a right triangle with one side of 2 and the other side of 4.5?
bitter hemlock
what is -2?
neon iron
it's cavalier axonometry
bitter hemlock
ok , i have no idea, you might want to give more context for this problem since at first glance it looks like a middle school geometry problem where you need to apply pythagorean theorem : )
sleek needle
im rly confused here, because when u mutiply out the matrices, u dont get the RHS
odd pagoda
yeah they messed up some signs
oh and the 2 and 1 are switched
just all around messed up
sleek needle
yeah they messed up some signs
we did this question before together, and remember we said to take Q-1 as the 'invertible'
and so Q^-1 is = S eg
well i did another question, but it defies what we said
look here, here they r using the same Q^-1, and Q, they arent defining an S and S^-1
odd pagoda
oh they did actually calculate QBQ^-1
sleek needle
oh they did actually calculate QBQ^-1
yh, but they didnt do that in the example i just posted now
which is making me rly confused
odd pagoda
they fucked up
sleek needle
they fucked up
the matrix answer for A for the 2nd question is corretc (ie the multiplcation of the matrices does give u the RHS)
so i guess it is then Q^-1BQ = A
and not QBQ^-1
they just wrote the answer wrong for the first question
...
odd pagoda
yes they just messed up the calculation
sleek needle
yes they just messed up the calculation
so all of what we said last few weeks when we did this was just nonsense then ^^
its just simply Q^-1BQ
odd pagoda
I dont remember what we said back then
sleek needle
it was this
odd pagoda
the matrix highlighted in yellow doesnt work if you just plug it into the supposed ode x'=Ax and calculate both sides
topaz sinewBOT
topaz sinewBOT
Available help channel!
rugged mango
Boys
chilly walrus
2^set is powerset right
rugged mango
YE
bitter hemlock
girls aren't allowed to help you?
rugged mango
NA
fluid belfry
we only have girl helpers
topaz sinewBOT
If you are done with this channel, please mark your problem as solved by typing .close
chilly walrus
goddamn
livid tusk
Ahahaha
rugged mango
Comon guys i need some help
livid tusk
Mate just say everyone
fluid belfry
@chilly walrus dont
rugged mango
Bruh guy = boy and girl
livid tusk
Bruh guy = boy and girl
Bro didnt pass biology
livid tusk
Really?
chilly walrus
<@474467399207223307> dont
a homeless guy came up and inserted a syringe in my veins. i think that's testosterone. i feel like i am ungirlifying.
rugged mango
it is
livid tusk
Actually yeah
rugged mango
the hell
rugged mango
u never heard a girl say to there friends that are girls, "Hey guys!"
So can i have some help 😄
chilly walrus
So can i have some help 😄
right away, do you see that that is true?
just think of a couple of examples in your head
chilly walrus
great
acoustic tangle
The empty set is irrelevant, can you describe what type of elements $2^A \cap 2^B$ has?
thorny flameBOT
A Lonely Bean
rugged mango
IDK
acoustic tangle
$2^A$ is the set of subsets of $A$ and $2^B$ is the set of subsets of $B$, so in $2^A \cap 2^B$ the elements are subsets of $A$ and $B$
thorny flameBOT
A Lonely Bean
acoustic tangle
But if some set is a subset of $A$ and $B$ simultaneously, then it should be a subset of $A \cap B$ as well, right?
thorny flameBOT
A Lonely Bean
acoustic tangle
So the elements from $2^A \cap 2^B$ are subsets of $A \cap B$, i.e., they also belong to $2^{A \cap B}$
thorny flameBOT
A Lonely Bean
acoustic tangle
So they equal wahoo
No they aren't equal, this only shows that $2^A \cap 2^B \subseteq 2^{A \cap B}$
thorny flameBOT
A Lonely Bean
rugged mango
Oh ok
acoustic tangle
Okay they are equal but it will require a separate proof
But you aren't asked to prove equality
topaz sinewBOT
rugged mango
Owen sort him out
strange whale
hey it's gonna close tim
green gulch
Why does it go from f(j) at the start and then my prof uses f(i) and the same with g(i) and then goes to g(j)
strange whale
you better get another channel
rugged mango
@strange whale You better shut up, how about that !?
strange whale
wtf
rugged mango
Joke lol
green gulch
U gokna get banned ans never understand maths dude
rugged mango
Ima make an alt cause if i do get banned since I rlly do need help man
green gulch
Yo platypus where do i go
rugged mango
Just a joke platypus 😄
topaz sinewBOT
Available help channel!
long tiger
hello
long tiger
I need help with a statistics question
how can I calculate the 0.125 quantile of a measurement series
I have the series 10 11 15 17 17 19 22 25 31 32 35 43 47 59 99
and my result is 11 as 0.125 quantil
is that correct
<@&286206848099549185>
<@&286206848099549185> :,)
topaz sinewBOT
@long tiger Has your question been resolved?
topaz sinewBOT
@long tiger Has your question been resolved?
violet mauve
hello again im back for more questions: when proving the surjectuivity of a quadratic function would it be considered formal proof that i wrote the quadratic as $a(x-b)^2+c$ and therefore $x=\pm \sqrt {y-c} + b$ and since y is inside a sqrt it can only be a positive value incl 0
topaz sinewBOT
hello again im back for more questions: when proving the surjectuivity of a quad...
thorny flameBOT
sup sup
sterile geyser
Are you proving that it's not surjective? Because what you're showing is that the range only consists of $y ≥ c$
thorny flameBOT
OssihLikesBlue
violet mauve
yes, and that range doesnt match with $\mathbb{R}$ which is the functions uhhh
thorny flameBOT
sup sup
ruby tree
Domain
I don't think you can use the domain of the partial inverse function to prove something about the surjectivity of a function...
ruby tree
You can prove that any quadratic function has an extremum
That restricts the image, which means it does not cover the whole codomain
violet mauve
i get the idea
but am i not doing the same thing here
codomain takes values from c to +inf in my case
which is $\neq$ to R
thorny flameBOT
sup sup
violet mauve
idk maybe im wrong
ruby tree
First, terminology
The codomain is what you define it to be
The image is the set of possible outputs
If the two are equal, then the function is surjective
violet mauve
well the image != codomain
violet mauve
and i found the image through the inverse function
in my case [-1/4; +inf[
trying to avoid derivatives because they werent on the lectures, trying to use only what i got
and this is the most "formal" way i could formulate it
ruby tree
You said "the image is the domain of the (partial) inverse function"
Which is correct, but how do you know the domain of sqrt is not R?
violet mauve
.close
midnight viper
Yo
topaz sinewBOT
@neon iron Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
Available help channel!
daring warren
Can someone help me solve this question? I am getting infinity but the final answer is -1
topaz sinewBOT
Can someone help me solve this question? I am getting infinity but the final ans...
drifting swift
how are you getting infinity
daring warren
I split the limit and then by using l hopitals rule for the first term in the subtraction part I get infinity
opal vault
I split the limit and then by using l hopitals rule for the first term in the su...
yeah, well for part 2 you'll get infinity as well, so you get infinity - infinity
So not solvable this way
daring warren
so how do I approach it?
opal vault
Here's a hint : put everything on the same denominator
drifting swift
I split the limit and then by using l hopitals rule for the first term in the su...
splitting yields ∞ - ∞
so that is no bueno
daring warren
I tried it but im not sure won’t I get infinity again?
opal vault
I tried it but im not sure won’t I get infinity again?
can you show what you did in this case?
daring warren
opal vault
I suggest you not to expand the numerator when bringing everything inside the fraction
$\frac{x^2-(x+1)\sqrt{x^2+1}}{x+1}$
thorny flameBOT
rafilou2003
opal vault
And now, an old trick when you're dealing with difference of square roots, you multiply by the...
daring warren
by the..?
opal vault
I don't want to spoil it, but for example, how do you get rid of square roots on the denominator : $\frac{1}{\sqrt{b}-\sqrt{a}}$?
thorny flameBOT
rafilou2003
daring warren
multiply with its conjugate?
opal vault
yes!
fair pulsar
please can you help me start this question i believe it is to do with coding but i dont know what to do with all the numbers
topaz sinewBOT
please can you help me start this question i believe it is to do with coding but...
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).
coral torrent
omg soz
fair pulsar
<@&286206848099549185>
topaz sinewBOT
@fair pulsar Has your question been resolved?
topaz sinewBOT
@fair pulsar Has your question been resolved?
true minnow
please can you help me start this question i believe it is to do with coding but...
so, given that the width is x and the length is y meters
area, which equals x*y, must be less than or equal 75.
the width must be between 3 and 9, but in the question it says that the width is x so
also, the fencing is 25 meters so 2x + y = 25
$3 \le x \le 9$ and $2x+y = 25$ and $xy \le 75$ must hold
thorny flameBOT
musava_ribica
true minnow
can you go from there?
topaz sinewBOT
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Available help channel!
jolly dragon
topaz sinewBOT
jolly dragon
What’s the rule?
half edge
Wdym what’s the rule?
Ur given a formula, and they provide the values of the sum and the ratio
Just plug in and solve
topaz sinewBOT
@jolly dragon Has your question been resolved?
topaz sinewBOT
@jolly dragon Has your question been resolved?
topaz sinewBOT
@jolly dragon Has your question been resolved?
pseudo sonnet
topaz sinewBOT
pseudo sonnet
!status
topaz sinewBOT
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
Maybe consider the derivatives of P?
pseudo sonnet
ah, I think I may have found something
P'(0) = a1
P''(0) = a2
etc
and then I just substitute these in?
vernal matrix
Kinda like that (but check the P''(0) value maybe 
)
pseudo sonnet
Kinda like that (but check the P''(0) value maybe <:catThink:1073406415575728200...
ah, P''(0) = 2*a2
graceful leaf
topaz sinewBOT
vernal matrix
Might help to break it down into smaller steps, as you have nested roots...
topaz sinewBOT
@graceful leaf Has your question been resolved?
graceful leaf
topaz sinewBOT
graceful leaf
how dis wrong plz
sonic dawn
right idea wrong execution
acoustic pecan
ik but if you pull the ^3 from the y, itll be 3 outside, not 1/3 to give 1/6
graceful leaf
o
topaz sinewBOT
@graceful leaf Has your question been resolved?
willow raptor
Can someone help me combine these fractions? I am messing up so hard
half edge
Well what’d u get for lcd
willow raptor
alr
half edge
Ping when done
willow raptor
u said set both fractions to that denom
half edge
“Get both fractions to have that denom”
half edge
U did, but u can’t just change denominator only
For example
If I had the fraction
2/5
and I wanted the denominator to be 5x
I can’t just change it to
2/5x
willow raptor
so what would happen to num
half edge
Same thing that u did to the denom
willow raptor
also multiplied by lcd?
half edge
Multiplied by the necessary factor to get the lcd
willow raptor
uhh
this is prob wrong but one sec
i prob misunderstood u here
cause that look very wrong
thorny flameBOT
Stephen
half edge
What’s the lcd here?
willow raptor
bd?
willow raptor
multiply top and bottom by bd?
half edge
What do u get in the denominator after multiplying the denominator of a/b by bd
willow raptor
b^2d?
willow raptor
oh i see
half edge
So what value must we multiply the top and bottom of a/b by to get denominator = bd
willow raptor
b^2
half edge
So how do we get from b to bd
willow raptor
multiply it by d
willow raptor
ad/bd
half edge
Perfect
willow raptor
oooooooooo
half edge
Now make the common denominator on c/d
half edge
idk how im struggling with this in cal 😢
A lack of proper understanding of the basics
So now we have
ad/bd + bc/bd
willow raptor
correct
half edge
What does it become after adding
willow raptor
ad+bc/bd
thorny flameBOT
Stephen
half edge
Common denom is x(x^2 + 5)
willow raptor
correct
half edge
How do we make 6/x to have that common denominator
willow raptor
i thought we wanted x^2+5
oh wait
bro im brain farting so hard ngl
we just multiply by x^2+5
half edge
Ye
willow raptor
so we do that to the top?
half edge
So what does the first fraction become
willow raptor
6(x^2+5/x(x^2+5)
willow raptor
just x this time?
half edge
Yes
willow raptor
ooooo
half edge
What does it become
half edge
Ye correct
willow raptor
which turns into 4x^2+30/x(x^2+5)
half edge
Yes
willow raptor
i will man
shut sand
topaz sinewBOT
crimson iron
well lets look at c for a second