so 72/180 is 0.4
#help-42
calm coralBOT
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obsidian void
'
obsidian void
this question is confusing me because i dont think any of these line up with sine of theta equalling -1
ivory pilot
Why do you think so
clear delta
$\f{7\pi}2 \neq 420\deg$
potent lotusBOT
hayliänus austrǎlis
obsidian void
how did i get that
obsidian void
Why do you think so
oh i see
i was counting degrees starting at the right line
going down
or wait
clear delta
you probably want to start working directly with radians
remembering that pi/2 is a quarter rotation
obsidian void
remembering that pi/2 is a quarter rotation
right good to remember
let me do it again
also do you start rotations from positive x going clockwise or counter clockwise
clear delta
positive is counterclockwise
obsidian void
ohh
that explains half of it
alright i got it on the second try
working with radians is much easier you're right
thank you
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✅ Original question: #help-42 message
obsidian void
did they mean to use sin^-1 in this
is theta exclusively for the input of angles
still haven
Wait what
dull wagon
options should've just been
theta = angle
still haven
I think u substitute theta for the angles
So sin 0 etc
Cause sin-1 is only from -1 to 1
still haven
Terrible question😭
obsidian void
it just tripped me up for a minute because ive never found a mess up in these before lol
alr well thank you
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fickle geyser
Does anyone know philosophy discord server?
calm coralBOT
Does anyone know philosophy discord server?
proven oxide
no but i know a math one
leaden thunder
Does anyone know philosophy discord server?
This isn't a math question
Don't abuse help channels
thorny stump
Does anyone know philosophy discord server?
You know there's a "discover" button where you can look that up, right?
sleek vessel
.close not a maths question
wheat wyvern
why is there a spike downwards at 5
calm coralBOT
why is there a spike downwards at 5
wheat wyvern
x = linspace(-2,6,1000);
for t = 1:1000
if x(t) < -1
y(t) = exp(x(t)+1)
elseif (-1 <= x(t)) & (x(t) <= 5)
y(t) = 2 + cos(pi*x(t))
elseif x(t) > 5
y(t) = 10 * (x(t) - 5)
endif
endfor
figure
plot(x,y)
Both should be meeting at 1 when x is 5
pallid halo
why should they meet at 1
if x(t) is just slightly more than 5 then x(t) - 5 is slightly more than 0
pallid halo
ah the +1 should help!
wheat wyvern
Thank you!
pallid halo
yw
wheat wyvern
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glad sinew
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glad sinew
why for miu=0 you dont plot points -sqrt(miu) and sqrt(miu)
because miu=0 is valid for these points
hiii!!
calm coralBOT
@glad sinew Has your question been resolved?
leaden thunder
mu = 0 implies sqrt(mu) = - sqrt(mu) = 0
you should also plug in mu = 0 to the differential equation and simplify
glad sinew
Thank you
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If you are done with this channel, please mark your problem as solved by typing .close
glad sinew
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old crater
How to show zn+1 < zn .
The exponential function is not yet discussed in the book . So i can't use its properties
velvet osprey
you want to show $c^{\frac{1}{n+1}} \overset?< c^{\frac{1}{n}}$.
potent lotusBOT
Ann
old crater
Yes
velvet osprey
are you allowed the claim of $a<b \iff a^k<b^k$, with $a,b>0$ and $k \in \bN$?
old crater
Haven't proved it yet
potent lotusBOT
Ann
velvet osprey
Haven't proved it yet
was it mentioned in the book
old crater
No
velvet osprey
ok then at least are we allowed to say that if p > 0 and c > 1 then c^p > 1
old crater
They have written (why?) after zn>1 and zn+1<zn
So i think we have to show both
In a proceeding example. They showed that lim(b^n)=0 , if 0<b<1.
And in this , they just wrote "we see that since 0<b<1 , then b^(n+1) < b^n
velvet osprey
what properties of exponents are you legally allowed access to
old crater
They haven't mentioned the exponentials even a single time
Only about squares and roots
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spice venture
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spice venture
spice venture
possible values of m,M are
i got f(x) = 192/pi^4 integral t^3/(2+sin^4t)
do i use sandwhich theorem or smth
wait lemme try that
wait
but they are asking integral f(x)
bruhhh
anyone help?
spice venture
so do i differentiate it?
i mean max should happen at x=1
and min at x=1/2
max value = 96
min = 8
@violet mauve
coral pond
Is this university-level math or high school math?
spice venture
high school
violet mauve
and min at x=1/2
No no just put x=1/2 for min value and x=1 for max
remote mural
high school
bro we will be hopefully university this year
spice venture
No no just put x=1/2 for min value and x=1 for max
yes thats what i did
spice venture
max value = 96
^
violet mauve
yes thats what i did
So min value< f'(x)<max value
Now integrate both sides from 1/2 to 1 wrt x
Sandwich theorem I guess this is called
Idk forgot the name
spice venture
Now integrate both sides from 1/2 to 1 wrt x
oh
oh alr i can get it from there
but bro
i tried sandwhich theorem in a different way
violet mauve
i tried sandwhich theorem in a different way
Yeah tell
spice venture
-1<sin^4t<3
1<2+sin^4t<3
3<1/(2+sin^4t)<1
3t^3<t^3/(2+sin^4t)<t^3
and then i integrated this
will this also work
mortal orbit
Here's a hint that I think could simplify the work (apart from the bounding of f')
Use the MVT on a primitive of f
That gives you $\int_{\frac 12} ^1 f(x)dx =\frac 12 f(c)$ for some $c\in \left(\frac12,1\right)$
violet mauve
will this also work
I mean you can try and see if it matches, I am not sure
potent lotusBOT
Rafilouyear2026
valid linden
i think i have a thought
let g'(x) =192x³/2 be another function, with g(1/2) =0
So like if compare f'x and g'x, well know that g'x is always greater than f'x, right?
if g'(x) is greater than f'(x) then g(x) grows more rapidly then f(x), and thus g(x) covers more area than f(x) {in 1/2 to 1}
Thus we have an upper bound
valid linden
you got it?
spice venture
Thus we have an upper bound
but how do u know that this is a sufficient condition and not a necessary condition?
valid linden
lemme think bro
valid linden
yea yea and in the same way 192x^3/3 will be lower bound
ya
spice venture
mb
spice venture
Use the MVT on a primitive of f
oh sorry bro im not so good with mean value theorem..i u nderstood what u said but not what to do with it
mortal orbit
oh sorry bro im not so good with mean value theorem..i u nderstood what u said b...
Once you have that information
valid linden
but how do u know that this is a sufficient condition and not a necessary condit...
i dont know how to prove that, it just came from intuition
mortal orbit
You just have to bound f(x) for x between 1/2 and 1
You know that $f(x) = \int_{\frac 12}^xf'(t)dt$
potent lotusBOT
Rafilouyear2026
valid linden
:)
mortal orbit
It's probably not the best bounds ever, I think the lower bound will be a bit inefficient, but you might get your answer with the upper bound
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last dome
Is the frequency of sine function defined by number of cycles per radian or number of cycles in 2pi ?
thorny stump
The number of radians per cycle
Sorry, you said frequency, so cycles per radian indeed
(a cycle is 2pi)
last dome
so for y=sinx, what's the frequency? Is it not 1?
thorny stump
In what unit are you measuring frequency?
main compass
frequency can be cycles per time or cycles per usual period of sine, I suppose.
thorny stump
Frequency is typically defined as some number of events per unit of time
In maths, we say y = sin(x) has a period of 2pi because the function repeats every 2pi units in x
Since frequency is synonym with 1/period, it would be 1/(2pi)
last dome
Frequency is typically defined as some number of events per unit of time
so it's number of cycles per period?
last dome
wdym 
thorny stump
In what context are you asking this?
last dome
let's say the period is pi, so the frequency would be 1/pi ...so frequency is number of cycles per period?
valid linden
i dont think frequency is even defined for y=sin(x) (if x an y are not time)
like frequency means how frequent an event is occuring
main compass
typically in cases like this frequency is implicitly 1/period.
valid linden
oh alr thnks
last dome
typically in cases like this frequency is implicitly 1/period.
in that case, for y=sinx the frequency is 1/2pi?
not 1?
main compass
let's say the period is pi, so the frequency would be 1/pi ...so frequency is nu...
cycles per period... kinda makes no sense or sounds redundant.
by definition, the period of a sinusoidal function is the distance between the starting points of two consecutive cycles, so by this definition a period always contains one cycle, period.
main compass
in that case, for y=sinx the frequency is 1/2pi?
I would say that is the frequency, yes, if there is no other context.
if there is, please reveal it now.
last dome
no it is just y=sinx
main compass
I know, but y = sin(x) is so generic an equation you would be able to see it in engineering, physics, computer science, math, etc.
depending on where you found this equation, there can be extra context to it.
last dome
it's in math
main compass
that's why helpees are encouraged to show full context if there is one.
last dome
cycles per period... kinda makes no sense or sounds redundant.
by definition, th...
so should I say, frequency is number of cycles per length/distance?
main compass
I'm not sure if I agree but I can't think exactly of why I disagree, so in the interests of not saying something horribly wrong, I will defer to future helpers. sorry.
calm coralBOT
@last dome Has your question been resolved?
slender socket
How can the derivative of 1/x^2 be positive everywhere except zero. I know that second derivative is positive everywhere except zero but if you look at the graph for x>0 the function is decreasing so the derivative must be decreasing
burnt ocean
The derivative is not +ve
pallid halo
indeed it's not
burnt ocean
In +ve x axis
old falcon
How can the derivative of 1/x^2 be positive everywhere except zero. I know that ...
so, youre right to doubt it, i'm curious why you came to that conclusion though.
main compass
could we have the context please?
slender socket
Ok doing number 7
old falcon
x + 1/x^2
main compass
ah there is an extra x!
main compass
okay yeah, fair. my bad.
slender socket
Oh wait no number 6
old falcon
i mean yea, its still not true
can you explain why you think its true, what you claimed, that its positive everywhere
slender socket
6/x^4 is the second derivative
main compass
oh God, is this meant to be 'examine the sign of f'''?
main compass
the font is inconsistent throughout the page. who wrote this??
old falcon
a program, probably
main compass
then it makes sense why OP was examining the second derivative, but makes no sense that they would refer to it as the first....
slender socket
not second derivative
But if the second derivative is positive isn't first deirvative increasing everywhere
old falcon
But if the second derivative is positive isn't first deirvative increasing every...
sure but that doesn't mean its positive
the function -e^(-x) is increasing everywhere and nowhere positive
calm coralBOT
@slender socket Has your question been resolved?
slender socket
the function -e^(-x) is increasing everywhere and nowhere positive
Doesn't that contradict theorem 4.7
old falcon
Doesn't that contradict theorem 4.7
what interval are you imagining?
because if f(x) = x^(-2) then f'(x) isn't continuous 'everywhere'
neither is f(x)
slender socket
what interval are you imagining?
I was thinking of the original problem
old falcon
right so, read the requirements of the theorem you posted
slender socket
Yes so if f'(x)<0 for a certain interval then f is strictly decreasing
For 1/x^2 f'(x) was decreasing from x> 0 and if you look at the graph of f it is decreasing
old falcon
For 1/x^2 f'(x) was decreasing from x> 0 and if you look at the graph of f it is...
this isnt right
for f(x) = x^(-2), for x>0, then f'(x) is negative and increasing
so, for x>0, f' < 0, and we have f decreasing there
slender socket
this isnt right
Doesn't this contract our theorem though?
old falcon
No, it doesnt.
main compass
maybe it helps to separate the concepts of increasing/decreasing from positive/negative if that is the confusion here.
slender socket
No, it doesnt.
How?
slender socket
maybe it helps to separate the concepts of increasing/decreasing from positive/n...
But for 1/x^2 isn't the the part for x> 0 decreasing?
old falcon
But for 1/x^2 isn't the the part for x> 0 decreasing?
it is
and the derivative is negative
main compass
negative but increasing. it starts off with a very steep downwards slope near x = 0, but gets shallower as x grows.
slender socket
negative but increasing. it starts off with a very steep downwards slope near x ...
Wait how is it increasing. Isn't a function increasing if the values get bigger as the inputs get bigger
main compass
oh I mean its derivative is increasing, sorry. not the function itself.
yes, the function itself is indeed decreasing as x grows.
slender socket
Wait I'm confused. Jan said it is decreasing you said it is increasing???
main compass
f is decreasing but f' is increasing. jan said the same thing!
main compass
for f(x) = x^(-2), for x>0, then f'(x) is negative and increasing
he mentioned that f' is negative and increasing here, and in the message after he said that f is decreasing.
which is correct!
slender socket
I'm finished f' is negative. I see that. How can you say it is increasing there?
main compass
negative but increasing. it starts off with a very steep downwards slope near x ...
^
slender socket
Oh I see. Increasing because it starts very negative and becomes less
main compass
or, if you want an algebraic proof, the derivative of x^(-2) = -2/(x^3).
as x grows, this fraction becomes less negative as x dominates. therefore it is increasing.
(for positive x.)
slender socket
Ok so is that why we say that since the second derivative is positive for this function it's first derivative is increasing everywhere
main compass
yes.
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crisp minnow
So my question is how woukd I know I needed to use u=(x^2+9)^1/2 for the first one and not just use u = den for the second one?
teal drift
I'd do x = 3tan(t) for the first integral
In general it is extremely useful to know one of these two:
- cosh²t - sinh²t = 1
- sec²t - 1 = tan²t
velvet osprey
in general btw for a given integral there may be more than 1 technique that works
calm coralBOT
@crisp minnow Has your question been resolved?
crisp minnow
I'd do x = 3tan(t) for the first integral
wHy? As in what does this help with and how did you come to this conclusion
my question answered
teal drift
Sure, that's the reason why
crisp minnow
so like when I would use trig sub vs u sub
teal drift
I thought you had been taught it by your teacher, my bad
crisp minnow
i have not
teal drift
so like when I would use trig sub vs u sub
When you have difference or sum of squares under square roots, trig substitution can be useful
But there's no general rule, and more important, there's usually more than one way of solving an integral
All comes with practice and seeing a lot of already solved examples (such as in YouTube), that can show you the different scenarios
mossy tide
So my question is how woukd I know I needed to use u=(x^2+9)^1/2 for the first o...
For the first one the numerator has a maximum power of 3 and denominators have max of 2 and we doin integration here so we will use x²+something into new variable to solve whole eqn by sub method
Maybe
@crisp minnow did you figure out 2nd one?
crisp minnow
Yes its hyperbolic identity
crisp sphinx
usually when one integrates, they want to try the easiest method first, then the hardest. in my opinion, the order is
u-sub -> trig sub -> integration by parts -> other bs (power series representation, etc.)
because u-sub and trig sub involve substitutions, but reversing a u-sub is generally easier (think about why!)
in the first one, du can easily be cancelled out with the original integrand, so a u-sub is possible. but in the second one, du has 6x in the numerator which won't cancel with anything. then when you go back to find x in terms of u, you end up with an absolute value, which is a mess. thus it's better to do a trig-sub there
someone might disagree with me and say trig sub is easier than u-sub. ultimately it comes down to what you find easier to do
crisp minnow
For this question why do we use the trig identity x=2tanu?
leaden thunder
,rotate
potent lotusBOT
leaden thunder
Because it puts the integral of the form where substitution makes the integral easy to solve
crisp minnow
Because it puts the integral of the form where substitution makes the integral e...
so we the the arctan standard form?
leaden thunder
I don't know what that means
teal drift
i don't think this is trig sub because there's no square root
Noone said there must be square roots for doing trig sub
crisp minnow
Noone said there must be square roots for doing trig sub
i know but its common when it has one
teal drift
Sure
crisp minnow
so the above is the inverse trig formula
teal drift
Inverse tangent, yes
Also known as arctan or tan^-1
That's very common in integrals, so make sure you recognise that each time you see it
crisp minnow
yeah
teal drift
Then no, from my experience they are not common at all, especially the one with arccos
There could be a few times where the one with arcsin is useful, so maybe learn that one
But otherwise no
crisp minnow
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pale prairie
Hi can someone review my proof :) I think i overcomplicated / done it unecessarily
pale prairie
(b) $\mathfrak{P}_\equiv$ is a partition of $X$\
potent lotusBOT
toast
pale prairie
\textit{Proof of (b)}. By definition, $\mathfrak{P}\equiv = {[x]\equiv: x \in X}$, where $[x]\equiv = {y : y \equiv x}$. Now, let $x \in X$ be arbitrarily selected. Observe that $x$ must be in $[x]\equiv$ as $x \equiv x$ by the reflexive axiom of $\equiv$, so every element of $X$ must be in at least one element of $\mathfrak{P}\equiv$. Suppose $x \in [x']\equiv$. Then $x \equiv x' \equiv x$. Now suppose we select $y \in [x]\equiv$. then $y \equiv x \equiv x'$ by transitivity, so $y \in [x']\equiv$, thus $[x]\equiv \subseteq [x']\equiv$. Let $z \in [x']\equiv$. Then $z \equiv x' \equiv x$, so $z \in [x]\equiv$. Thus $[x']\equiv \subseteq [x]\equiv$ so $[x']\equiv = [x]\equiv$. Thus each element $x$ can only exist in at most one element of $\mathfrak{P}\equiv$. Thus each element of $X$ can only exist in exactly one element of $\mathfrak{P}\equiv$, thus $\mathfrak{P}_\equiv$ is a partition of $X$.
potent lotusBOT
toast
calm coralBOT
@pale prairie Has your question been resolved?
elder pawn
\textit{Proof of (b)}. By definition, $\mathfrak{P}_\equiv = \{[x]_\equiv: x \in...
the “at most one” part is not proven correctly
it goes “if two things have the property then theyre equal”
in light of that, you should prove that if x in [y] and x in [z] for some y,z then [y]=[z]
pale prairie
it goes “if two things have the property then theyre equal”
ah
pale prairie
the “at most one” part is not proven correctly
so just out of cuirosity, what would be the biggest mistake in my proof?
i think i approached it wrong, but if you were to like take off points what doesnt make sense
my idea was like if x is in two equvialence classes, then they are the same equvialence class
pale prairie
in light of that, you should prove that if x in [y] and x in [z] for some y,z th...
but ye this makes more sense than what i did
elder pawn
my idea was like if x is in two equvialence classes, then they are the same equv...
its the correct idea but slightly wrong execution
hmm actually im wrong. your proof is correct but uses a ‘less popular’ definition of uniqueness
your question reminded me of my older post which explains two equivalent definitions of uniqueness
i tried enforcing the more popular definition here without realizing that you used the less popular one
translated to your problem, the less popular def goes “x is in [x], and if x is in [y] for some y then [x]=[y]” which is exactly what you proved
calm coralBOT
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calm coralBOT
elder pawn
.reopen
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cunning reef
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cunning reef
i might be missing something, but this seems really easy
by vietas we get c^4 = a^2 =b
then from p(1) = 0 we have c^4 + c^2 + c + 1 = 0
so either c = +-i or c = -1
but c cant be imaginary otherwise its conjugate wont be a root so c = -1?
gleaming cedar
I think you have it
cunning reef
so the sum is 1
gleaming cedar
yea
calm coralBOT
plucky pumice
Is this channel still open to help?
covert thunder
by vietas we get c^4 = a^2 =b
what?
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covert thunder
a^2 = -b + 2b = b and a = c^2
ok that makes sense, but how are you getting c = +-i and c = -1 from c^4 + c^2 + c + 1 = 0
covert thunder
shit
cunning reef
ok that makes sense, but how are you getting c = +-i and c = -1 from c^4 + c^2 +...
oh wait
did i factorize it wrong
;-;
covert thunder
I plugged that equation into wolframalpha and it only has complex roots
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quasi quarry
Does anyone know how to make a delta-epsilom proof on lim_x→0 (1/x)=infinite
robust sedge
Let N > 0 be given, and choose δ such that ..., so that for any 0 < x < δ we have 1/x > N
calm coralBOT
@quasi quarry Has your question been resolved?
obsidian cedar
Requests arrive at an edge server according to a Poisson process with rate 4 requests per second.
- Compute the probability that no requests and exactly one request arrive in 1 second.
- Let T be the time until the next request arrives. Compute P(T > 0.2).
- Compute the probability that at least one request arrives in 50 ms (0.05 seconds).
calm coralBOT
@obsidian cedar Has your question been resolved?
calm coralBOT
@obsidian cedar Has your question been resolved?
calm coralBOT
@obsidian cedar Has your question been resolved?
obsidian cedar
<@&286206848099549185>
ebon vessel
Requests arrive at an edge server according to a Poisson process with rate 4 req...
what’s your definition of a Poisson process?
ebon vessel
hum this does not pin it down much, there are multiple “equivalent” definitions for this thing
k im going to assume it’s this one because it’s one i know and i think it applies best here
obsidian cedar
Yes
ebon vessel
Requests arrive at an edge server according to a Poisson process with rate 4 req...
I think the 3rd bullet in what i just sent allows you to answer 1. and 3.
obsidian cedar
I think the 3rd bullet in what i just sent allows you to answer 1. and 3.
But I don't have to do the exercise in machine mode
ebon vessel
But I don't have to do the exercise in machine mode
well, it's more like once you understand what this property means 1. and 3. are plug and chug questions imo
in these kind of process events can happen at any time on the line (it's "continuous", a subset of R) but if you restrict yourself to counting the events happening in any interval of length t, the number of events will be distributed like a Poisson random variable with parameter \lambda times t
A poisson r.v. make sense because any number of events could happen in the interval {0,1,2,…} and that’s the values a Poisson can take. Further the longer the interval or the higher the rate and the higher the expected number of event in the interval will be because E[Poisson(\lambda t)]=\lambda t
ebon vessel
But I don't have to do the exercise in machine mode
Can you link what I just sent to your problem 1.
calm coralBOT
@obsidian cedar Has your question been resolved?
frozen vortex
hi!!!
zero idea on how to start
calm coralBOT
hi!!!
zero idea on how to start
primal smelt
do you know what a test statistic is?
calm coralBOT
@frozen vortex Has your question been resolved?
cunning robin
hasty fiber
hi!!!
zero idea on how to start
start by stating your null and alternative hypotheses
frozen vortex
start by stating your null and alternative hypotheses
ohh okokok
thank you
.close
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clear elm
How would I prove this?
calm coralBOT
How would I **prove** this?
clear elm
But it's asking to prove the following inequalities for all numbers x, y.
I've proved the previous yet idk really how to encounter this one
This is wjay I thought of doing
But this doesn't really prove it right?
clear elm
Yeah I guess what I did doesn't really help provei t
Hmmm
Yeah idk how to go about this question tbh
keen flower
i think cross-multiplying does it
graceful dust
yea i would just bash some algebra and see what happens if i wasn't sure where to start
clear elm
Yeah but wouldn't that be
Oh wait
keen flower
cross multiply both the hypothesis a/b < c/d and the goal a/b < (a+c)/(b+d), you will see how similar they are
graceful dust
you want to prove a(b+d) < b(a+c). and we also have ad < bc by hypothesis
clear elm
YEah okay I proved it I think
by cross multiplying
You get ab + ad < ba + bc
Where then you can simplify ab and ba
To get ad < bc
Thanks for your help!
.close
calm coralBOT
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steady panther
can someone help me make a kmap
calm coralBOT
can someone help me make a kmap
Asking the actual question right away is more likely to get responses.
Asking "Can I ask...?" or "Does anyone know about...?" doesn't give people enough information to decide whether they can help, and answering can feel like a promise to help with the actual question, which they might find themselves unable to.
steady panther
C
i already simplified it
its the same thing with first term removed
but not sure how to make a kmap out of it
swift laurel
do you need help with constructing the kmap itself or with making groups?
steady panther
constructing
i think i can make the groups but idk how to go about constructing it
i can only make it for basic ones like the first one
swift laurel
can you make a truth table for it?
steady panther
no 😭 I can transfer a truth table to Kmap but for the last one I don't know how to go about making it
for this
swift laurel
if you need to you can make a separate column for parts of the expression and then combine them
steady panther
what does that mean
ok so i tried making a kmap but i'm not sure if this is right
i used demorgans on the first term to get AB' + AC' + AD' + A'B'C'D'
so my kmap is
CD/AB
00 01 11 10
00 1 0 1 1
01 0 0 1 1
11 0 0 0 1
10 0 0 1 1
i think
and i circled top left with top right, bottom two, top four right, and last column
are those the right groupings
wait i just realized
if i circle bottom right two, right column, top four, and top left just by itself it gives me correct answer
i dont get it tho that shouldn't be right
because circling the top left by itself is breaking the rule of trying to get the maximum amount in a circle
calm coralBOT
@steady panther Has your question been resolved?
gusty estuary
because circling the top left by itself is breaking the rule of trying to get th...
1 can be the maximum
steady panther
yeah but in this case you can also go for 2 right? if you wrapped 0000 to 1000
gusty estuary
idk what wrap means
iirc, the circles must have a number of 1's inside that equals a power of two, right?
steady panther
yeah
wrap as in like
the ends can connect right
like the right side technically meets the left and top meets bottom
so top left can connect with top right and form a pair instead of being solo
steady panther
oou i didn't even see the yellow connection
steady panther
yes the deep red
gusty estuary
🙂
steady panther
dark red: notB notC notD
yellow: A notD
green: A notB
orange: A notC
combining yellow green orange gives AB'C'D'
and then you're left with B'C'D' and there's no A'
or did I not do dark red properly
because A changes but B'C'D' don't change
calm coralBOT
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untold thorn
I don't even know what a rank is
I have the solution pdf too. Should I send it?
untold thorn
I can't understand what a rank is after researching and reading about it
limpid lagoon
rank is the amount of "independent information" a system or matrix, etc. has
untold thorn
Like no. of independence between pair of rows or pair of columns?
limpid lagoon
for example if you had a system where you had two equations: x=2 and 2x=4, the rank would be 1 because both give the same answer
pallid halo
probably you should learn what rank is, before attempting to answer a question about rank
see the relevant khan academy video?
calm coralBOT
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tall quarry
I'm going to crash out I don't know how to do ii and iii
calm coralBOT
I'm going to crash out I don't know how to do ii and iii
flat tulip
This is a linear equation so b with just be 1
tall quarry
This is a linear equation so b with just be 1
wait why
flat tulip
wait why
the degree of a linear equation is one
for finding a you can write the given equation in slope intercept form
tall quarry
for finding a you can write the given equation in slope intercept form
do i sub in values of x and y?
flat tulip
Yeah in formula for slope
tall quarry
so does the graph for i still apply
flat tulip
Basically the experiment was one which was supposed to show a linear relation between x and y. Say, voltage and current
there were small innacuracies in reading thats why some of these readings are not aligned with the graph you have drawn
tall quarry
no as in
i need to make y=ax^b in linear
so i did lny=blnx + lna
than my axis's are lny and lnx
flat tulip
I think that you don't need ln for this question
timid pond
Hello
woeful tiger
I think that you don't need ln for this question
it's in the form of a linear equation no?
tall quarry
.close
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pure breach
calm coralBOT
dusky flax
wasnt this an advanced qn 
spice venture
cause each dm is at a different distance and contributes different pressure?
spice venture
wasnt this an advanced qn <:opencry:586078614865444865>
🤔 was it? i dont remember
tbh no idea how to solve it even tho i know u have to integrate
pure breach
wasnt this an advanced qn <:opencry:586078614865444865>
no clue
pure breach
cause each dm is at a different distance and contributes different pressure?
uhh but that doesnt matter? since inside the sphere the layers above R/2 wont contribute any force
and the force applied by the inner part is fixed for a certain m??
spice venture
wait why wont layers above R/2 contribute force?
spice venture
yea exactly
pure breach
wait why wont layers above R/2 contribute force?
shell theorem
pure breach
why R/2 though
oh fuck mb in my workbook its R/2 instead of centre
they ammended it a lil bit
pure breach
tbh no idea how to solve it even tho i know u have to integrate
i get what they assumed but apparently at the surface P=0??
spice venture
i get what they assumed but apparently at the surface P=0??
gravitational COMPRESSION
at surface there is nothing above
to compress it
pure breach
applying weight
why would they apply weight
weight exists due to field
atleast thats what my understanding was
spice venture
like
force is the cause for pressure right
and in this case surrounding particles r giving reaction force
and now if u say that the particles inside r giving reaction force to the surface, i would say yes but its not compression
calm coralBOT
@pure breach Has your question been resolved?
pure breach
and in this case surrounding particles r giving reaction force
?? hmm maybe
dusky flax
? isnt the compression due to the field
yeah
net force exerted by outer shell on the inner sphere is zero but pressure is not zero
pure breach
net force exerted by outer shell on the inner sphere is zero but pressure is not...
oh
aisa hai
dusky flax
like trying to squeeze an iron ball with hands
pure breach
ic
ty
now i get it little little
okay i got it
every layer exerts a different field and hence diff pressure
therefore the pressure of the outer layers has to be calculated using integration
dusky flax
considering a patch of the inner sphere
each of the layers exert a pulling force on the patch which gets balanced by the normal force
pure breach
normals will get involved 
pure breach
therefore the pressure of the outer layers has to be calculated using integratio...
this intuition is correct right
pure breach
considering a patch of the inner sphere
each of the layers exert a pulling force...
the upper layers right
dusky flax
yeah
i think pressure refers to pressure exerted by normal force on the surface of the inner sphere then
wait what
spice venture
i think pressure refers to pressure exerted by normal force on the surface of th...
thats what i was saying..
spice venture
aur karo irodov aur ss krotov
dusky flax
okayy i think i kind of get it
wait i need to draw
yeah i think pressure on the inner sphere is exerted by normal force
topmost layer gets pulled and counters by upward normal force (N1)
middle layer gets pulled (+ pushed down by N1) and counters by upward normal force (N2)
inner layer gets pushed down by N2
remote mural
intereseting
quick talon
Wait did you study gauss’s gravitational theorem ? It makes this much easier
@pure breach
calm coralBOT
@pure breach Has your question been resolved?
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plush kindle
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plush kindle
it is saying that a,x,y,z,b are in AP then x+y+z=15 and if then are in HP then 1/x+1/y+1/z=5/3 then show that a=1 and b=9
I'm sorry for last night, I got sleepy
calm coralBOT
@plush kindle Has your question been resolved?
calm coralBOT
@plush kindle Has your question been resolved?
final flower
it is saying that a,x,y,z,b are in AP then x+y+z=15 and if then are in HP then 1...
So x+y+z=15 and 1/x + 1/y +1/z=5/3. x,y,z in both equation are the same variable, right?
I asked this since last night someone said they're different
plush kindle
In the given question to me says same
@final flower
Should it would be different?
final flower
if x,y,z are and AP and x,y,z are also in HP
Then I don't think there exists such x,y,z in this case
final flower
I dunno, ask the one who made the question
final flower
I wanted to feel this logic actually
x,y,z in AP
x=a-q
y=a
z=a+q
=> y=a=5
Now x,y,z in HP
x=1/(b+p), y=1/b, z=1/(b-p)
1/x+1/y+1/z = 3b = 3•1/5
potent lotusBOT
calm coralBOT
@plush kindle Has your question been resolved?
tall snow
So x+y+z=15 and 1/x + 1/y +1/z=5/3. x,y,z in both equation are the same variable...
Different
calm coralBOT
@plush kindle Has your question been resolved?
hollow totem
What is the average of a and b?
umbral gorge
What is the average of a and b?
!help
calm coralBOT
What is the average of a and b?
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
hollow totem
proud light
Idk
plush kindle
.close
calm coralBOT
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frigid aurora
My bad
calm coralBOT
frigid aurora
.close
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radiant notch
So like. I got a test tmrw about thales, but theres this figure that i NEED to know how it works. (I cant use my notebook cuz it somehow isnt explained. Could someone please help? I recreated the question on paint from memory and i need to calculate (RO) PLEASE
radiant notch
oh
alpine cobalt
Is that a random line in OP?
radiant notch
i forgot to add a letter
steep zinc
THALES
radiant notch
Is that a random line in OP?
its like KP
steep zinc
Bruh lemme do something
oh okay
steep zinc
helper enthusiasist im see
steep zinc
didnt know math community was THIS exited
-# oh that's only me
alpine cobalt
2 is better than one tho
No its not, there was chaos
alpine cobalt
Ok so iguess OTP is 90
steep zinc
didnt know math even HAD a community
you're in one
radiant notch
anyways, i need help
alpine cobalt
Right?
steep zinc
steep zinc
anyways, i need help
-# everyone knows that
alpine cobalt
<:opencry:586078614865444865>
Go back
radiant notch
Ok so iguess OTP is 90
what
alpine cobalt
Right
radiant notch
do I have to use the angle ?
steep zinc
So like. I got a test tmrw about thales, but theres this figure that i NEED to k...
what's the green part, i need to know that
i think this lacks some measurements
alpine cobalt
How is K defined
radiant notch
what's the green part, i need to know that
imagine a "K" next to the P
radiant notch
How is K defined
KP
alpine cobalt
Yea but is there anything specific
steep zinc
like, that kinda lacks some information here
radiant notch
Yea but is there anything specific
RS is parallel to TP
alpine cobalt
Yea
radiant notch
its 2.4
alpine cobalt
Bruh
radiant notch
sorry, i dont think theres much
steep zinc
try to remember again
alpine cobalt
Yea
radiant notch
i dont think theres anything else with KP
alpine cobalt
then its literally unsolvable
steep zinc
as im guessing, if we let Q be the intersection of OP an RS, KP = PQ?
alpine cobalt
maybe
steep zinc
i think that's what the KP is for
radiant notch
i dont think theres a Q in the figure
alpine cobalt
bruh
steep zinc
i dont think theres a Q in the figure
read again
alpine cobalt
xd
radiant notch
as im guessing, if we let Q be the intersection of OP an RS, KP = PQ?
brb
alpine cobalt
is this calculus?
radiant notch
im fucking lost
alpine cobalt
xD
steep zinc
E is the intersection of the 2 lines
alpine cobalt
when did you pull out geogebra xD
alpine cobalt
xD
radiant notch
so like the intersection is the "perpendiculaire"?
radiant notch
E is the intersection of the 2 lines
is this considered as comedy for mathers?
steep zinc
is this considered as comedy for mathers?
no?
alpine cobalt
i like to laugh
alpine cobalt
im in 3e btw
what is 3e
radiant notch
what is 3e
when youre 41 yo
alpine cobalt
???
radiant notch
backwards
forest pulsar
hello
alpine cobalt
-# NOOOOOOOOOOOO
steep zinc
?
radiant notch
can yall PLEASE help me make it solvable?
alpine cobalt
cannot help
radiant notch
awh
steep zinc
why did the role change color xD
you really have to ping the mods for that?
calm coralBOT
@radiant notch Has your question been resolved?
calm coralBOT
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zinc condor
Hi. The question asked us to find the orthogonal trajectories of the familiy of curves x=k*y^2, where k is an arbitrary constant. I approached the problem as shown in the picture, but the correct answer is x^2 + 1/2+y^2 = c. I dont undesrtand why my answer is wrong, I found a family of curves p, orthogonal to the intial curve
zinc condor
Hi. The question asked us to find the orthogonal trajectories of the familiy of ...
Does a single curve from the orthogonal family of curves need to be orthogonal to all the intial curves at once, not only to one, is that the problem?
rustic osprey
Hi. The question asked us to find the orthogonal trajectories of the familiy of ...
The curve needs to be perpendicular at every curve that it intersects at the point of intersection. But $k$ varies for these curves (you treated it as a constant).
potent lotusBOT
Civil Service Pigeon
calm coralBOT
@zinc condor Has your question been resolved?
zinc condor
The curve needs to be perpendicular at every curve that it intersects at the poi...
Okay, I get that I found the orthogonal family of a single curve
But then how do I get the family whose curves are orthogonal to all the initial curves?
calm coralBOT
@zinc condor Has your question been resolved?
leaden thunder
But then how do I get the family whose curves are orthogonal to all the initial ...
You need to show your definition of orthogonal for functions
plush kindle
calm coralBOT
plush kindle
if I replace y=mx
we get x.mx
√x^2|m|
so it depends on m hence i can say that it is not differentiable
atomic flare
the easiest thing to do is verify the cauchy-riemann equations
so i would do that first
i dont exactly remember what they are
atomic flare
so it depends on m hence i can say that it is not differentiable
fun fact: even without the |m| that is still not differentiable at x=0
plush kindle
.close
calm coralBOT
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Available help channel!
teal moss
Why is the s(t) graph connected at t=30 here?
calm coralBOT
Why is the s(t) graph connected at t=30 here?
teal moss
is s not supposed to be 360 not 180 here?
jolly pilot
Why is the s(t) graph connected at t=30 here?
wdym why is s(t) connected? the graph ofc has to be continuous
your car doesnt teleport itself
finite oasis
,w 1/5 * 30^2 = 12*30
potent lotusBOT
jolly pilot
there is a +c in the integration thats missing there. An appropriate choice of c would be necessary for you
calm coralBOT
@teal moss Has your question been resolved?
golden quest
$|x-2| = \frac{1}{|x-2|}$
calm coralBOT
$|x-2| = \frac{1}{|x-2|}$
potent lotusBOT
Hurbet IV
golden quest
i was able to solve this however my teacher only gave me 3/4 marks
velvet osprey
i was able to solve this however my teacher only gave me 3/4 marks
show your solution so we can see where you may have lost a mark
also do you have the mark scheme on hand
golden quest
sorry i have no marking scheme but he did write what i was missing on the test
velvet osprey
ok so show the solution and his comment
golden quest
i dont have the test rn but this is essentially what i did
i solved it in two ways just to make sure
his comment was "DOMAIN" in a large circle in red
:D
🙂 🔫
the rejection part was written out fully on the test
i just couldnt be bothered on latex
velvet osprey
maybe he docked you a mark for treating x=2 as a valid x value to plug in instead of declaring x can't be equal to 2?
calm coralBOT
@golden quest Has your question been resolved?
golden quest
maybe he docked you a mark for treating x=2 as a valid x value to plug in instea...
mm i did kind of prove that
x = 2 is invaluid
with the working out beneath it no?
maybe u are right
stating that $x \neq 2$ is probably very importabnt
potent lotusBOT
Hurbet IV
barren plover
what is the meta theory we use in mathematical logic. i am now taking the course and we have used the axiom of choice a few times but we want to show something like compactness about models that not necessarily satisfy the axiom and yet we use it as part of something more basic.
i have taken set theory last year but when defining the axiom we used first order logic (for example the axiom replacement we used a property), yet now to define the logic we use set thoery, why does it work?
calm coralBOT
what is the meta theory we use in mathematical logic. i am now taking the course...
@barren plover Has your question been resolved?
calm coralBOT
@barren plover Has your question been resolved?
calm coralBOT
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plush kindle
main kraken
Hello,
My sibling is in 10th Grade, and still struggling with Geometry, which geometry book is best for it, because there are soo many options and ratings are also very low, which book is also available an e-book form.
fleet raven
Are you sure they need a full book solely for geometry? I would recommend Gelfand's Geometry or Lang & Murrow High-School Geometry
These are good for in depth understanding of the subject, if you're looking for questions and application worksheets then you should go on brilliant learning and check out some of the mathematics past papers--they have some very good geometry questions in them
calm coralBOT
@main kraken Has your question been resolved?
frank flower
how
clear delta
$s^2 - 7sc + 12c^2 < 0$ 🤔
potent lotusBOT
schrödinger's kitten
frank flower
$s^2 - 7sc + 12c^2 < 0$ 🤔
idk what to do here
half trench
you could probably get it all in terms of sin2x
clear delta
looks kinda like a quadratic to me
frank flower
you could probably get it all in terms of sin2x
so i make sinxcosx into sin2x?
is that how it works
half trench
so i make sinxcosx into sin2x?
it might actually be better to make it all cosx or sinx
because cos^2x+sin^2x=1
clear delta
i kinda feel like you can just factor ti
frank flower
it might actually be better to make it all cosx or sinx
but i'm confused on the step
like what do i do first
half trench
i kinda feel like you can just factor ti
actually yeah because its in the form of a binomial expansion
half trench
like what do i do first
think about what (x+y)^2 is
frank flower
think about what (x+y)^2 is
yeah i see it
i'm so dumb bro
but it still has 7 and 12
frank flower
(sinx-cosx) squared?
half trench
ok then think of it as x^2-7x+12
no what is this factorised
frank flower
no what is this factorised
i actually can't figure it out
how do you factorize this
half trench
what 2 numbers add to -7 and multiply to 12
frank flower
3 and 4?
half trench
yeah -3 and -4
frank flower
idk how to factorize hold up
half trench
so its (x-3)(x-4)
frank flower
now i see it
half trench
yeah so you just substitute x for sinx and put cosx as the other term in the binomial
frank flower
so it turns into just (x-3)(x-4) or do i have to add sin and cos squared too?
so it's (sinx-3)(cosx-4)?
half trench
no the form is (sinx+acosx)(sinx+bcosx)
frank flower
no the form is (sinx+acosx)(sinx+bcosx)
wait how i am so confused
half trench
if this was (sinx+cosx)(sinx+2cosx) for example
it would expand to be sin^2x + 2cosxsinx + cosxsinx + 2cos^2x
which is sin^2x + 3cosxsinx + 2cos^2x
do you see the pattern
half trench
no the first item in each bracket is sin
the second is cos
thats the point
so youre close
half trench
and thats just less than 0
frank flower
so it's done here?
half trench
you need to take each bracket and find the boundaries of x
half trench
if (sinx - 3cosx)(sinx - 4cosx) = 0 then you can take each bracket separately equal to 0 and find x
frank flower
i get that but idk how to countinue further i got sinx-3cos<0 and sinx-4cos<0
is it sinx<3cos?
and the same for other one
half trench
ye
frank flower
so x=(3cos,4cos)
frank flower
so i square it
and turn sinx into 1-cosx squared
and then from there 1=10cosx squared
and after cosx=+-1/rooting10
half trench
yes
half trench
do it for both brackets
and make sure you get the right angle domain
think about the unit circle for that
yeah this is a tough question
clear delta
it's an involved question with a lot of subcomponents
frank flower
it's an involved question with a lot of subcomponents
i saw it
full arrow
how to solve this monstrosity? i dont know, this is in indonesia
calm coralBOT
Available help channel!
solid marten
lol 😂 how do i solve this
calm coralBOT
lol 😂 how do i solve this
thorny stump
Trigonometry
solid marten
yes i know. theres an angle so...
thorny stump
An angle is not the only thing you need to apply trigonometry
You need a triangle, preferably right-angled
solid marten
yes i see that
thorny stump
Mark the center of the large circle and try joining points to get a right triangle
(btw they most likely mean that the "point on the small circle" is also on the segment joining the two circle centers, otherwise this question has no single solution)
velvet osprey
is it just me or is the problem underspecified
thorny stump
It is, hence my remark
solid marten
ah the thing is realistically this should be fairly below my level yet im struggling with this 😂 smh
solid marten
what abouyt this ?
thorny stump
Looks correct
solid marten
Looks correct
how do I know its not like this? it depends on where the tangent touches the circle surely?
<@&286206848099549185>
desert relic
yeah looks right
solid marten
smh man what one
i got two different "looks correct" both for different solutions
what one is correct and what one isnt? and furthermore why
is it because i can not assume that the tangent lines touch the large circle directly beneath the centre of the large circle?
desert relic
oh wait no
desert relic
what abouyt this ?
how can this work
solid marten
lol 😂 how do i solve this
i have no clue. this is all the information given in the question. I dont remember any circle theorem so just trying to analyse it using trig and hoping i dont need circle theorems.
desert relic
opposite tangents can only be mutually at 90 degrees to the centre when they're parallel lines
opposite as in originiting from the same place
desert relic
what abouyt this ?
like here, the tangent can only be the hypotenuse if the point was at infinity
solid marten
the tangent line cant be the longest length then when we have 2 tangents originating from the same place intersecting a circles circumference?
desert relic
what abouyt this ?
O cannot be the centre of the circle, you basically have to make another triangle which goes from that chord to the centre
desert relic
like basically if you draw a chord connecting these two tangent points
solid marten
yeah ngl i appreciate u bro but u have lost me
where can i find online a rigorous explanation for this all
scarlet magnet
yeah ngl i appreciate u bro but u have lost me
-# so find yourself... 🗣🔥
scarlet magnet
What are u tryna find?
desert relic
yeah ngl i appreciate u bro but u have lost me
yeah I'm sorry man, am not at my best right now
solid marten
lol 😂 how do i solve this
@scarlet magnet original question is here
solid marten
yeah I'm sorry man, am not at my best right now
nah mate i wasnt trying to insult you dont apologise lol honestly its not like you havent given me things to think about and lookup 😂 its chill thanks man
scarlet magnet
lol 😂 how do i solve this
Lemme get a paper, doesn't seem too bad. One sec
@solid marten this is what I'm getting
scarlet magnet
<@1290318450220335188> this is what I'm getting
,rotate
potent lotusBOT
