Thank You for your help. I'm understanding is as best I can. It's hard to grasp sometimes.
#help-10
wise hedge
I have a question about the Greek letter Theta specifically but the whole Greek alphabet in general. Regarding the letter Theta, for exampe, I've seen the letter Theta written as a zero with a horizontal line through the middle. Sometimes It extends outside the zero and sometimes it only approaches the bounds of the zero. Is there a precise way to draw these symbols?
obtuse pebbleBOT
I have a question about the Greek letter Theta specifically but the whole Greek ...
static beacon
$\theta$
warm shaleBOT
Mortta
static beacon
$\Theta$
nocturne minnow
I have a question about the Greek letter Theta specifically but the whole Greek ...
No
warm shaleBOT
Mortta
nocturne minnow
As long as it gets the point accross
wise hedge
Ah, okay, but that makes 3 ways It's been drawn. Horizontal line extends through, extends to, and falls short of.
static beacon
nocturne minnow
Ah, okay, but that makes 3 ways It's been drawn. Horizontal line extends through...
One upper case
And lower case
The most common used the lower case one
static beacon
Top is upper bottom is lower
wise hedge
Okay, that explains 2 of them.
wise hedge
The horizontal line extends through the boundaries of the circle.
Okay, I've seen it but good enough. Thank You again.
.close
ruby shadow
Is there a kinematic equation for determining when an object has to stop?
ruby shadow
I have for finding the time it takes for reaching a certain point:
delta x = v0 t + 1/2 a t ^2
and how my equation looks for this is
d = 0 * 2.88 + 1/2 * 3.12 + 2.88^2
and I got 12.939264
how would I use this (or another equation) to find the distance that I have to stop breaking if
tardy epoch
Is there a kinematic equation for determining when an object has to stop?
What's the definition of stop
ruby shadow
What's the definition of stop
reach a velocity of 0
nocturne minnow
What's the definition of stop
The opposite of go
ruby shadow
but is there a formula for this?
me and a couple of people have been trying to figure it out
teal turret
Can u show the full problem
Vf = vi + at may help ?
But it’s tough to say without context
nocturne minnow
Those are the primary kinematic equations
tardy epoch
reach a velocity of 0
Use one of the equations dld sent and solve for v=0
That's your equation
static beacon
but is there a formula for this?
Would a have to be negative?
nocturne minnow
That depends on the context
teal turret
Can u send the problem
obtuse pebbleBOT
@ruby shadow Has your question been resolved?
ruby shadow
Can u send the problem
Well I am solving it this way: delta x = initial velocity (9, max speed of robot = 9 ft/sec) *time (-2.88, time to slow down) + 1/2 * -3.12 (slowing down, loosing velocity) * -2.88^2
teal turret
I have for finding the time it takes for reaching a certain point:
Wdym by certain point? Is it a specific distance?
teal turret
Im still unsure as to what you’re trying to do
teal turret
how would I use this (or another equation) to find the distance that I have to s...
What does this mean
ruby shadow
Im still unsure as to what you’re trying to do
Ok so I am trying to find the distance of which I need to start breaking inorder to reach a velocity of 0
teal turret
You can start braking at any distance and eventually reach a velocity of 0, right? What’s the constraint
Again, is there an actual textbook problem this is based on? I still feel there’s missing context
obtuse pebbleBOT
@ruby shadow Has your question been resolved?
ruby shadow
Again, is there an actual textbook problem this is based on? I still feel there’...
No there is is not a textbook problem. I am doing this for the robotics team
.close
elfin burrow
how can there be infinitely many graphs with a finite number of vertices?
obtuse pebbleBOT
how can there be infinitely many graphs with a finite number of vertices?
@elfin burrow Has your question been resolved?
obtuse pebbleBOT
@elfin burrow Has your question been resolved?
glossy basalt
just passing by
"non simple graphs?"
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
shadow lava
obtuse pebbleBOT
shadow lava
How would you personally go about factoring this? Would it involve moving -y^2 to be the last term in the denominator? Or doesn’t really matter
high lily
if it makes you feel more comfortable
shadow lava
if it makes you feel more comfortable
I’m actually not sure how to do it with this one.. as far as I can tell only the denominator can be factored
high lily
for convenience lets do \
moving $-y^2$ to be the last term \
to get an order you're more used to
$$2x^2 + xy - y^2$$
warm shaleBOT
ℝamonov
high lily
diamond method or whatever method of factorisation you'd use can still be applied here
view this as a quadratic in x
and you can treat y as a constant
identify the pair of values that multiply to -2y^2
and sum to y
its not that much different to factorising
$$2x^2 + x - 1$$
where you'd find the pair that multiply to -2 and sum to 1
meager mantle
are u sure the numerator of 7x+y isnt 7(x+y)?
warm shaleBOT
ℝamonov
meager mantle
are u sure the numerator of 7x+y isnt 7(x+y)?
bc if it is, itll be hella easier
shadow lava
diamond method or whatever method of factorisation you'd use can still be applie...
I solved with diamond but it was strange with the y, I’m not used to that
And normally i don’t want ^2 as last term
First term only
shadow lava
shadow lava
identify the pair of values that multiply to -2y^2
and sum to y
Thank you!
nocturne minnow
You realized, I think it was mentioned, you didn't have to factor. I was already given to you factored
shadow lava
You realized, I think it was mentioned, you didn't have to factor. I was already...
With the numerator added
Interesting how the denominator ended up being the exact same like that
nocturne minnow
Because the denominator was already factored
You never needed to expand the denominator
shadow lava
😂
“Simplify the expression”
// Proceeds to break it down and build it back up again
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
lunar summit
How can I isolate this diagonal square of values from a matrix
obtuse pebbleBOT
How can I isolate this diagonal square of values from a matrix
obtuse pebbleBOT
@lunar summit Has your question been resolved?
karmic hedge
obtuse pebbleBOT
https://gyazo.com/ed2a3597fbfe1053bd4dcfb3050c924f?token=4a4bc269cdbf32e364c8705...
karmic hedge
I know that they are laws of identity but Idk what they are equal to
royal basin
they are not called identity
if you can't figure out what p & F is equal to, make a 1-atom truth table to remind yourself
likewise for p or T
royal basin
yes, but the ones fpr p & F and for p or T aren't called identity laws, they're called something else
if you can't figure out what p & F is equal to, make a 1-atom truth table to remind yourself
karmic hedge
Ok thx I had never heard of that
so for the question I say "Based on the fact that T or p = T and F and p = F for all values of p these are in fact laws"?
obtuse pebbleBOT
@karmic hedge Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
chrome star
Okay I'm getting frustrated now, I keep getting stuck can someone help me again I'm sorry
obtuse pebbleBOT
Okay I'm getting frustrated now, I keep getting stuck can someone help me again ...
chrome star
timid silo
Hmm
royal basin
is this the original problem?
chrome star
Yes
timid silo
I think you are over complicating it a bit
royal basin
yeah you are making your life more complicated than it needs to be
chrome star
:sobb
royal basin
rationalize before adding
chrome star
Ohh
But I thought it's not allowed
Because my teacher told me to do that
Okay I'm mad at my teacher
royal basin
your teacher specifically told you NOT to rationalize before adding?
timid silo
That's so weirdly specific... There is no way
royal basin
it is never 'not allowed' to rationalize a fraction's denominator.
chrome star
He didn't say that it's not allowed but when my classmate solved it on the board and rationalized it, the teacher stopped him there
And said that it should be this and that
Idk maybe he's breaking it into pieces
timid silo
Well your teacher is being ooga booga
royal basin
He didn't say that it's not allowed but when my classmate solved it on the board...
maybe your classmate screwed up in some way but it was execution and not planning?
royal basin
$\frac{\sin(7\pi/4)}{1 + \cos(7\pi/4)} + \frac{1 + \cos(7\pi/6)}{\sin(5\pi/3)}$
warm shaleBOT
Ann
timid silo
Yeah just do the series of annoying algebra
chrome star
But I tried to photomath it
royal basin
just to make sure, have i transcribed the problem correctly?
chrome star
just to make sure, have i transcribed the problem correctly?
Yes
chrome star
But I tried to photomath it
It showed a different answer
chrome star
royal basin
same thing.
royal basin
(6 - 2sqrt(3))/3 = 2 - 2sqrt(3)/3
chrome star
Ohhh
timid silo
Added the fractions
chrome star
Oh I'm sorry I'm dumb
timid silo
It's okay, no need to call yourself dumb over that lmao
kind bison
A chess player entered a chess tournament with 12 rounds. In how many ways can he finish the
tournament with 7 wins, 2 draws, and 3 losses?
obtuse pebbleBOT
A chess player entered a chess tournament with 12 rounds. In how many ways can h...
drifting wraith
you divide 12! by 7! and 2! and 3!
alternatively you choose 3 losses out of 12 and choose 7 wins out of 9 remaining
kind bison
So 12!/(7!)(2!)(3!)
drifting wraith
yes
kind bison
ok tysm
turbid wing
alternatively you choose 3 losses out of 12 and choose 7 wins out of 9 remaining
but there's the possibility of draws too so we would need make many cases for that
your first method is better
drifting wraith
i think you're making things up
it's the same method, it's maybe faster to think of
turbid wing
oh yes it gives the same answer
kind bison
how do you solve problems like that
turbid wing
really sorry
kind bison
but different situations
kind bison
cause im confused on how to do problems about permutations
turbid wing
cause im confused on how to do problems about permutations
the most basic way is too brute force and make cases. But this problem was same as "How many distinct words can you make from 7 A's , 2 B's and 3 C's ?"
karmic hedge
obtuse pebbleBOT
https://gyazo.com/555153caa03de01dcc91e8c90eadb059?token=c7f94200ab30170d9575e50...
karmic hedge
Im confused about b)
I know that p → q = ¬p V q but Idk the name of that law
is it even a law?
deft gust
I am not entirely sure, but if you negate it twice, shouldn’t you be able to obtain it? Because the negation of p implies q is p and not q
karmic hedge
I am not entirely sure, but if you negate it twice, shouldn’t you be able to obt...
I dont really understand, which rule? The rule of negation wont change the operator..
deft gust
I haven’t learn this math in school, so I don’t know. But if there is a law where the negation of p implies q is p and not q, then you can apply de Morgan’s laws to obtain not p or q
karmic hedge
hmm yes that would solve it I just dont know the name of the law that changes p → q to ¬p V q
deft gust
Does that have a name in itself?
karmic hedge
Im not sure, I know that its a logical equivalence
obtuse pebbleBOT
@karmic hedge Has your question been resolved?
obtuse pebbleBOT
@karmic hedge Has your question been resolved?
misty iron
I know that p → q = ¬p V q but Idk the name of that law
Yeah, it is not a law it is just a logically equivalent statement. You can say that we use the inversion law once we write the ¬p → q = ¬(¬p) V q
candid dome
I know that p → q = ¬p V q but Idk the name of that law
i think they call it the equivalence law/ relation
obtuse pebbleBOT
karmic hedge
.reopen
obtuse pebbleBOT
✅
karmic hedge
so I got:
(¬p) → q ≡ (¬(¬p)) ∨ q equivalence law
≡ p ∨ q double negation
Is this correct?
candid dome
Is this correct?
yup
timid silo
wooo
sleek fulcrum
obtuse pebbleBOT
sleek fulcrum
How do I find tan tan 46 in terms of K?
atomic bobcat
i think ur tan 44 is wrong
atomic bobcat
that's correct
sleek fulcrum
how do i solve tan tan 46 from here?
feral sentinel
obtuse pebbleBOT
feral sentinel
yes
royal basin
also what's lg? is it log_10 or log_2?
feral sentinel
err lemme write it down cant visualize lol
royal basin
f_3(n) = n^3 * (partial sum of a convergent series) = O(n^3)
feral sentinel
is a partial sum an arthimetic series
royal basin
no
warm shaleBOT
feral sentinel
oh lol
feral sentinel
f_3(n) = n^3 * (partial sum of a convergent series) = O(n^3)
wait how did u know that this is a partial sum
royal basin
it's n^3 sum[i=1, n^3] i/3^i
and i can tell you that sum[i=1, infty] i/3^i is convergent, though it would take some work to find what to
warm shaleBOT
royal basin
log_n(n!) = log(n!)/log(n) ~ (n log(n) - n - 1/2 log(2pi n))/log(n) by stirling
feral sentinel
,w stirlings approximation
royal basin
lol
feral sentinel
i wanna see the meth 
royal basin
you can look it up on wikipedia
feral sentinel
,w stirlings approximations formula
warm shaleBOT
Requested by HellO#6239
feral sentinel
okay
royal basin
your thing should be O(n)
the factorial one
ish
er
O(n) for just the log factorial
so O(n^3)?
feral sentinel
log_n(n!) = log(n!)/log(n) ~ (n log(n) - n - 1/2 log(2pi n))/log(n) by stirling
easier reference
feral sentinel
so O(n^3)?
ah yes i got this
i cant do anything to f_4 right?
so jsut O(n * log(log(n)))
okay got it
royal basin
incorrect
nobody said f'(x_0) had to exist
it may not
yes
no, differentiability at one point doesn't imply differentiability in a neighborhood thereof
ah wait hold on
hm. hold up. yeah. i think we only need differentiability at x0.
haughty coyote
hm. hold up. yeah. i think we only need differentiability at x0.
It's sufficient to do a proof by contradiction if f'(x0) != 0
royal basin
haughty coyote
No
royal basin
no, differentiability at one point doesn't imply differentiability in a neighbor...
.
also the word 'holds' does not belong there
you are confusing definedness with differentiability...
haughty coyote
You can make f be approximately a line near x0, but make it jagged everywhere else in a way that prevents differentiability anywhere else, but is small enough to still allow differentiability at x0
royal basin
there's this famous function called the Weierstrass function, which is notable for being continuous everywhere but differentiable nowhere.
the function f(x) = x * W(x) will be differentiable at 0 and nowhere else.
novel knoll
it doesn't even have to be continious in any interval around x_0
royal basin
there's this famous function called the Weierstrass function [which i denoted W(x)], which is notable for being continuous everywhere but differentiable nowhere.
the product rule doesn't apply.
yes f'(0) = W(0) but no it's not by the product rule.
novel helm
I need help in finding the collinear of this
obtuse pebbleBOT
I need help in finding the collinear of this
iron crypt
Hello guys,
Could you help me with this problem. I have already used the Cramer' s method but i got wrong results.
Thank you in advance.
royal basin
@iron crypt this channel is occupied, please open your own. see #❓how-to-get-help for instructions
sour jasper
I need help in finding the collinear of this
If P, D, and H are collinear, what does that say about the slope of line DH versus the slope of line PD?
novel helm
I dont know?
sour jasper
For P, D, and H to be collinear, they must lie on the same line. So, lines PD and DH are the same line.
sour jasper
Do you remember the slope formula?
novel helm
y=mx+b
or m= rise/run
The problem I face here is that they just gave me this question before discussing it in class
and this is the last question I have
frozen rune
I need help solving this, using either Fermat or Euler
obtuse pebbleBOT
I need help solving this, using either Fermat or Euler
frozen rune
$37^{ 8442126}-1 \mod 49$
warm shaleBOT
Hek
frozen rune
Without the minus 1 I would probably get it right, but I don't know how to deal with the -1 in the conversion.
royal basin
just calculate 37^8442126 mod 49 and then subtract 1...?
frozen rune
Oh, as simple as that ? I know that a * b mod x is the same as a mod x * b mod x, but did not know how to deal with minus and plus
Would someone be so kind and tell me the result, just to check if I am right? Or possibly provide an online calculator for such tasks?
.close
prime yacht
How do I eval $sin(\frac{\pi}{3})$ without a calc
obtuse pebbleBOT
How do I eval $sin(\frac{\pi}{3})$ without a calc
warm shaleBOT
OceanBro
timber fox
unit circle
prime yacht
do I need to know the unit circle or somethin?
we haven't learnt that yet @timber fox
timber fox
learn it then
prime yacht
Wait, but if we haven't learnt it yet (it's going to be soon), wouldn't it want us to use some other method of evaluating
Cuz we haven't learnt the unit circle yet, so I'm assuming we don't use the unit circle here
timber fox
you can play around with angles on the x axis
vagrant magnet
how do i find c, apparently its -2/3 i am getting 2/3
obtuse pebbleBOT
how do i find c, apparently its -2/3 i am getting 2/3
whole dock
it actually can be both
whole dock
if we multiply -1 with itself what do we get?
whole dock
is it 2 in the numerator
vagrant magnet
v > 0 btw
woeful cove
Doesn't matter.
sage geode
$$v = \frac{4}{(\lambda{t} - c)^2}$$
$$(\lambda{t} - c)^2 = \frac{4}{v}$$
$$\lambda{t} - c = \pm\frac{2}{\sqrt{v}}$$
$$c = \lambda{t} \pm \frac{2}{\sqrt{v}}$$
warm shaleBOT
A Lonely Bean
vagrant magnet
ik that
vagrant magnet
what about this
what about this, i just solved a differential eq to get this
woeful cove
Mind giving me more context/ the question itself?
sage geode
Doesn't matter.
Matters as it ensures existence of the square root though
vagrant magnet
if v > 0 then it is only 2 / sqrt(v) then no plus minus?
sage geode
There can be minus in front of the sqrt
woeful cove
Matters as it ensures existence of the square root though
Well we know it's "equal" to nine so does it really matter
obtuse pebbleBOT
@vagrant magnet Has your question been resolved?
vagrant magnet
how do i find c, apparently its -2/3 i am getting 2/3
how do i get that in this form
if c = -2/3
?
obtuse pebbleBOT
@vagrant magnet Has your question been resolved?
obtuse pebbleBOT
@vagrant magnet Has your question been resolved?
prime oracle
What is the sum of all quadratic residues (between $1$ and $100$) modulo $101$?
It's equivalent to : $x^2\equiv{a}[101]$
•We know that we have exactly:
$$(\frac{101-1}{2})=50$$ quadratic residues .
So what about the sum ?
obtuse pebbleBOT
What is the sum of all quadratic residues (between $1$ and $100$) modulo $101$?
...
warm shaleBOT
Pierre de Fermat
timid silo
hint: -1 is a square mod 101
obtuse pebbleBOT
@prime oracle Has your question been resolved?
prime oracle
hint: -1 is a square mod 101
$x^2\equiv{-1}[101]$ ?
warm shaleBOT
Pierre de Fermat
timid silo
yeah
prime oracle
But how can I do that with the sum ?....
timid silo
if $a$ is a square, what do we know about $-a$?
warm shaleBOT
Toby
prime oracle
This the ... quadratic residues...?
prime oracle
\pmod{101}$$$$2^2 \equiv 4 \equiv -97 \pmod{101}$$$$3^2 \equiv 9 \equiv -92 \pmod{101}$$$$4^2 \equiv 16 \equiv -85 \pmod{101}$$$$5^2 \equiv 25 \equiv -76 \pmod{101}$$$$6^2 \equiv 36 \equiv -65 \pmod{101}$$$$7^2 \equiv 49 \equiv -52 \pmod{101}$$$$8^2 \equiv 64 \equiv -37 \pmod{101}$$$$9^2 \equiv 81 \equiv -20 \pmod{101}$$$$10^2 \equiv 100 \equiv -1 \pmod{101}$$ with sommation we have $-240$
warm shaleBOT
Pierre de Fermat
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
timid silo
you do not need to calculate everything
have you proved that the product of two squares is a square?
timid silo
in what way?
timid silo
there are more squares than that
timid silo
**Pierre de Fermat**
you've said there are 50
you can do this question without calculating 50 squares
prime oracle
On [1;100] is mean
timid silo
huh?
prime oracle
you can do this question without calculating 50 squares
How ?
prime oracle
With $a=50$ ?
warm shaleBOT
Pierre de Fermat
timid silo
a can be any square
prime oracle
9 for exemple
timid silo
sure
prime oracle
so what is a+(-a)?
It's 0
prime oracle
😶
obtuse pebbleBOT
@prime oracle Has your question been resolved?
shut trellis
we know that -a is a square too
out of curiosity why is it that -a is also a residue?
timid silo
hint: -1 is a square mod 101
.
timid silo
yea
flint moss
it says B has the bases b1 and b2, A has the bases a1 and a2
construct the transformationmatrix from B to A
obtuse pebbleBOT
it says B has the bases b1 and b2, A has the bases a1 and a2
construct the trans...
flint moss
did i do it correctly here or am i off by a mile?
damn a German would be really helpful in this situation 
obtuse pebbleBOT
@flint moss Has your question been resolved?
obtuse pebbleBOT
@flint moss Has your question been resolved?
obtuse pebbleBOT
@flint moss Has your question been resolved?
obtuse pebbleBOT
@flint moss Has your question been resolved?
sage dagger
If anyone is bothered enough to put this into a calculator can they check if they also got 12.3?
obtuse pebbleBOT
If anyone is bothered enough to put this into a calculator can they check if the...
sand chasm
obtuse pebbleBOT
obtuse pebbleBOT
@sand chasm Has your question been resolved?
sand chasm
How do I write the Greek letters in here?
can u answer
obtuse pebbleBOT
@sand chasm Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
ancient acorn
Let W be a subset of R³ containing the vectors (x,y,z) which satisfy 3x²+y²-z²=0.
This is not a subspace because it's not closed under addition.
What'd be a subspace of R³ containing W?
obtuse pebbleBOT
Let W be a subset of R³ containing the vectors (x,y,z) which satisfy 3x²+y²-z²=0...
ancient acorn
Yeh I was gonna add a non trivial subset
frosty spoke
basically the problem here is that you can construct 3 linearly independent vectors that satisfy that equation
and therefore they have to span R3
ancient acorn
I actually think that's the only subspace that works
Darn. How would I go about proving that?
warm canopy
spanW is going to be your smallest one that works, this may end up being R^3
obsidian matrix
So I am confused on this question
obtuse pebbleBOT
So I am confused on this question
obsidian matrix
I am not sure how to solve it. It looks as if I can uuse arctaan'
if i manipulate it
but not sure how.
timber fox
thought about u sub?
versed turret
I am not sure how to solve it. It looks as if I can uuse arctaan'
Your intuition is right.
Rewrite the inside as $\frac{x^{1/2}}{(x^{3/2})^2 + 1}$
obsidian matrix
Ah u sub sounds familiar
warm shaleBOT
Castroploiin¹
timber fox
Ah u sub sounds familiar
try playing around with some substitutions, you can make more than one
just remember what your integrating the integrand with respect to
versed turret
.close
timid silo
obtuse pebbleBOT
misty iron
Why can't I use "In"
You are substituting the expression inside the square root and not the entire denominator itself.
What you end up with after the substitution you make is $\int\frac{1}{\sqrt{t}}dt$ and not with $\int\frac{1}{t}dt$.
warm shaleBOT
Bono my tires are gone
obtuse pebbleBOT
@timid silo Has your question been resolved?
trim jay
Question asks to convert into cartesian form
obtuse pebbleBOT
Question asks to convert into cartesian form
trim jay
how do i do that, as i only know the formula is r(cos + i sin)
misty iron
Question asks to convert into cartesian form
I have never seen such notation before but if I had to guess then what this means is you have something in polar coordinates that has a radius of 3 units and angle -pi/2.
misty iron
how do i do that, as i only know the formula is r(cos + i sin)
Yes, this should work.
trim jay
what ive got myself is 2.450
i think i've applied that formula incorrectly
since the answer should be -3i
misty iron
what ive got myself is 2.450
Yeah, you don't end up with with a neat real number in this case.
Drawing a diagram will be helpful.
trim jay
argan dragram?
misty iron
Yeah.
misty iron
Mhm. Looks good to me.
trim jay
this lets me know that theres not going to be any real numbers
how should i work this out?
misty iron
Well you know that the real part will be zero.
And we know the r
And we know the angle.
So our answer will be r*isin(theta).
misty iron
Mhm, the cos represents the real part.
trim jay
i cant just plot this formula into my calculator can i?
oh wait. i can.
but theres a problem, why is it when i put in 3(sin(-pi/2)) it comes out -3 but when i go with 3(sin(270)） it doesnt do the same?
misty iron
Hmm, probably because your calculator is set for radians and not for degrees.
trim jay
ah, so when its set to radians whenever i have to do trigo functions i'll have to use radians
fair enough
thanks alot !
.close
lethal blaze
Hallo
timid silo
.open
frosty spoke
6 sqrt(2)
timid silo
hmm
frosty spoke
the diameter is 12 sqrt(2)
lethal blaze
Why is 12 the diameter?
lethal blaze
Disregard the line in the middle because im the one who put that there
frosty spoke
12 sqrt(2) is the diamater
use the pythagorean theorem
the diameter is the length of the diagonal of the square
obtuse pebbleBOT
lethal blaze
.reopen
obtuse pebbleBOT
✅
lethal blaze
Then the diameter of this is 16.97
fluid snow
When f' has a zero point of even degree, that means that f has a saddle point there, right?
obtuse pebbleBOT
When f' has a zero point of even degree, that means that f has a saddle point th...
fluid snow
If f' has a double zero point, then f should behave like x^3 at that point, right?
royal basin
youre gonna need to be more precise in what you mean by "degree of a zero point" unless you want to ONLY consider this for polynomials.
fluid snow
Yes, let's only look at polynomial functions for now
royal basin
yeah, sure, if f' has a root r of multiplicity m, then that means f(x)-f(r) has the same root but with multiplicity m+1
gonna need a definition of saddle point here
fluid snow
yeah, sure, if f' has a root r of multiplicity m, then that means f(x)-f(r) has ...
Yeah, but we only want to look at f(x), right?
royal basin
i mean sure
fluid snow
gonna need a definition of saddle point here
$x_0$ is a saddle point if $f'(x_0) = 0$ and $f'(x_0 + \epsilon)$, $f'(x_0 - \epsilon)$ for some small $\epsilon > 0$ are of the same sign
royal basin
are you sure you are not missing anything from this?
fluid snow
fluid snow
ok then the answer to your original question appears to be yes
Why did we need the definition?
royal basin
well i asked for it to ensure we're both on the same page
but also you should not be shocked at needing to consult the definitions of things when doing math in general
fluid snow
but also you should not be shocked at needing to consult the definitions of thin...
Yeah of course
So if f' has a root r of multiplicity m, then f(x) - f(r) has this root with multiplicity m + 1, thus for f(x) this will be shifted up by f(r) and since m is even so m + 1 odd, we have a saddle point, right?
fluid snow
So when we find a zero of f' and we want to find extrema, and it's of even degree, we don't need the second derivative test (or checking the sign left and right to the zero)
This could save some time in an exam
thanks
.close
timid silo
is it meant to be continuous
gusty heath
Um, this is "Determining Constants that Make a Limit Exist". I think I am supposed to try using direct substitution to see if both sides of the limit agree
this may sound dumb but I wasn't sure if it was correct to plug 2 into both c and x
sorry this is the condition
timid silo
oh okay
timid silo
for the limit to exist $\lim_{x \to 2^+} = \lim_{x \to 2^-}$ so find the value(s) of $c$ for when $\lim_{x \to 2^-} \l(\f14 c^2 x^2 +3 \r) = \lim_{x \to 2^+} \l(c^2 x^2 \r)$
warm shaleBOT
♡A(lex)♡
gusty heath
well okay, good news is I understand both sides have to agree, bad news is I'm not sure how to find the value of c, I tried just examining one side at a time. and Came up with the
left side limit = 7
right side limit = 16
and when x = 2 (as c + 9) the limit = 11.
I directly substituted into c with the given value of 2, with the ID law
does that make sense?
timid silo
here is the thing
let's dissect this bit by bit
how did you get the number 7 (and 16)?
can you write out your steps and what you did?
gusty heath
ok so if x<2, so approaching from the left side, it is worth
so then using the sum law I ended up with 2 limits
both as x --> 2 from the left
1/4(c)^2(x)^2 + 3
I used the power rule to bring out the exponent of c and x
and then I think I can use the Identity rule to sub 2 for x, but I wasn't sure if that was true for c.
shy flax
Hi
Can any one proof second line with cauchy schwarz?
obtuse pebbleBOT
@gusty heath Has your question been resolved?
keen lodge
idk if this stupidly easy or if im dumb someone helpp
obtuse pebbleBOT
idk if this stupidly easy or if im dumb someone helpp
timid silo
idk if this stupidly easy or if im dumb someone helpp
looks correct
keen lodge
looks correct
how is it solved??
timid silo
how is it solved??
by looking at the graph
keen lodge
but how would 30 degrees coordinate with 16 minutes
keen lodge
idk if this stupidly easy or if im dumb someone helpp
<@&286206848099549185>
somber sorrel
16 minutes...
somber sorrel
idk if this stupidly easy or if im dumb someone helpp
90 to 60 the difference is 30 degrees, and look in graphs it crosses 60 degrees at 16th min.
Simple...
keen lodge
thank u sooo much i was just rlly confused because the whole thing was algebra 3 so i was confused why this question was there
thank uu!
.close
jolly bramble
Hey, So i wanna start fresh with math. I researched and got some help to design this path to learn math
obtuse pebbleBOT
Hey, So i wanna start fresh with math. I researched and got some help to design ...
jolly bramble
Basic Mathematics
Pre-Algebra
Geometry
Algebra 1
High School Geometry
Algebra 2
Trigonometry
College Algebra
Statistics & Probability
Pre Calculus
Differential Calculus
Integral Calculus
Calculus 1
Calculus 2
Linear Algebra
Discrete Math```I would love to get some feedback
meager sapphire
jolly bramble
I wanna go in order from basics to advanced
gleaming ridge
For the initial topics Khan Academy is the best, for calculus Paul's notes are really good
For book recommendations check #book-recommendations
green field
Is there any way of doing this without L'hopital?
obtuse pebbleBOT
Is there any way of doing this without L'hopital?
green field
sorry for bad writing, i had to use the mouse
green field
I tried to convert the x+1 into x(1+1/x) but that end up in a dead end anyway
timber fox
can you show working for that step
because you would get something like
something * sin
and if you divide by something, then you would have sin / 1/something
green field
timber fox
ok that looks good
green field
idk if it is too confusing
timber fox
you see the last line
green field
but ended up with the same result
green field
0?
timber fox
right indeterminate form
and if we have the x there
then lets just divide top and bottom by it also
then we have lhopital setup
timid yacht
the question was about doing it without lhopital
timber fox
NOOOOOO
timid yacht
did you learn the limit of sinx/x
by the famous(?, dunno how they say it in english) limits
green field
you mean sin(x/x) or sin(x)/x?
timid yacht
xd, the second
distant moth
Whats the answer for this?
green field
2pi
green field
this is supposed to be previous to learning L'hopital, its from a lot of limits exercises
distant moth
This way you dont need l hopital
green field
1/pi?
green field
I will try
timid yacht
but maybe I'm just dumb and can't remember
check in your notes, that used to be one of the starting examples
because ur gonna need it in a lot of exercises
heres a video, which i believe doesnt use any lhopital to proving
green field
is this legal?
i used this from my notes
but dont know if I made some illegality XD
timid yacht
so u did learn sin(x)/x as x goes zero
green field
oh so you meant infinitesimals? I think that's how they are called
timid yacht
wdym
green field
sinx is equivalent to x when x tends to 0
so I changed sin(t) for t then I delete it with the denominator
But I don't know if the variable change I made is good or if I made some mistake
timid yacht
it seems good, but u dont need to change the variable if ur not sure how to use it, you can just do this:
sry, i wrote it when i thought its an n, not pi
green field
sry, i wrote it when i thought its an n, not pi
yh, my writing sucks, blame on me
I never thought on multiplying and dividing for 2pi/x
spark coral
is this correct/the right way to go about this? Just starting my proofs class, so not really sure if this is correct
obtuse pebbleBOT
is this correct/the right way to go about this? Just starting my proofs class, s...
kind hawk
it often is better to start at the beginning and end where you want. here: $a=b \mod n$ gives $a=kn+b$, $c=d \mod n$ gives $c=qn+d$, so $$ac = (kn+b)(qn+d) = kqn^2+knd+bqn+bd = n(kqn+kd+qb)+bd$$ which is exactly the form you want
warm shaleBOT
Denascite
kind hawk
it looks like yours is probably equivalent but it definitely is longer so it seems more complicated
hmm
I don't see how you jump from your last equation to the three conditions (i), (ii) and (iii)
I mean that's true but comes from nowhere
and the last paragraph is wrong. "since (iii) is equivalent to what we want to show, we can just assume it's true"
spark coral
I factored each term so (d), (b), (c), (a) are on their own, so then I pulled them out of the equation? Not sure how to prove that algebraically though, I just know its something you can do
spark coral
and the last paragraph is wrong. "since (iii) is equivalent to what we want to s...
is this what I should say instead?
not sure what's wrong with it though
kind hawk
no the point is that paraphrased you said that. but you can't just assume that what you want to prove is true
spark coral
So should I just say something like "Since (iii) is equivalent to ..., if (i) and (ii) hold, then (iii) holds as well." ? Not sure how to deal with the recursion there where it depends on itself
spark coral
ok then where did I go wrong?
kind hawk
I don't see how you jump from your last equation to the three conditions (i), (i...
well this jump is very questionable
in general you made it much harder by kinda starting at the end
it's harder to see which logical steps etc you are doing and in which direction you are going etc
obtuse pebbleBOT
@spark coral Has your question been resolved?
spark coral
in general you made it much harder by kinda starting at the end
wdym tho starting at the end?
kind hawk
you start with ac=bd mod n and say this is equivalent to (...) which is equivalent to (...) .... until you get to (...) which you then know is true
instead of starting at the beginning, namely a=b mod n and c=d mod n, and then doing steps until you finally at the end go to ac=bd mod n
like I did
spark coral
ah I see
fallow venture
My question is with regards to an exercise I'm working on, which I have screenshotted to include here. I have been struggling with Big O, Omega, and Theta for years now and it's never made sense to me. I would appreciate if someone could help me understand how to prove Big Theta (and thus by extension, Big O and Big Theta) across the board by teaching me how to do it in this problem.
obtuse pebbleBOT
My question is with regards to an exercise I'm working on, which I have screensh...
fallow venture
I do not know how to show that these things are true
My biggest issue so far in learning is that everyone uses a different example to demonstrate how it works and each time there's a point at which I fail to understand how the numbers/equations being used came to fruition. I have no understanding of how to set up these proofs as a result.
maybe i'll just finally pay for chegg lol...
obtuse pebbleBOT
@fallow venture Has your question been resolved?
obtuse pebbleBOT
@fallow venture Has your question been resolved?
obtuse pebbleBOT
@fallow venture Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
half pecan
Show that the set Q + Q √ 3 is a field
obtuse pebbleBOT
Show that the set Q + Q √ 3 is a field
half pecan
I can kinda understand how to show Q root(3) is a field
but not sure how to go about Q + Q root (3)
Q being the set of rational numbers by the way
obtuse pebbleBOT
@half pecan Has your question been resolved?
obtuse pebbleBOT
@half pecan Has your question been resolved?
obtuse pebbleBOT
@half pecan Has your question been resolved?
obtuse pebbleBOT
@half pecan Has your question been resolved?
half pecan
?
neon eagle
wtf does Qsqrt 3 mean
tardy epoch
Show that the set Q + Q √ 3 is a field
You need to define your notation
half pecan
Q as in the set of all rational numbers
tardy epoch
And
neon eagle
yes but what is Q sqrt 3
half pecan
I'm assuming just the set of all rational numbers with a root 3
there's no explanation
what i posted is literally the question i got
frosty spoke
probably all rational multiples of sqrt 3
neon eagle
oh ok so it's the set Q and then sqrt 3 as well?
tardy epoch
what i posted is literally the question i got
Show the screenshot
neon eagle
^
tardy epoch
Otherwise it's just
https://math.stackexchange.com/questions/1581493/what-does-the-following-notation-mathbbq-sqrt3-mean
half pecan
i can't find it anymore as I submitted the assignment already
but it was literally that
Show that the set Q + Q √ 3 is a field
exactly that
tardy epoch
probably all rational multiples of sqrt 3
Probably this then
half pecan
probably all rational multiples of sqrt 3
shit yea probably
crazy cause it's the first homework
and fool didn't even go over it in the first class
neon eagle
is $\frac{1}{\sqrt{3}}$ in the set tho
warm shaleBOT
ed
half pecan
not sure
how i went about it was
i had Q be the set {a + b | a,b in Q}
and Q root 3 be the set { a + b root 3 | a,b in Q}
neon eagle
maybe it just meant that then
half pecan
and i let 2a + b + broot 3 be an element of Q + Q root 3
then i used that element to prove it's closed under addition/ multiplicatoin
etc
neon eagle
yes keep going
addition is commutative and so is multiplication so thats done
then show every element has a multiplicative inverse and additive inverse also in the set
half pecan
yea I showed the identity properties as well
and for commutative , associative and distributive i just said since Q + Qroot3 is a subset of R it holds
half pecan
sounds good then
yea that's weird
i haven't taken a proof class in 4 months
so i was also confused about the Q root 3
obtuse pebbleBOT
@half pecan Has your question been resolved?
outer sail
For this question:
obtuse pebbleBOT
For this question:
outer sail
I calculated the derivative to be 3yx^2 + y^2
subbing in values 7,8 i got 1201. Can anyone see any immediate faults ive made? Ive not really learnt 'partial derivatives' i just differentiated it and am hoping its right
high lily
how are you getting an odd number for you final answer
when taking the partial derivative wrt, you pretty much treat the other variables as constant
so your partial derivative is fine
you evaluation however is off
outer sail
how are you getting an odd number for you final answer
where have i gone wrong. If my differentiation is correct 🙏 , i got 3yx^2 +y^2
y^2 is 64
its 3* yx^2
3 is odd
high lily
3 is oddd, the product isnt
outer sail
im lost mate
outer sail
this is why i asked, i subbed in x for y and y for x
soo. thankyou lmao 😄
im a goose
high lily
yeh and what's you get
trail musk
Sin(z) ~ z about 0
So sin((x-y)/2) ~ (x-y)/2
So then we get:
4|(x-y)/2|
= 2|x-y|
It's the asymptotic equivalence
Lim x->0 sinx/x = 1
copper shell
from an integral calculus practice sheet, am i missing something? how do i calculate this without saying that obviously 1/sqrt(n^2 + a^2) converges to 0?
obtuse pebbleBOT
from an integral calculus practice sheet, am i missing something? how do i calcu...
atomic bobcat
umm sandwich theorem
copper shell
umm sandwich theorem
i dont think that would work cuz you'd have 0 <= S <= 1 where s is the sum
timid silo
do you have to calculate its value or just show it converges?
copper shell
i have to calculate its value
atomic bobcat
are you sure that it converge to 0?
copper shell
im mainly guessing but it makes sense to me, i dont know how to prove it though, especially using integrals somehow
atomic bobcat
nah
cause when i use squeeze theorem its value lies between 1 and 1
its limit is one
north ore
Can someone solve this equation?
a = ?
ok it converges to 1/2 log(3 + 2√2)
atomic bobcat
?
rich tapir
,ask integral 1/(1+x^2) from 0 to 1
atomic bobcat
is 1 wrong?
warm shaleBOT
rich tapir
,ask integral 1/(1+x^2) from 0 to 1
was my guess
timid silo
,w integral 1/sqrt(n²+x²) dx from 0 to n
atomic bobcat
i still think that it converge to 1
timid silo
it doesnt, i even plugged in a huge number for n
copper shell
,w integral 1/sqrt(n²+x²) dx from 0 to n
interesting, this is probably it
or perhaps from 1 to n since the first term is 1/sqrt(n^2 +1)
timid silo
thats the upper bound
the lower bound has borders 1 to n+1
but i guess if you let n go to inf for both, it gets the same value
atomic bobcat
umm....i maybe be wrong then...but i was pretty sure that it converge to 1.. so let's ask helpers
timid silo
not sure how to integrate that thing though
rich tapir
my real analysis course has a similar problem
timid silo
rich tapir
oops doxed myself
timid silo
rich tapir
timid silo
yeah answer is arcoth(√2)
atomic bobcat
okie
rich tapir
,ask integral 1/(1+x^2) from 0 to 1
just realized that i forgot the sqrt 🥹🥹
timid silo
but he said its integral calculus
obtuse pebbleBOT
@copper shell Has your question been resolved?
copper shell
this seems to be the way, yeah
obtuse pebbleBOT
copper shell
many thanks
obtuse pebbleBOT
Available help channel!
rapid girder
i have found the equation in General Form
obtuse pebbleBOT
i have found the equation in General Form
rapid girder
now i need to transform it in double intercept form then compare the equation with the given one and find the value of a and b
just help me how to convert these equations
ivory trout
i have found the equation in General Form
two lines are perpendicular when m * m' = 1
given a line y = mx + q
ivory trout
find the point of intersection of these two lines
rapid girder
Resulting Equation is 3x - 2y = 5
ivory trout
first
rapid girder
(3,2)
M = -2/3 and M' = 3/2
by using Slope Point Formulae
i.e. y - y1 = m ( x - x1)
Therefore 3x - 2y = 5
oh i had a idea in Bathroom
3x - 2y = 5
or (3x - 2y)/5 = 1
or 3x/5 - 2y/5 = 1
or x/5/3 + y/-5/2 = 1 --------- (i)
comparing (i) with x/a + y/b = 1
oh i got it
.clo;se
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
tardy moon
Could anyone help me with this equation? That’s what I did but kinda couldn’t finish it. Do you have any ideas I could try?
obtuse pebbleBOT
Could anyone help me with this equation? That’s what I did but kinda couldn’t fi...
obtuse pebbleBOT
@tardy moon Has your question been resolved?
tardy moon
No need to continue it, I wonder. If there might be an easier wait to do it that I don’t see and no need for all those a^4 and whatever
obtuse pebbleBOT
@tardy moon Has your question been resolved?
tardy moon
.close
trim haven
How do I expand the function f=x^2 with fourier series in the interval (1,3)
trim haven
i also have to express the parseval identity for it
river compass
I have a Black box system, from which I can realize experiments by setting some experimental parameters (X0, X1, X2...) to some value inside their respective domains (known), and obtaining a result Y. I have already realized a Full Factorial experiment, and using it, I have obtained a set of Regressors that could explain the known data. These regressors are in the form of symbolic functions, and should be differentiable. I also have a "score" for each regressor, which would be my confidence I have on their fit.
From this set of experiments, regressors, and black box, I want to design new experiments. Ideally, I would want to disprove with new data as many regressors as possible, so my intuition is to do something like in clustering and try to find parameters such that the different expected results of the regressors are maximally separate. What would be a way of finding this, ideally without doing something numerical method search. I have tried figuring out information matrix methods, but I do not know enough about this to turn a symbolic model like f(x0,x3) = x3^(2*x0-5) into an information matrix
obtuse pebbleBOT
I have a Black box system, from which I can realize experiments by setting some ...
@river compass Has your question been resolved?
obtuse pebbleBOT
@river compass Has your question been resolved?
obtuse pebbleBOT
@river compass Has your question been resolved?
river compass
<@&286206848099549185>
vestal ridge
STOP FUCKING @ PLEASE THANKS BRO
river compass
what?
timid silo
he is an angry helper